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DEVELOPMENT OF A RATIONAL DESIGN APPROACH (LRFD phi) FOR DRILLED SHAFTS CONSIDERING REDUNDANCY, SPATIAL VARIABILITY, AND TESTING
COST
by
JOHANNA KARINA OTERO
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2007
2
© 2007 Johanna Karina Otero
3
To my parents Maria Isabel Sanchez and Rafael Otero who have supported me all the way since the beginning of my studies, and to Enrique who accompanied me on this last stage
4
ACKNOWLEDGMENTS
I would especially thank to my advisor, Dr. Ralph Ellis, for his generous time and
commitment. His permanent conviction on my professional capacity during my doctoral work
made this research a reality. Also, thanks to Dr. McVay for to share part of his geotechnical
knowledge. Special thanks go to Dr. Guerly for his supervision and technical support on the
stochastic world.
I would like to acknowledge Dr. Horhota and the Florida Department of Transportation
(FDOT) State Material Office for providing the funding and help for this research project.
Thanks also go to Farouque, Haki and Enrique who assisted me on different stages of the project
investigation.
5
TABLE OF CONTENTS page
ACKNOWLEDGMENTS ...............................................................................................................4
LIST OF TABLES...........................................................................................................................8
LIST OF FIGURES .......................................................................................................................10
ABSTRACT...................................................................................................................................12
CHAPTER
1 INTRODUCTION ..................................................................................................................13
Introduction.............................................................................................................................13 Background.............................................................................................................................13
Site Characterization .......................................................................................................14 Subsoil Exploration .........................................................................................................14
Geotechnical variability ...........................................................................................14 Conventional geotechnical modeling .......................................................................15
LRFD...............................................................................................................................15 FMOS First Order Second Moment .........................................................................19 Reliability index .......................................................................................................20 Solving for the resistance factor...............................................................................21
Problem Statement..................................................................................................................23 Objectives ...............................................................................................................................24 Methods ..................................................................................................................................24
2 LITERATURE REVIEW .......................................................................................................27
Static and Dynamic Field testing of Drilled Shafts ................................................................27 Modeling Spatial Variability in Pile Capacity for Reliability-Based Design.........................28 Reliability-Based Foundation Design for Transmission Line Structures ...............................29 Transportation Research Board Circular E-C079...................................................................30 Estimation for Stochastic Soils Models..................................................................................31 Practice of Sequential Gaussian Simulation ...........................................................................31 Bearing Capacity of a Rough Rigid Strip Footing on Cohesive Soil-a Probabilistic
Study ...................................................................................................................................32
3 DATA COLLECTION ...........................................................................................................35
Existent Data Collection .........................................................................................................35 New Field Data Collection .....................................................................................................36
The Fuller Warren Bridge (District 2).............................................................................37 17th Street Bridge Fort Lauderdale (District 4)................................................................38
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4 GEOSTATISTICS AND NUMERICAL MODEL ................................................................45
Geostatistics............................................................................................................................45 (Semi) Variogram............................................................................................................46
Semivariogram models.............................................................................................47 Anisotropy................................................................................................................48 Covariance and correlogram ....................................................................................49
Kriging.............................................................................................................................49 Types of Kriging ......................................................................................................51
Stochastic Simulation ......................................................................................................53 Sequential Gaussian simulation ...............................................................................53
Software...........................................................................................................................54 Numerical Models ..................................................................................................................55
FLAC3D (Fast Lagrangian Analysis of Continua) .........................................................57
5 DATA ANALYSIS ................................................................................................................65
Cases Studies ..........................................................................................................................65 Fuller Warren..........................................................................................................................65
Summary Statistics ..........................................................................................................65 Spatial Continuity............................................................................................................66 Fuller Warren Semivariogram.........................................................................................67
17th Street Bridge ....................................................................................................................68 Summary Statistics ..........................................................................................................68 17th Street Bridge Semivariogram ...................................................................................68 17th Street Bridge Simple Kriging ...................................................................................69 17th Street Bridge Sequential Gaussian Simulation.........................................................69 17th Street Bridge Random Field Model..........................................................................69 17th Street Bridge Finite Elements Analysis....................................................................70 17th Street Bridge Determinist Capacity..........................................................................71 17th Street Bridge Parametric Study ................................................................................71 17th Street Bridge Comparison of Deterministic and Predicted End Bearing .................73 17th Street Bridge LRFD Phi Factors ..............................................................................73
6 COST ANALYSIS .................................................................................................................95
Factor Influencing Cost ..........................................................................................................95 Drilled Shaft Cost and Excavation .........................................................................................96 Soil Boring Test Costs ............................................................................................................97 Relative Costs Analysis ..........................................................................................................97
Drilled Shaft Cost ............................................................................................................97 Drilled Shaft Excavation .................................................................................................98 Boring Test Cost..............................................................................................................98
7 CONCLUSIONS AND RECOMMENDATIONS...............................................................105
7
APPENDIX
A DATA FROM STATIC AND DYNAMIC FIELD TESTING OF DRILLED SHAFTS (FULLER WARREN AND 17TH STREET BRIDGE) ........................................................107
B SOIL BORING DATA FROM FIELD INVESTIGATION PROCESSED BY MSO.........111
C SOIL BORING INFORMATION PROCESSED ................................................................128
D FREQUENCY DISTRIBUTIONS .......................................................................................131
E SGS RANDOM FIELD TABLES........................................................................................140
F FLAC3D PROGRAMMING MODELS ..............................................................................150
G UNIT COST DATA .............................................................................................................157
LIST OF REFERENCES.............................................................................................................159
BIOGRAPHICAL SKETCH .......................................................................................................161
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LIST OF TABLES
Table page 2-1 LRFD φ Factors, Probability of Failure (Pf) and Fs Based on Reliability φ for
Nearest Boring Approach. .................................................................................................34
2-2 LRFD φ Factors, Probability of Failure (Pf) and Fs Based on Reliability φ for Random Selection ..............................................................................................................34
3-1 Measured Unit End Bearing from Load Tests. ..................................................................39
3-2 17th Street Bridge Soil Boring Data (State Project No. 86180-1522)...............................40
3-3 Fuller Warren State Materials Office Soil Laboratory Data..............................................41
4-1 Commercially Available Numerical Programs for Rock Mechanics Study. .....................59
4-2 Sequential Gaussian Simulation Data Values....................................................................60
4-3 WINSLIB SGS Example Results.......................................................................................60
5-1 Fuller Warren Bridge Soil Boring Information. ................................................................77
5-2 Fuller Warren Soil Boring Modified Data. ........................................................................78
5-3 Table 17th Street Bridge Soil Boring Information. ............................................................80
5-4 17th Street Bridge Wingslib Results...................................................................................81
5-5 Material Properties.............................................................................................................81
5-6 17TH Street Bridge Cohesion Mean Results Values from Simulations..............................81
5-7 17TH Street Bridge End Bearing Capacity Mean Values from FLAC3D ..........................81
5-8 17TH Street Mean, Standard, and COV of Predicted End Bearing Capacity Bias .............81
5-9 17TH Street Bridge φ Values for different Reliability Index β FOSM (Traditional)..........82
5-10 17TH Street Bridge φ Values for different Reliability Index β FOSM (Modified) ............82
5-11 17th Street Bridge COV and λ............................................................................................82
6-1 FDOT Item Average Unit Cost Database. .........................................................................99
6-2 Summary of Drilled Shaft of 48” Diameter (0455 88 5). ..................................................99
6-3 Summary of Excavation Shaft of 48” Diameter (0455 122 5)...........................................99
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6-4 Summary of Soil Lab from 2003 to 2007 ..........................................................................99
6-5 Summary of Drilled Shaft Cost (Material, labor) for φ Factors FOSM..........................100
6-6 Summary of Drilled Shaft Cost (Material, labor) for φ Factors FOSM (Modified) ........100
6-7 Summary of Drilled Shaft Cost Excavation for φ Factors FOSM ...................................100
6-8 Summary of Drilled Shaft Cost Excavation for φ Factors FOSM (Modified).................100
6-9 Average Cost for a 1 foot length and 4 feet Diameter Drilled Shaft, (One Soil Boring) .............................................................................................................................101
6-10 Average Cost for a 1 foot length 4 feet Diameter Drilled Shaft, (Five Soil Boring).......101
6-11 LRFD φ Factors, Probability of Failure and Fs Based on Reliability, β for Nearest Boring Approach..............................................................................................................101
A-1 Fuller Warren Bridge Soil Boring Data. ..........................................................................107
A-2 17th Street Bridge Soil Boring Data. ................................................................................109
B-1 17th Street Soil Boring Data. ............................................................................................111
B-2 Fuller Warren Soil Boring Data.......................................................................................123
C-1 17th Street Bridge Processed Soil Boring Data. ...............................................................128
C-2 Fuller Warren Bridge Processed Soil Boring Data. .........................................................130
E-1 17th Street Bridge SGS (1feet). ........................................................................................140
E-2 17th Street Bridge SGS (5feet). ........................................................................................142
E-3 17th Street Bridge SGS (12 feet). .....................................................................................144
E-4 17th Street Bridge SGS (20feet). ......................................................................................148
F-1 FLAC Results...................................................................................................................150
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LIST OF FIGURES
Figure page 1-1 Location of Boundaries between Materials. ......................................................................26
1-2 Litho Logical Heterogeneity. .............................................................................................26
1-3 Inherent Spatial Soil Variability. .......................................................................................26
3-1 Load Test Bridge Locations...............................................................................................43
3-2 Fuller Warren Bridge Shaft Locations. ..............................................................................43
3-3 Fuller Warren Bridge during Site Inspection.....................................................................44
3-4 17th Street Bridge Load Test Location. ..............................................................................44
4-1 Semivariogram Model. ......................................................................................................61
4-2 Most popular Semivariogram Models. ..............................................................................61
4-3 Semivariogram and Covariance.........................................................................................62
4-4 Numerical Approaches to Model an Excavation in a Rock Mass .....................................63
4-5 WINSLIB SGS Example Location Data Values. ..............................................................63
4-6 WINSLIB SGS Example Results Graph............................................................................64
5-1 Fuller Warren Soil Boring Location. .................................................................................83
5-2 Fuller Warren Histogram CB1...........................................................................................83
5-3 Fuller Warren Histogram CB2...........................................................................................84
5-4 Fuller Warren Histogram CB3...........................................................................................84
5-5 Fuller Warren New Borings Frequency Distribution qu, qt and RQD. .............................85
5-6 Frequency Distribution for quqt.........................................................................................86
5-7 Fuller Warren Bridge quqt and E Correlation....................................................................86
5-8 17th Street Soil Boring Locations.......................................................................................87
5-9 17th Street Frequency Distribution.....................................................................................88
5-10 17th Street Semivariogram .................................................................................................89
11
5-11 17th Street Bridge Correlation quqt vs E. ...........................................................................90
5-12 17th Street Bridge FLAC Model Grid ................................................................................91
5-13 17th Street Axial Force vs Pile Displacement ....................................................................92
5-14 17th Street Correlation Length vs Cohesion Mean.............................................................93
5-15 17th Street Correlation Length vs Total Bearing Capacity.................................................93
5-16 17TH Street Correlation length vs End Bearing Capacity...................................................94
6-1 FDOT Basis of Estimates Handbook Description for the Item 455 88 “Drilled Shaft”. .102
6-2 FDOT Basis of Estimates Handbook Description for the Item 455 122 “Unclassified Shaft Excavation”. ...........................................................................................................103
6-3 Example of the 2006 Item Average Unit Cost for the Items 455 88 5 and 455 122 5.....104
D-1 Total Capacity Frequency Distribution 5 feet Correlation Length ..................................131
D-2 Total Capacity Frequency Distribution 12 feet Correlation Length ................................131
D-3 Fuller Warren Bridge Old and New Borings. ..................................................................132
D-4 Fuller Warren Bridge Old Borings. .................................................................................133
D-5 Fuller Warren Bridge New Borings.................................................................................134
D-6 17th Street Bridge Old and New Borings. ........................................................................135
D-7 17th Street Bridge New Borings. ......................................................................................136
D-8 Fuller Warren Bridge New Boring CB1. .........................................................................137
D-9 Fuller Warren New Boring CB2. .....................................................................................138
D-10 Fuller Warren New Boring CB3 ......................................................................................139
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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
DEVELOPMENT OF A RATIONAL DESIGN APPROACH (LRFD phi) FOR DRILLED SHAFTS CONSIDERING REDUNDANCY, SPATIAL VARIABILITY, AND TESTING
COST
By
Johanna Karina Otero
December 2007
Chair: Ralph Ellis Cochair: Michael McVay Major: Civil Engineering
New designs move toward larger single shaft, so the need to improve LRFD resistance
factors, φ, for non- redundant shaft, emerge. In general geotechnical design practice involve
analysis using representatives values of design parameters,(like strength, recoveries, etc), usually
an average or lowest value obtained from field and laboratory test results. It followed by an
application of a suitable factor of safety. In nature soil parameter varies in horizontally and
vertically direction, so our research used the same soil boring parameters, but this time use
information obtained from sites localized close to the design site instead using the whole site
average. Random soil models were created based on geostatistics analysis using soil parameters.
The created random soil models were used on a finite element program that modeling a three feet
diameter, twenty feet long drilled shaft, giving the drilled shaft capacity for each random soil
model and a suitable, φ, factor.
13
CHAPTER 1 INTRODUCTION
Introduction
This research initiative was based on the need to improve the LRFD resistance factors, φ,
for non- redundant shaft design, due the new designs methods moves toward larger single shaft
design (e.g. Cross –Town, New River, etc).
Most geotechnical analysis in general practice involve analysis using representatives
values of design parameters,(like strength, recoveries, compressibility, etc), usually an average or
the lowest value obtained from field and laboratory test results, and it followed by an application
of a suitable factor of safety to get an allowable loading condition. However, in nature soil
parameter varies in both horizontally and vertically direction.
Our case used the same soil boring parameters than those used on most geotechnical
analyses, but this time use information obtained from sites localized close to the design site
instead using the whole site average. Random soil models were created based on geostatistics
analysis using soil parameters. The created random soil models were used on a finite element
program that modeling a six feet diameter, twenty feet long drilled shaft, giving the drilled shaft
capacity for each random soil model.
Additionally, a cost comparison between using the actual method involving an increment
on the drilled shaft construction due to using a bigger LRFD resistance factors, φ. And using the
proposed LRFD resistance factors, φ, but with an increment on additional field coring of rock
around the location where the shaft will be is accomplished.
Background
Foundation design depends basically on the engineering properties of the soil or rock that
is supporting the foundation. But the soil characteristics at any site frequently are non-
14
homogeneous, that means that the soil profile may vary. Therefore, for estimate the natural soil
or rock in-situ properties, it is necessary to pass by two phases; site characterization and subsoil
exploration.
Site Characterization
On this phase, the engineer glances for formation of the soil origin and alterations that
usually are caused by the environment processes, like chemical weathering and the introduction
of new substances. Those alterations vary on space and time. If the engineer has an
understanding of soil formation and later alteration of geotechnical materials, he will have a
better acknowledge of the material variability and the behavior that it could have during
construction process and structure lifetime.
Subsoil Exploration
This phase is where the engineer obtains information that assists him/her on calculations of
the load bearing capacity of the foundation, estimation of the possible settlement of a structure,
establishing foundation problems, choosing the appropriate foundation type, and determining
construction methods for changing subsoil condition. The subsoil phase has three basic steps;
collection of preliminary information, reconnaissance and site.
Geotechnical variability
Natural soils are rarely homogeneous and highly variable in their properties. This soil
variability can be classified into three main categories. The first is the location of boundaries
between materials (see Figure 1-1). The second is litho logical heterogeneity that is the locations
of anomalies, or areas of significantly differences properties, within a single material type (see
Figure 1-2). And the third is inherent spatial soil variability (see Figure 1-3). Soil and rock
material vary so that a property measures at two different points will have different values,
assuming no error on measurement.
15
Conventional geotechnical modeling
The conventional method of modeling soil structures is to evaluate the results from field
testing studies and then to make soil profiles. In theses profiles, each layer is assumed to be
homogeneous with singles values for the engineering properties of each layer. This properties
information is obtained from in situ soil testing and lab testing. This information is evaluated
later by the engineer and a single conservative value is chosen to represent the property of the
material. The variability normally is not quantified.
The usual design practice for soil design is deterministic. This involves the estimation of
ultimate bearing capacity using average values of design parameters and application of a suitable
factor of safety (F) to arrive an allowable bearing capacity (Griffiths & Fenton 1999).
LRFD
The purpose of foundation design is to guarantee that a system achieves adequately in its
design life. However, there are some uncertainties on the two phases described above, (site
characterization and subsoil exploration) that make it impossible to ensure that any unfortunate
performance will occur under all possible circumstances.
Foundation failures are always undesirable events. They occur for diverse reasons,
negligence, lack of knowledge, greed, etc. The probability of failure is often higher for projects
involving new materials, technology, and extreme parameters (larger shaft diameter) for which
there is little or no prior experience. Therefore, the design provisions include built-in safety
margins: load effects are usually overestimated and resistances are underestimated. In load and
resistance factor design (LRFD), load components are multiplied by load factors and resistance is
multiplied by a resistance factor. The basic equation is:
φRn >∑γi Qi (1-1)
16
Where γi is a load factor applied to load components Qi and φ is resistance factor applied
to the resistance (measured of load carrying capacity) Rn . In words it equation says that the
capacity of the foundation (modified by the factor φ) must be larger than the total effect of all the
loads acting on it.
The mention above design formulas are developed by code committees with input from
practicing engineers, researchers, and scientists. However, things are changing and there are new
requirements that need to be satisfied, for example moving toward larger single shaft
construction. New rules are required, for example “field coring of rock at the location of the as
built non-redundant shaft” (FDOT Structures Bulletin, 2005). Similar to cycles, new requirement
results could improve the formulas over again.
The goal of load and resistance factor design (LRFD) analysis is to develop factors that
decrease the nominal resistance to give a design with an acceptable and consistent probability of
failure. To accomplish this, an equation that incorporates and relates together all of the variables
that affect the potential for failure of the structure, must be developed for each limit state. The
parameters of load and resistance are considered as random variables, with the variation modeled
using the available statistical data. A random variable is a parameter that can take different
values that are not predictable. An example is compressive strength of the soil, qu that can be
determined using a testing machine.
There are three levels of probabilistic design: Levels I, II, and III (Withiam et al. 1998;
Nowak and Collins 2000). The Level I method is the least accurate. It is sufficient here to point
out that only Level III is a fully probabilistic method. Level III requires complex statistical data
beyond what is generally available in geotechnical and structural engineering practice. Level II
and Level I probabilistic methods are more viable approaches for geotechnical and structural
17
design. In Level I design methods; safety is measured in terms of a safety factor, or the ratio of
nominal (design) resistance and nominal (design) load. In Level II, safety is expressed in terms
of the reliability index, β. The Level II approach generally requires iterative techniques best
performed using computer algorithms. But for simple cases, there are available closed-form
solutions to estimate β. Closed-form analytical procedures to estimate load and resistance factors
should be considered approximate, with the exception of very simple cases where an exact
closed-form solution exists (Calibration to Determine Load and Resistance Factors for
Geotechnical and Structural Design 2005).
For LRFD calibration purposes, statistical characterization should focus on the prediction
of load or resistance relative to what is actually measured in a structure. Therefore, this statistical
characterization is typically applied to the ratio of the measured to predicted value, termed the
bias. The predicted (nominal) value is calculated using the design model being investigated. Note
that the term bias factor (or bias) is typically defined as the ratio of the mean of the measured
value divided by the nominal (predicted) value. However, for the purposes described herein, the
term bias is used to refer to individual measured values of load or resistance divided by the
predicted value corresponding to that measured value.
Regardless of the level of probabilistic design used to perform LRFD calibration, the steps
needed to conduct a calibration are as follows:
• Develop the limit state equation to be evaluated, so that the correct random variables are considered. Each limit state equation must be developed based on a prescribed failure.
• Statistically characterize the data. Key parameters include the mean, standard deviation, and coefficient of variation (COV) as well as the type of distribution that best fits the data (i.e., often normal or lognormal).
• Determine load and resistance factors using reliability theory. It must be recognized that the accuracy of the results of a reliability theory analysis is directly dependent on the adequacy, in terms of quantity and quality, of the input data used. The final decision made
18
regarding the magnitude of the load and resistance factor selected for a given limit state must consider the adequacy of the data. If the adequacy of the input data is questionable, the final load and resistance factor combination selected should be more heavily weighted toward a level of safety that is consistent with past successful design practice, using the reliability theory results to increase coming as to whether or not past practice is conservative or nonconservative exists (Calibration to Determine Load and Resistance Factors for Geotechnical and Structural Design 2005).
Current assessment of drilled shaft skin and tip resistance is performed on laboratory rock
core samples (unconfined compression, split tension, and intact Young’s Modulus) recovered
from a site. Generally, all the samples are averaged over the whole site using either a log normal
distribution or arithmetic mean throwing out one standard deviation above and below.
Unfortunately, these methods don’t account for spatial variability of strength and voids, i.e.
recoveries at a specific locale, which is important for end bearing for a particular shaft. For this
stage a probabilistic approach (Monte Carlo, Bayesian etc.) will be developed to identify the
local strength, recovery, etc. for a specific shaft (i.e. use data near location) as well as for the
whole site. From the specific locale data, LRFD resistance factors, φ, may be determined for end
bearing based. The LRFD resistance factors, φ, for end bearing will also be determined using the
geometric mean (lognormal) from the whole site as well. The FDOT online Internet Foundation
Database (e.g. Osterberg, Statnamic results) has sufficient laboratory data to determine LRFD
resistance factors,φ, for end bearing on a site basis, but not for a specific location within a site.
Additionally, there are many methods have been developed to calibrate the LRFD
resistance factors using statistical data. FOSM (First Order Second Moment) is popular because
it does not require a computer program to find the results. FORM (First Order Reliability
Method) is more complicated that FOSM and iterates to find a solution. Each of these methods
results in a different set of resistance factors. The one used on this research was the FOSM.
19
FMOS First Order Second Moment
FOSM state for First Order Second Moment, First Order because use the first-order terms
in the Taylor series expansion, Second moment because only means and variance are needed.
It has been used (NCHRP 507, 2004) to calibrate LRFD factors using a statistical dataset
containing the measured and predicted resistances. The bias of member i of the dataset is
defined as,
n
mi r
r=λ . (1-2)
where λi is the bias, rm is the measured resistance, and rn is the nominal resistance. Each
element in the dataset will have a corresponding bias. The average of these biases is found with
the following equation.
NE i
R∑=
λλ ][ (1-3)
where N is the number of elements within the dataset. The standard deviation of the
dataset is,
( )1
][ 2
−
−= ∑
NE Ri
R
λλσ λ (1-4)
The coefficient of variation (COV) of the bias data is,
][][
R
RR E
COVλ
σλ λ= (1-5)
The reliability index is found using a function of the two random variables R, resistance
and Q load. Assuming RN and QN are normally distributed, this combined function would be,
NNNN QRQRg −=),( (1-6)
20
When QN is larger then RN, g() is negative. Therefore, failure can be defined as when g()
is less then or equal to zero. However, FOSM assumes that the load and resistance random
variables are lognormal random variables, this limits the load and resistance values to only
positive numbers.
Now considering the relationship between a normally distributed random variable RN, and
a lognormal random variable R,
( ) N
R
RReR N
==
ln. (1-7)
Writing the g(R,Q) equation in terms of lognormal random variables yields,
( ) ( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛=−=
QRQRQRg lnlnln),( (1-8)
This equation is equivalent to the first definition of g(R,Q). When R is less then Q g() will
still be negative. The g(R,Q) function is a random variable.
⎟⎟⎠
⎞⎜⎜⎝
⎛==
QRQRgG ln),( (1-9)
Yet, R/Q is a lognormal random variable. Therefore the distribution of ln(R/Q) is normal.
This results in the random variable G having a normal distribution.
Reliability index
The reliability index (β) is defined as the mean value of G (E[G]) divided by the lognormal
standard deviation of G (ζG).
G
GEζ
β ][= (1-10)
As previously defined,
)ln()ln( QRG −= (1-11)
21
with R and Q being lognormal random variables. This yield,
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+=
−=
22 ])[(1][ln
])[(1][ln][
)][ln()][ln(][
N
N
N
N
QCOVQE
RCOVREGE
QEREGE
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
+=
2
2
])[(1][
])[(1][ln][
Nn
NN
RCOVQE
QCOVREGE (1-12)
With RN and QN being normally distributed, so that E[RN] and E[QN] are the normal
means. The coefficients of variation are also calculated using the normal means and normal
standard deviations.
)]])[(1)(])[(1ln[( 22NNG QCOVRCOV ++=ζ . (1-13)
This results in the reliability index being defined as:
)]])[(1)(])[(1ln[(
])[(1][
])[(1][ln
22
2
2
NN
NN
NN
QCOVRCOV
RCOVQE
QCOVRE
++
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
+
=β (1-14)
Solving for the resistance factor
The following derivation for the resistance factor is based largely on NHI 1998. Solving
for the resistance factor begins with the fundamental LRFD equation.
∑ ⋅≥⋅ iin qr γφ (1-15)
In this equation rn stands for the nominal resistance. Solving for the resistance factor and
plugging in the bias yields:
22
][][
][][
1
R
Nn
RnN
RnN
iin
EREr
ErRErR
qr
λ
λλ
γφ
=
⋅=⋅=
⋅⋅≥ ∑
(1-16)
∑ ⋅⋅≥ iiN
R qRE
E γλφ][][ (1-17)
E[RN] is the expected value of the normally distributed resistance random variable. The
next step involves solving the reliability index equation previously derived (equation 1-14) for
the E[RN] term.
)])[(1()])[(1(
][][
2
2
)]])[(1)(])[(1ln[( 22
N
N
QCOVRCOVN
N
RCOVQCOV
eQERENNT
++
⋅=
++⋅β
(1-18)
This is then substituted into the fundamental LRFD equitation .
)]])[(1)(])[(1ln[(
2
2
22
][
)])[(1()])[(1(][
NNT QCOVRCOVN
iiN
NR
eQE
qRCOVQCOVE
++⋅⋅
⋅⋅++
⋅=
∑β
γλφ (1-19)
NHI 1998 represents the coefficient of variation of the load as,
222 ])[(])[(])[( QLCOVQDCOVQCOV += (1-20)
and rewriting this equation for dead and live loads yields,
)]])[(])[(1)(])[(1ln[(
2
22
222
][
)()])[(1(
)])[(])[(1(][
QLCOVQDCOVRCOVN
LQLDQDN
R
NTeQE
qqRCOV
QLCOVQDCOVE
+++⋅⋅
⋅+⋅⋅+
++⋅
=β
γγλφ (1-21)
With,
23
LQLDQDN qEqEQE ⋅+⋅= ][][][ λλ (1-22)
Where λQD and λQL are the dead and live load bias factors respectively. This results in,
)]])[(])[(1)(])[(1ln[(
2
22
222
])[][(
)()])[(1(
)])[(])[(1(][
QLCOVQDCOVRCOVQL
L
DQD
QLL
DQD
NR
NTeEqqE
RCOVQLCOVQDCOVE
+++⋅⋅+⋅
+⋅⋅+
++⋅
=βλλ
γγλφ (1-23)
This equation is used to calibrate the resistance factor using the FOSM method. It is
dependent on the target reliability index and the ratio of dead to live load.
Problem Statement
In the last 20 years, the use of drilled shaft foundations as an alternative to driven piles for
supporting bridges has become common practice. Reasons for their use are: 1) higher resistance
to lateral loads such as wind loads (e.g. hurricanes etc.) and ship impacts, 2) need to minimize
construction noise and vibration in urban areas, 3) right of way constrains which require minimal
foundation footprints and 4) the economy of replacing large number of piles with a single or few
drilled shaft with out pile caps. Also with the introduction of larger and more autonomous
equipment, and the aspiration to reduce costs, shaft diameters have been getting larger and
larger.
Due to the loss of foundation redundancy or the move toward larger single shaft
construction (e.g. Cross-Town, New River, Ringling, etc.), field coring of rock at the location of
the as built non-redundant shaft is now required (FDOT Structures Bulletin, 2005). However, to
accurately assess skin and end bearing of a non-redundant shaft, the need for coring in the
vicinity of a proposed shaft during the design phase is also of strong interest. For instance, the
thickness of limestone layers, recoveries (voids), strength and compressibility in the near vicinity
of the shaft may significantly improve the LRFD resistance factors, φ, for design. Consequently,
24
there is a strong need to assess the LRFD resistance factors, φ, for shaft design, e.g. end bearing,
based on the frequency distribution of strengths, recoveries and compressibility data for the
whole site vs. a specific location, especially for non-redundant shafts. In addition, there is the
question as to the number of cores, samples etc. to ensure a specific reliability.
Fortunately, a probabilistic based LRFD resistance factor assessment answers the latter
questions. For instance, using a Monte Carlo or Bayesian theory, strength, compressibility, etc.,
statistical (mean, standard deviation, etc.) properties for a specific shaft or for the whole site may
be generated from core and laboratory data near a specific shaft or over the whole site. Using
random sampling, kriging, Sequential Gaussian simulation, end bearing, etc. may be computed
for a specific shaft or for all the shafts on the site. It is expected that the difference in LRFD
resistance factors for end bearing will be significant different if applied at a specific location vs.
the whole site.
Objectives
1. To estimate the influence of the spatial variability of a site on the selection of Load Resistance Factor Design.
2. To assess the resistance factors, φ, for drilled shaft design applying the modified FOSM (First Order Second Moment), based on the frequency distribution of strengths, recoveries, compressibility data and spatial variability.
3. To calculate testing cost and compare those against the final shaft built cost. This comparison will be done by assuming spatial variability testing influences.
Methods
The method used in this research was the Empirical. It explains the data collected through
the development of a model that hypothesizes about the relationship between the data and
relevant variables of the environment. The empirical research is grounded in reality rather than in
25
some abstract territory. The base for this research was soil data, and was done in five stages.
Therefore, the abstract was replaced by collected data.
The five research stages were literature review, lab and field data collection, data analysis,
LRFD resistance factor development and cost comparison. Each of these stages will be explained
in details in further chapters.
26
Figure 1-1. Location of Boundaries between Materials.
Figure 1-2. Litho Logical Heterogeneity.
Figure 1-3. Inherent Spatial Soil Variability.
-70
-65
-60
-55
-50
-45
-400.00 20.00 40.00 60.00 80.00 100.00 120.00
qu (tsf)
Dept
h (ft
)
Peat lenses
Bedrock
Material A
Material B
Material C
27
CHAPTER 2 LITERATURE REVIEW
The LRFD resistance factors,φ, for end bearing, is determinate without have into account
spatial variability of strength and voids. On larger single shaft construction, spatial variability is
important due to large cost involves on construction. The basis for below literature review was
spatial variability, Reliability-Based Design, LRFD resistance factor design, and limestone
parameters.
Static and Dynamic Field testing of Drilled Shafts
The “Static and Dynamic Field testing of drilled shafts” (FDOT and UF) past geotechnical
research, is the first part of this research. One of the principal founding of that study was the
proposed LRFD resistance factor, φ, and ASD factor of safety for O’Neill end bearing. However,
that research required include additional rock properties to the study (i.e. mass modulus of the
rock) or simply add variables that can improve the LRFD resistance factor that were reached (i.e.
spatial variability).
The “Static and Dynamic Field testing of drilled shafts” basically shows the necessity of
have into account the drilled shaft unit bearing on design. It due many designers either neglected
or uses a small nominal value. However, evident from the Osterberg tip results significant end
bearing has been generated on drilled shaft founded in Florida Limestone.
The study follows the O’Neill tip resistance model, which identify tip resistance vs. tip
displacement. The approach is dependent on the rocks’ compressibility (i.e., Young’s Modulus,
E) and strength (qu) characteristics.
The procedure used there was the computation of all the tip resistances vs. tip displacement
for the entire Osterberg tests available at that moment (six locations in total). It had two different
approaches for each location, nearest boring (between 100 ft) and Random Selection based on all
28
the site selection. For each available test, a comparison between measured and predicted FDOT
failure resistance is made. Furthermore, the same comparison was complete for nearest boring
and random selection.
The LRFD specifications as approved by AASHTO recommend the use of load factors to
account for uncertainty in the load, and resistance factor to account for uncertainty in the
materials. Therefore, this research followed the AASHTO recommendation saying that a
probabilistic approach for estimating resistance factors be used on a database of measured and
predicted values. From that procedure LRFD φ factors, Probability of failure (Pf) and Fs Based
on Reliability φ for nearest boring and random selection approach were calculated. Table 2-1
and Table 2-2 showed the results obtained in the Static and Dynamic Field testing of drilled
shafts research. On the first column is the Reliability for drilled shafts. The Second column is the
LRFD factor. And, the fourth and fifth columns pertain to probability of failure and factor of
safety.
Comparing the LRFD factor from nearest boring and random selection results, the nearest
boring has higher resistance factor for the same design approach. Based on this study results
evidently, the use of the nearest boring greatly diminished the variability of rock properties and
the subsequent mobilized unit end bearing.
Modeling Spatial Variability in Pile Capacity for Reliability-Based Design
The American Petroleum Institute (API) recommends using site-specific data for soil
properties when developing pile capacity profiles for offshore structures (API 1993). However,
there are many situations where this site-specific information is not available or would be costly
and time consuming to obtain. It is therefore advantageous to be able to predict the expected pile
29
capacity at a site that does not have a site-specific soil boring by using the properties of the
offshore field as a whole.
This paper does the introduction to the development of a site-specific model for predicting
axial side capacity, which is the first step for a achieving the same level of reliability in design at
a site whether or not a soil boring has been drilled at that site by using the properties of the
offshore fields as a whole. This paper developed a similar procedure to the “Static and Dynamic
Field Testing of Drilled Shaft” analysis. But, instead predicting axial side capacity the named
study predicted end bearing capacity.
The model provides a methodology to predict site specific pile capacity profiles with depth
and to quantify the uncertainty associated with these predictions. The process of model
development consists of the following steps: (1) establish a conceptual geological model; (2)
compile geotechnical data to relate the geological model to pile capacity; (3) develop a
quantitative model describing spatial trends and variability in pile capacity; and (4) calibrate the
quantitative model with geotechnical data.
The models are part of a reliability-based methodology for design offshore pile
foundations without site-specific geotechnical data that could be used on a lot of cases. The
paper is completed with three examples of the application of the model on real cases.
Reliability-Based Foundation Design for Transmission Line Structures
The Electric Power Research Institute published on 1988, three volumes on Reliability-
Based Foundation Design for Transmission Line Structure, Volume 1 “Geotechnical Site
Characterization Strategy”; and Volume 3 “Uncertainties in Soil Property Measurement”. Each
of those volumes focused on geotechnical problems. The first volume explained on its second
chapter “Geotechnical Material Variability” a guide for to do Geotechnical modeling having into
30
account the material variability. Also, explained reasons for geotechnical material variability and
random field models that could be helpful for this research.
The second chapter titled “Geotechnical Material Variability” explained topics like reasons
for geotechnical variability, conventional subsurface geotechnical modeling, and random field
models. Also, shows a procedure (statistical model) for to quantify variability of the soil and
measurement errors. It procedure is alternative to the conventional subsurface modeling that
requires a great deal of engineering judgment to interpret the results of discrete measurement and
generalized them over depth and lateral extent. The procedure consist on uses a consistent
mathematical model, such as a random field model. Explanations of some steps that should be
followed for to do the model are on that chapter also. The steps are basically to analyze spatial
variability, trend, distribution of the property about its mean and correlation.
Transportation Research Board Circular E-C079
The Transportation Research Board Circular E-C079, published on September 2005,
described a complete procedure for to calibrate and determine the load and resistance factors for
geotechnical and structural design. It included all the steps that will necessary to follow. Also, it
provides alternatives for to do the calibration of the model after the factors have been obtained.
The circular document guides the reader starting in an overview of the calibration approach
through the final selection of Load and Resistance Factors. In the course, explain with examples
and applications, the limit state equation development, some calibration concepts, the target
reliability index selection, statistical consideration of calibration and characterization, how
estimate the load and resistance factors, and calibrations using the Monte Carlo method with
different variables.
It text will be useful in the process of developing the phi factor. The application of the
Monte Carlo method is an option for to have a simulation of the data obtained. It due the data
31
obtained on the field is reduced due the costs implied on its acquisition. Also, some guidance on
statistical characterization will be used as technique of estimating the load and resistance factor
would be applied.
Estimation for Stochastic Soils Models
The Journal of Geotechnical and Geoenvironmental Engineering paper, published in 1999
by Gordon A. Fenton, talked about the uncertainty in spatial soil variation and how to quantify it
rationally. It described how the mean and variance are not sufficient for to make a reliability
study, that each day more clients and engineers are interested in more sophisticated models and
rational soil correlation structures. This paper clarified reasonable correlations models.
Explained how soils are best represented using fractal or finite scale models. Also, explained
how the soil parameters will be estimated have been selected the model.
The papers give solution to questions by looking at a number of tools which aid in
selecting appropriate stochastic models. These tools included the sample covariance, spectral
density, variance function, variogram, and wavelet variance functions. Additionally, common
models, corresponding to finite scale and fractal models, are investigated and estimation
techniques discussed.
Practice of Sequential Gaussian Simulation
The Geostatistics Banff, published on 2004 a Marek Nowak and Georges Verly paper. It
described the practice of sequential Gaussian simulation within the mining industry. The paper
shows a process for simulation with the objective of reducing the mistakes that could be
undetected due to the lack of theory of simulation in practice. The paper described four of the
most important aspects of the process, like, a gradual trend adjustment, a modified bootstrap
approach, a number of pre and post simulation check. All of the approaches, solutions and
32
checks presented in this paper are simple, flexible, and can be easily implemented in other
industries.
Bearing Capacity of a Rough Rigid Strip Footing on Cohesive Soil-a Probabilistic Study
The paper indicates the use of a probabilistic study on the bearing capacity of a rough rigid
strip footing on a cohesive soil. The first step on this paper was to use statistics help for to create
random field model. The parameters used for this purpose were Young modulus E, Poison ratio
and undrained shear strength. The first two were held constant and the shear strength is modeled
as a random variable. It is assumed to be characterized by a lognormal distribution. And this
information was used for to get the spatial correlation function and the correlation coefficient
length needed for to generate random fields. After getting the random fields a finite element
method was used for to recreated the footing and get the bearing capacity of it. The researcher of
this paper was not working with real data if not with assumed statistical properties (our case is
using real field data). The last stage of this paper was the Monte Carlo simulation for each set of
assumed statistical properties. Each realization, while having the same underlying statistics, had
fairly different spatial pattern of shear strength values beneath the footing and hence, a different
value of bearing capacity. Our research followed a very similar procedure that the used on this
investigation paper, but the differences are that this paper did all the analysis based on assumed
statistical properties and our research are real soil properties obtained from the field and instead
using a strip footing our is thirty two length drilled shaft. This paper was very helpful in the
description of their procedure and the results obtained.
Additionally to these papers mentioned are about twenty to thirty more that made
contributions to the investigations, the most relevant are, “Observations on Geotechnical
reliability-based design development in North America”, “Spatial Trends in Rock Strength-can
they be Determined from core holes?”, and “Drilled Shaft Design for Transmission structures
33
Using LRFD and MRFD” and the rest of them are mentioned on the references or through the
research.
34
Table 2-1. LRFD φ Factors, Probability of Failure (Pf) and Fs Based on Reliability φ for Nearest Boring Approach (FDOT & UF 2003).
Reliability, β LRFD φ Pf (%) Factor of Safety 2.0 0.86 8.5 1.652.5 0.71 1.0 1.983.0 0.60 0.1 2.373.5 0.50 0.01 2.844.0 0.42 0.002 3.404.5 0.35 0.0002 4.07
Table 2-2. LRFD φ Factors, Probability of Failure (Pf) and Fs Based on Reliability φ for Random Selection (FDOT & UF 2003).
Reliability, β LRFD φ Pf (%) Factor of Safety 2.0 0.56 8.5 2.602.5 0.43 1.0 3.323.0 0.33 0.1 4.243.5 0.26 0.01 5.424.0 0.21 0.002 6.924.5 0.16 0.0002 8.84
35
CHAPTER 3 DATA COLLECTION
The Data Collection was divided in two different research stages. The first one, the existent
data was recollected from diverse resources, like Florida Department of Transportation database,
University of Florida past researches, and soil labs maps. And secondly, the data obtained from
the soil borings from the field and processed on the FDOT Materials lab. Both new and old data
was analyzed and it made contribution to the final investigation.
Existent Data Collection
The existent lab data was gathered from different resources like, the FDOT database,
University of Florida Geotechnical Department, and Florida Department of Transportation
Districts past projects. Among the data that was gathered are strengths (qu-qt), recoveries and
compressibility, as well as load testing information. The used data was taken from four of the
seven projects available around Florida that at the time of the initial investigation had available
load test information and additionally any soil boring data, which were relevant to the research.
These four projects that had the requirements described in the last paragraph were Apalachicola
Bridge (Calhoun), Victory Bridge (Chattahooch), Fuller Warren Bridge (Jacksonville) and 17th
Street Causeway (Fort Lauderdale). The localization around Florida of the mentioned bridges is
showed in Figure 3-1.
The other three sites that appear in the location map as a white shadow belong to bridges
that had some load test information at the time of the initial investigation, but the load test shafts
were set in a soil different to limestone.
The data obtained from each one of the bridges showed on the figure is the Measured Unit
End Bearing from Osterberg Load Tests. A summary of this information is showed in the Table
3-1. The table contains in the first column the bridges names, the shaft number and length in the
36
second and third columns respectively. The fourth is for the unknown friction and the bottom
movement on the fifth. The last four columns belong to information about the failure status and
the values for each type of the failure. The mobilized bearing is described as a value less than the
shaft diameter over thirty shaft displacement value. FDOT failure is when the displacement is
exact that displacement rate and Maximum over it.
The values used in the investigation from the above table were the Bottom movement,
FDOT failure, Maximum failure and Mobilized bearing value. Those results were compared with
the Predicted unit end bearings obtained from the finite element model for the different random
fields created using the information obtained from the soil boring lab results. The lab results used
on the random field creation includes strengths (qu-qt), recoveries (REC) and compressibility for
to predict the Unit End bearing.
An example from the 17th Street Bridge is the Table 3-2. The Figure shows the bridge
name with the state project number on the title. The first row includes the soil boring name and
location along the bridge. The first column describes the elevation of the sample, and the other
six columns show the strengths (qu and qt), recovery and RQD. This is just one unsystematic
example but the complete tables used for each one of the mentioned bridges are illustrated on the
APPENDIX A.
New Field Data Collection
The second stage for data collection was the information obtained from the new soil
borings on the bridges field. The bridge site selection was done using a preliminary research for
the mentioned bridges. It includes details as the accessibility to the site (not to be under water),
that the site were on limestone rock, the selected location had to have strength data, that the load
test have preferably a FDOT end bearing failure, and last but not lest that the O-Cell were on the
tip of the drilled shaft. Due to theses details some of the seven projects were not used. Those are
37
the bridges showed on the Figure 3-1 with a white shadow. The principal two recurrent failed
details were that the load test locations were offshore, and that the load test results did not reach
the tip movement (end bearing failure criteria).After the preliminary selection the finally four
selected sites or bridges were:
• Apalachicola River Bridge (District 3) • Victory Bridge (District 3) • Fuller Warren Bridge (District 2) • 17th Street Bridge (District 4)
The field exploration was accomplished by Universal a soil exploration company in
Jacksonville and Fort Lauderdale. And the rock cores obtained from Universal were tested at the
State Materials Office soil lab district 2 (Gainesville Fl.). Consequently, strength values,
recoveries and compressibility records were obtained from them and subsequently were used to
establish LRFD resistance factors for end bearing for each specific site location.
From the pre-selected sites name above, just two of them were tested. It is the case of
Fuller Warren Bridge Jacksonville (District 2) and 17th Street Bridge Fort Lauderdale (District
4). The data obtained from each bridge is showed in the APPENDIX B but an example of the
data obtained from the State Material Office lab is showed in the Table 3-3. In this table is
illustrated the information for each rock core took from the field, as length, diameter, depth, unit
mass, qu, qt, recovery, RQD, density, etc. The data obtained from theses tables was used on the
simulation of random fields and later on the model on the finite element program.
The next couple of paragraphs are dedicated to relevant information about the two bridges
selected for the research.
The Fuller Warren Bridge (District 2)
It is localized over the St. Johns River in downtown Jacksonville on the Interstate Highway
95 (I-95). It replaced the old Gilmore Street Bridge. It has four Load tests LT-1, LT-2, LT-3 and
38
LT-4. In the Figure 3-2 are showed the plan view and the soil profile indicating the mentioned
shaft load tests localization. Only the load test LT-4 was used on this research. Additionally, in
the Figure 3-3 are couple of pictures under the Fuller Warren Bridge during the site inspection.
These pictures shows the position of the load test LT4 where the additional soils boring were
realized around.
17th Street Bridge Fort Lauderdale (District 4)
This is a bascule replacement bridge for the old movable bridge on S.E. 17th Street
Causeway over the intercostals waterway in Fort Lauderdale, located on Broward County. The
17th Street Causeway Bridge has four Osterberg Load tests LTSO-1, LTSO-2, LTSO-3 and
LTSO-4. The only load test used was the LTSO4. Figure 3-4 shows pictures where the load test
LTSO4 is localized.
Data collection for the Fuller Warren Bridge was realized by the Jacksonville Universal
Engineering Science firm. The soil samples were taken to State Materials Office soil lab district
2 (Gainesville Fl.) were all the necessary lab exploration were realized. The same procedure was
followed with the 17th Street Bridge Fort Lauderdale but the firm in charge to do the soil
exploration was PSI Engineering.
39
Table 3-1. Measured Unit End Bearing from Load Tests.
Shaft
Name
Shaft Length (ft)
Unknown Friction (ft)
Bottom Move. (in)
Failure Status
Mobilized Bearing (tsf)
FDOT Failure (tsf)
Max. Failure (tsf)
LSTSO 1 119.4 5.2 0.624 Both x x xLSTSO 2 142.0 9.1 1.95 Tip Fail x x xLSTSO 3 100.1 11.1 1.89 Both 41.5 x x
17th Street Bridge
LSTSO 4 77.5 2.6 3.53 Tip Fail x x 66.4Test 1 64.2 0 4.41 Tip Fail x 61.7 90.3Test 2 101.2 0 2.97 Tip Fail x 28 39Test 4 113.9 0 3.2 Tip Fail x 22.4 30.2
Acosta Bridge
Test 5A 87.8 0 5.577 Tip Fail x 18.5 29.446-11A 85.0 0 5.977 Both x 72.6 9253-2 72.0 0 2.1 Both 70 x x57-10 84.0 0 1.7 Both 60 x x59-8 134.0 9 1.3 Both 65 x x62-5 89.2 0 2.69 Both x 38 40
ApalachicolaBridge
69-7 99.1 0 4.46 Both x 36 44LT-1 41.0 0 0.23 Skin
Fail 87 x x
LT-2 27.9 0 2.56 Both x 80.8 89.5LT-3a 120.7 0 2.94 Both x 34 34
Fuller Warren Bridge
LT-4 66.8 0 3.12 Both x 34 7026-2 38.4 9.8 0.4 Skin
Fail x x x
52-4 54.5 4.33 2.9 Both x 139.2 x
Gandy Bridge
91-4 74.7 6.7 2.5 Both x 42.9 xHillsborough
Bridge 4-14 70.8 7.33 1.74 Both x x x
3-1 33.2 0 0.5 Both 109 x x3-2 38.6 9.66 0.4 Skin
Fail x x x
10-2 46.6 7.7 2.367 Both x 45 x19-1 45.0 0 0.528 Both 124.4 x x
Victory Bridge
19-2 50.7 12.14 0.4 Skin Fail
x x x
40
Table 3-2. 17th Street Bridge Soil Boring Data (State Project No. 86180-1522). BB-1 (32+93) S-4 (33+00)
EL (ft) qu REC RQD qt REC RQD EL (ft) qu REC RQD qt REC RQD-65 32.2 30 22 -32 211.2 68.3 -72 27.34 67 28 -36 116.9 19.4 -85 114.2 13 7
BB-4 (34+81) BB-9 (35+06) EL (ft) qu REC RQD qt REC RQD EL (ft) qu REC RQD qt REC RQD
-69 32.74 22 5 -115 26.5 5-88 28.8 35 10 -131 24.63 43
-131 32.9 43S-12 (35+29) BB-7 (35+44) EL (ft) Qu REC RQD qt REC RQD EL (ft) qu REC RQD qt REC RQD
-32 211 -49 43.5 18 4-32 68.34 -65 414 20 7 -49 117 -72 37.8 -49 19.4 -82 120.8 98 38 -72 19.6 -82 26.3 98 38
-92 82.98 98 38 -102 117.47 66 7 -108 82.44 35 8 -131 140.6 35 10 -131 64.6 35 10
BB-11 (35+53) BB-8 (36+10) EL (ft) qu REC RQD qt REC RQD EL (ft) qu REC RQD qt REC RQD
-36 379.4 38 35 143.97 38 35 -39 361.3 6 5 -36 189.01 38 38 -46 158.7 48 19 55 48 19-36 112.6 38 35 -46 272.7 48 19 53.99 48 19-75 26.3 33 -46 76.78 48 19-98 27.04 60 23 68.7 60 23 -56 285.0 50 12 40.4 50 12-98 140.01 60 23 -95 14.04 17 5
Table 3-3. Fuller Warren State Materials Office Soil Laboratory Data.
State Materials Office Rock Core Effective/Revised: 4/27/05
Foundations Laboratory Unconfined Compression-Split
Tensile By: G.J. Page 1 of 1
Boring /Core Samp.
No. Depth Top
(ft) Depth
Bot. (ft) Test Date Length
(in) Dia. (in) Wet Wt.
(g) Wet Unit
Wt. (pcf)
L/D Ratio Corr. Factor
CB-3/1 1U 41' 8/21/2006 4.8380 2.3950 853.2 149.1 2.02 1.00 2U 4.4327 2.3835 740.4 142.6 1.86 1.01 3T 2.4345 2.3100 335.2 125.2 1.05 4T 2.4350 2.3785 375.0 132.0 1.02 5T 46' 2.3500 2.3730 409.9 150.2 0.99 CB-3/2 1T 46' 8/21/2006 2.4165 2.2995 308.4 117.1 1.05 2U 4.3357 2.3655 774.8 154.9 1.83 1.01 3T 8/22/2006 2.3220 2.3760 406.1 150.3 0.98 4U 4.8068 2.3820 806.8 143.5 2.02 1.00 5T 2.3535 2.3720 400.6 146.7 0.99 6U 4.8825 2.3895 799.2 139.1 2.04 1.00 7T 2.3395 2.3870 393.8 143.3 0.98 8U 51' 4.8715 2.3890 865.4 151.0 2.04 1.00CB-3/3 1T 51' 8/22/2006 2.3315 2.3510 380.8 143.3 0.99 2U 4.8632 2.3610 838.4 150.0 2.06 1.00 3T 2.4395 2.3110 376.5 140.2 1.06 4T 2.4330 2.3555 378.1 135.9 1.03 5U 4.8955 2.3430 734.4 132.5 2.09 1.00 6T 2.4855 2.3285 366.7 132.0 1.07 7T 2.4545 2.3375 328.7 118.9 1.05 8U 4.8125 2.3360 672.7 124.2 2.06 1.00 9T 2.3865 2.3230 332.8 125.3 1.03 10T 2.1210 2.3185 291.7 124.1 0.91 11U 4.7020 2.3455 676.5 126.9 2.00 1.00
41
12T 56' 2.4110 2.3595 369.5 133.5 1.02
Table 3-3. Continued.
Boring /Core
Samp.No. w (%)
Dry Unit Wt.(pcf)
Max. Load (lbs.)
S.T. Strength (psi)
q(u) (psi)
Displ. @ Fail (in)
Strain @ Fail (%)
%Recov./%RQD
Tare Wt. (g)
Wet Wt. (g)
Dry Wt. (g)
CB-3/1 1U 5.32 141.6 6782 1505.6 0.0522 1.08 72/50 430.3 1281.5 1238.5 2U 11.14 128.3 3530 784.1 0.0634 1.43 72/50 430.7 1168.7 1094.7 3T 26.01 99.3 368 41.6 0.0633 72/50 366.1 698.4 629.8 4T 16.40 113.4 1378 151.5 0.0687 72/50 431.4 805.4 752.7 5T 9.07 137.8 3224 368.0 0.0515 72/50 428.3 837.2 803.2
CB-3/2 1T 26.50 92.5 204 23.4 0.0743 77/67 428.1 735.5 671.1 2U 7.46 144.2 5720 1287.5 0.0549 1.27 77/67 430.2 1196.6 1143.4 3T 8.10 139.0 1552 179.0 0.0415 77/67 430.3 835.8 805.4 4U 11.63 128.5 3252 729.8 0.0541 1.13 77/67 431.4 1237.8 1153.8 5T 10.86 132.4 1623 185.1 0.0468 77/67 371.5 771.6 732.4 6U 13.79 122.2 4229 943.0 0.0563 1.15 77/67 433.1 1230.0 1133.4 7T 11.05 129.0 1715 195.5 0.0419 77/67 312.1 703.9 664.9 8U 8.31 139.4 5690 1269.3 0.0454 0.93 77/67 375.9 1239.0 1172.8
CB-3/3 1T 9.56 130.8 379 44.0 0.0410 100/92 366.0 746.4 713.2 2U 8.71 138.0 3187 727.9 0.0630 1.30 100/92 370.8 1207.2 1140.2 3T 4.54 134.1 120 13.5 0.0237 100/92 370.6 746.2 729.9 4T 14.37 118.8 243 27.0 0.0276 100/92 425.7 802.9 755.5 5U 18.48 111.9 501 116.1 0.0297 0.61 100/92 430.6 1164.0 1049.6 6T 19.11 110.8 169 18.6 0.0236 100/92 424.6 790.5 731.8 7T 28.86 92.3 88 9.7 0.0209 100/92 430.4 758.6 685.1 8U 27.47 97.5 731 170.5 0.0455 0.95 100/92 302.8 972.4 828.1 9T 24.01 101.1 287 32.9 0.0422 100/92 425.0 756.6 692.4 10T 23.05 100.8 93 12.1 0.0402 100/92 410.1 701.0 646.5 11U 23.97 102.3 433 100.3 0.0348 0.74 100/92 428.2 1103.6 973.0
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12T 17.63 113.5 437 48.9 0.0324 100/92 428.4 797.4 742.1
43
Figure 3-1. Load Test Bridge Locations.
Figure 3-2. Fuller Warren Bridge Shaft Locations.
LT-1 LT-2LT-3
LT-4
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Figure 3-3. Fuller Warren Bridge during Site Inspection.
Figure 3-4. 17th Street Bridge Load Test Location.
45
CHAPTER 4 GEOSTATISTICS AND NUMERICAL MODEL
Geostatistics
Geostatistics were first developed to provide better estimates of ore reserves. In coal
mining, they have been used to evaluate energy content, sulfur, ash, and other quality attributes
of deposits. In fact, Geostatistics can be used to study many properties that vary in space, but are
measured at distinct locations. Field Researches as diverse as hydrology, forestry, air pollution,
and global warming have all made extensive use of Geostatistics. (Ledvina et al., 1994;
Armstrong, 1998).
The Geostatistics term has been used amply in mining design but just a few of times in
geotechnical. Since it will be not a clear word, let me recall two definitions: “Geostatistics: study
of phenomena that vary in space and/or time” (Deutsch, 2002) and “Geostatistics offers a way of
describing the spatial continuity of natural phenomena and provides adaptations of classical
regression techniques to take advantage of this continuity.” (Isaaks and Srivastava, 1989).
Geostatistics deals with spatially auto correlated data. It is data that has correlation between
elements of a random variable separated from them by a given interval.
The basic idea of Geostatistics is this. Suppose the goal is to determine the cohesion in a
limestone field. If two core holes are drilled just 1 ft apart from each other, one would expect that
their cohesion values would be very similar. If a third hole is drilled 10 ft away, the cohesion
value might be expected to change a little, but still be close the original value. As more holes are
drilled further and further away, a distance is eventually reached where the first holes no longer
help predict the cohesion value.
Between the basic elements of Geostatistics are:
• (Semi) variogram analysis – characterization of spatial correlation.
46
• Kriging – optimal interpolation; generates best linear unbiased estimate at each location; employs semivariogram model.
• Stochastic simulation – generation of multiple equally probable images of the variable; also employs semivariogram model.
(Semi) Variogram
Establishing the spatial correlation structure of a site having erratic variation in its soil
properties would require an extensive amount of subsoil exploration, which may not be feasible
in many projects due to the high costs (Fenton & Griffiths 1999). One of the most common
methods for to estimate the correlation coefficient length is the semivariogram.
The semivariogram is a statistic that appraises the average decrease in similarity between
two random variables as the distance between the variables increases. It describe how spatial
continuity change as a function of distance and direction.
Significant terminology is used to describe the important features of the semivariogram
model, these terms are:
• Sill: The semi variance value at which the variogram levels off. Also it is used to refer to the “amplitude” of a certain component of the semivariogram. For the plot above, “sill” could refer to the overall sill (1.0) or to the difference (0.8) between the overall sill and the nugget (0.2). Meaning depends on context.
• Range: The lag distance at which the semivariogram (or semivariogram component) reaches the sill value. Presumably, autocorrelation is essentially zero beyond the range.
• Nugget: In theory the semivariogram value at the origin (0 lag) should be zero. If it is significantly different from zero for lags very close to zero, then this semivariogram value is referred to as the nugget. The nugget represents variability at distances smaller than the typical sample spacing, including measurement error. The ratio of the nugget effect to the sill is often referred to as the relative nugget effect and is usually quoted in percentage.
• Trend: If the empirical semivariogram continues climbing steadily beyond the global variance value, this is often indicative of a significant spatial trend in the variable, resulting in a negative correlation between variable values separated by large lags. Three options for dealing with lag include: 1) Fit a trend surface and work with residuals from the trend 2) Try to find a “trend-free” direction and use the variogram in that direction as the variogram for the “random” component of the variable 3) ignore the problem and use a linear or power variogram. See Figure 4-1.
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Semivariogram models
For the sake of kriging (or stochastic simulation), we need to replace the empirical
semivariogram with an acceptable semivariogram model. Part of the reason for this is that the
kriging algorithm will need access to semivariogram values for lag distances other than those
used in the empirical semivariogram. More importantly, the semivariogram models used in the
kriging process need to obey certain numerical properties in order for the kriging equations to be
solvable. (Technically, the semivariogram model needs to be non-negative definite, in order the
system of kriging equations to be non-singular.) Therefore, geostatisticians choose from a palette
of acceptable or licit semivariogram models.
Using h to represent lag distance, a to represent (practical) range, and c to represent sill,
the five most frequently used models are:
The nugget model represents the discontinuity at the origin due to small-scale variation.
On its own it would represent a purely random variable, with no spatial correlation. The
spherical model actually reaches the specified sill value, c, at the specified range, a. The
exponential and Gaussian approach the sill asymptotically, with a representing the practical
48
range, the distance at which the semi variance reaches 95% of the sill value. The Gaussian
model, with its parabolic behavior at the origin, represents very smoothly varying properties.
(However, using the Gaussian model alone without a nugget effect can lead to numerical
instabilities in the kriging process.) The spherical and exponential models exhibit linear behavior
the origin, appropriate for representing properties with a higher level of short-range variability.
Examples of this model are showed in Figure 4-2.
Anisotropy
The omni directional semivariogram is that one that for which the directional tolerance is
larger enough that the direction of any particular separation vector become unimportant. It
contains all possible directions combined into a single variogram. The calculation of the
omnidirectional semivariogram does not imply that the spatial continuity is the same in all
directions. It provides a starting point for to establishing some of the parameter required for
sample semivariogram calculations.
In many cases, a random variable shows different autocorrelation structures in different
directions, and an anisotropic semivariogram model should be developed to reflect these
differences. The most commonly employed model for anisotropy is geometric anisotropy, with
the semivariogram reaching the same sill in all directions, but at different ranges. In geological
settings, the most prominent form of anisotropy is a strong contrast in ranges in the
(stratigraphically) vertical and horizontal directions, with the vertical semivariogram reaching
the sill in a much shorter distance than the horizontal semivariogram. In some settings, there may
also be significant lateral anisotropy, often reflecting prominent directionality in the depositional
setting.
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Covariance and correlogram
There are two other tools used on describing spatial continuity these are the Covariance
and Correlation function. Though these two are equally useful, the semivariogram however is the
most traditional. Under the condition of second-order stationary (spatially constant mean and
variance), the covariance function, correlogram, and semivariogram obey the following
relationships:
C(0) = Cov(Z(u),Z(u))= Var(Z(u))
ρ(h) = C(h) C(0)
γ (h)= C(0)-C(h)
In words, the lag-zero covariance should be equal to the global variance of the variable
under consideration; the correlogram should look like the covariance function scaled by the
variance, and the semivariogram should look like the covariance function turned upside down.
The representation is showed in Figure 4-3.
Unlike time series analysts, who prefer to work with either the covariance function or the
correlogram, geostatisticians typically work with the semivariogram. This is primarily because
the semivariogram, which averages squared differences of the variable, tends to filter the
influence of a spatially varying mean.
Kriging
Kriging technique was named after a South African mining engineer named Daniel
Gerhardus Krige who develops the method in an attempt to more accurately predict ore reserves.
Kriging is a group of geostatistical techniques to interpolate the value Z(x0) of a random
field Z(x) (e.g. the elevation Z of the landscape as a function of the geographic location x) at an
unobserved location x0 from observations of the random field at
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nearby locations . Kriging computes the best linear unbiased estimator of
Z(x0) based on a stochastic model of the spatial dependence quantified either by the variogram
γ(x,y) or by expectation μ(x) = E[Z(x)] and the covariance function c(x,y) of the random field. It
have been demonstrated that kriging is not possible without knowledge of the semivariogram or
the covariance.
The kriging estimator is given by a linear combination
of the observed values zi = Z(xi) with weights chosen such that the
variance (also called kriging variance or kriging error):
(with w0(x0) = − 1) of the prediction error is minimized subject to the unbiased
ness condition:
Depending on the stochastic properties of the random field different types of kriging apply.
For the different types of kriging the unbiased ness condition is rewritten into different linear
constraints for the weights wi.
The kriging variance must not be confused with the variance of the kriging predictor
itself.
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Types of Kriging
Classical types of kriging are:
• Simple kriging assuming a known constant trend: μ(x) = 0. • Ordinary kriging assuming an unknown constant trend: μ(x) = μ.
• Universal Kriging assuming a general linear trend model • IRFk-Kriging assuming μ(x) to be an unknown polynomial in x. • Indicator Kriging using indicator functions instead of the process itself, in order to
estimate transition probabilities. • Multiple indicator kriging is a version of indicator kriging working with a family of
indicators. However, MIK has fallen out of favor as an interpolation technique in recent years. This is due to some inherent difficulties related to operation and model validation. Conditional Simulation is fast becoming the accepted replacement technique in this case.
• Disjunctive Kriging is a nonlinear generalization of kriging. • Lognormal Kriging interpolates positive data by means of logarithms.
For this research we were focused in two of theses types, Simple and Ordinary Kriging
Simple Kriging
Simple kriging is the most basic form of kriging in the sense that the model is the simplest
in its mathematical formulation.
The kriging weights of simple kriging have no unbiasedness condition and are given by the
simple kriging equation system:
• Simple Kriging Interpolation
The interpolation by simple kriging is given by:
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• Simple Kriging Error
The kriging error is given by:
which leads to the generalized least squares version of the Gauss-Markov theorem
(Chiles&Delfiner 1999, p. 159):
Ordinary Kriging
Ordinary kriging is an estimation method that is often associated with the acronym
B.L.U.E. for “best linear unbiased estimator.” Ordinary kriging is “linear” because its estimates
are weighted linear combinations of the available data; it is “unbiased” since it tries to have mR,
the mean residual or error, equal to 0; it is “best” because it aims at minimizing σ2R, the variance
of the errors. The distinguish feature of ordinary kriging, is its aim of minimizing the error
variance. In ordinary kriging, it is used a probability model in which the bias and the error
variance can both be calculated and then choose weights for the nearby samples that ensure that
the average error for our model, m̃R, is exactly cero and that our modeled error variance,σ̃R, is
minimized.
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Stochastic Simulation
Stochastic Simulation is the process of building alternative, equally probable, high
resolution models of the spatial distribution of the random variable in study. The simulation is
called conditional if the resulting realizations honor data values at their locations.
Simulation differs from kriging in two primary aspects:
• In kriging the goal is to provide a best local estimate of the variable without specific regard to the resulting spatial statistics of the estimates taken together. In simulation, reproduction of global features and statistics take precedence over local accuracy. Kriging provides a set of local representations, where local accuracy prevails. Simulation provides alternative global representations, where reproduction of patterns of spatial continuity prevails.
• Kriging provides only an incomplete measure of local accuracy and no appreciation of joint accuracy when several locations are considered together. Simulations are designed specifically to provide such measures of accuracy, both local and involving several locations. These measures are given by the differences between alternative simulated values at any location (local accuracy)or the alternative simulated fields (global or joint accuracy).
Sequential Gaussian simulation
There are many algorithms that can be devised to create stochastic simulations (1) matrix
approaches (LU Decomposition), which are not extensively used because of size restrictions (an
N x N matrix must be solved where N, the number of locations, could be in the millions), (2)
turning bands methods where the variable is simulated on 1-D lines and then combined into a 3-
D model; not commonly used because of artifacts, (3) spectral method using FFTs can be CPU
fast, but honoring conditioning data requires an expensive kriging step, (4) fractal which are not
used extensively because of the restrictive assumption of self-similarity, and (5) moving average
methods, which are infrequently used due to CPU requirements. The common approach adopted
in recent times is the sequential Gaussian simulation (SGS) approach. This method is simple,
flexible, and reasonable efficient.
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Sequential Gaussian Simulation is the most straightforward algorithm for generating
realizations of a multivariate Gaussian field. It is provided by the sequential simulation principle
of including all data available within a neighborhood of the point on question, including the
original data and all previously simulated values. Each variable is simulated sequentially
according to its normal cdf fully characterized through a Simple Kriging system.
The detailed steps in Sequential Gaussian Simulation are:
• Determine the univariate cdf representative of the entire study area and not only of the sample data available.
• Transform data to “normal space” • Establish grid network and coordinate system (Zrel-space) • Assign data to the nearest grid node (take the closest of multiple data assigned to the same
node) • Determine a random path through all of the grid nodes • Find nearby data and previously simulated grid nodes • Construct the conditional distribution by kriging • Draw simulated value from conditional distribution • Check results • Back transform (Statios 2001)
By using different random number seeds the order of visiting locations is varied and,
therefore, multiple realizations can be obtained. In other words, since the simulated values are
added to the data set, the values available for use in simulation are partly dependent on the
locations at which simulations have already been made and, because of this, the values simulated
at any one location vary as the available data vary.
Software
The wide range of public domain and low cost software now available means that the tools
of Geostatistics are readily available to the geotechnical. Widely used public domain software
packages include WINGSLIB Geostatistical Software Library, and Gstat , the first one used for
the case studies presented in this research. In addition, several commercial GISystems include
55
geostatistical functions and there is a range of commercial geostatistical packages. Before
starting using the WINGSLIB software, a manual check test was realized. All the steps described
on the Sequential Gaussian Simulation process, were followed and the results were positive.
The data required for to do simulation using SGS in WINGSLIB software were:
• The variable to be simulated (Cohesion Values) • The Semivariogram structure to be used • The maximum and minimum of original data that should be used to simulate a grid node. • Data Variance • X, Y and Z coordinates for the available data • Definition of the grid system • The number of previously simulated point to use for the simulation of another node. • Type of kriging to be used.
This manual check was realized to demonstrate that the results obtained from the Wingslib
software are the same or similar to those obtained doing the process manually.
The example in 2D used eight data values, showed in Table 4-2. The location on a plan
view of data values is illustrated in Figure 4-5. The WINGSLIB results values are in Table 4-3
and those same results are represented in Figure 4-6.
As you observe in Table 4-3 the last two values correspond to the coordinates X,Y (0,2)
and X,Y (2,0). Using WINSLIB the results were 198.95 and 5.52 respectively. And doing the
process manually the results are 198.52 and 5.95 respectively. The difference is very small
comparing the two results. So, it was proved that using WINGSLIB the results obtained are
similarly to those that are obtained doing the process manually.
Numerical Models
Numerical models are available for the user in form of computer codes or programs. A
numerical model program is capable of: (1) solving the equations of equilibrium, (2) satisfying
the strain compatibility equations, and (3) following certain constitutive equations - when
56
prescribed boundary conditions are set forth. The program will produce displacements and stress
changes associated in addition to many other quantities of interest for geotechnical design.
To select the appropriate for each case it is necessary to survey within the wide number of
options and to select one that fit to each case. At this time there are three approaches to model
engineering problems: Continuum, Discrete, and Hybrid. In the Continuum approach, there is no
chance for a failure surface to be explicitly developed since model elements cannot separate at
the boundaries except on pre-defined boundaries like “interfaces” (see Figure 4-4). In the
Discrete approach, elements are ready to separate on boundaries but discontinuity (failure
surface) cannot propagate through the elements, they are still modeled as continuum (see Figure
4-4 c). Finally, the Hybrid approach, as the name implies, incorporates both the Discrete and
Continuum approaches (see Figure 4-4 e).
The numerical solution methods include:
Continuum methods:
• Finite Difference Method (FDM). • Finite Element Method (FEM). • Boundary Element Method (BEM).
Discrete methods
• Discrete Element Method (DEM). • Discrete Fracture Network (DFN) methods.
Hybrid continuum/discrete models
• Hybrid FEM/BEM. • Hybrid FEM/DEM. • Other hybrid models.
57
From a survey made on South Africa (SIMRAC 1999) a list of many numerical models
program available for the use in rock mechanics worldwide is showed in Table 4-1.
FLAC3D (Fast Lagrangian Analysis of Continua)
Flac3D is a powerful Three-dimensional continuum program for modeling soil, rock and
structural behavior. The FLAC3D can model non-linear systems as they evolve in time (Itasca
2002). Used interactively or in batch mode, FLAC is a general analysis and design tool for
geotechnical, civil, and mining engineers that can be applied to a broad range of problems in
engineering studies. The explicit finite difference formulation of the code makes FLAC3D
ideally suited for modeling geomechanical problems that consist of several stages, such as
sequential excavation, backfilling and loading.
The formulation can accommodate large displacements and strains and non-linear material
behavior, even if yield or failure occurs over a large area or if total collapse occurs. FLAC3D
uses an explicit finite difference time-marching scheme to solve the equations of equilibrium.
The equation of motion is solved to drive new velocities and displacements from stress and
forces. Velocities are then used to calculate the strain rates, from there a new stresses can be
calculated through the constitutive equation. These calculations are carried out over one time
step, during which velocities are assumed to be constant. The advantage of using the explicit
formulation is that the numerical scheme stays stable even when the physical system is unstable.
This is particularly advantageous, when modeling “non-linear”, “large strain” behavior and
actual “physical instability”. The disadvantage of the time-marching explicit scheme of the
FLAC3D is that calculation times can be longer than those of implicit formulations.
Materials are represented by polyhedral elements within a three-dimensional grid that is
adjusted by the user to fit the shape of the object to be modeled. Each element behaves according
to a prescribed linear or nonlinear stress/strain law in response to applied forces or boundary
58
restraints. The material can yield and flow and the grid can deform (in large-strain mode) and
move with the material that is represented. The explicit, Lagrangian calculation scheme and the
mixed-discretization zoning technique used in FLAC3D ensure that plastic collapse and flow are
modeled very accurately. Because no matrices are formed, large three-dimensional calculations
can be made without excessive memory requirements. The drawbacks of the explicit formulation
are overcome by automatic inertia scaling and automatic damping that does not influence the
mode of failure. FLAC3D offers an ideal analysis tool for solution of three-dimensional
problems in geotechnical engineering.
The FLAC3D has many constitutive models built in. The user has the option of choosing
the most relevant constitutive model for his problem.
The following FLAC3D material models are the most used:
• Elastic, isotropic;
• Drucker-Prager plasticity;
• Mohr-Coulomb plasticity;
• Strain-hardening / softening Mohr-Coulomb plasticity;
• Bi-linear strain-hardening / softening ubiquitous-joint plasticity
59
Table 4-1. Commercially Available Numerical Programs for Rock Mechanics Study.
Program Source Type(a) Use Complexity BESOL/ MINAP_97
Mining Stress Systems
2D BEM Common Simple
BESOL/MS Mining Stress Systems
3D BEM Common Simple
CSIR Minap32 CSIR Miningtek 2D BEM Academic Simple DIGS CSIR Miningtek 2D BEM Research Specialist Elfen CSIR Miningtek 2D FEM Testing Beta Mediocre Examine Rocscience Inc. 3D BEM Rare Mediocre FLAC Itasca Consulting
Group Inc. 2D FDM Common Advanced
FLAC3D Group Inc. 3D FDM Rare Complex Map3D Mine Modeling
Ltd. 3D BEM Moderate Mediocre
MINIFFT CSIR Miningtek 3D BEM Research Specialist MINSIM CSIR Miningtek 3D BEM Common Simple PFC2D Itasca Consulting
Group Inc. 2D DEM Rare Complex
PFC3D Itasca Consulting Group Inc.
2D DEM Rare Complex
Phase Rocscience Inc. 3D DEM Rare Simple 3DEC Itasca Consulting
Group Inc. 2D BEM Rare Complex
UDEC Itasca Consulting Group Inc.
3D DEM Moderate Advanced
WAVE CSIR Miningtek 2D- 3D FDM Research Specialist PLAXIS Plaxis BV 2D- 3D FEM Moderate Moderate ANSYS ANSYS, Inc. 3D FEM Rare Mediocre ABAQUS ABAQUS, Inc. 3D FEM Rare Mediocre ALGOR ALGOR, Inc. 3D FEM Rare Mediocre (a) BEM: Boundary Element Method; FDM: Finite Difference Method; DEM: Distinct Element Method; FEM:
Finite Element Method.
60
Table 4-2. Sequential Gaussian Simulation Data Values. X Coordinate Y Coordinate Values
0 0 80 0 1 190 1 0 10 1 1 80 1 2 200 2 1 5 2 2 80
Table 4-3. WINSLIB SGS Example Results. X Coordinate Y Coordinate Values
0 0 80 0 1 190 1 0 10 1 1 80 1 2 200 2 1 5 2 2 80 0 2 198.95 2 0 5.52
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Figure 4-1. Semivariogram Model.
Figure 4-2. Most popular Semivariogram Models.
62
Figure 4-3. Semivariogram and Covariance.
63
Figure 4-4. Numerical Approaches to Model an Excavation in a Rock Mass (Jing 2003).
Figure 4-5. WINSLIB SGS Example Location Data Values.
64
Figure 4-6. WINSLIB SGS Example Results Graph.
65
CHAPTER 5 DATA ANALYSIS
Cases Studies
In this research, two case studies are presented. The first case study is an analysis of the
Fuller Warren Bridge in Jacksonville Florida. The second case study is the 17th Street Bridge in
Fort Lauderdale Florida. Both of them were field sites with performed Drilled Shaft Load Test in
Limestone. The data analysis followed the theory description showed on the CHAPTER 4.
The main purpose was to generate random fields using Sequential Gaussian Simulation
(SGS) that was based on the best suited Semivariogram. Each realization, while having the same
statistics (Semivariogram), will have quite difference spatial pattern properties of cohesion, bulk
and shear values on the soil and hence a difference value of end bearing capacity. This was
followed by a finite element model analysis using the random fields obtained on the SGS results.
Fuller Warren
Summary Statistics
The data obtained from the FDOT soil labs are shown in APPENDIX B. It was necessary
to transforms these tables to a different format accepted by the software (APPENDIX C). Some
of the properties showed on these tables, like qu, qt, and, RQD were used on statistics analysis.
The Fuller Warren field data was obtained from three different borings, localized
strategically near to Load Test LT4 in the Southwest side of the Bridge. Each of these boring
CB1, CB2, and CB3 has its own information like qu, qt, RQD, and depth. An example is showed
in Table 5-1. The same data was presented in a different format and it is showed in Table 5-2.
Additionally, the soil boring location is showed in Figure 5-1.
The raw data for each boring was analyzed through histograms, frequency distribution and
summary statistics realization. The histograms for each soil boring CB1, CB2 and CB3 are
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showed in Figure 5-2 to Figure 5-4. These three boring histograms illustrate clearly a difference
tendency on properties values from elevation 55 feet and below. This behavior suggests a limit
for two different layers on the soil. Additionally, an example of frequency distribution (for qu, qt
and RQD), and statistics summary for all new borings (CB1, CB2 and CB3) is showed in
Figure 5-5. It shows that the most suitable frequency distribution is the lognormal. The complete
set of graphs showing each of the boring data in all sites for the same bridge are showed in
APPENDIX D.
The frequency distributions comparing all data (past FDOT research), new data (CB1,CB2
and CB3) and a combination of both is showed in Figure 5-6. The figure showed how the
standard deviation from the combination of old and new data is reduced from 25.66 to 20.32-tsf
when more data values (new data) are added.
Several attempts have been made to obtain the classical statistical properties of the soil,
such as the mean value, COV, and probability distribution, throughout geotechnical engineering
practice. These statistical characteristics have been discussed by several authors and most of
them have implemented distribution models like normal, lognormal, and beta for to curve fit
results of field data. This implies that these distributions are can be used to fitted soil properties
distribution results obtained under field conditions.
Accorded to the obtained results showed in Figure 5-5, the majority of the “closes fitted”
distribution model selected for the Fuller Warren site were Lognormal and Beta.
Spatial Continuity
Spatial continuity exists in most earth science data sets. Two data sets close to each other
are more likely to have similar values than two data sets that are far apart. When we look at a
data graph or posting, the values do not appear to be randomly located, but rather, low values
tend to be near and high values tend to be near other high values. That is the case for each of the
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three soil borings that shows a clear vertical difference between qu, qt and RQD values from -35
to -55 feet depth and -55 to -65 feet depth (Figure 5-2 to Figure 5-4)
The h-scatterplot is another tool used for to analyze vertical spatial continuity. It explains
all possible pair of data whose locations are separated by a certain distance in a particular
direction. On this research, the h-scatterplots, the x-coordinate of a point correspond to the
(qu)^.5(qt)^.5/2 value and the y-coordinate to the (qu)^.5(qt)^.5 value a distance of 1.5 feet away
in a vertical direction.
One of the essential features of an h-scatterplot is the fatness of the cloud of points. And a
way to summarizing this feature is the Correlation Coefficient. As the cloud of points gets fatter,
we expect the correlation coefficient to decrease. The relationship between the correlation
coefficient of an h-scatterplot and h is called the correlogram. Other indices of spatial continuity
are the Semivariogram that is the relationship between the moment of inertia of an h-scatterplot
and h. And the Covariance function that is the relationship between the covariance of an h-
scatterplot and h.
Although the h-scatterplot contain much more information than any of the three summary
statistics (semivariogram, correlogram and covariance function), it is very common to bypass the
actual h-scatterplot and go directly to any of these three to describe spatial continuity.
Fuller Warren Semivariogram
Due to the small amount of soil boring location (just three CB1,CB2 and CB3) and the big
length between them (35 to 45 feet apart), any real representative correlation length was founded
for this bridge data. There are two possibilities to use the Fuller Warren data. The first is to add
two or three more soil boring to the site or secondly, to use the correlation length of 12 feet like
that one founded on the 17th Street Bridge. It is not the best solution but it could represent a
68
better approximation. Since, not real correlation was founded neither Kriging nor Sequential,
Gaussian Simulation was performed on this bridge.
17th Street Bridge
Summary Statistics
The 17th Street Bridge field data was obtained from six different borings localized
strategically near to Load Test LT4 in the Northeast side of the Bridge (see Figure 5-8). Each of
these boring has its own information like qu, qt, RQD, and depth (see Table 5-3). The rest of the
borings soil data is available in APPENDIX B.
The Frequency distributions, for both individual borings, and the complete field site are
showed in the Figure 5-9. No pattern like that layers differences on the Fuller Warren bridge data
was found in this bridge data.
It was discovered from the statistic study that a Proportional Effect is present on the 17th
Street bridge data analysis. Proportional effect on statistics is used when the variance or
semivariogram of a random variable (qu^0.5*qt^0.5/2 in this case) is proportional to the square
of its mean. (Hans Wackernagel 2003). This phenomenon is often an argument to postulate the
log normality of the random variable.
17th Street Bridge Semivariogram
The semivariogram for the 17th Street Bridge was realized using two directions, horizontal
and vertical. The initial idea was to use just one semivariogram for all the data, but after
reviewing the statistic results it was noted that there were two different ranges for each direction.
The semivariogram range was found to be 12 feet distance. The nugget effects that represent the
random measurement error, was fount to be 0.3 of the total sill (Figure 5-10).
69
17th Street Bridge Simple Kriging
The Simple kriging was performed using the cohesion (qu)0.5 (qt)0.5 /2 information from the
soil borings, for each soil borings. The results obtained from simple kriging were used as a step
on the Sequential Gaussian Simulation process.
17th Street Bridge Sequential Gaussian Simulation
The Sequential Gaussian Simulation (SGS) for the 17th Street Bridge was done using the
WINGSLIB software. A small part of the results obtained from the Wingslib is showed in Table
5-4, but the complete table is presented in the APPENDIX E. The results showed on these tables,
are the coordinates for each grid point on space and the correspondent simulated cohesion value
for each grid point.
17th Street Bridge Random Field Model
The behavior of a drilled shaft on limestone rock is influenced by the strengths parameters,
qu and qt, Poisson ratio (υ) and Young modulus (E). While the parameter E and υ, influence the
computed settlement, the bearing capacity depends primarily on the strengths qu and qt
parameters (Gordon & Griffiths 2001). In the present research the Poisson ratio was held
constant and the strengths in the forms (qu^0.5qt^0.5)/2 are modeled as a random variable. After
obtaining the random field the E parameter is calculated from the correlation equation
E=165.06*(qu^0.5qt^0.5)/2+300000. The correlation square ratio between E and
(qu^0.5qt^0.5)/2 for the 17th Street Bridge is 0.6126 (Figure 5-11).
The spatial correlation lengths, or the range from the semivariogram, describe the distance
over which the spatial random values will tend to be correlated. From the 17th Street bridge
semivariogram the ranges on the horizontal and vertical direction were taken, like most of the
soil field the isotropy was not assumed. The random fields were created using the parameters
from the semivariogram showed in Figure 5-10. The range for the vertical direction was 6 feet
70
and for the horizontal direction was 12 feet. Also a nugget effect of 0.3 was used on both
directions. Each random field, while having the same semivariogram parameters, will have quite
different spatial pattern of cohesion values, due to the dissimilar seed used, and hence a different
value of bearing capacity.
The software used on the random field, based on semivariogram parameters, calculation
was the WINGSLIB, and a different seed was used in each calculation. Examples of the random
field and summary tables are founded in APPENDIX E. On these tables is showed the statistics
of the results obtained using different seed values, like mean, standard deviation, etc. It is noticed
that having the same parameter, but with different seed, the final results will change.
17th Street Bridge Finite Elements Analysis
The load-deflection response of a single concrete pile foundation is calculated for loading
in the axial direction. The pile is three feet diameter by twenty feet of length embedded in
limestone rock layer. The properties of the concrete pile and the limestone that are kept constant
are showed in Table. 5-5.
As it was described on CHAPTER 4 the software used for the modeling procedure was
FLAC3D. A modified example founded on the FLAC3D manual was used as support of the
current model.
The soil block model used to simulate our specimen was introduced in the computer
program with the following parameter: the coordinates axes were localized on the lower left
corner and the z-axis oriented along the pile axis and upward. The top of the model, at z=40 feet
is free surface. The base of the model, at z=0, is fixed in the z direction, and roller boundaries are
imposed on the sides of the model, at x=30 feet and y=30 feet (see Figure 5-12).The finite
element mesh consists of square elements of equal size (1.5 x 1.5 x 2.0 feet). Each element has
its own properties, cohesion, bulk, shear and Young modulus.
71
The axial-bearing capacity of a pile is a function of the skin friction resistance along the
pile shaft and the end-bearing capacity at the pile tip. The skin friction resistance is modeled by
placing an interface between the pile walls and the rock. The friction and cohesion properties of
the interface represent the frictional resistance between the concrete and the limestone. For this
model a friction angle of 5° and cohesion of 30000 (tsf) are assumed for the interfaces properties.
The ultimate bearing capacity of the pile in the axial direction is calculated by applying a
vertical velocity at the top of the pile. Many thousand of time steps are required to propagate a
loading through the model. If the velocity is applied suddenly, the inertial effects will dominate
initially and make it more difficult to identify the steady state response of the system. The axial
stress at the top of the pile is calculated and stored. It is plotted versus the axial displacement at
the pile top and an example is showed in the Figure 5-13.
Combined damping is used for this stage of the analysis because this type of damping is
more efficient at removing kinetic energy from the model for the prescribed loading condition.
Three different correlation lengths were used on this study, 1,5, and 12 feet. The 12 feet
was the length that the semivariogram recommend to use, but to see the behavior on the final
capacity, it was necessary to compare the 12 feet with other lengths.
17th Street Bridge Determinist Capacity
The estimated total failure bearing and the End bearing capacities for the determinist soil
properties by the finite element method were 1260 (tons), and 235 (tons) respectively.
Deterministic soil properties mean an average of all soil properties values from the site.
17th Street Bridge Parametric Study
Thirty to forty realizations of statistical soil properties for each one of the correlation
lengths were completed. Each realization, while having the same underlying statistics, will have
quite different spatial pattern of cohesion, bulk, and shear, and hence, a different value of bearing
72
capacity. The results obtained from each simulation were compiled and are showed in the
APPENDIX E. A summary graph is in the Figure 5-14. In the figure the values on the x direction
are the correlation length 1, 5, and 12 feet respectively. On the Y direction are the cohesion mean
of forty simulations, for each one of the correlation length. The values used in Figure 5-14 are
also showed in Table 5-6.
The cohesion means shows a higher value for the correlation length of 12 feet and a small
cohesion value for the 1 foot correlation length. The row data cohesion mean value is 42647
(PSF), and it is showed that the one foot correlation length cohesion mean value is the closest
one to the raw data, and the twelve feet the isolated. The explanation for this is that the smallest
the correlation length, the smallest the coefficient of variation of the simulated data from the
sequential Gaussian simulation program.
The same tendency on the cohesion behavior is showed on the end bearing capacity
obtained from the finite element method Figure 5-15. But in this case the deterministic capacity
value is 235 (tons). Therefore, this case is inversed to the cohesion graph. The twelve feet
capacity value is approximated to the deterministic capacity value and the one foot is far-away.
The explanation for the lower capacity values for one and five feet correlation lengths lies in the
fact that as the spatial correlation length decreased, the weakest trail becomes increasingly
tortuous, and its length correspondingly longer. As a result the weakest trail starts to look for
shorter ways cutting through higher strength materials (Griffiths & Fenton 1999). If there were a
correlation length bigger than 12 feet correlation length, the result could be bigger or smaller but
in any case far away from the determinist value; it is because it allows enough variability for a
failure surface to develop which deviates significantly from the deterministic results.
73
Consequently, the optimum failure path will be the same as in the uniform material. In our case
the result that tends to that result, is the correlation length suggested by the semivariogram.
In the APPENDIX G is show all the programming models used on this research, for to
obtain the bearing capacity for each one of the soil simulations. Additionally, the results graphs
and tables are in this same appendix.
17th Street Bridge Comparison of Deterministic and Predicted End Bearing
Table 5-7 shows a comparison of Simulated and deterministic End Bearing capacity from
the finite elements program. Each correlation has its own predicted End bearing and it is
compared with the End bearing capacity obtained from the deterministic value So, for one, five,
and twelve feet correlation lengths the predicted End Bearing are 218.36, 218.375, and 238.125
tons respectively compared to 235 from the deterministic result.
17th Street Bridge LRFD Phi Factors
According the explanation in CHAPTER 1, the goal of resistance factor design (LRFD)
analysis is to develop factors that decrease the nominal resistance to give a design with an
acceptable and consistent probability of failure. Where load components are multiplied by load
factors and resistance is multiplied by a resistance factor. The basic equation is:
φRn > ∑γi Qi
where γi is a load factor applied to load components Qi and φ is resistance factor applied to
the resistance (measured of load carrying capacity) Rn. In words it equation says that the
capacity of the foundation (modified by the factor φ) must be larger than the total effect of all the
loads acting on it.
FOSM method has been used (NCHRP 507, 2004) to calibrate LRFD factors using a
statistical dataset containing the measured and predicted resistances. It assumes that the load and
74
resistance are modeled as lognormal random variables. This limits the load and resistance values
to only positive numbers.
The next equation is used to calibrate the resistance factor using the FOSM method. It is
dependent on the target reliability index and the ratio of dead to live load.
)]])[(])[(1)(])[(1ln[(
2
22
222
])[][(
)()])[(1(
)])[(])[(1(][
QLCOVQDCOVRCOVQL
L
DQD
QLL
DQD
NR
NTeEqqE
RCOVQLCOVQDCOVE
+++⋅⋅+⋅
+⋅⋅+
++⋅
=βλλ
γγλφ
In the 17th Street Bridge instead using it for to calibrate the resistance factor as a method, it
was used for to account for differences or variability based on correlation lengths.
The FOSM equation was used for to get Phi factor for different correlation length, but
instead using a measured value it was used the deterministic value obtained from the same finite
element program. It allows seeing the differences on the phi factor, based on spatial variability
and reliability index.
To account for spatial variability on the 17th Street Bridge, a total of forty End bearing
values were predicted for five and twelve feet correlation length, and thirty values for the one
foot length case. Additionally, the deterministic value was obtained using the same program.
From the predicted and deterministic values at all the correlation length, the mean λΡ, standard
deviationσΡ, and coefficient of variation COVR, were found for the design approach (Table 5-8).
Using the computed mean, λΡ, and coefficient of variation COVR, for each correlation
length, the LRFD resistance factor, φ, were determined for different values of reliability index, β.
The results are shown in Table 5-9.
75
Additionally, a Modified FOSM equation was also used, due to a NCHRP 507 report that
shows that the resistance factors developed by FORM (First Order Reliability Method) tend to be
10 to 15% greater than the factors developed using the FOSM method. This means that the
FOSM resistance factors are conservative (it is recognized that the FORM resistance factors are
more accurate). Since the purpose of LRFD is to design based off of the probability of failure, it
is more beneficial to have accurate resistance factors.
The modified FOSM equation is based on a past (Styler 2006) research, which stated that
the published FOSM equation had an error that offered results consistently lower than actual
resistance factors. The modified equation is:
)]])[(][][2])[(
])[(])[(])[(])[(1)(])[(1ln[(
2
222
2
22222
2
222
2
22222
2
2
])[][(
)()])[(1(
)])[(][][2])[(
])[(])[(])[(])[(1(
][
⎟⎟⎠
⎞⎜⎜⎝
⎛++
⎟⎟⎠
⎞⎜⎜⎝
⎛+
++⋅
⋅+⋅
+⋅⋅+
⎟⎟⎠
⎞⎜⎜⎝
⎛++
⎟⎟⎠
⎞⎜⎜⎝
⎛+
+
⋅=
QLQLQDL
DQD
L
D
QLQLQDQDL
D
T
EEEqqE
COVECOVEqq
RCOV
QLL
DQD
QLL
DQD
QLQLQDL
DQD
L
D
QLQLQDQDL
D
R
eEqqE
RCOV
EEEqqE
COVECOVEqq
E
λλλλ
λλλλβ
λλ
γγλλλλ
λλλλ
λφ
The modified FOSM equation is still in terms of the target reliability index and the dead to
live load ratio. Results from the 17TH Street Bridge using the modified equation are illustrated in
Table 5-10. It is shown that positively the values using the new equation are a little higher than
those using the traditional FOSM equation.
The results for the phi factors show a proportional inversely relationship with correlation
length, a bigger value when the correlation length is minor and small value when the length is
larger. This result explanation lies in the fact that with smaller correlation distances better
knowledge of the proximity soil properties, so a bigger factor could be used.
76
The modified FOSM results are slightly bigger than the traditional, and based on Styler
2006 theory, closer to accurate results.
Table 5-1. Fuller Warren Bridge Soil Boring Information.
Boring /Core
Samp.No. w (%)
Dry Unit Wt.(pcf)
Max. Load (lbs.)
S.T. Strength (psi)
q(u) (psi)
Displ. @ Fail (in)
Strain @ Fail (%)
%Recov./%RQD
Tare Wt. (g)
Wet Wt. (g)
Dry Wt. (g)
CB-3/1 1U 5.32 141.6 6782 1505.6 0.0522 1.08 72/50 430.3 1281.5 1238.5 2U 11.14 128.3 3530 784.1 0.0634 1.43 72/50 430.7 1168.7 1094.7 3T 26.01 99.3 368 41.6 0.0633 72/50 366.1 698.4 629.8 4T 16.40 113.4 1378 151.5 0.0687 72/50 431.4 805.4 752.7 5T 9.07 137.8 3224 368.0 0.0515 72/50 428.3 837.2 803.2
CB-3/2 1T 26.50 92.5 204 23.4 0.0743 77/67 428.1 735.5 671.1 2U 7.46 144.2 5720 1287.5 0.0549 1.27 77/67 430.2 1196.6 1143.4 3T 8.10 139.0 1552 179.0 0.0415 77/67 430.3 835.8 805.4 4U 11.63 128.5 3252 729.8 0.0541 1.13 77/67 431.4 1237.8 1153.8 5T 10.86 132.4 1623 185.1 0.0468 77/67 371.5 771.6 732.4 6U 13.79 122.2 4229 943.0 0.0563 1.15 77/67 433.1 1230.0 1133.4 7T 11.05 129.0 1715 195.5 0.0419 77/67 312.1 703.9 664.9 8U 8.31 139.4 5690 1269.3 0.0454 0.93 77/67 375.9 1239.0 1172.8
CB-3/3 1T 9.56 130.8 379 44.0 0.0410 100/92 366.0 746.4 713.2 2U 8.71 138.0 3187 727.9 0.0630 1.30 100/92 370.8 1207.2 1140.2 3T 4.54 134.1 120 13.5 0.0237 100/92 370.6 746.2 729.9 4T 14.37 118.8 243 27.0 0.0276 100/92 425.7 802.9 755.5 5U 18.48 111.9 501 116.1 0.0297 0.61 100/92 430.6 1164.0 1049.6 6T 19.11 110.8 169 18.6 0.0236 100/92 424.6 790.5 731.8 7T 28.86 92.3 88 9.7 0.0209 100/92 430.4 758.6 685.1 8U 27.47 97.5 731 170.5 0.0455 0.95 100/92 302.8 972.4 828.1 9T 24.01 101.1 287 32.9 0.0422 100/92 425.0 756.6 692.4 10T 23.05 100.8 93 12.1 0.0402 100/92 410.1 701.0 646.5 11U 23.97 102.3 433 100.3 0.0348 0.74 100/92 428.2 1103.6 973.0
77
12T 17.63 113.5 437 48.9 0.0324 100/92 428.4 797.4 742.1
Table 5-2. Fuller Warren Soil Boring Modified Data. Name of Boring
CB-1 (New) CB-2 (New) CB-3 (New) Distance from Load Test (ft)
30 25 15 EL. (ft)
qu (tsf)
qt (tsf) RQD Ei (psi) EL. (ft)
qu (tsf)
qt (tsf) RQD Ei (psi)
EL. (ft)
qu (tsf)
qt (tsf) RQD Ei (psi)
-40.5 15.36 31.21 37 20725.93 -37.58 42.57 25.23 23 48974.00 -41 108.40 3.00 50 139525.37 -40.5 96.14 2.14 37 93362.29 -37.58 4.36 23 -41 56.45 10.91 50 55345.75 -40.5 6.36 37 -42.58 18.66 3.54 52 30083.74 -41 26.50 50 -45.5 143.30 9.07 74 108694.81 -42.58 56.42 1.76 52 75668.97 -46 92.70 1.69 67 102818.36 -45.5 59.24 7.21 74 20329.10 -42.58 15.32 52 -46 52.55 12.89 67 64868.52 -45.5 52.29 15.85 74 50938.20 -42.58 10.34 52 -46 67.90 13.33 67 81761.47 -45.5 68.09 18.33 74 87522.73 -47.58 64.77 18.36 87 81523.95 -46 91.39 14.08 67 136076.85 -45.5 13.65 74 163837.76 -47.58 65.12 8.41 87 75899.59 -51 52.41 3.17 92 56192.28 -50.5 113.41 18.62 48 143167.10 -47.58 37.24 8.51 87 38959.02 -51 8.36 0.97 92 19141.58 -50.5 11.95 48 -47.58 140.06 10.11 87 152082.74 -51 12.28 1.94 92 18051.95 -50.5 1.86 48 -47.58 8.29 1.91 87 15682.83 -51 7.22 1.34 92 13564.22 -50.5 0.89 48 -47.58 78.44 0.84 87 69402.72 -51 0.70 92 -50.5 1.44 48 -52.58 15.68 5.49 98 24923.43 -51 2.37 92
78
-55.5 12.56 1.37 77 16123.94 -52.58 10.61 1.82 98 14642.92 -51 0.87 92
Table 5 2. Continued. Name of Boring
CB-1 (New) CB-2 (New) CB-3 (New) Distance from Load Test (ft)
30 25 15 EL. (ft) EL. (ft)
EL. (ft)
EL. (ft) EL. (ft) EL. (ft)
EL. (ft)
EL. (ft)
EL. (ft) EL. (ft)
EL. (ft)
EL. (ft)
EL. (ft)
EL. (ft) EL. (ft)
-55.5 22.01 0.91 77 33646.94 -52.58 9.08 1.28 98 13980.61 -51 3.52 92 -55.5 22.92 2.58 77 28351.18 -52.58 18.88 1.90 98 21191.30 -56 27.07 1.30 60 35561.05-55.5 11.89 1.77 77 13580.10 -52.58 20.99 1.40 98 20221.36 -56 19.84 2.93 60 24011.06-55.5 2.00 77 -52.58 16.81 1.36 98 21522.93 -56 14.39 2.74 60 13791.05-60.5 7.08 1.05 67 6509.45 -52.58 1.04 98 -56 1.75 60 -60.5 7.36 0.66 67 8173.66 -52.58 1.64 98 -56 1.42 60 -60.5 8.59 0.25 67 10247.30 -57.58 16.72 1.77 47 26059.97 -61 9.09 1.09 100 11308.89-60.5 7.57 1.05 67 11768.07 -57.58 10.80 47 11899.08 -61 9.33 0.87 100 9220.15-60.5 0.93 67 -57.58 18.28 47 19700.99 -61 9.89 1.37 100 11249.80-65.5 3.02 0.40 38 3832.10 -62.58 11.08 1.14 77 11334.53 -61 9.80 1.32 100 11165.85-65.5 0.40 38 -62.58 9.44 1.44 77 12460.26 -61 8.10 0.40 100 10801.59-65.5 0.43 38 -62.58 9.59 1.24 77 13170.90 -61 5.90 100 9630.65-65.5 0.25 38 -62.58 10.08 0.97 77 14308.84 -61 3.96 100 8026.87
-62.58 7.49 0.42 77 15724.97 -66 5.99 0.81 45 8732.30
79
-66 8.04 0.69 45 10850.17
Table 5-3. Table 17th Street Bridge Soil Boring Information.
Boring /Core
Samp.No. w (%)
Dry Unit Wt.(pcf)
Max. Load (lbs.)
S.T. Strength (psi)
q(u) (psi)
Displ. @ Fail (in)
Strain @ Fail (%)
%Recov./%RQD
Tare Wt. (g)
Wet Wt. (g)
Dry Wt. (g)
9/1 1T 6.88 93.3 1279.5 144.8 0.1211 98/64 76.3 349.6 332 2U 6.62 119.7 4586 1014.4 0.0481 0.99 98/64 77 803.8 758.7 3T 9.36 107.7 1349.6 139.6 0.1402 98/64 75.4 429.4 399.1 4U 7.87 127.8 5926.1 1283.9 0.0533 1.39 98/64 77.1 684.2 639.9 5T 6.88 133.4 3102.2 378.2 0.0323 98/64 75.1 435.4 412.2 7U 5.95 123.0 4364.8 971.6 0.0426 1.02 98/64 74.2 695.5 660.6 8T 5.68 122.8 2644.6 361.6 0.1008 98/64 77.9 373.6 357.7 9T 4.30 128.2 3740 437.2 0.1115 98/64 76.3 430.4 415.8 10U 1.86 145.8 16570 3651.9 0.0723 2.00 98/64 75.6 682.5 671.4
9/2 2U 3.66 130.4 4704.7 1032.8 0.0302 0.74 62/8 75.5 716.1 693.5 3T 1.84 143.2 5139.4 553.9 0.0406 62/8 76.3 502.5 494.8 4T 2.50 145.2 4575.3 556.0 0.0323 62/8 77.1 461.8 452.4 5T 1.55 134.0 3925.7 447.4 0.0201 62/8 77.9 450.6 444.9
9/3 1T 0.90 138.6 3660 416.8 0.0345 87/33 75.1 458.1 454.7 2T 1.16 151.6 5147.2 598.8 0.0344 87/33 75.4 486.6 481.9 3U 1.62 151.8 8931.8 2022.7 0.0411 0.86 87/33 77 930.4 916.8 4T 1.15 150.1 4117.4 469.1 0.0385 87/33 76.1 489.7 485 5U 2.26 149.6 12046.9 2714.5 0.0564 1.24 87/33 77.1 881.4 863.6 6T 3.71 132.2 1619.8 335.6 0.0306 87/33 76.5 431.4 418.7 7U 3.83 136.8 4587.7 1005.8 0.0652 1.67 87/33 81.6 724.1 700.4
80
8T 2.53 104.3 1663.5 225.2 0.1097 87/33 75.7 318.7 312.7
81
Table 5-4. 17th Street Bridge Wingslib Results. X Coordinate Y Coordinate Z Coordinate Cohesion Simulated
0 0 0 9.593 1.5 0 18.59
27 3 0 11.100 9 0 30.109 19.5 2 7.380 13.5 6 35.320 0 10 36.60
22.5 22.5 10 19.250 19.5 14 14.42
Table. 5-5 Material Properties Bulk (psf) Shear (psf) Friction Cohesion (psf)
1.40E+07 8.80E+06 15 77421.791.40E+07 8.80E+06 15 70154.741.40E+07 8.80E+06 15 54409.31.40E+07 8.80E+06 15 60513.671.40E+07 8.80E+06 15 67786.841.40E+07 8.80E+06 15 62980.131.40E+07 8.80E+06 15 50742.81.40E+07 8.80E+06 15 53058.951.40E+07 8.80E+06 15 68361.91.40E+07 8.80E+06 15 79498.88
Table 5-6. 17TH Street Bridge Cohesion Mean Results Values from Simulations Correlation Length (ft) Cohesion Mean (psf)
1 42695 5 42931
12 43731 Raw Data 42647
Table 5-7. 17TH Street Bridge End Bearing Capacity Mean Values from FLAC3D Correlation Length (ft) End Bearing Capacity (tons))
1 216.36 5 218.37
12 238.12 Deterministic 235
Table 5-8. 17TH Street Mean, Standard, and COV of Predicted End Bearing Capacity Bias Correlation Length (ft) Mean Standard Deviation COV
1 1.089557 0.120611 0.1106985 1.104859 0.181206 0.164009
12 1.012976 0.172597 0.170386
82
Table 5-9. 17TH Street Bridge φ Values for different Reliability Index β FOSM (Traditional) Correlation Length (ft) β 2.5 β 3.0 β 3.5 β 4.0
1 0.773 0.684 0.605 0.5355 0.726 0.633 0.553 0.482
12 0.658 0.573 0.500 0.435 Table 5-10. 17TH Street Bridge φ Values for different Reliability Index β FOSM (Modified) Correlation Length (ft) β 2.5 β 3.0 β 3.5 β 4.0
1 0.957 0.887 0.822 0.7625 0.868 0.788 0.715 0.650
12 0.785 0.710 0.643 0.582 Table 5-11. 17th Street Bridge COV and λ Correlation Length (ft) COV λ
1 0.1106975 0.12061125 0.1640086 0.18120632
12 0.17038627 0.17259719
83
2 3
1
40 ft
35 ft55 ft
N
2 3
1
40 ft
35 ft55 ft
N
Figure 5-1. Fuller Warren Soil Boring Location.
CB-1 Elevation vs. qu, qt,RQD,qb
-20.000.00
20.0040.0060.0080.00
100.00120.00140.00160.00
-70-65-60-55-50-45-40-35Elevation (ft)
qu (t
sf),
qt (t
sf),
RQ
D
qu (tsf) qt (tsf) Recovery qb(tsf) (FDOT) quqt
Figure 5-2. Fuller Warren Histogram CB1.
84
CB-2 Elevation vs. qu, qt,RQD,qb
0.0020.0040.0060.0080.00
100.00120.00140.00160.00
-70-65-60-55-50-45-40-35
Elevation (ft)
qu (t
sf),
qt (t
sf),
RQ
D
qu (tsf) qt (tsf) Recovery qb(tsf) (FDOT) quqt
Figure 5-3. Fuller Warren Histogram CB2.
CB-3 Elevation vs. qu, qt,RQD,qb
0.00
20.00
40.00
60.00
80.00
100.00
120.00
-70-65-60-55-50-45-40-35
Elevation (ft)
qu (t
sf),
qt (t
sf),
RQ
D
qu (tsf) qt (tsf) Recovery qb(tsf) (FDOT) quqt
Figure 5-4. Fuller Warren Histogram CB3.
85
0 50 100 1500
0.01
0.02
0.03
0.04
qu0 10 20 30 40
0
0.1
0.2
0.3
0.4
qt
0 50 1000
0.01
0.02
0.03
RQD
QU QT RQD MEAN = 33.2623 4.9771 70.5119 STD = 35.5262 6.7102 21.6325 MNPDFEXP = 30.9262 4.9163 29.2225 STDPDFEXP = 28.4992 4.7548 25.2514 MNPDFLOG = 27.5770 4.0548 56.0055 STDPDFLOG = 25.9415 4.9143 17.7774 MNPDFGAM = 31.4924 4.8403 58.0390 STDPDFGAM = 27.7417 5.1162 17.8002 MNPDFRAYL = 42.9191 7.3741 45.8545 STDPDFRAYL = 22.4075 3.8534 23.3869 sqerrorNORM = 1.0e-005 * 0.7224 0.0185 0.0003 sqerrorEXP = 1.0e-005 * 0.3605 0.0020 0.0043 sqerrorLOGN = 1.0e-005 * 0.1938 0.0000 0.0093 sqerrorGAM = 1.0e-005 * 0.3299 0.0037 0.0041 sqerrorRAYL = 1.0e-005 * 0.5839 0.0968 0.0009 Figure 5-5. Fuller Warren New Borings Frequency Distribution qu, qt and RQD.
86
0 20 40 60 80 100 1200
0.05
0.1
Frequency Distribution Old Borings
quqt (tsf)0 20 40 60 80 100
0
0.05
0.1
Frequency Distribution New borings
quqt (Tsf)
0 20 40 60 80 100 1200
0.05
0.1
Frequency Distribution New+Old Borings
quqt (tsf)
MEAN = 40.4560 11.8474 18.7135 STD = 25.6634 12.0870 20.3264 Figure 5-6. Frequency Distribution for quqt.
quqt vs Ei (psf) y = 383.66x + 1E+06R2 = 0.6645
0
5000000
10000000
15000000
20000000
25000000
0 10000 20000 30000 40000 50000
quqt (psf
E (p
sf)
Figure 5-7 Fuller Warren Bridge quqt and E Correlation
87
Figure 5-8. 17th Street Soil Boring Locations (SMO 2007).
88
0 100 200 3000
0.005
0.01
0.015
qu0.5qt0.5/20 20 40 60 80
0
0.01
0.02
0.03
0.04
0.05
qt(tsf)
0 20 40 600
0.01
0.02
0.03
0.04
0.05
qu (tsf)
Figure 5-9. 17th Street Frequency Distribution
89
Figure 5-10. 17th Street Semivariogram.
90
quqt vs Ey = 165.06x + 3E+06
R2 = 0.6126
0
5000000
10000000
15000000
20000000
25000000
30000000
35000000
40000000
0 50000 100000 150000 200000
quqt
E
Series1Linear (Series1)
Figure 5-11. 17th Street Bridge Correlation quqt vs E.
91
Figure 5-12. 17th Street Bridge FLAC Model Grid
92
Figure 5-13. 17th Street Axial Force vs Pile Displacement
93
Correlation Length vs Cohesion Mean
42600
42800
43000
43200
43400
43600
43800
0 2 4 6 8 10 12 14
Correlation Length (feet)
Coh
esio
n M
ean
(lbs)
Figure 5-14. 17th Street Correlation Length vs Cohesion Mean
Correlation Length vs Total Bearing Capacity Mean
1150.00
1155.00
1160.00
1165.00
1170.00
1175.00
1180.00
1185.00
1190.00
1195.00
1200.00
0 2 4 6 8 10 12 14
Correlation length (ft)
Tota
l Bea
ring
Cap
city
Mea
n (t
ons)
Figure 5-15. 17th Street Correlation Length vs Total Bearing Capacity
94
Correlation Length vs End Bearing Capacity Mean
210.00
215.00
220.00
225.00
230.00
235.00
240.00
0 2 4 6 8 10 12 14
Correlation length (ft)
End
Bea
ring
Cap
city
Mea
n (t
ons)
Figure 5-16. 17TH Street Correlation length vs End Bearing Capacity
95
CHAPTER 6 COST ANALYSIS
The principal initiative of the cost analysis is to find a cost comparison between the
different φ factors obtained from this Geostatistics study. This study compared results from the
three correlation lengths to the deterministic result. The first one used the soil parameter from the
borings made around the specific drilled shaft, and the deterministic used the design parameters
from soil borings over the whole site. Moreover, the cost analysis is divided in two stages. The
first stage includes the materials, labor and equipment cost of the drilled shaft construction and
the second stage includes the costs of additional borings around each drilled shaft.
Factor Influencing Cost
Several factors influence the final costs of a drilled shaft construction, among them are:
Subsurface and site conditions Geometry of Drilled Shaft Specification, including inspection procedures Weather conditions Location of work as related to travel and living cost of crew Governmental regulation Availability of optimum equipment Experience of the contractor Insurance and bonding
These factors are just a sample of all the variables that could influence a drilled shaft
construction costs. This cost analysis assembles most of these influence variables in three big
groups. Those are: 1) Drilled Shaft Construction, 2) Drilled Shaft Excavation and 3) Boring Test
Costs.
The drilled shaft construction includes the costs of: concrete, steel, temporary casing,
labor, materials, equipment and incidentals necessary to complete the drilled shaft. The second
group includes all the work related to the drilled shaft excavation. Finally, the boring test cost
96
includes the soil boring auger and the laboratory analysis. It will depend basically on the number
of tests to be performed.
Drilled Shaft Cost and Excavation
The analysis is based on the Florida Department of Transportation average unit cost
database. The database item descriptions are presented in the Basis of Estimates Handbook
(Figure 6-1). This document was created with the purpose of presenting a standard method of
documenting the design quantities for construction paid items. The handbook also presents the
standard method of calculating quantities for many paid items that require special methods of
measurement.
The FDOT Item Average Unit Cost Database is numerated from item 000 to 1999 and the
items are categorized by paid item range. Table 6-1 shows this categorization. The used items for
this research were in the Road &Bridge category from 100 to 577. These items are 455 88 5
Drilled Shaft and 455 122 5 Excavation Unclassified shaft. The item 455 88 5 is specified for a
Drilled Shaft of 48” diameter. Figure 6-1 shows the FDOT Basis of Estimates Handbook
description for this item. The analyzed drilled shaft in this research was 36” of diameter.
However, due to the lack of information for this diameter on the FDOT data base, data from a
48” diameter shaft was used instead. The same procedure was used on the item 455 122
Unclassified Shaft Excavation. Figure 6-2 shows the description of this item. The quantity on
this item is measured as the depth of excavation from the ground to tip of the shaft measured in
linear feet.
The Basis Estimates Handbook is divided by years. Therefore, data from 2002 to 2006
were used. An example of the 2006 Item average Unit Cost for the items 455 88 5 and 455 122 5
are showed in the Figure 6-3. The complete data information is presented in APPENDIX G.
97
Moreover, the summary of the Drilled Shaft and Excavation shaft of 48’ diameter are presented
in Table 6-2 and Table 6-3.
Soil Boring Test Costs
The rates for soil laboratory tests are based on the State Material Office cost database. The
available FDOT data from 2003 through 2006 divided annually was used for the analysis. Table
6-4 shows the most common soil test used for Drilled Shaft studies and at the same time used on
the 17th Street Bridge. Additionally, the cost of obtaining the soil samples in a rock soil from 0’
to 50’ is $26.25/LF and from 50’-100’ is $30.63/LF. These costs are based on actual (2007) cost
from FDOT District 4.
Relative Costs Analysis
The analysis was divided into three groups: 1) Drilled Shaft Cost, 2) Drilled Shaft
Excavation and 3) Boring Test Cost.
Drilled Shaft Cost
All the cost analysis will be based on a one foot length by four feet diameter drilled shaft
in lime rock soil. The total Drilled Shaft construction cost was $267.97 per linear feet. This result
was compared with the costs generated by the used of the new φ factors presented previously in
CHAPTER 5. Those φ factors accounted for three correlation lengths, and four reliability indices
(Table 5-10). It is assumed that each φ factors represent a percentage of the deterministic value.
For example from Table 5-10 , a value with a correlation length of 5 feet and a reliability index
of 3.0 the φ factor is 0.788. Therefore, this value represents the 100/78.88% of the total
determinist cost corresponding to this φ factor. Consequently, the total cost of the determinist
value of $267.97 multiply by 1/0.788 will derive on $423.33 per linear feet. This cost
98
corresponds to the use of a specific φ factor. The complete sets of results are presented in Table
6-5 and Table 6-6.
Drilled Shaft Excavation
The same procedure followed on the Drilled Shaft Construction Cost section was followed
for the Drilled Shaft Excavation. The cost analysis for the excavation item is also based on a one
foot length by four feet diameter drilled shaft on lime rock. This excavation cost is $173.92 per
linear feet. The complete set of cost results are presented in
Table 6-7, and Table 6-8.
Boring Test Cost
This analysis was based on the influence of number of soil borings around the drilled shaft.
The average of the Drilled Shaft construction cost, Excavation, and soil lab test cost presented in
Table 6-2 to Table 6-4 are shown in Table 6-9. The total construction cost assuming just one soil
boring test was $267.97 per linear feet, the excavation $173.92 and the laboratory soil test costs
$24.5 per linear feet. The average auger cost of $30.63 per linear feet was obtained from FDOT
District 4 (Table 6-9). The total is $497.02 per linear feet assuming one soil boring per drilled
shaft.
Under the same circumstances but assuming five soil borings around the drilled shaft, the
total cost per linear feet was $717.54 per linear feet (Table 6-10). The difference was $220.52
per linear feet. If the drilled shaft is 20 feet long as the 17th Street Bridge case, the differences
will result on $4,410.4.
99
Table 6-1. FDOT Item Average Unit Cost Database. ITEM CATEGORY
100 to 577 Roadway & Bridge 579 to 590 Landscape 600 to 715 Traffic Operations 721 to 770 Peripherals 800 to 899 Mass Transit 900 to 999 Special Use
1000 to 1999 Utility Table 6-2. Summary of Drilled Shaft of 48” Diameter (0455 88 5). Year No. of Contracts Weighted Average Total Quantity (LF) Total Amount
2006 4 $356.66 2456 $875,956.96 2005 3 $204.33 1087 $222,106.71 2004 6 $277.60 2533 $703,106.80
2002-2003 10 $233.29 3488 $813,715.52 Average $267.97 Table 6-3. Summary of Excavation Shaft of 48” Diameter (0455 122 5). Year No. of Contracts Weighted Average Total Quantity (LF) Total Amount
2006 3 $328.19 2380 $781,092.20 2005 2 $170.14 1011 $172,011.54 2004 5 $77.78 2128 $165,515.84
2002-2003 9 $119.58 3270 $391,026.60 Average $173.92 Table 6-4. Summary of Soil Lab from 2003 to 2007
Test Name Moisture Content ($)
Specific Gravity ($)
Split Tensile ($)
Unconfined Compression ($) Average ($)
2003-2004 8 57.37 89 83.63 2382004-2005 8.15 55.83 95.83 85.38 245.192005-2006 8.43 57.24 95.72 87.80 249.192006-2007 8.15 57.34 95.37 86.63 247.49
Average 8.1825 56.945 93.98 85.86 244.9675
100
Table 6-5. Summary of Drilled Shaft Cost (Material, labor) for φ Factors FOSM Correlation Length (ft) β 2.5 β 3.0 β 3.5 β 4.0
1 $346.66 $391.77 $442.93 $500.885 $369.10 $423.33 $484.58 $555.95
12 $407.25 $467.66 $535.94 $616.02 Table 6-6. Summary of Drilled Shaft Cost (Material, labor) for φ Factors FOSM (Modified) Correlation Length (ft) β 2.5 β 3.0 β 3.5 β 4.0
1 $280.01 $302.11 $326.00 $351.675 $308.72 $340.06 $374.78 $412.26
12 $341.36 $377.42 $416.75 $460.43 Table 6-7. Summary of Drilled Shaft Cost Excavation for φ Factors FOSM Correlation Length (ft) β 2.5 β 3.0 β 3.5 β 4.0
1 $224.99 $254.27 $287.47 $325.085 $239.56 $274.76 $314.50 $360.83
12 $264.32 $303.53 $347.84 $399.82 Table 6-8. Summary of Drilled Shaft Cost Excavation for φ Factors FOSM (Modified) Correlation Length (ft) β 2.5 β 3.0 β 3.5 β 4.0
1 $181.73 $196.08 $211.58 $228.245 $200.37 $220.71 $243.24 $267.57
12 $221.55 $244.96 $270.48 $298.83
101
Table 6-9. Average Cost for a 1 foot length and 4 feet Diameter Drilled Shaft, (One Soil Boring) Average Drilled Shaft Cost / LF $267.97Average Drilled Shaft Excavation Cost/ LF $173.92Average of four Soil Tests Cost/ LF $24.5(*)Average of Auger Soil Boring/ LF $30.63TOTAL/ LF $497.02(*) Assuming a set of soil tests every 10 ft. Table 6-10. Average Cost for a 1 foot length 4 feet Diameter Drilled Shaft, (Five Soil Boring) Average Drilled Shaft Cost / LF $267.97 Average Drilled Shaft Excavation Cost/ LF $173.92 Average of four Soil Tests Cost/ LF $122.5 Average of Auger Soil Boring/ LF $153.15 TOTAL/ LF $717.54 Table 6-11. LRFD φ Factors, Probability of Failure and Fs Based on Reliability, β for Nearest
Boring Approach (McVay and Ellis 2001)
Reliability, β LRFD, φ Pf(%) Factor of Safety 2.0 0.86 8.5 1.65 2.5 0.71 1.0 1.98 3.0 0.60 0.1 2.37 3.5 0.50 0.01 2.84 4.0 0.42 0.002 3.40 4.5 0.35 0.0002 4.07
102
Figure 6-1. FDOT Basis of Estimates Handbook Description for the Item 455 88 “Drilled Shaft”.
103
Figure 6-2. FDOT Basis of Estimates Handbook Description for the Item 455 122 “Unclassified
Shaft Excavation”.
104
Figure 6-3. Example of the 2006 Item Average Unit Cost for the Items 455 88 5 and 455 122 5.
105
CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS
A probabilistic study on the end bearing capacity of a axially loaded drilled shaft, on soil
with randomly varying cohesion, bulk, and shear have been realized. Random field theory
using Sequential Gaussian simulation has been combined with a finite element program.
The results were compared with the deterministic result obtained from the same software.
The objective of this procedure was to see the variability of the φ, factor with spatial
variability. Additional cost analyses based on result were completed.
The following conclusions can be made:
• The cohesion means obtained from the sequential Gaussian simulation program
shows a higher value for bigger correlation length, and a small cohesion mean
value for minor correlation length. The explanation to this phenomenon is that the
smallest the correlation length the smallest the coefficient of variation for
simulation exist.
• The end bearing capacity mean, obtained from the finite element program, is bigger
for larger correlation lengths, and smaller for minor correlation lengths. It is
because as the spatial correlation length decreased, the weakest trail becomes
increasingly tortuous, and its length correspondingly longer. As a result the weakest
trail starts to look for shorter ways cutting through higher strength materials
• A smaller resistance factors, φ, were obtained for larger correlation lengths, it because the bigger uncertainties with distances (spatial variability).
• Resistance factors, φ, obtained with correlation lengths valued bigger than the founded using the semivariogram takes to variable results.
• The drilled shaft construction costs, like materials, labor and equipment, and excavations are less when using the obtained resistance factors, φ. But, the increase
106
on soil boring cost are around twice bigger than the saving achieved from the construction cost.
The research was based in just one bridge information; more investigation should be
realized using more sites. The spatial variability can be better define with more information, so
as more the number of sampling the better the design parameter definitions and the bigger the
resistance factors, φ, used. The number of sampling for to get a bigger factor should be at least
four, for a correct semivariogram definition, additionally, the distances between them should be
as close as possible.
107
APPENDIX A DATA FROM STATIC AND DYNAMIC FIELD TESTING OF DRILLED SHAFTS (FULLER
WARREN AND 17TH STREET BRIDGE)
Table A-1. Fuller Warren Bridge Soil Boring Data.
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-35 96.5 62 32 -15 54.5 80 47-35 27.8 62 32 -15 12.5 80 47-40 70.5 41 8 -20 98.5 43 20-40 13.7 41 8 -20 6.1 43 20
-25 89 100-25 9.1 100
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-35 92 25 25 -45 82 87 51-35 13.9 25 25 -45 17.2 87 51-45 68.5 30 17-45 24.35 30 17
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-35 56.5 25 17 -20 95 50 47-35 8.4 25 17 -20 9.9 50 47
-25 82 48 19-25 12.95 48 19
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-20 244.5 70 49 -15 258 100-20 54.05 70 49 -15 25.2 100-25 104 100 -20 22.5 87 47
-20 5.6 87 47-22 117.5 77 25
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-30 92.5 32 17 -45 28.75-30 16.75 32 17
jBL-4
BL-11 BL-13
BL-20 BL-23
BL-36 BL-37
BW-1 BW-3
BL-2
108
Table A-1. Continued.
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-25 44.8 -35 31.85 27-30 32.75 -40 27.4-35 29.95
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-30 43 20 42-30 9.55 20 42
Dep.(ft) qu REC RQD qt REC RQD Dep.(ft) qu REC RQD qt REC RQD-20 596.2 38 38 -23 65.4 15 10
284 -28 30.8401.6 -28 34.6 52 3317.4 24.660.2 33.380.9 14
-25 110.5 11-30 43.4 63 26 -33 58.5
32.252.987.715.86.6
-35 50.4-35 87.7 73 66
85.177.920.429.412
23.617.918.318.247.8
-40 55.1
Added Boring (Hole 1: Near Boring BL-1) Added Boring (Hole 2: Near Boring BL-1)
BW-5 BW-12
BW-14
109
Table A-2. 17th Street Bridge Soil Boring Data.
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-65 32.2 30 22 -32 211.2 68.3-72 27.34 67 28 -36 116.9 19.4-85 114.2 13 7
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-69 32.74 22 5 -115 26.5 5-88 28.8 35 10 -131 24.63 43
-131 32.9 43
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-32 211 -49 43.5 18 4-32 68.34 -65 414 20 7-49 117 -72 37.8-49 19.4 -82 120.8 98 38-72 19.6 -82 26.3 98 38
-92 82.98 98 38-102 117.47 66 7-108 82.44 35 8
-131 140.6 35 10-131 64.6 35 10
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-36 379.4 38 35 143.97 38 35 -39 361.3 6 5-36 189.01 38 38 -46 158.7 48 19 55 48 19-36 112.6 38 35 -46 272.7 48 19 53.99 48 19-75 26.3 33 -46 76.78 48 19-98 27.04 60 23 68.7 60 23 -56 285.02 50 12 40.4 50 12-98 140.01 60 23 -95 14.04 17 5
j
BB-7 (35+44)
BB-11 (35+53)
BB-9 (35+06)
S-12 (35+29)
BB-1 (32+93) S-4 (33+00)
BB-4 (34+81)
BB-8 (36+10)
110
Table A-2. Continued.
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-36 283.4 45.8 13.5 148.76 45.8 13.5 -66 432 33 28-36 52.64 45.8 13.5 -66 45.24 33 28-49 444.3 69 36 49.84 69 36-49 212.84 69 36 60.5 69 36-49 65.7 69 36-56 377.6 84 59-56 381.6 84 59-56 320.6 84 59-105 219.04 31 7
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-49 51.4 -39 389 63 31-49 17.5-72 38.34-72 7.7
EL.(ft) qu REC RQD qt REC RQD EL.(ft) qu REC RQD qt REC RQD-49 64.95 42 17 -56 26.54 85 59-66 152.5 45 24 -72 281.3 80-82 58.2 45 24 -79 331.4 47-82 12.4 51 13-92 365.4 57 10-92 101.4 57 10-125 19.2 45 31-125 20.95 45 31-125 31.04 45 31
Dep.(ft) qu REC RQD qt REC RQD Dep.(ft) qu REC RQD qt REC RQD-53 51.7 50.5 50.5
58.559.986.1
-58 58.6-58 20.1 47 40.5-64 46.1 53 53-64 250.1 56.5 53
28.213.58.4
-69 9.8-77 122.5 33 17-77 357.9-90 14.5 23.5 13-109 41.5 22 13
Added Boring (34+81, 10' North+)
N-17 (36+19)
BB-6 (38+07) N-25 (38+38)
S-15 (37+10) N-14 (35+55)
BB-10 (36+07)
111
APPENDIX B SOIL BORING DATA FROM FIELD INVESTIGATION PROCESSED BY MSO
Table B-1. 17th Street Soil Boring Data.
BORING SAMP DEPTH DEPTH TEST LENGTH DIA. WET WET L / D CORR.NO. TOP BOT. DATE MASS UNIT MASS RATIO FACTOR
CORE (ft) (ft) (in) (in) (g) (pcf)
4/1 1T 52.0 4/9/2007 2.4615 2.3955 337.2 115.8 1.032U 4/9/2007 4.6333 2.3962 635.7 115.9 1.93 1.003U 4/9/2007 4.7535 2.3960 704.3 125.2 1.98 1.004T 4/9/2007 2.3770 2.3830 336.4 120.9 1.005U 4/9/2007 4.9210 2.3985 788.7 135.1 2.05 1.006T 4/9/2007 2.5933 2.3880 383.0 125.6 1.097U 4/9/2007 4.4755 2.3945 660.8 124.9 1.87 1.018U 4/9/2007 4.7955 2.3960 764.9 134.8 2.00 1.009T 4/9/2007 1.9430 2.4010 305.4 132.3 0.81
10U 4/9/2007 4.9680 2.3980 785.4 133.4 2.07 1.0011T 57.0 4/9/2007 2.0933 2.3970 319.2 128.7 0.87
4/2 1T 57.0 4/9/2007 2.4955 2.3990 300.0 101.3 1.042U 4/9/2007 4.3760 2.3830 533.4 104.1 1.84 1.013T 4/9/2007 2.6210 2.3815 333.7 108.9 1.104T 4/9/2007 2.4920 2.4035 391.4 131.9 1.045U 4/9/2007 3.9130 2.3560 532.2 118.9 1.66 1.026T 4/9/2007 2.4735 2.3430 332.9 118.9 1.067T 4/9/2007 2.4045 2.3990 378.1 132.5 1.008T 4/9/2007 2.6580 2.3955 392.5 124.8 1.119U 62.0 4/9/2007 4.8115 2.3820 710.5 126.2 2.02 1.00
4/3 1T 62.0 4/9/2007 1.8750 2.3630 217.7 100.9 0.792U 4/9/2007 3.6345 2.3990 656.7 152.3 1.52 1.043U 4/9/2007 3.6035 2.3945 619.6 145.5 1.50 1.044T 4/10/2007 2.3630 2.3580 287.3 106.1 1.005T 67.0 4/10/2007 2.4010 2.3610 280.1 101.5 1.02
4/4 1T 67.0 4/10/2007 2.3499 2.3780 353.1 128.9 0.992U 4/10/2007 5.0140 2.3475 682.8 119.9 2.14 1.003T 4/10/2007 2.4170 2.2935 310.4 118.4 1.054U 4/10/2007 3.4240 2.3803 413.5 103.4 1.44 1.055T 4/10/2007 2.2945 2.3507 276.5 105.8 0.986T 4/10/2007 2.1785 2.3897 249.5 97.3 0.917T 4/10/2007 2.4660 2.3578 287.5 101.7 1.058U 4/10/2007 4.5855 2.3688 543.1 102.4 1.94 1.009T 72.0 4/10/2007 2.2500 2.3417 264.6 104.0 0.96
BORING SAMP DEPTH DEPTH TEST LENGTH DIA. WET WET L / D CORR.NO. TOP BOT. DATE MASS UNIT MASS RATIO FACTOR
CORE (ft) (ft) (in) (in) (g) (pcf)
4/5 1U 72.0 4/10/2007 4.3355 2.3968 769.5 149.9 1.81 1.012U 4/10/2007 4.1755 2.3973 752.0 152.0 1.74 1.023T 4/10/2007 2.7900 2.3953 513.1 155.5 1.164T 4/10/2007 2.3720 2.4007 427.7 151.8 0.995T 4/10/2007 2.1110 2.4037 370.3 147.3 0.886T 77.0 4/10/2007 2.1705 2.3942 358.7 139.8 0.91
4/6 1U 77.0 4/10/2007 4.4615 2.3982 789.5 149.2 1.86 1.012U 4/10/2007 3.6695 2.3942 651.7 150.3 1.53 1.043T 82.0 4/10/2007 2.4030 2.3955 395.8 139.2 1.00
4/7 1T 82.0 4/10/2007 2.6260 2.4087 468.2 149.1 1.092U 4/10/2007 4.9695 2.3965 862.9 146.6 2.07 1.003U 87.0 4/10/2007 3.9910 2.4072 711.8 149.3 1.66 1.02
4/8 NA 87.0 92.0 4/10/2007
Effective/Revised Date: 12/22/05
By: B.W. Page 1 of 1
STATE MATERIALS OFFICE
Foundations Laboratory
Rock CoreUnconfined Compression-
Split Tensile
112
Table B-1. Continued.
BORING SAMP. w DRY MAX. S. T. q (u) STRAIN % RECOV. TARE WET DRYNO. UNIT MASS LOAD STRENGTH @ FAIL. WT. WT. WT.
CORE (%) (pcf) (lbs) (psi) (psi) (in) (%) % RQD (g) (g) (g)
4/1 1T 10.00 105.3 1375.2 148.5 0.0527 100 / 77 75.4 411.9 381.32U 9.77 105.6 3357.2 741.4 0.0425 0.92 " 75.5 710.5 6543U 9.90 113.9 5394.3 1195.3 0.0505 1.06 " 76.2 778.8 715.54T 12.15 107.8 1498.2 168.4 0.0398 " 75 411 374.65U 9.64 123.3 7650.7 1693.3 0.0548 1.11 " 77 861.7 792.76T 11.33 112.8 438.4 45.1 0.0319 " 76.4 455.8 417.27U 10.13 113.4 4492.3 989.3 0.0344 0.77 " 74.9 726 666.18U 7.30 125.6 7813 1732.9 0.0623 1.30 " 75.6 838.2 786.39T 7.02 123.6 2047.2 279.4 0.0643 " 77 381.8 361.8
10U 6.09 125.7 6338.7 1403.5 0.0486 0.98 " 75.5 840.8 796.911T 8.00 119.2 1733.3 219.9 0.0443 " 75.6 394.3 370.7
4/2 1T 3.21 98.2 1414.2 150.4 0.1128 90 / 48 77.7 377 367.72U 3.08 101.0 1978.9 439.0 0.0355 0.81 " 75.9 595.4 579.93T 4.33 104.4 1262.1 128.7 0.0891 " 76 401.6 388.14T 10.79 119.0 3328 353.7 0.0556 " 76.9 467 4295U 8.51 109.5 2030.7 454.7 0.0354 0.90 " 76 585.9 545.96T 4.33 114.0 2302.1 252.9 0.0906 " 75.7 405.8 392.17T 7.02 123.8 2290.3 252.8 0.0902 " 77.5 450.9 426.48T 10.64 112.8 2816.1 281.6 0.0969 " 76.1 454.5 418.19U 5.61 119.5 3170.6 711.5 0.0553 1.15 " 75.1 780.8 743.3
4/3 1T 3.09 97.8 1280.1 183.9 0.0246 82 / 14 77.9 294.5 2882U 2.22 149.0 6791.7 1447.0 0.0489 1.35 " 74.9 700 686.43U 0.75 144.4 9992.7 2134.8 0.0458 1.27 " 74.8 691.7 687.14T 0.76 105.3 1260.9 144.1 0.0434 " 75 352.3 350.25T 1.28 100.2 812.9 91.3 0.0452 " 77.5 354.4 350.9
4/4 1T 4.95 122.8 2832.6 322.7 0.0400 87 / 34 76.2 430.3 413.62U 9.54 109.4 2457.9 567.9 0.0247 0.49 " 75 756 696.73T 6.11 111.6 1563.5 179.6 0.0658 " 75.5 384.8 3674U 6.50 97.1 1591.8 341.7 0.0329 0.96 " 75.4 486.6 461.55T 4.48 101.2 1743.1 205.7 0.0986 " 77.9 353.1 341.36T 3.31 94.2 688.7 84.2 0.0312 " 77.1 327.1 319.17T 3.95 97.9 963.8 105.5 0.0704 " 75.8 362.8 351.98U 4.70 97.8 1058.1 239.1 0.0223 0.49 " 76.9 607.4 583.69T 6.26 97.9 1296.7 156.7 0.1132 " 77.9 339.4 324
BORING SAMP. w DRY MAX. S. T. q (u) STRAIN % RECOV. TARE WET DRYNO. UNIT MASS LOAD STRENGTH @ FAIL. WT. WT. WT.
CORE (%) (pcf) (lbs) (psi) (psi) (in) (%) % RQD (g) (g) (g)
4/5 1U 2.84 145.7 10309.5 2256.4 0.0540 1.25 58 / 25 75.5 832.4 811.52U 2.83 147.8 10395.3 2262.9 0.0506 1.21 " 75.1 826 805.33T 2.01 152.4 4593 437.5 0.0638 " 75.7 587.1 5774T 1.76 149.1 3913.4 437.5 0.0460 " 76 503.1 495.75T 2.05 144.3 2823.3 354.2 0.0309 " 76.9 445.3 437.96T 3.57 135.0 3007.5 368.4 0.0760 " 77.7 435 422.7
4/6 1U 1.86 146.5 10446.5 2292.1 0.0512 1.15 77.5 865.4 8512U 1.96 147.4 10971.3 2351.0 0.0473 1.29 75.6 727.2 714.73T 1.46 137.2 3324.5 367.7 0.0283 75.5 471.3 465.6
4/7 1T 1.52 146.8 4003.3 402.9 0.0483 42 / 20 77 539.1 532.22U 1.32 144.7 16231.4 3598.5 0.0498 1.00 " 76.1 910.4 899.53U 2.34 145.9 10079.6 2161.3 0.0438 1.10 " 74.9 786.6 770.3
12 / 0
DISPL. @ FAIL.
DISPL. @ FAIL.
Project Number:Lab Number:Bridge Number:LIMS Number:
17th Street BridgeLocation:Date Received:Tested by:
113
Table B-1. Continued.
BORING SAMP DEPTH DEPTH TEST LENGTH DIA. WET WET L / D CORR.NO. TOP BOT. DATE MASS UNIT MASS RATIO FACTOR
CORE (ft) (ft) (in) (in) (g) (pcf)
5/1 1T 52.0 2.4015 2.3885 330.1 116.9 1.012T 2.4510 2.3675 333.5 117.7 1.043U 4.2535 2.4005 665.8 131.8 1.77 1.024T 2.3715 2.3815 380.4 137.2 1.005U 4.2280 2.3980 677.2 135.1 1.76 1.026T 2.1840 2.3965 325.2 125.8 0.917U 3.9255 2.3800 595.6 129.9 1.65 1.038U 4.1990 2.3780 628.0 128.3 1.77 1.029T 2.3305 2.2213 342.5 144.5 1.05
10U 3.7045 2.3075 486.8 119.7 1.61 1.0311T 2.5410 2.3835 360.8 121.2 1.0712T 57.0 2.2945 2.3860 342.5 127.2 0.9613U 3.6425 2.4065 621.9 143.0 1.51 1.04
5/2 1U 57.0 4.1540 2.3005 625.3 138.0 1.81 1.012T 2.3740 2.3655 353.0 128.9 1.003T 1.9955 2.3900 278.7 118.6 0.834U 3.7010 2.3695 529.2 123.5 1.56 1.035T 62.0 2.1560 2.4000 300.6 117.4 0.90
5/3 1U 62.0 4.8695 2.3820 854.4 150.0 2.04 1.002T 2.3920 2.3970 392.7 138.6 1.003T 2.2700 2.3490 229.5 88.9 0.974T 67.0 2.1725 2.3970 338.8 131.7 0.91
5/4 1T 67.0 1.8100 2.2860 195.0 100.0 0.792T 1.6915 2.3205 155.7 82.9 0.733T 72.0 1.8465 2.3020 185.0 91.7 0.80
BORING SAMP DEPTH DEPTH TEST LENGTH DIA. WET WET L / D CORR.NO. TOP BOT. DATE MASS UNIT MASS RATIO FACTOR
CORE (ft) (ft) (in) (in) (g) (pcf)
5/5 1T 72.0 1.8750 2.3860 320.2 145.5 0.792U 3.3513 2.3965 606.8 152.9 1.40 1.053T 2.4415 2.4000 345.7 119.2 1.024U 4.8035 2.4030 881.2 154.1 2.00 1.005U 4.9085 2.4010 819.0 140.4 2.04 1.006T 1.8025 2.4070 316.5 147.0 0.757U 4.0455 2.3900 687.6 144.3 1.69 1.028T 2.1895 2.4005 385.6 148.2 0.919U 4.6335 2.3990 826.1 150.3 1.93 1.00
10U 77.0 3.8715 2.4000 650.9 141.6 1.61 1.03
5/6 1T 77.0 2.2060 2.4065 405.9 154.1 0.922U 4.7255 2.3990 835.7 149.0 1.97 1.003T 2.1880 2.3830 357.1 139.4 0.924U 82.0 3.6900 2.3870 657.5 151.7 1.55 1.04
5/7 1T 82.0 2.2215 2.3845 382.2 146.8 0.932U 87.0 3.6250 2.3885 630.9 148.0 1.52 1.04
STATE MATERIALS OFFICE
Foundations Laboratory
Rock CoreUnconfined Compression-
Split Tensile
Effective/Revised Date: 12/22/05
By: B.W. Page 1 of 1
114
Table B-1. Continued.
BORING SAMP. w DRY MAX. S. T. q (u) STRAIN % RECOV. TARE WET DRYNO. UNIT MASS LOAD STRENGTH @ FAIL. WT. WT. WT.
CORE (%) (pcf) (lbs) (psi) (psi) (in) (%) % RQD (g) (g) (g)
5/1 1T 9.04 107.2 1772.1 196.7 0.1135 100 / 82 75.1 405.7 378.32T 8.16 108.9 1390.3 152.5 0.0964 " 75.5 408.2 383.13U 7.50 122.6 5753.4 1252.0 0.0315 0.74 " 74.9 737.4 691.24T 8.21 126.8 3673.9 414.1 0.0638 " 77 456.7 427.95U 8.35 124.7 8109.5 1767.1 0.0604 1.43 " 77.9 751.3 699.46T 7.19 117.3 713.9 86.8 0.0394 " 76.9 401.8 3807U 8.49 119.8 3836.9 841.0 0.0407 1.04 " 77.5 670.7 624.38U 8.10 118.7 3195.3 708.2 0.0228 0.54 " 75 700.7 653.89T 6.93 135.1 2784.1 342.4 0.0873 " 75.4 416.6 394.5
10U 5.13 113.9 2008 466.4 0.0066 0.18 " 75.8 561.1 537.411T 4.94 115.5 1703.3 179.0 0.0854 " 77.9 415.5 399.612T 4.32 121.9 3028.1 352.1 0.0565 " 77.1 417.7 403.613U 1.36 141.1 10398.8 2201.4 0.0585 1.61 " 76.9 696.5 688.2
5/2 1U 3.97 132.7 2665.4 633.1 0.0563 1.36 70 / 20 77.7 700.6 676.82T 0.98 127.6 1608.2 182.3 0.0440 " 76 417 413.73T 1.26 117.1 1573.5 210.0 0.0374 " 77.5 342.1 338.84U 6.90 115.6 3880 851.3 0.1273 3.44 " 76.2 573.2 541.15T 4.45 112.4 1110.3 136.6 0.0307 " 75.7 362 349.8
5/3 1U 1.79 147.4 9570.4 2147.7 0.0630 1.29 77 / 15 75.7 928.5 913.52T 1.21 136.9 3920.7 435.3 0.0381 " 75.5 468.1 463.43T 2.01 87.1 1000.5 119.5 0.0812 " 75.1 303.6 299.14T 1.90 129.2 2292.2 280.2 0.0588 " 75.6 413.6 407.3
5/4 1T 3.62 96.5 982.8 151.2 0.1229 52 / 0 76 270.8 2642T 2.72 80.7 392 63.6 0.1238 " 75.9 226.7 222.73T 4.61 87.7 273.8 41.0 0.0446 " 75.7 259.6 251.5
BORING SAMP. w DRY MAX. S. T. q (u) STRAIN % RECOV. TARE WET DRYNO. UNIT MASS LOAD STRENGTH @ FAIL. WT. WT. WT.
CORE (%) (pcf) (lbs) (psi) (psi) (in) (%) % RQD (g) (g) (g)
5/5 1T 1.23 143.7 2179.8 310.2 0.0172 80 / 63 77.3 397 393.12U 1.90 150.1 5546.2 1169.2 0.0425 1.27 " 75.6 680.2 668.93T 2.38 116.5 920.9 100.1 0.0247 " 76.3 419.8 411.84U 2.26 150.7 10731.9 2366.3 0.0558 1.16 " 74.9 955.4 935.95U 3.05 136.2 3268.8 722.0 0.0271 0.55 " 77 894.1 869.96T 2.66 143.2 2258.7 331.4 0.0873 " 76.4 392.7 384.57U 2.77 140.4 4315.8 941.5 0.0426 1.05 " 76.2 751.7 733.58T 1.96 145.4 2358.6 285.7 0.0325 " 77.6 462.3 454.99U 2.18 147.1 6641.7 1463.2 0.0554 1.20 " 75.5 900.7 883.1
10U 2.95 137.5 5546.1 1191.7 0.0395 1.02 " 78.3 728 709.4
5/6 1T 0.87 152.8 3107.5 372.6 0.0300 66 / 30 76.5 482.7 479.22U 1.30 147.1 8502.2 1877.6 0.0544 1.15 " 75 910.9 900.23T 2.21 136.4 3750.5 457.9 0.0485 " 74.2 429.6 421.94U 2.13 148.5 10165.4 2194.3 0.0512 1.39 " 81.6 739.1 725.4
5/7 1T 2.44 143.3 5093 612.1 0.0387 37 / 8 76 458.5 449.42U 2.22 144.8 9645.3 2073.6 0.0472 1.30 " 76.2 707.3 693.6
17th Street BridgeLocation:Date Received:Tested by:
DISPL. @ FAIL.
DISPL. @ FAIL.
Project Number:Lab Number:Bridge Number:LIMS Number:
115
Table B-1. Continued.
BORING SAMP DEPTH DEPTH TEST LENGTH DIA. WET WET L / D CORR.NO. TOP BOT. DATE MASS UNIT MASS RATIO FACTOR
CORE (ft) (ft) (in) (in) (g) (pcf)
6/1 1T 52.0 1.9870 2.3910 272.5 116.4 0.832U 5.2945 2.3465 756.2 125.8 2.26 1.003T 2.3995 2.3670 372.9 134.5 1.014T 2.1695 2.3813 357.0 140.8 0.915U 4.9755 2.3908 790.4 134.8 2.08 1.006T 2.2120 2.3722 349.7 136.3 0.937U 4.1560 2.3880 660.8 135.2 1.74 1.028T 2.4715 2.3530 358.4 127.0 1.059U 4.3230 2.3750 677.5 134.8 1.82 1.0110T 2.4515 2.2730 337.6 129.3 1.0811T 57.0 2.3845 2.1530 323.7 142.1 1.11
6/2 1U 57.0 3.8650 2.4130 588.3 126.8 1.60 1.032T 2.2650 2.3790 349.6 132.3 0.953T 2.3615 2.3400 259.4 97.3 1.014T 2.3770 2.3775 406.5 146.7 1.005U 4.5670 2.4130 735.5 134.2 1.89 1.016T 2.2730 2.3795 349.3 131.6 0.967T 62.0 2.3500 2.3665 351.0 129.4 0.99
6/3 1T 62.0 2.1080 2.3765 250.8 102.2 0.892U 3.5275 2.3957 615.8 147.5 1.47 1.043U 3.4635 2.3770 591.4 146.6 1.46 1.044T 2.4800 2.3557 257.6 90.8 1.055U 4.3140 2.3707 551.0 110.2 1.82 1.016T 1.8850 2.3350 219.7 103.7 0.817U 4.4285 2.3725 565.7 110.1 1.87 1.018T 2.2850 2.3757 274.3 103.2 0.969U 67.0 5.2080 2.3627 658.6 109.9 2.20 1.00
6/4 1U 67.0 4.4235 2.3710 487.7 95.1 1.87 1.012T 2.3640 2.3732 294.7 107.4 1.003T 1.9045 2.3665 233.8 106.3 0.804U 3.9975 2.3658 463.7 100.5 1.69 1.025T 2.2850 2.3908 270.8 100.6 0.966T 2.3470 2.3717 270.5 99.4 0.997T 2.2670 2.3843 270.2 101.7 0.958T 72.0 1.9775 2.3643 236.3 103.7 0.84
6/5 1U 72.0 4.3710 2.3745 714.5 140.6 1.84 1.012T 2.0435 2.3770 368.4 154.8 0.863U 4.5400 2.3770 665.7 125.9 1.91 1.014T 2.6210 2.3900 449.9 145.8 1.105T 2.3695 2.3440 318.7 118.7 1.016U 4.4540 2.3820 584.7 112.2 1.87 1.017T 1.9690 2.3915 259.2 111.6 0.828U 77.0 4.4395 2.3930 672.2 128.3 1.86 1.01
6/6 1T 77.0 2.3335 2.3855 407.0 148.7 0.982U 3.9965 2.3740 674.5 145.3 1.68 1.023T 82.0 2.0250 2.3805 333.5 141.0 0.85
STATE MATERIALS OFFICE
Foundations Laboratory
Rock CoreUnconfined Compression-
Split Tensile
Effective/Revised Date: 12/22/05
By: B.W. Page 1 of 1
116
Table B-1. Continued.
BORING SAMP. w DRY MAX. S. T. q (u) STRAIN % RECOV. TARE WET DRYNO. UNIT MASS LOAD STRENGTH @ FAIL. WT. WT. WT.
CORE (%) (pcf) (lbs) (psi) (psi) (in) (%) % RQD (g) (g) (g)
6/1 1T 9.24 106.5 1758.5 235.6 0.1252 100 / 62 76.3 326.9 305.72U 8.39 116.1 2846.5 658.3 0.0200 0.38 " 76.2 830.3 771.93T 14.53 117.5 3201.6 358.9 0.0836 " 75.4 446.6 399.54T 6.55 132.1 3330.8 410.4 0.0511 " 75 419.9 398.75U 8.96 123.7 5693.3 1268.2 0.0350 0.70 " 76.9 845.8 782.66T 5.51 129.2 1942.3 235.6 0.0616 " 75 408.2 390.87U 8.79 124.3 2542.3 557.7 0.0308 0.74 " 76 734.1 680.98T 12.07 113.4 2583.7 282.8 0.0851 " 76.3 433.9 395.49U 9.90 122.6 3311.5 738.8 0.0275 0.64 " 76.4 749 688.410T 14.18 113.2 788.4 90.1 0.0271 " 77.7 414.3 372.511T 6.19 133.8 2896.2 359.1 0.0964 " 75.7 398.1 379.3
6/2 1U 2.60 123.6 4409.9 936.4 0.1758 4.55 72 / 37 77.5 642.6 628.32T 8.56 121.9 1745.3 206.2 0.0705 " 75.7 424.5 3973T 3.87 93.7 871.7 100.4 0.1053 " 74.9 329.9 320.44T 3.40 141.9 6055 682.1 0.0486 " 75.6 474.2 461.15U 7.51 124.8 3801.2 825.6 0.0303 0.66 " 76.5 805.5 754.66T 11.67 117.9 2097.8 246.9 0.0430 " 74.2 420.5 384.37T 5.12 123.1 2339.3 267.8 0.0591 " 75.7 410.1 393.8
6/3 1T 1.29 100.9 1389.6 176.6 0.0688 80 / 51 74.9 325.3 322.12U 1.43 145.5 10020.2 2131.3 0.1268 3.59 " 75.6 679.3 670.83U 1.92 143.8 4800.3 1035.5 0.0311 0.90 " 76 665.3 654.24T 4.35 87.0 1040.9 113.4 0.1196 " 75.7 332.3 321.65U 3.56 106.4 1966 440.2 0.0205 0.48 " 77.7 618.9 600.36T 3.85 99.8 866.3 125.3 0.1288 " 74.2 292.6 284.57U 3.51 106.3 2473.7 554.8 0.4020 9.08 " 75.7 632.6 613.78T 3.45 99.7 1302.4 152.7 0.0788 " 76.5 349 339.99U 2.83 106.9 1828 416.9 0.0357 0.69 " 75.4 722.6 704.8
6/4 1U 2.63 92.7 1289.8 289.6 0.2128 4.81 68 / 30 76.3 552.9 540.72T 2.05 105.2 1123.7 127.5 0.0449 " 77.2 370.6 364.73T 3.76 102.5 1072.1 151.4 0.0605 " 74.9 298.2 290.14U 2.78 97.8 1081.4 240.7 0.0544 1.36 " 77 535.4 5235T 2.50 98.1 892.6 104.0 0.0590 " 76.2 343.1 336.66T 3.18 96.3 1147.1 131.2 0.0634 " 76.4 345.6 337.37T 3.76 98.0 1148.7 135.3 0.0905 " 76.3 343.8 334.18T 3.36 100.3 1509.8 205.6 0.1603 " 75.1 303 295.6
6/5 1U 1.23 138.9 6235.5 1393.7 0.0445 1.02 80 / 60 81.6 796.1 787.42T 1.24 152.9 3890.2 509.9 0.0562 " 76.9 445.3 440.83U 1.53 124.0 6375.1 1428.6 0.0322 0.71 " 75 740.7 730.74T 1.35 143.8 2505 254.6 0.0378 " 75.5 525.4 519.45T 1.05 117.5 2201.1 252.3 0.1374 " 77.1 395.8 392.56U 1.69 110.4 2312.3 514.6 0.0550 1.23 " 75.5 660.2 650.57T 0.78 110.8 1209.9 163.6 0.0332 " 76 335.2 333.28U 1.65 126.2 2716.5 598.4 0.0979 2.21 " 76.2 748.4 737.5
1T 1.80 146.0 5188.1 593.3 0.0366 48 / 17 74.8 481.5 474.32U 1.37 143.3 3525.6 778.9 0.0294 0.74 " 76.1 750.6 741.53T 0.89 139.7 3676.3 485.5 0.0483 " 76.2 406.1 403.2
17th Street BridgeLocation:Date Received:Tested by:
DISPL. @ FAIL.
Project Number:Lab Number:Bridge Number:LIMS Number:
117
Table B-1. Continued.
BORING SAMP DEPTH DEPTH TEST LENGTH DIA. WET WET L / D CORR.NO. TOP BOT. DATE MASS UNIT MASS RATIO FACTOR
CORE (ft) (ft) (in) (in) (g) (pcf)
7/1 1T 52.0 1.9905 2.3980 285.2 120.9 0.832U 57.0 3.7880 2.3845 633.0 142.6 1.59 1.03
7/2 1T 57.0 2.2260 2.3560 293.3 115.1 0.942T 1.9940 2.3500 293.5 129.3 0.853U 4.3135 2.3815 693.7 137.5 1.81 1.014T 2.2580 2.3835 403.4 152.5 0.955U 4.6970 2.3950 841.0 151.4 1.96 1.006T 2.0550 2.3970 364.0 149.5 0.867T 1.7540 2.3670 254.8 125.8 0.748T 2.1750 2.3915 334.1 130.3 0.919T 2.4540 2.3975 412.3 141.8 1.02
10U 4.2085 2.3010 612.9 133.4 1.83 1.0111T 2.4605 2.3720 375.3 131.5 1.0412U 5.0075 2.3880 763.2 129.6 2.10 1.0013T 62.0 2.2130 2.3675 337.6 132.0 0.93
7/3 1T 62.0 2.2015 2.2940 223.3 93.5 0.962T 67.0 2.3255 2.3015 229.1 90.2 1.01
7/4 67.0 72.0 NA SAND
7/5 1T 72.0 2.4535 2.3843 376.1 130.8 1.033T 2.1355 2.3915 366.2 145.4 0.894T 2.1765 2.3920 388.8 151.4 0.915U 3.8825 2.3842 674.7 148.3 1.63 1.036U 4.1465 2.3872 735.6 151.0 1.74 1.027U 3.7250 2.3710 576.4 133.5 1.57 1.038T 1.4850 2.3715 226.6 131.6 0.639U 77.0 3.9970 2.3770 670.0 143.9 1.68 1.02
7/6 1T 77.0 2.0110 2.3840 364.4 154.6 0.842T 2.1070 2.3953 378.2 151.7 0.883U 3.6625 2.3932 646.9 149.6 1.53 1.044U 82.0 3.9280 2.3900 685.7 148.2 1.64 1.03
7/7 1T 82.0 2.1955 2.3965 390.7 150.3 0.922T 87.0 2.2945 2.3890 384.8 142.5 0.96
7/8 1T 87.0 92.0 2.3110 2.3970 338.9 123.8 0.96
Effective/Revised Date: 12/22/05
By: B.W. Page 1 of 1
STATE MATERIALS OFFICE
Foundations Laboratory
Rock CoreUnconfined Compression-
Split Tensile
118
Table B-1. Continued.
BORING SAMP. w DRY MAX. S. T. q (u) STRAIN % RECOV. TARE WET DRYNO. UNIT MASS LOAD STRENGTH @ FAIL. WT. WT. WT.
CORE (%) (pcf) (lbs) (psi) (psi) (in) (%) % RQD (g) (g) (g)
7/1 1T 3.56 116.7 2871 382.9 0.0986 52 / 10 77 359.2 349.52U 1.25 140.8 11000 2389.1 0.0734 1.94 " 77.2 711 703.2
7/2 1T 2.67 112.1 1725.4 209.4 0.1515 93 / 50 74.1 366.6 3592T 5.61 122.4 2714.9 368.8 0.0663 " 75.9 364 348.73U 4.11 132.1 6379.5 1414.5 0.0646 1.50 " 74.5 765.9 738.64T 3.25 147.7 4748.7 561.7 0.0388 " 75.9 476.1 463.55U 0.53 150.6 13108.8 2903.0 0.0698 1.49 " 76.1 891.1 886.86T 1.68 147.1 3542.8 457.9 0.0347 " 76.3 438.4 432.47T 6.38 118.2 2918.9 447.6 0.0936 " 75.7 329.3 314.18T 5.88 123.0 3484.4 426.5 0.0672 " 75 406.1 387.79T 1.90 139.1 4411.4 477.3 0.0591 " 76 488.2 480.5
10U 3.85 128.5 4195.6 997.8 0.0359 0.85 " 75 682 659.511T 2.11 128.8 2239.8 244.3 0.0287 " 75.4 448.7 44112U 6.12 122.2 4652.1 1038.7 0.0314 0.63 " 76.9 834.4 790.713T 1.78 129.7 2716.6 330.1 0.0326 " 76.2 408.7 402.9
7/3 1T 0.63 92.9 1277.5 161.0 0.1324 42 / 0 74 297.2 295.82T 0.75 89.5 1871.7 222.6 0.1413 " 77 333.2 331.3
7/4 50 / 0
7/5 1T 1.19 129.3 3141.3 341.9 0.0411 83 / 54 74.2 448.9 444.53T 1.27 143.6 2780.1 346.6 0.0292 " 75.7 442.1 437.54T 1.09 149.8 3555.4 434.8 0.0262 " 75.7 464.6 460.45U 0.90 147.0 10908.5 2378.3 0.0542 1.40 " 74.9 746.5 740.56U 1.37 149.0 11900.5 2611.5 0.0548 1.32 " 75.6 809.4 799.57U 1.94 131.0 3889.5 853.0 0.0300 0.81 " 76.2 607.2 597.18T 1.49 129.7 2100.7 379.7 0.0599 " 74.9 300.4 297.19U 1.15 142.3 9887.3 2178.6 0.0468 1.17 " 76.4 743.1 735.5
7/6 1T 1.36 152.6 5727.5 760.5 0.0456 67 27 77.7 442 437.12T 0.83 150.5 3472.4 438.0 0.0288 " 77.5 456 452.93U 1.16 147.9 11070.3 2373.7 0.0550 1.50 " 76.5 722.2 714.84U 1.02 146.7 7211.3 1566.7 0.0737 1.88 " 76.3 722.8 716.3
7/7 1T 1.98 147.4 5630.4 681.3 0.0402 43 / 7 76 466.8 459.22T 2.15 139.5 3660.1 425.1 0.0219 " 75.7 460.5 452.4
7/8 1T 1.38 122.1 1884.9 216.6 0.0368 23 / 8 77 416 411.4
DISPL. @ FAIL.
Project Number:Lab Number:Bridge Number:LIMS Number:
17th Street BridgeLocation:Date Received:Tested by:
119
Table B-1. Continued.
BORING SAMP DEPTH DEPTH TEST LENGTH DIA. WET WET L / D CORR.NO. TOP BOT. DATE MASS UNIT MASS RATIO FACTOR
CORE (ft) (ft) (in) (in) (g) (pcf)
8/1 1T 52.0 2.1765 2.3665 290.2 115.5 0.922U 3.9035 2.3900 669.1 145.6 1.63 1.033T 2.3245 2.3913 249.4 91.0 0.974U 4.3995 2.3833 494.8 96.0 1.85 1.016U 4.4095 2.3905 745.8 143.6 1.84 1.017T 1.5920 2.3745 233.4 126.1 0.678U 57.0 3.8605 2.3753 560.6 124.8 1.63 1.03
8/2 1T 57.0 2.3260 2.3933 357.7 130.2 0.972U 4.5345 2.3895 712.2 133.4 1.90 1.013T 2.0255 2.3955 316.4 132.0 0.854U 4.0815 2.3973 631.0 130.5 1.70 1.025T 2.3285 2.4045 344.4 124.1 0.976U 62.0 4.0865 2.3912 570.2 118.4 1.71 1.02
8/3 1U 62.0 4.4460 2.3633 510.1 99.6 1.88 1.012T 2.0945 2.3863 259.6 105.6 0.883T 2.3430 2.3708 262.8 96.8 0.994T 2.3025 2.3858 254.1 94.0 0.975T 1.8790 2.3665 313.8 144.6 0.796U 4.7045 2.3860 852.5 154.4 1.97 1.007T 2.2252 2.3870 405.1 155.0 0.938U 4.3420 2.3868 789.6 154.8 1.82 1.019T 2.4615 2.3933 432.8 148.9 1.03
10U 4.7155 2.3927 801.4 144.0 1.97 1.0011T 67.0 2.0520 2.3777 327.5 136.9 0.86
8/4 1U 67.0 4.5165 2.3643 761.0 146.2 1.91 1.013T 2.3610 2.3775 283.3 103.0 0.994T 2.1220 2.3710 253.2 103.0 0.895U 5.0405 2.3805 576.3 97.9 2.12 1.006T 72.0 2.0905 2.3848 250.7 102.3 0.88
8/5 1U 72.0 3.9240 2.3735 700.6 153.7 1.65 1.032T 2.0870 2.3748 327.2 134.8 0.884U 4.2615 2.3708 731.2 148.1 1.80 1.015U 4.7125 2.3745 826.9 151.0 1.98 1.006T 1.8625 2.3745 301.7 139.4 0.787T 2.1330 2.3822 341.4 136.8 0.908U 77.0 3.7315 2.3673 659.3 152.9 1.58 1.03
8/6 77.0 82.0 NA
8/7 1T 82.0 87.0 2.2285 2.3755 406.0 156.6 0.94
8/8 87.0 92.0 NA
Effective/Revised Date: 12/22/05
By: B.W. Page 1 of 1
STATE MATERIALS OFFICE
Foundations Laboratory
Rock CoreUnconfined Compression-
Split Tensile
120
Table B-1. Continued.
BORING SAMP. w DRY MAX. S. T. q (u) STRAIN % RECOV. TARE WET DRYNO. UNIT MASS LOAD STRENGTH @ FAIL. WT. WT. WT.
CORE (%) (pcf) (lbs) (psi) (psi) (in) (%) % RQD (g) (g) (g)
8/1 1T 1.90 113.3 2768.5 342.2 0.0618 85 / 40 75.7 364.9 359.52U 2.44 142.1 10983.7 2384.1 0.0540 1.38 " 77.7 744.5 728.63T 10.29 82.5 587.3 67.3 0.0477 " 75.7 324.4 301.24U 7.44 89.4 1094.7 243.0 0.0406 0.92 " 74.9 567.2 533.16U 7.06 134.1 5410.4 1193.5 0.0393 0.89 " 76 820.8 771.77T 10.37 114.3 1071 180.4 0.0374 " 74.9 305.8 284.18U 11.92 111.5 2448.3 537.6 0.0545 1.41 " 76.5 630.5 571.5
8/2 1T 2.12 127.5 3284.3 375.6 0.0476 61 / 38 74.2 431.4 4242U 1.46 131.5 4159.5 921.6 0.0346 0.76 " 77.2 784.8 774.63T 2.34 129.0 3120.2 409.4 0.0254 " 75.7 390.7 383.54U 6.00 123.1 5359 1162.9 0.0502 1.23 " 75.4 703 667.55T 2.24 121.4 3494.8 397.4 0.0457 " 77 420 412.56U 8.08 109.5 3299 719.9 0.0796 1.95 " 76.3 636.6 594.7
8/3 1U 0.88 98.8 1058 239.4 0.0282 0.63 85 / 63 76.2 579.1 574.72T 1.89 103.6 1465.3 186.6 0.1091 " 76.4 334.8 3303T 3.30 93.7 1507.4 172.8 0.1471 " 75.1 334.9 326.64T 3.32 91.0 1277.5 148.0 0.0729 " 76.3 325.4 317.45T 1.00 143.2 3369.1 482.3 0.0248 " 76.1 389.3 386.26U 1.16 152.6 9120.5 2036.4 0.0488 1.04 " 81.6 936.2 926.47T 1.02 153.4 5483.6 657.2 0.0370 " 76.2 481 476.98U 0.92 153.4 8597.7 1899.0 0.0384 0.88 " 77.1 866.5 859.39T 1.12 147.2 4848.9 524.0 0.0444 " 76.9 509.8 505
10U 1.16 142.3 6241.3 1385.6 0.0423 0.90 " 74.8 875.8 866.611T 0.90 135.7 3860.6 503.7 0.0599 " 76.1 401.7 398.8
8/4 1U 1.68 143.8 4166.6 943.8 0.0503 1.11 73 / 46 76.3 832.3 819.83T 2.74 100.2 1869 212.0 0.0974 " 75.6 352.6 345.24T 3.10 99.9 1096.2 138.7 0.0710 " 75.5 318.4 311.15U 1.69 96.2 1103.9 248.0 0.0730 1.45 " 77.9 636.9 627.66T 1.76 100.5 1599.8 204.3 0.0898 " 74.2 322.9 318.6
8/5 1U 0.78 152.5 10016 2208.2 0.0569 1.45 73 / 38 76.1 774.6 769.22T 0.80 133.8 3009.1 386.5 0.0311 " 75.7 401.9 399.34U 1.16 146.4 8808.2 1968.7 0.0691 1.62 " 81.6 807.3 7995U 1.09 149.3 6129.3 1382.9 0.0542 1.15 " 76.2 902.9 8946T 1.00 138.0 3366.1 484.5 0.0270 " 76.5 378.2 375.27T 1.72 134.5 2593.7 325.0 0.1258 " 75.7 412.3 406.68U 0.73 151.8 9882.5 2175.2 0.0924 2.48 " 77.2 727.7 723
8/6 23 / 0
8/7 1T 1.91 153.7 7095.3 853.3 0.0373 30 / 0 76.9 483 475.4
8/8 6 / 0
DISPL. @ FAIL.
Project Number:Lab Number:Bridge Number:LIMS Number:
17th Street BridgeLocation:Date Received:Tested by:
121
Table B-1. Continued.
BORING SAMP DEPTH DEPTH TEST LENGTH DIA. WET WET L / D CORR.NO. TOP BOT. DATE MASS UNIT MASS RATIO FACTOR
CORE (ft) (ft) (in) (in) (g) (pcf)
9/1 1T 52.0 2.3675 2.3758 274.8 99.7 1.002U 4.8455 2.3993 734.1 127.7 2.02 1.003T 2.5725 2.3918 357.3 117.8 1.084U 3.8405 2.3895 623.0 137.8 1.61 1.035T 2.2010 2.3723 364.2 142.6 0.937U 4.1760 2.3723 631.5 130.3 1.76 1.028T 1.9400 2.4003 299.0 129.8 0.819T 2.2845 2.3838 357.8 133.7 0.96
10U 57.0 3.6120 2.3605 616.1 148.5 1.53 1.04
9/2 2U 57.0 4.0595 2.3835 642.7 135.2 1.70 1.023T 2.4610 2.4002 426.2 145.8 1.034T 2.1900 2.3923 384.5 148.8 0.925T 62.0 2.3480 2.3793 372.9 136.1 0.99
9/3 1T 62.0 2.3540 2.3748 382.8 139.9 0.992T 2.3030 2.3762 411.0 153.3 0.973U 4.7730 2.3712 853.7 154.3 2.01 1.004T 2.3620 2.3657 413.8 151.8 1.005U 4.5455 2.3710 806.2 153.0 1.92 1.016T 2.2490 2.3638 355.2 137.1 0.957U 3.9055 2.3790 647.2 142.0 1.64 1.038T 67.0 2.0000 2.3515 243.9 107.0 0.85
9/4 1T 67.0 2.0470 2.3715 332.2 140.0 0.862U 4.8350 2.3870 751.7 132.4 2.03 1.003T 2.0110 2.3808 227.2 96.7 0.844T 2.2550 2.3907 274.4 103.3 0.945T 2.0905 2.3708 248.0 102.4 0.886U 3.6590 2.3763 436.6 102.5 1.54 1.047T 72.0 1.9035 2.3728 228.5 103.4 0.80
9/5 1T 72.0 2.1880 2.3832 366.2 142.9 0.922U 4.5405 2.3837 780.4 146.7 1.90 1.013T 2.2630 2.3797 404.8 153.2 0.954U 4.4335 2.3853 712.6 137.0 1.86 1.015U 77.0 4.8720 2.3825 861.7 151.1 2.04 1.00
9/6 1U 77.0 3.6205 2.3862 662.8 156.0 1.52 1.042T 2.4180 2.3888 439.7 154.6 1.013T 82.0 1.9630 2.3873 356.4 154.5 0.82
9/7 1U 82.0 87.0 4.2860 2.3872 770.9 153.1 1.80 1.01
STATE MATERIALS OFFICE
Foundations Laboratory
Rock CoreUnconfined Compression-
Split Tensile
Effective/Revised Date: 12/22/05
By: B.W. Page 1 of 1
122
Table B-1. Continued.
BORING SAMP. w DRY MAX. S. T. q (u) STRAIN % RECOV. TARE WET DRYNO. UNIT MASS LOAD STRENGTH @ FAIL. WT. WT. WT.
CORE (%) (pcf) (lbs) (psi) (psi) (in) (%) % RQD (g) (g) (g)
9/1 1T 6.88 93.3 1279.5 144.8 0.1211 98 / 64 76.3 349.6 3322U 6.62 119.7 4586 1014.4 0.0481 0.99 " 77 803.8 758.73T 9.36 107.7 1349.6 139.6 0.1402 " 75.4 429.4 399.14U 7.87 127.8 5926.1 1283.9 0.0533 1.39 " 77.1 684.2 639.95T 6.88 133.4 3102.2 378.2 0.0323 " 75.1 435.4 412.27U 5.95 123.0 4364.8 971.6 0.0426 1.02 " 74.2 695.5 660.68T 5.68 122.8 2644.6 361.6 0.1008 " 77.9 373.6 357.79T 4.30 128.2 3740 437.2 0.1115 " 76.3 430.4 415.8
10U 1.86 145.8 16570 3651.9 0.0723 2.00 " 75.6 682.5 671.4
9/2 2U 3.66 130.4 4704.7 1032.8 0.0302 0.74 62 / 8 75.5 716.1 693.53T 1.84 143.2 5139.4 553.9 0.0406 " 76.3 502.5 494.84T 2.50 145.2 4575.3 556.0 0.0323 " 77.1 461.8 452.45T 1.55 134.0 3925.7 447.4 0.0201 " 77.9 450.6 444.9
9/3 1T 0.90 138.6 3660 416.8 0.0345 87 / 33 75.1 458.1 454.72T 1.16 151.6 5147.2 598.8 0.0344 " 75.4 486.6 481.93U 1.62 151.8 8931.8 2022.7 0.0411 0.86 " 77 930.4 916.84T 1.15 150.1 4117.4 469.1 0.0385 " 76.1 489.7 4855U 2.26 149.6 12046.9 2714.5 0.0564 1.24 " 77.1 881.4 863.66T 3.71 132.2 1619.8 335.6 0.0306 " 76.5 431.4 418.77U 3.83 136.8 4587.7 1005.8 0.0652 1.67 " 81.6 724.1 700.48T 2.53 104.3 1663.5 225.2 0.1097 " 75.7 318.7 312.7
9/4 1T 1.34 138.1 3476.3 455.9 0.0404 68 / 17 76.2 408.3 403.92U 1.15 130.8 6042.2 1350.2 0.0451 0.93 " 76.3 823.9 815.43T 4.01 93.0 802.1 106.7 0.0909 " 77.2 302.8 294.14T 2.98 100.3 1647 194.5 0.1026 " 75.7 348.9 3415T 3.21 99.2 986.8 126.8 0.0723 " 75.9 320.5 312.96U 2.15 100.3 848.3 184.7 0.0877 2.40 " 76.1 508.6 499.57T 2.27 101.1 1367.3 192.7 0.0828 " 76.2 301.9 296.9
9/5 1T 0.97 141.6 3361 410.3 0.0543 80 / 37 72.2 437.2 433.72U 1.04 145.2 6839.4 1523.5 0.0341 0.75 " 76.6 856.4 848.43T 1.09 151.6 5095.1 602.3 0.0367 " 76.7 477.2 472.94U 1.21 135.4 6111.7 1355.4 0.0470 1.06 " 76.1 776.6 768.25U 1.20 149.3 7936.3 1780.2 0.0341 0.70 " 76.3 937.8 927.6
9/6 1U 1.97 152.9 9747.7 2099.6 0.0406 1.12 47 / 16 76.7 737.9 725.12T 1.62 152.1 5475.7 603.5 0.0583 " 76.4 515.7 508.73T 1.54 152.2 4377.4 594.7 0.0467 " 79 435.5 430.1
9/7 1U 1.09 151.4 8963.4 1975.7 0.0694 1.62 30 / 13 77.3 844.1 835.8
17th Street BridgeLocation:Date Received:Tested by:
DISPL. @ FAIL.
Project Number:Lab Number:Bridge Number:LIMS Number:
123
Table B-2. Fuller Warren Soil Boring Data
BORING SAMP DEPTH DEPTH TEST LENGTH DIA. WET WET L / D CORR.NO. TOP BOT. DATE WT. UNIT WT RATIO FACTOR
CORE (ft) (ft) (in) (in) (g) (pcf)
CB-1/1 1T 40.50 8/10/2006 2.3420 2.4850 463.4 155.4 0.942U 4.8177 2.4610 799.3 132.9 1.96 1.003T 2.4465 2.4200 374.3 126.7 1.014T 2.3805 2.4200 396.3 137.9 0.985U 45.50 4.1642 2.4765 751.1 142.6 1.68 1.02
CB-1/2 1U 45.50 8/10/2006 3.6302 2.4545 679.5 150.7 1.48 1.042T 2.4455 2.4625 442.7 144.8 0.993U 4.5233 2.4315 750.0 136.0 1.86 1.014T 2.3470 2.4250 399.4 140.4 0.975U 4.6885 2.4535 805.6 138.5 1.91 1.016T 2.1235 2.4700 384.2 143.9 0.867T 2.5135 2.4600 454.9 145.1 1.028U 4.8195 2.4570 848.6 141.5 1.96 1.009T 2.5560 2.4640 472.0 147.5 1.04
10U 50.50 4.7962 2.4740 892.8 147.5 1.94 1.00
CB-1/3 1T 50.50 8/10/2006 2.4945 2.4510 464.0 150.2 1.022U 4.7732 2.4630 911.1 152.6 1.94 1.003T 2.4785 2.4495 451.5 147.2 1.014T 8/11/2006 2.4555 2.4545 388.3 127.3 1.005T 2.3780 2.4340 355.0 122.2 0.986T 55.50 2.4080 2.4240 346.0 118.6 0.99
CB-1/4 1U 55.50 8/14/2006 4.7672 2.3530 693.6 127.5 2.03 1.002T 2.5350 2.3975 384.2 127.9 1.063T 2.5305 2.4060 353.4 117.0 1.054U 4.8415 2.4215 758.8 129.6 2.00 1.005T 2.2020 2.4115 341.0 129.2 0.916U 4.8682 2.4230 766.8 130.1 2.01 1.007T 2.3085 2.4170 345.1 124.1 0.968U 4.7217 2.4350 727.1 126.0 1.94 1.009T 60.50 2.5060 2.4400 393.8 128.0 1.03
CB-1/5 1T 60.50 8/14/2006 2.3600 2.0160 227.1 114.8 1.172T 2.0215 2.1000 207.7 113.0 0.963T 2.4585 2.2185 285.8 114.6 1.114U 4.0008 2.0860 420.4 117.1 1.92 1.015U 4.8755 2.2955 597.1 112.7 2.12 1.006T 2.4770 2.4000 349.0 118.6 1.037U 4.8537 2.4230 680.3 115.8 2.00 1.008U 4.6912 2.4060 665.3 118.8 1.95 1.009T 65.50 2.4465 2.3815 326.2 114.0 1.03
CB-1/6 1T 65.50 8/15/2006 2.5280 2.3400 328.9 115.3 1.082T 2.3860 2.2185 296.0 122.3 1.083U 4.8008 2.3850 675.2 119.9 2.01 1.004T 2.3295 2.4040 344.1 124.0 0.975T 70.50 2.3140 2.3200 303.5 118.2 1.00
Effective/Revised Date: 4/27/05
By: G.J. Page 1 of 1
STATE MATERIALS OFFICE
Foundations Laboratory
Rock CoreUnconfined Compression-
Split Tensile
124
Table B-2. Continued. CB-18/9/2006
BORING SAMP. w DRY MAX. S. T. q (u) STRAIN % RECOV. TARE WET DRYNO. UNIT WT LOAD STRENGTH @ FAIL. WT. WT. WT.
CORE (%) (pcf) (lbs) (psi) (psi) (in) (%) % RQD (g) (g) (g)
CB-1/1 1T 3.35 150.4 3963.2 433.5 0.0640 67/37 427.1 873.8 859.32U 16.73 113.8 1017.4 213.3 0.0497 1.03 431.1 1224.3 1110.63T 23.01 103.0 276.8 29.8 0.0464 410.1 781.1 711.74T 15.60 119.3 799.8 88.4 0.0445 425.5 821.1 767.75U 10.93 128.6 6578.2 1335.3 0.0609 1.46 433 1181.1 1107.4
CB-1/2 1U 8.01 139.5 9815.4 1990.3 0.0699 1.93 94/74 424.3 1098.2 1048.22T 10.47 131.1 1191 125.9 0.0443 418.9 861 819.13U 14.44 118.9 3855 822.8 0.0496 1.10 302.8 1051.7 957.24T 11.77 125.6 896 100.2 0.0512 370.7 769.5 727.55U 14.05 121.4 3453 726.2 0.0672 1.43 435.2 1239.4 1140.36T 11.39 129.1 1814 220.2 0.0509 328.3 711.6 672.47T 11.43 130.2 2473 254.6 0.0558 434.1 887.6 841.18U 11.42 127.0 4494 945.7 0.0522 1.08 368.9 1201.4 1116.19T 11.39 132.4 1875 189.6 0.0411 429.5 900.9 852.7
10U #DIV/0! #DIV/0! * #VALUE! * #VALUE!
CB-1/3 1T 8.79 138.1 2483.1 258.6 0.0504 60/48 377.8 840.9 803.52U 8.31 140.9 7533 1575.1 0.0527 1.10 372.3 1279.6 12103T 9.49 134.5 1582 165.9 0.0408 428.2 878.2 839.24T 16.13 109.6 245 25.9 0.0289 427.1 814.5 760.75T 24.16 98.5 112 12.4 0.0213 372.3 726.9 657.96T 31.27 90.4 183 19.9 0.0297 435.2 780.7 698.4
CB-1/4 1U 26.38 100.9 759 174.5 0.0516 1.08 92/77 427.1 1118.4 974.12T 23.05 103.9 181 19.0 0.0223 372.4 756.2 684.33T 30.80 89.5 121 12.7 0.0393 435.3 780.1 698.94U 22.23 106.1 1408 305.7 0.0440 0.91 419 1165.6 1029.85T 22.22 105.7 299 35.9 0.0278 364.9 705.4 643.56U 22.05 106.6 1468 318.3 0.0547 1.12 308.2 1073.8 935.57T 27.86 97.1 215 24.6 0.0356 313.1 657.8 582.78U 25.34 100.5 772 165.1 0.0576 1.22 373.2 1098.8 952.19T 23.43 103.7 267 27.8 0.0440 425.5 819 744.3
CB-1/5 1T 36.30 84.3 109 14.6 0.0336 90/67 315.2 542 481.62T 41.19 80.0 61 9.2 0.0242 431.1 637.8 577.53T 45.34 78.8 29 3.4 0.0173 432.5 716.5 627.94U 37.67 85.1 338 98.4 0.0608 1.52 370.4 789.6 674.95U 36.26 82.7 423 102.3 0.0610 1.25 370.6 965.9 807.56T 33.82 88.7 136 14.5 0.0386 376.5 724.3 636.47U 34.34 86.2 550 119.3 0.0565 1.16 312 990.3 816.98U 29.72 91.6 479 105.1 0.0420 0.90 300.9 965.2 8139T 30.54 87.4 119 13.0 0.0401 371.3 697 620.8
CB-1/6 1T 29.23 89.2 51.7 5.6 0.0276 58/38 315.2 643.7 569.42T 27.22 96.1 46 5.5 0.0407 431.3 726.7 663.53U 28.98 93.0 187 41.9 0.0531 1.11 370.4 1045.1 893.54T 21.96 101.7 53 6.0 0.0284 364.9 708.7 646.85T 25.61 94.1 30 3.5 0.0372 432.5 735.6 673.8
DISPL. @ FAIL.
Fuller WarrenProject Number:Lab Number:Bridge Number:LIMS Number:
JC
Location:Date Received:Tested by:
125
Table B-2. Continued.
BORING SAMP DEPTH DEPTH TEST LENGTH DIA. WET WET L / D CORR.NO. TOP BOT. DATE WT. UNIT WT RATIO FACTOR
CORE (ft) (ft) (in) (in) (g) (pcf)
CB-2/1 1U 37.58 8/16/2006 4.0513 2.3715 674.2 143.5 1.71 1.022T 2.4250 2.3875 437.6 153.6 1.023T 42.58 2.4635 2.3500 390.2 139.1 1.05
CB-2/2 1T 42.58 8/16/2006 2.2305 2.3730 359.4 138.8 0.942U 4.8233 2.3865 806.6 142.4 2.02 1.003T 2.2735 2.3440 328.3 127.5 0.974U 8/17/2006 4.7352 2.3685 756.7 138.2 2.00 1.005T 2.4425 2.3845 413.1 144.3 1.026T 47.58 2.4775 2.3770 429.6 148.9 1.04
CB-2/3 1T 47.58 8/17/2006 2.3155 2.3325 393.3 151.4 0.992U 4.6713 2.3815 790.1 144.7 1.96 1.003T 2.4450 2.3890 415.2 144.3 1.024U 2.6913 2.3880 784.5 247.9 1.13 1.095T 2.3950 2.3885 401.6 142.6 1.006U 4.7383 2.3925 769.6 137.6 1.98 1.007T 2.4370 2.3935 401.1 139.4 1.028U 4.9098 2.3895 872.3 150.9 2.05 1.009T 2.2950 2.3770 310.1 116.0 0.97
10U 4.7280 2.3760 630.4 114.6 1.99 1.0011T 2.3950 2.3630 294.3 106.7 1.0112U 52.58 4.7902 2.3810 834.4 149.0 2.01 1.00
CB-2/4 1T 52.58 8/17/2006 2.3575 2.3365 383.7 144.6 1.012U 4.7825 2.3870 798.5 142.1 2.00 1.003U 4.7328 2.3500 775.3 143.9 2.01 1.004T 8/18/2006 2.3815 2.3675 367.4 133.5 1.015U 4.6380 2.3510 701.1 132.7 1.97 1.006T 2.3035 2.3635 327.9 123.6 0.977U 4.6880 2.3645 655.3 121.3 1.98 1.008T 2.2875 2.3445 312.6 120.6 0.989U 4.7233 2.3485 662.1 123.3 2.01 1.0010T 2.3315 2.3390 330.5 125.7 1.0011T 2.3140 2.3530 340.4 128.9 0.9812U 4.8088 2.3595 699.7 126.8 2.04 1.0013T 2.5235 2.3475 359.1 125.3 1.0714T 57.58 2.5360 2.3615 357.3 122.5 1.07
CB-2/5 1U 57.58 8/18/2006 4.8678 2.3470 705.9 127.7 2.07 1.002T 2.4855 2.3655 363.3 126.7 1.053U 4.7017 2.3590 677.6 125.6 1.99 1.004T 2.3865 2.3325 350.0 130.8 1.025U 62.58 4.9502 2.3395 718.3 128.6 2.12 1.00
CB-2/6 1T 62.58 8/18/2006 2.3460 2.3535 294.3 109.9 1.002U 4.7983 2.3545 623.0 113.6 2.04 1.003T 2.3445 2.3675 301.1 111.1 0.994U 4.7540 2.3515 627.6 115.8 2.02 1.005T 2.3380 2.3355 311.5 118.5 1.006U 4.6223 2.3500 629.1 119.5 1.97 1.007U 4.8098 2.3650 654.8 118.1 2.03 1.008T 2.3175 2.3130 312.8 122.4 1.009U 4.8382 2.3155 654.1 122.3 2.09 1.0010T 67.58 2.4185 2.3000 323.1 122.5 1.05
STATE MATERIALS OFFICE
Foundations Laboratory
Rock CoreUnconfined Compression-
Split Tensile
Effective/Revised Date: 4/27/05
By: G.J. Page 1 of 1
126
Table B-2. Continued.
BORING SAMP DEPTH DEPTH TEST LENGTH DIA. WET WET L / D CORR.NO. TOP BOT. DATE WT. UNIT WT RATIO FACTOR
CORE (ft) (ft) (in) (in) (g) (pcf)
CB-3/1 1U 41' 8/21/2006 4.8380 2.3950 853.2 149.1 2.02 1.002U 4.4327 2.3835 740.4 142.6 1.86 1.013T 2.4345 2.3100 335.2 125.2 1.054T 2.4350 2.3785 375.0 132.0 1.025T 46' 2.3500 2.3730 409.9 150.2 0.99
CB-3/2 1T 46' 8/21/2006 2.4165 2.2995 308.4 117.1 1.052U 4.3357 2.3655 774.8 154.9 1.83 1.013T 8/22/2006 2.3220 2.3760 406.1 150.3 0.984U 4.8068 2.3820 806.8 143.5 2.02 1.005T 2.3535 2.3720 400.6 146.7 0.996U 4.8825 2.3895 799.2 139.1 2.04 1.007T 2.3395 2.3870 393.8 143.3 0.988U 51' 4.8715 2.3890 865.4 151.0 2.04 1.00
CB-3/3 1T 51' 8/22/2006 2.3315 2.3510 380.8 143.3 0.992U 4.8632 2.3610 838.4 150.0 2.06 1.003T 2.4395 2.3110 376.5 140.2 1.064T 2.4330 2.3555 378.1 135.9 1.035U 4.8955 2.3430 734.4 132.5 2.09 1.006T 2.4855 2.3285 366.7 132.0 1.077T 2.4545 2.3375 328.7 118.9 1.058U 4.8125 2.3360 672.7 124.2 2.06 1.009T 2.3865 2.3230 332.8 125.3 1.0310T 2.1210 2.3185 291.7 124.1 0.9111U 4.7020 2.3455 676.5 126.9 2.00 1.0012T 56' 2.4110 2.3595 369.5 133.5 1.02
CB-3/4 1T 56' 8/25/2006 2.4285 2.3140 361.2 134.7 1.052T 2.4045 2.3495 360.4 131.7 1.023U 4.7600 2.3470 716.7 132.6 2.03 1.004T 2.3475 2.3350 351.6 133.2 1.015U 4.8043 2.3400 701.4 129.3 2.05 1.006U 4.8840 2.3575 697.0 124.5 2.07 1.007T 2.4785 2.3545 368.8 130.2 1.058T 61' 2.4740 2.3655 330.1 115.7 1.05
CB-3/5 1T 61' 8/29/2006 2.3695 2.3380 291.2 109.1 1.012U 4.7328 2.3555 593.2 109.6 2.01 1.003T 2.2640 2.3445 282.7 110.2 0.974U 4.7637 2.3380 606.0 112.9 2.04 1.005U 4.5473 2.3420 570.4 110.9 1.94 1.006U 4.7163 2.3305 605.3 114.6 2.02 1.007T 2.3420 2.5030 330.6 109.3 0.948U 4.7265 2.3425 626.8 117.2 2.02 1.009T 2.3560 2.3405 313.9 118.0 1.01
10U 4.6853 2.3125 627.2 121.4 2.03 1.0011U 4.6542 2.2635 600.2 122.1 2.06 1.0012T 66' 2.5205 2.3035 313.7 113.8 1.09
CB-3/6 1T 66' 8/29/2006 2.3570 2.3525 329.7 122.6 1.002U 4.5855 2.3315 637.4 124.0 1.97 1.003T 2.4500 2.3325 331.8 120.7 1.054U 71' 4.7435 2.3535 651.6 120.3 2.02 1.00
Effective/Revised Date: 4/27/05
By: G.J. Page 1 of 1
STATE MATERIALS OFFICE
Foundations Laboratory
Rock CoreUnconfined Compression-
Split Tensile
127
Table B-2. Continued. CB-3
8/10/2006
BORING SAMP. w DRY MAX. S. T. q (u) STRAIN % RECOV. TARE WET DRYNO. UNIT WT LOAD STRENGTH @ FAIL. WT. WT. WT.
CORE (%) (pcf) (lbs) (psi) (psi) (in) (%) % RQD (g) (g) (g)
CB-3/1 1U 5.32 141.6 6782 1505.6 0.0522 1.08 72/50 430.3 1281.5 1238.52U 11.14 128.3 3530 784.1 0.0634 1.43 430.7 1168.7 1094.73T 26.01 99.3 368 41.6 0.0633 366.1 698.4 629.84T 16.40 113.4 1378 151.5 0.0687 431.4 805.4 752.75T 9.07 137.8 3224 368.0 0.0515 428.3 837.2 803.2
CB-3/2 1T 26.50 92.5 204 23.4 0.0743 77/67 428.1 735.5 671.12U 7.46 144.2 5720 1287.5 0.0549 1.27 430.2 1196.6 1143.43T 8.10 139.0 1552 179.0 0.0415 430.3 835.8 805.44U 11.63 128.5 3252 729.8 0.0541 1.13 431.4 1237.8 1153.85T 10.86 132.4 1623 185.1 0.0468 371.5 771.6 732.46U 13.79 122.2 4229 943.0 0.0563 1.15 433.1 1230.0 1133.47T 11.05 129.0 1715 195.5 0.0419 312.1 703.9 664.98U 8.31 139.4 5690 1269.3 0.0454 0.93 375.9 1239.0 1172.8
CB-3/3 1T 9.56 130.8 379 44.0 0.0410 100/92 366.0 746.4 713.22U 8.71 138.0 3187 727.9 0.0630 1.30 370.8 1207.2 1140.23T 4.54 134.1 120 13.5 0.0237 370.6 746.2 729.94T 14.37 118.8 243 27.0 0.0276 425.7 802.9 755.55U 18.48 111.9 501 116.1 0.0297 0.61 430.6 1164.0 1049.66T 19.11 110.8 169 18.6 0.0236 424.6 790.5 731.87T 28.86 92.3 88 9.7 0.0209 430.4 758.6 685.18U 27.47 97.5 731 170.5 0.0455 0.95 302.8 972.4 828.19T 24.01 101.1 287 32.9 0.0422 425.0 756.6 692.410T 23.05 100.8 93 12.1 0.0402 410.1 701.0 646.511U 23.97 102.3 433 100.3 0.0348 0.74 428.2 1103.6 973.012T 17.63 113.5 437 48.9 0.0324 428.4 797.4 742.1
CB-3/4 1T 19.83 112.4 159 18.0 0.0444 85/60 371.3 730.3 670.92T 19.85 109.9 361 40.6 0.0204 377.9 737.8 678.23U 20.45 110.1 1627 376.0 0.0503 1.06 304.2 1019.9 898.44T 21.49 109.7 328 38.1 0.0311 435.2 786.3 724.25U 24.66 103.7 1185 275.5 0.0551 1.15 370.7 1070.4 9326U 26.73 98.3 873 199.9 0.0708 1.45 419 1113.1 966.77T 25.87 103.4 223 24.3 0.0379 375.9 743.7 668.18T 37.81 83.9 181 19.7 0.0368 366 695.5 605.1
CB-3/5 1T 40.81 77.4 131 15.1 0.0392 100/100 366.0 656.5 572.32U 41.51 77.4 550 126.2 0.0528 1.12 371.4 963.6 789.93T 40.60 78.4 101 12.1 0.0494 375.9 657.8 576.44U 38.32 81.6 556 129.5 0.0669 1.40 435.3 1039.9 872.45U 39.91 79.3 594 137.3 0.0557 1.22 419.0 988.0 825.76U 34.81 85.0 581 136.1 0.0575 1.22 304.2 908.0 752.17T 30.13 84.0 175 19.0 0.0442 370.6 699.3 623.28U 29.44 90.6 485 112.5 0.0492 1.04 377.9 1002.2 860.29T 32.05 89.3 159 18.4 0.0365 427.2 740.3 664.3
10U 26.49 96.0 344 81.9 0.0398 0.85 375.3 1001.3 870.211U 26.54 96.5 221 55.0 0.0319 0.69 433.0 1032.3 906.612T 28.11 88.8 51 5.6 0.0220 371.5 684.6 615.9
CB-3/6 1T 20.39 101.8 98 11.2 0.0234 58/45 431.4 760.8 705.02U 21.02 102.5 356 83.1 0.0437 0.95 428.5 1064.8 954.33T 24.32 97.1 86 9.5 0.0405 428.2 759.4 694.64U 24.31 96.8 486 111.7 0.0488 1.03 430.4 1080.9 953.7
DISPL. @ FAIL.
Fuller WarrenProject Number:Lab Number:Bridge Number:LIMS Number:
JC
Location:Date Received:Tested by:
APPENDIX C SOIL BORING INFORMATION PROCESSED
Table C-1. 17th Street Bridge Processed Soil Boring Data.
128
1 2 3
EL. (ft) qt (tsf) qu (tsf) quqt(tsf) Ei (psi) EL. (ft) qt (tsf) qu (tsf) quqt(tsf) Ei (psi) EL. (ft) qt (tsf) qu (tsf) quqt(tsf) Ei (psi)-52 10.69 53.38 11.94 80829.45 -52 10.98 127.23 18.69 123700.43 -52 16.97 47.39 14.18 174256.09-53 12.12 86.06 16.15 112508.32 -53 29.82 127.23 30.80 123700.43 -53 25.84 47.39 17.50 174256.09-54 3.24 121.92 9.95 152060.87 -54 6.25 60.55 9.73 81116.67 -54 29.55 91.31 25.97 180288.98-55 3.24 71.23 7.60 128709.26 -56 24.65 50.99 17.73 130425.71 -54.5 16.97 40.15 13.05 75248.87-56 20.11 124.77 25.05 133386.84 -57 12.89 33.58 10.40 261797.27 -55 20.36 53.19 16.46 116133.00-57 15.83 101.05 20.00 143472.97 -58 25.35 158.50 31.70 137071.11 -56 6.49 53.19 9.29 116133.00
-57.5 10.83 31.61 9.25 54116.25 -60 13.13 45.58 12.23 46711.83 -57 25.86 67.42 20.88 20587.29-58 9.27 31.61 8.56 54116.25 -60 15.12 61.29 15.22 24748.90 -59 14.85 67.42 15.82 20587.29-59 25.47 32.74 14.44 50258.73 -62 9.84 154.63 19.50 166002.00 -60 7.23 67.42 11.04 20587.29-60 18.21 32.74 12.21 50258.73 -64 31.34 154.63 34.81 166002.00 -60.5 49.11 59.45 27.02 124443.40-61 20.27 51.23 16.11 61906.50 -65 8.60 154.63 18.23 166002.00 -61.5 17.78 59.45 16.25 124443.40-62 13.24 104.18 18.57 107548.83 -66 20.18 154.63 27.93 166002.00 -62 19.28 59.45 16.93 124443.40-65 10.37 153.71 19.96 167965.36 -67 10.89 84.19 15.14 92242.77 -62.5 12.71 153.46 22.09 59292.48-66 6.57 40.89 8.20 115282.48 -69 4.58 84.19 9.82 92242.77 -63 12.71 74.55 15.39 115316.42-67 23.23 40.89 15.41 115282.48 -72 2.95 84.19 7.88 92242.77 -64 8.17 31.69 8.04 92628.95-68 12.93 24.60 8.92 35563.47 -73 22.33 84.19 21.68 92242.77 -65 9.02 39.95 9.49 6111.94-69 14.81 17.22 7.99 49175.58 -74 7.20 170.37 17.52 203698.80 -66 11.00 30.02 9.08 60825.36-70 7.60 17.22 5.72 49175.58 -75 23.86 51.98 17.61 130769.50 -67 9.18 20.85 6.92 6020.61-72 11.28 17.22 6.97 49175.58 -76 20.57 67.79 18.67 89410.93 -69 10.90 17.33 6.87 17687.90
-77 20.57 105.35 23.28 122375.59 -70 7.49 17.33 5.70 17687.90-77 26.83 85.80 23.99 116801.38 -71 9.74 17.33 6.50 17687.90-78 26.83 135.18 30.11 163096.18 -72 14.80 100.35 19.27 136894.81-80 32.97 157.99 36.09 158144.06 -73 36.71 102.86 30.72 201419.69-85 44.07 149.30 40.56 159257.64 -75 18.17 37.05 12.97 41673.40
-77 11.78 43.09 11.26 27136.26-78 42.72 56.08 24.47 105885.43-82 34.96 56.08 22.14 105885.43
CB-6 (New)CB-4 (New) CB-5 (New)
Table C-1. Continued.
129
4 5 6
EL. (ft) qt (tsf) qu (tsf) quqt(tsf) Ei (psi) EL. (ft) qt (tsf) qu (tsf) quqt(tsf) Ei (psi) EL. (ft) qt (tsf) qu (tsf) quqt(tsf) Ei (psi)-52 27.57 172.01 34.43 123378.55 -52 24.64 171.66 32.52 172341.16 -52 10.43 73.03 13.80 102183.65
-57.5 15.08 101.85 19.59 94451.43 -54 4.84 17.49 4.60 26327.58 -53 10.05 92.44 15.24 92509.46-58 26.56 101.85 26.00 94451.43 -55 12.99 85.93 16.70 133906.89 -54 27.23 69.96 21.82 95248.98-59 40.44 209.01 45.97 195348.15 -57 12.99 38.71 11.21 38084.20 -55 26.03 69.96 21.34 95248.98-60 32.97 209.01 41.50 195348.15 -58 27.04 66.36 21.18 120782.02 -55.5 31.48 262.94 45.49 182445.65-61 30.71 71.84 23.48 116969.04 -60 29.48 83.73 24.84 94551.15 -56 39.88 74.36 27.23 138835.66-62 34.37 71.84 24.84 116969.04 -61 28.61 51.83 19.26 36950.25 -59 40.03 74.36 27.28 138835.66-63 17.59 74.79 18.14 165651.22 -62 13.44 17.24 7.61 37794.70 -61 32.21 74.36 24.47 138835.66-64 23.77 74.79 21.08 165651.22 -63 12.44 17.24 7.32 37794.70 -62 30.01 145.63 33.05 234895.75-65 11.59 74.79 14.72 165651.22 -64 10.66 146.62 19.77 196312.18 -62.5 43.11 145.63 39.62 234895.75-67 16.03 74.79 17.31 165651.22 -65 34.73 146.62 35.68 196312.18 -63.5 33.77 195.44 40.62 218771.42-72 24.61 171.24 32.46 170366.07 -66 47.32 136.73 40.22 214724.74 -65 24.16 72.42 20.91 60246.07-73 31.30 171.24 36.61 170366.07 -67 37.73 99.77 30.68 154467.47 -67 16.21 97.22 19.85 144754.85-74 31.30 188.03 38.36 197601.72 -68 36.27 67.95 24.82 84740.90 -67.5 32.82 97.22 28.24 144754.85-75 27.34 61.42 20.49 105915.18 -69 15.26 67.95 16.10 84740.90 -68.5 7.68 97.22 13.66 144754.85-77 27.34 156.86 32.74 186067.63 -70 9.99 17.86 6.68 17126.44 -69 14.00 97.22 18.45 144754.85-78 54.76 156.86 46.34 186067.63 -72 14.71 158.99 24.18 152286.14 -70 9.13 13.30 5.51 7704.23-80 31.54 170.90 36.71 158064.46 -73 27.83 141.75 31.40 121415.11 -72 13.88 13.30 6.79 7704.23-81 31.54 112.80 29.82 83499.76 -76 34.89 99.57 29.47 120236.98 -73 29.54 109.69 28.46 202857.23-83 49.05 112.80 37.19 83499.76 -77 23.40 156.61 30.27 87842.81 -75 43.37 97.59 32.53 127850.72-87 30.61 112.80 29.38 83499.76 -87 61.43 156.61 49.04 87842.81 -76 43.37 128.18 37.28 254347.86-90 15.60 112.80 20.97 83499.76 -80 43.45 151.17 40.52 187232.64
-82 42.82 142.25 39.02 122014.76
CB-7 (New) CB-8 (New) CB-9 (New)
130
Table C-2. Fuller Warren Bridge Processed Soil Boring Data.
EL. (ft) qu (tsf) qt (tsf) Recovery quqt(tsf) Ei (psi)-40.5 15.36 31.21 67 10.95 20725.93-42.5 96.14 2.14 67 7.18 93362.29-45.5 143.30 9.07 94 18.02 108694.81-46.5 59.24 7.21 94 10.34 20329.10-47.5 52.29 15.85 94 14.40 50938.20-48.5 68.09 18.33 94 17.67 87522.73-50.5 113.41 18.62 60 22.97 143167.10-55.5 12.56 1.37 92 2.07 16123.94-56.5 22.01 0.91 92 2.24 33646.94-57.5 22.92 2.58 92 3.85 28351.18-58.5 11.89 1.77 92 2.29 13580.10-60.5 7.08 1.05 90 1.37 6509.45-61.5 7.36 0.66 90 1.10 8173.66-62.5 8.59 0.25 90 0.73 10247.30-63.5 7.57 1.05 90 1.41 11768.07-65.5 3.02 0.40 58 0.55 3832.10
EL. (ft) qu (tsf) qt (tsf) Recovery quqt(tsf) Ei (psi)-37.58 42.57 25.23 25 16.39 48974.00-42.58 18.66 3.54 68 4.06 30083.74-43.58 56.42 1.76 68 4.98 75668.97-47.58 64.77 18.36 90 17.24 81523.95-48.58 65.12 8.41 90 11.70 75899.59-49.58 37.24 8.51 90 8.90 38959.02-50.58 140.06 10.11 90 18.82 152082.74-51.58 8.29 1.91 90 1.99 15682.83
-52 78.44 0.84 90 4.05 69402.72-52.58 15.68 5.49 98 4.64 24923.43-53.58 10.61 1.82 98 2.20 14642.92-54.58 9.08 1.28 98 1.71 13980.61-55.58 18.88 1.90 98 2.99 21191.30-56.58 20.99 1.40 98 2.71 20221.36
-57 16.81 1.36 98 2.39 21522.93-57.58 16.72 1.77 80 2.72 26059.97-62.58 11.08 1.14 77 1.78 11334.53-63.58 9.44 1.44 77 1.84 12460.26-64.58 9.59 1.24 77 1.72 13170.90-65.58 10.08 0.97 77 1.56 14308.84-66.58 7.49 0.42 77 0.89 15724.97
EL. (ft) qu (tsf) qt (tsf) Recovery quqt(tsf) Ei (psi)-41 108.40 3.00 72 9.01 139525.37-42 56.45 10.91 72 12.41 55345.75-46 92.70 1.69 77 6.25 102818.36-47 52.55 12.89 77 13.01 64868.52-48 67.90 13.33 77 15.04 81761.47-49 91.39 14.08 77 17.93 136076.85-51 52.41 3.17 100 6.44 56192.28-52 8.36 0.97 100 1.42 19141.58-53 12.28 1.94 100 2.44 18051.95-54 7.22 1.34 100 1.55 13564.22-56 27.07 1.30 85 2.97 35561.05-57 19.84 2.93 85 3.81 24011.06-58 14.39 2.74 85 3.14 13791.05-61 9.09 1.09 100 1.57 11308.89-62 9.33 0.87 100 1.42 9220.15-63 9.89 1.37 100 1.84 11249.80-64 9.80 1.32 100 1.80 11165.85-65 8.10 0.40 100 0.90 10801.59-66 5.99 0.81 58 1.10 8732.30-67 8.04 0.69 58 1.18 10850.17
CB-3 (New)15
CB-1 (New)30
CB-2 (New)25
131
APPENDIX D FREQUENCY DISTRIBUTIONS
Figure D-1. Total Capacity Frequency Distribution 5 feet Correlation Length
Figure D-2. Total Capacity Frequency Distribution 12 feet Correlation Length
500 520 540 560 580 600 620 640 660 680 7000
0.005
0.01
0.015
0.02
0.025
0.03
550 560 570 580 590 600 610 620 6300
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
132
0 200 400 6000
0.005
0.01
0.015
0.02
0.025
qu0 20 40 60
0
0.1
0.2
0.3
0.4
qt
0 50 1000
0.01
0.02
0.03
0.04
RQD
FullerWarren MEAN = 56.6495 8.4384 63.0673 STD = 78.6970 10.6514 25.6656 SKEW = 4.0955 1.8064 -0.1906 KURT = 24.6259 6.3517 1.9980 MNPDFEXP = 56.6321 8.3339 29.6672 STDPDFEXP = 56.5155 8.0886 25.1402 SKPDFEXP = 1.9848 1.7879 1.4168 KUPDFEXP = 8.7361 6.8332 3.5806 MNPDFLOG = 53.7941 6.7613 46.0365 STDPDFLOG = 66.7919 8.8546 20.5086 SKPDFLOG = 3.1883 2.5116 1.2676 KUPDFLOG = 16.7575 9.8725 3.1364 sqerrorNORM = 1.0e-005 * 0.1896 0.0147 0.0008 sqerrorEXP = 1.0e-006 * 0.4337 0.0909 0.0524 sqerrorLOGN = 1.0e-006 * 0.0867 0.1634 0.1023 Figure D-3. Fuller Warren Bridge Old and New Borings.
133
0 200 400 6000
0.005
0.01
0.015qu
0 20 40 600
0.02
0.04
0.06
0.08qt
0 20 40 60 800
0.02
0.04
0.06RQD
FullerWarren MEAN = 84.0846 21.0250 31.8000 STD = 103.4132 12.8320 15.8931 SKEW = 3.1996 0.8896 0.3480 KURT = 14.4114 3.2306 2.1762 MNPDFEXP = 83.5399 16.3554 20.5342 STDPDFEXP = 82.2767 14.0040 17.1492 SKPDFEXP = 1.8272 1.2029 1.2207 KUPDFEXP = 7.2899 3.5943 3.4034 MNPDFLOG = 78.7380 19.3564 27.8348 STDPDFLOG = 79.1172 11.3702 13.9045 SKPDFLOG = 2.4872 1.2153 1.0484 KUPDFLOG = 11.0840 4.0844 3.3541 sqerrorNORM = sqerrorNORM = 1.0e-005 * 0.1173 0.0002 0.0009 sqerrorEXP = 1.0e-006 * 0.6094 0.0027 0.0002 sqerrorLOGN = 1.0e-006 * 0.3260 0.0093 0.0001 Figure D-4. Fuller Warren Bridge Old Borings.
134
0 50 100 1500
0.01
0.02
0.03
0.04
qu0 10 20 30 40
0
0.1
0.2
0.3
0.4
qt
0 50 1000
0.01
0.02
0.03
RQD
FullerWarren MEAN = 33.2623 4.9771 70.5119 STD = 35.5262 6.7102 21.6325 SKEW = 1.4909 1.9667 -0.2355 KURT = 4.3762 6.4417 1.9256 MNPDFEXP = 30.9262 4.9163 29.2225 STDPDFEXP = 28.4992 4.7548 25.2514 SKPDFEXP = 1.4166 1.8230 1.5131 KUPDFEXP = 4.7127 6.9671 3.7210 MNPDFLOG = 27.5770 4.0548 56.0055 STDPDFLOG = 25.9415 4.9143 17.7774 SKPDFLOG = 1.8682 2.5286 1.2478 KUPDFLOG = 6.5454 10.3575 2.8813 MNPDFGAM = 31.4924 4.8403 58.0390 STDPDFGAM = 27.7417 5.1162 17.8002 SKPDFGAM = 1.3825 1.9486 1.0286 KUPDFGAM = 4.6979 7.1993 2.6588 sqerrorNORM = 1.0e-005 * 0.7224 0.0185 0.0003 sqerrorEXP = 1.0e-005 * 0.3605 0.0020 0.0043 sqerrorLOGN = 1.0e-005 * 0.1938 0.0000 0.0093 sqerrorGAM = 1.0e-005 * 0.3299 0.0037 0.0041 Figure D-5. Fuller Warren Bridge New Borings.
135
0 100 200 3000
0.005
0.01
0.015
quqt/20 20 40 60 80
0
0.01
0.02
0.03
0.04
0.05
qt (tsf)
0 20 40 600
0.01
0.02
0.03
0.04
0.05
qu(tsf)
MEAN = 1.0e+004 * 0.0060 0.0006 6.2192 STD = 1.0e+004 * 0.0042 0.0006 4.8059 SKEW = 0.5721 0.8510 0.7210 KURT = 2.4376 2.2529 2.3001 MNPDFEXP = 1.0e+004 * 0.0042 0.0005 4.5972 STDPDFEXP = 1.0e+004 * 0.0035 0.0004 3.9074 SKPDFEXP = 1.1923 1.2702 1.1766 KUPDFEXP = 3.4116 3.8305 3.4654 MNPDFLOG = 1.0e+004 * 0.0043 0.0004 4.8072 STDPDFLOG = 1.0e+004 * 0.0032 0.0004 3.4648 SKPDFLOG = 1.3965 1.6554 1.3606 KUPDFLOG = 4.0138 5.1557 4.1142 MNPDFGAM = 1.0e+004 * 0.0049 0.0005 5.3568 STDPDFGAM = 1.0e+004 * 0.0033 0.0004 3.6765 SKPDFGAM = 0.9666 1.2516 0.9698 KUPDFGAM = 3.0719 3.7974 3.1902 sqerrorNORM = 1.0e-005 * 0.1110 0.0016 0.0279 sqerrorEXP = 1.0e-006 * 0.1716 0.0205 0.8014 sqerrorLOGN = 1.0e-006 * 0.0112 0.0037 0.7291 Figure D-6. 17th Street Bridge Old and New Borings.
136
0 50 100 1500
0.01
0.02
0.03
0.04
qu (tsf)0 10 20 30 40
0
0.1
0.2
0.3
0.4
qt (tsf)
0 0.5 1 1.5 2
x 105
0
2
4
6x 10-5
Ei (psi)
MEAN = 1.0e+004 * 0.0033 0.0005 4.0354 STD = 1.0e+004 * 0.0036 0.0007 4.1662 SKEW = 1.4909 1.9667 1.5006 KURT = 4.3762 6.4417 4.2151 MNPDFEXP = 1.0e+004 * 0.0031 0.0005 3.6832 STDPDFEXP = 1.0e+004 * 0.0028 0.0005 3.3610 SKPDFEXP = 1.4166 1.8230 1.3552 KUPDFEXP = 4.7127 6.9671 4.4338 MNPDFLOG = 1.0e+004 * 0.0028 0.0004 3.3867 STDPDFLOG = 1.0e+004 * 0.0026 0.0005 2.9839 SKPDFLOG = 1.8682 2.5286 1.7647 KUPDFLOG = 6.5454 10.3575 6.1003 MNPDFGAM = 1.0e+004 * 0.0031 0.0005 3.8192 STDPDFGAM = 1.0e+004 * 0.0028 0.0005 3.2012 SKPDFGAM = 1.3825 1.9486 1.2998 KUPDFGAM = 4.6979 7.1993 4.4234 sqerrorNORM = 1.0e-005 * 0.7224 0.0185 0.0003 sqerrorEXP = 1.0e-005 * 0.3605 0.0020 0.0043 sqerrorLOGN = 1.0e-005 * 0.1938 0.0000 0.0093 sqerrorGAM = 1.0e-005 * 0.3299 0.0037 0.0041 Figure D-7. 17th Street Bridge New Borings.
137
0 50 100 1500
0.01
0.02
0.03
0.04
0 10 20 30 400
0.1
0.2
0.3
0.4
0 20 40 60 800
0.02
0.04
0.06
0.08
0.1
FullerWarren MEAN = 40.6770 5.6533 59.0000 STD = 43.8454 7.7969 16.2741 SKEW = 1.1377 1.7369 -0.2460 KURT = 3.0363 5.4691 1.3395 MNPDFEXP = 35.4210 5.5212 22.4767 STDPDFEXP = 31.5161 5.2677 19.7376 SKPDFEXP = 1.2780 1.7062 1.5784 KUPDFEXP = 4.0350 6.2048 3.8275 MNPDFLOG = 29.4949 4.1192 46.3333 STDPDFLOG = 29.1923 5.4296 13.3009 SKPDFLOG = 1.7745 2.4799 1.3628 KUPDFLOG = 5.7006 9.4714 2.7984 MNPDFGAM = 35.1343 5.2196 47.4964 STDPDFGAM = 31.6539 5.8278 13.2912 SKPDFGAM = 1.2908 1.9324 1.2163 KUPDFGAM = 4.0534 6.6096 2.6321 sqerrorNORM = 1.0e-005 * 0.6799 0.0320 0.0000 sqerrorEXP = 1.0e-005 * 0.3160 0.0222 0.0074 sqerrorLOGN = 1.0e-005 * 0.2110 0.0085 0.0160 sqerrorGAM = 1.0e-005 * 0.3215 0.0209 0.0077 Figure D-8. Fuller Warren Bridge New Boring CB1.
138
0 50 100 1500
0.02
0.04
0.06
0 10 20 300
0.1
0.2
0.3
0.4
0 50 1000
0.01
0.02
0.03
0.04
0.05
FullerWarren EAN = 30.3093 5.0613 74.5000 STD = 32.0428 6.2900 23.5584 SKEW = 2.0375 1.8282 -0.7659 KURT = 7.0180 5.6542 2.4186 MNPDFEXP = 28.8431 4.9667 28.9120 STDPDFEXP = 27.0370 4.7615 25.2984 SKPDFEXP = 1.5024 1.7542 1.5628 KUPDFEXP = 5.1612 6.4929 3.8012 MNPDFLOG = 27.2953 4.3067 51.6272 STDPDFLOG = 23.2056 4.7122 19.8380 SKPDFLOG = 1.9139 2.3214 1.4651 KUPDFLOG = 7.2505 9.2016 2.9963 MNPDFGAM = 29.8271 4.9493 54.7557 STDPDFGAM = 24.1703 4.8362 19.5059 SKPDFGAM = 1.4061 1.7783 1.2851 KUPDFGAM = 5.1809 6.5286 2.7296 sqerrorNORM = 1.0e-004 * 0.2195 0.0025 0.0032 sqerrorEXP = 1.0e-004 * 0.1553 0.0008 0.0003 sqerrorLOGN = 1.0e-005 * 0.9675 0.0110 0.0006 sqerrorGAM = 1.0e-004 * 0.1333 0.0025 0.0006 Figure D-9. Fuller Warren New Boring CB2.
139
0 50 100 1500
0.02
0.04
0.06
0 10 20 300
0.1
0.2
0.3
0.4
0 50 1000
0.01
0.02
0.03
0.04
0.05
FullerWarren MEAN = 30.9569 4.2200 77.3793 STD = 33.1697 6.0748 20.3354 SKEW = 1.1429 2.3112 -0.2341 KURT = 2.8870 7.9730 1.4244 MNPDFEXP = 26.9212 4.1906 28.6658 STDPDFEXP = 23.9281 4.0814 25.3287 SKPDFEXP = 1.2791 1.9112 1.5975 KUPDFEXP = 4.0327 7.5835 3.8601 MNPDFLOG = 23.4179 3.5494 60.1970 STDPDFLOG = 21.6499 4.0810 16.9897 SKPDFLOG = 1.7166 2.6733 1.4052 KUPDFLOG = 5.5971 11.9322 2.7615 MNPDFGAM = 27.2903 4.1714 61.5707 STDPDFGAM = 23.7335 4.2676 16.9482 SKPDFGAM = 1.2574 1.9894 1.2835 KUPDFGAM = 4.0039 7.7753 2.6131 sqerrorNORM = 1.0e-004 * 0.2302 0.0009 0.0131 sqerrorEXP = 1.0e-004 * 0.1278 0.0024 0.0073 sqerrorLOGN = 1.0e-005 * 0.7795 0.0204 0.0453 sqerrorGAM = 1.0e-004 * 0.1260 0.0028 0.0077 Figure D-10. Fuller Warren New Boring CB3
140
APPENDIX E SGS RANDOM FIELD TABLES
Table E-1. 17th Street Bridge SGS (1feet). A
PSF
Mean 42562.48642Standard Error 219.7863813Median 39538.838Mode 38500Standard Deviation 21150.94231Sample Variance 447362360.5Kurtosis -0.507237829Skewness 0.48869983Range 99365.73316Minimum 598.72084Maximum 99964.454Sum 394171186.8Count 9261
BPSF
Mean 42658.43886Standard Error 221.5141441Median 39514.378Mode 41800Standard Deviation 21317.21199Sample Variance 454423526.9Kurtosis -0.568971001Skewness 0.480259697Range 98794.59432Minimum 1077.72768Maximum 99872.322Sum 395059802.3Count 9261
CPSF
Mean 42503.73487Standard Error 223.6157448Median 39001.786Mode 49700Standard Deviation 21519.45762Sample Variance 463087056.4Kurtosis -0.581050641Skewness 0.497640383Range 99866.79713Minimum 117.150872Maximum 99983.948Sum 393627088.6Count 9261
DPSF
Mean 42557.4383Standard Error 220.0553434Median 39532.284Mode 11399.9996Standard Deviation 21176.82563Sample Variance 448457943.8Kurtosis -0.580991141Skewness 0.47042905Range 98897.99504Minimum 862.72496Maximum 99760.72Sum 394124436.1Count 9261
141
Table E-1. Continued. E
PSF
Mean 42518.58199Standard Error 219.4444741Median 39411.644Mode 48900.002Standard Deviation 21118.03918Sample Variance 445971578.7Kurtosis -0.526496513Skewness 0.488121523Range 99546.9086Minimum 430.7594Maximum 99977.668Sum 393764587.8Count 9261
FPSF
Mean 43109.75042Standard Error 223.6009188Median 39677.666Mode 38500Standard Deviation 21518.03086Sample Variance 463025652Kurtosis -0.575002397Skewness 0.468898326Range 99622.97688Minimum 375.72712Maximum 99998.704Sum 399239398.7Count 9261
GPSF
Mean 42377.27821Standard Error 219.7337363Median 39054.524Mode 15199.9998Standard Deviation 21145.87606Sample Variance 447148074.4Kurtosis -0.568985276Skewness 0.486387424Range 99352.60342Minimum 622.84458Maximum 99975.448Sum 392455973.5Count 9261
HPSF
Mean 42587.84604Standard Error 220.7370971Median 39504.638Mode 15199.9998Standard Deviation 21242.43358Sample Variance 451240984.2Kurtosis -0.544309321Skewness 0.478158775Range 99739.27387Minimum 191.482126Maximum 99930.756Sum 394406042.2Count 9261
IPSF
Mean 42446.51502Standard Error 221.3665243Median 39289.578Mode 38500Standard Deviation 21303.00593Sample Variance 453818061.7Kurtosis -0.564645925Skewness 0.495661419Range 99259.75486Minimum 631.13714Maximum 99890.892Sum 393097175.6Count 9261
142
Table E-2. 17th Street Bridge SGS (5feet). A
PSF
Mean 45806.79179Standard Error 222.6907591Median 42021.988Mode 49700Standard Deviation 21430.44246Sample Variance 459263864Kurtosis -0.689609294Skewness 0.381837804Range 99308.9843Minimum 594.1977Maximum 99903.182Sum 424216698.7Count 9261
BPSF
Mean 41246.08288Standard Error 217.5866605Median 38500Mode 41800Standard Deviation 20939.25418Sample Variance 438452365.5Kurtosis -0.448952677Skewness 0.545106492Range 98730.14074Minimum 1258.95726Maximum 99989.098Sum 381979973.5Count 9261
CPSF
Mean 45632.38736Standard Error 224.5743392Median 42031.22Mode 30800Standard Deviation 21611.70708Sample Variance 467065883.1Kurtosis -0.69715789Skewness 0.35706524Range 97915.1958Minimum 2035.8922Maximum 99951.088Sum 422601539.3Count 9261
DPSF
Mean 42598.52685Standard Error 217.1910467Median 39472.638Mode 15199.9998Standard Deviation 20901.18264Sample Variance 436859435.9Kurtosis -0.532426787Skewness 0.498080027Range 99879.66534Minimum 109.310656Maximum 99988.976Sum 394504957.1Count 9261
143
Table E-2. Continued. E
PSF
Mean 44489.19162Standard Error 222.650213Median 41394.268Mode 48900.002Standard Deviation 21426.54054Sample Variance 459096639.7Kurtosis -0.649152833Skewness 0.41713792Range 99747.25472Minimum 223.29528Maximum 99970.55Sum 412014403.6Count 9261
GPSF
Mean 41666.77162Standard Error 216.0629871Median 38692.49Mode 49700Standard Deviation 20792.62486Sample Variance 432333248.4Kurtosis -0.514976359Skewness 0.501212334Range 99806.4971Minimum 67.244902Maximum 99873.742Sum 385875971.9Count 9261
HPSF
Mean 42756.64801Standard Error 224.632869Median 39366.7Mode 49700Standard Deviation 21617.33964Sample Variance 467309373.1Kurtosis -0.551513094Skewness 0.508615793Range 99542.12376Minimum 371.65624Maximum 99913.78Sum 395969317.2
IPSF
Mean 43683.07808Standard Error 222.3762153Median 39940.616Mode 48900.002Standard Deviation 21400.17263Sample Variance 457967388.5Kurtosis -0.63673678Skewness 0.421260262Range 99744.20568Minimum 158.764318Maximum 99902.97Sum 404548986.1Count 9261
JPSF
Mean 41831.42157Standard Error 216.718847Median 38761.494Mode 48900.002Standard Deviation 20855.74094Sample Variance 434961930Kurtosis -0.50047995Skewness 0.533206704Range 99290.7898Minimum 697.6282Maximum 99988.418Sum 387400795.2Count 9261
144
Table E-3. 17th Street Bridge SGS (12 feet). A B C
PSF PSF PSF
Mean 41584.65934 Mean 52111.7188 Mean 39762.78304Standard Error 205.8633641 Standard Error 233.0037394 Standard Error 212.0978036Median 38963.996 Median 49829.998 Median 36918.004Mode 49700 Mode 48900.002 Mode 15199.9998Standard Deviation 19811.07343 Standard Deviation 22422.90273 Standard Deviation 20411.03904Sample Variance 392478630.3 Sample Variance 502786566.9 Sample Variance 416610514.6Kurtosis -0.457306535 Kurtosis -0.9338627 Kurtosis -0.264671923Skewness 0.493885727 Skewness 0.102754863 Skewness 0.646850373Range 99151.57972 Range 99192.8432 Range 99913.70662Minimum 611.08428 Minimum 732.4568 Minimum 62.269382Maximum 99762.664 Maximum 99925.3 Maximum 99975.976Sum 385115530.2 Sum 482606627.8 Sum 368243133.8Count 9261 Count 9261 Count 9261
D E FPSF PSF PSF
Mean 39355.34143 Mean 46573.85942 Mean 40064.89254Standard Error 215.9959574 Standard Error 232.6746559 Standard Error 212.0271793Median 36115.68 Median 42937.85 Median 37300Mode 11399.9996 Mode 49700 Mode 38500Standard Deviation 20786.17431 Standard Deviation 22391.23368 Standard Deviation 20404.24257Sample Variance 432065042.7 Sample Variance 501367345.7 Sample Variance 416333114.8Kurtosis -0.386909561 Kurtosis -0.802132918 Kurtosis -0.443063463Skewness 0.640670637 Skewness 0.28637968 Skewness 0.530885072Range 99816.1107 Range 99937.26621 Range 99619.43411Minimum 87.5993 Minimum 14.7757856 Minimum 97.851888Maximum 99903.71 Maximum 99952.042 Maximum 99717.286Sum 364469817 Sum 431320512.1 Sum 371040969.8Count 9261 Count 9261 Count 9261
G H JPSF PSF PSF
Mean 37173.00379 Mean 47907.34312 Mean 41663.39521Standard Error 208.7527541 Standard Error 228.4042742 Standard Error 220.5532068Median 34311.524 Median 43876.092 Median 38535.546Mode 11399.9996 Mode 49700 Mode 11399.9996Standard Deviation 20089.13124 Standard Deviation 21980.27739 Standard Deviation 21224.73707Sample Variance 403573194.1 Sample Variance 483132594.2 Sample Variance 450489463.6Kurtosis -0.17153857 Kurtosis -0.80052981 Kurtosis -0.530291652Skewness 0.714709268 Skewness 0.300035536 Skewness 0.522353319Range 99077.68402 Range 98726.572 Range 99212.07664Minimum 339.23998 Minimum 1247.8 Minimum 480.66536Maximum 99416.924 Maximum 99974.372 Maximum 99692.742Sum 344259188.1 Sum 443669904.7 Sum 385844703.1Count 9261 Count 9261 Count 9261
145
Table E-3. Continued. AA BB Z
PSF PSF PSF
Mean 42900.29827 Mean 42408.97909 Mean 46519.50275Standard Error 219.2799472 Standard Error 218.869694 Standard Error 223.6012514Median 39601.91 Median 39127.61 Median 42316.284Mode 15199.9998 Mode 48900.002 Mode 49700Standard Deviation 21102.20608 Standard Deviation 21062.72574 Standard Deviation 21518.06286Sample Variance 445303101.5 Sample Variance 443638415.5 Sample Variance 463027029.4Kurtosis -0.643142448 Kurtosis -0.538154163 Kurtosis -0.695072802Skewness 0.430785494 Skewness 0.49509214 Skewness 0.381873107Range 99267.1778 Range 99698.04192 Range 99382.08064Minimum 550.6242 Minimum 212.13808 Minimum 559.82136Maximum 99817.802 Maximum 99910.18 Maximum 99941.902Sum 397299662.3 Sum 392749555.3 Sum 430817115Count 9261 Count 9261 Count 9261
I K LPSF PSF PSF
Mean 43704.58521 Mean 39506.03724 Mean 44470.57504Standard Error 214.6861676 Standard Error 199.8427351 Standard Error 224.9408061Median 39961.776 Median 37021.622 Median 41004.174Mode 41800 Mode 38500 Mode 49700Standard Deviation 20660.12788 Standard Deviation 19231.68367 Standard Deviation 21646.97368Sample Variance 426840884.2 Sample Variance 369857657 Sample Variance 468591469.6Kurtosis -0.585301651 Kurtosis -0.35014142 Kurtosis -0.659852085Skewness 0.445114079 Skewness 0.56895775 Skewness 0.436021337Range 98805.25304 Range 99826.24379 Range 99576.18214Minimum 1054.96096 Minimum 143.53621 Minimum 260.83786Maximum 99860.214 Maximum 99969.78 Maximum 99837.02Sum 404748163.6 Sum 365865410.8 Sum 411841995.5Count 9261 Count 9261 Count 9261
LL M NPSF PSF PSF
Mean 52001.27262 Mean 47226.12953 Mean 46392.57197Standard Error 231.0221144 Standard Error 228.5146525 Standard Error 235.8458747Median 49700 Median 43423.728 Median 42452.282Mode 49700 Mode 41800 Mode 48900.002Standard Deviation 22232.20286 Standard Deviation 21990.89954 Standard Deviation 22696.41304Sample Variance 494270843.9 Sample Variance 483599662.6 Sample Variance 515127164.7Kurtosis -0.875814507 Kurtosis -0.743959545 Kurtosis -0.793047923Skewness 0.140331985 Skewness 0.347746576 Skewness 0.343204355Range 99156.84372 Range 96633.395 Range 99050.74032Minimum 837.24428 Minimum 3327.115 Minimum 935.39768Maximum 99994.088 Maximum 99960.51 Maximum 99986.138Sum 481583785.7 Sum 437361185.5 Sum 429641609Count 9261 Count 9261 Count 9261
146
Table E-3. Continued. Ñ O P
PSF PSF PSF
Mean 51470.31861 Mean 41320.25623 Mean 40438.14456Standard Error 236.2322652 Standard Error 206.1301759 Standard Error 215.9221412Median 49608.578 Median 38500 Median 37335.826Mode 49700 Mode 32200 Mode 11399.9996Standard Deviation 22733.59697 Standard Deviation 19836.74982 Standard Deviation 20779.07069Sample Variance 516816431.2 Sample Variance 393496643.2 Sample Variance 431769778.5Kurtosis -0.913495054 Kurtosis -0.37199239 Kurtosis -0.492837597Skewness 0.171190865 Skewness 0.55984348 Skewness 0.533478348Range 99976.04256 Range 99177.92682 Range 99853.50113Minimum 18.9974382 Minimum 734.86918 Minimum 94.534874Maximum 99995.04 Maximum 99912.796 Maximum 99948.036Sum 476666620.7 Sum 382666892.9 Sum 374497656.8Count 9261 Count 9261 Count 9261
Q R SPSF PSF PSF
Mean 47042.63871 Mean 44797.74259 Mean 45763.25705Standard Error 223.6413497 Standard Error 231.159873 Standard Error 222.6925403Median 43499.474 Median 41342.338 Median 42281.89Mode 48900.002 Mode 38500 Mode 48900.002Standard Deviation 21521.92168 Standard Deviation 22245.45993 Standard Deviation 21430.61387Sample Variance 463193112.9 Sample Variance 494860487.6 Sample Variance 459271211Kurtosis -0.740545222 Kurtosis -0.671942245 Kurtosis -0.75114585Skewness 0.319788177 Skewness 0.424328387 Skewness 0.319107618Range 97029.068 Range 99524.53918 Range 99124.16976Minimum 2876.152 Minimum 393.21682 Minimum 841.91824Maximum 99905.22 Maximum 99917.756 Maximum 99966.088Sum 435661877.1 Sum 414871894.1 Sum 423813523.6Count 9261 Count 9261 Count 9261
T U VPSF PSF PSF
Mean 44061.74486 Mean 48102.4208 Mean 37070.10498Standard Error 218.5590664 Standard Error 221.9101921 Standard Error 198.1461848Median 41032.302 Median 44215.9 Median 34927.44Mode 48900.002 Mode 38500 Mode 15199.9998Standard Deviation 21032.83278 Standard Deviation 21355.32531 Standard Deviation 19068.4177Sample Variance 442380054.7 Sample Variance 456049919.2 Sample Variance 363604553.7Kurtosis -0.626614687 Kurtosis -0.74765644 Kurtosis -0.200228081Skewness 0.424741976 Skewness 0.29905297 Skewness 0.659719139Range 99303.45 Range 98855.61356 Range 99517.49996Minimum 617.266 Minimum 1139.09244 Minimum 375.12404Maximum 99920.716 Maximum 99994.706 Maximum 99892.624Sum 408055819.2 Sum 445476519 Sum 343306242.2Count 9261 Count 9261 Count 9261
147
Table E-3. Continued. W X Y
PSF PSF PSF
Mean 44963.57643 Mean 42967.49829 Mean 47554.61147Standard Error 222.873721 Standard Error 222.1398912 Standard Error 248.1298149Median 41800 Median 39449.822 Median 43413.186Mode 49700 Mode 49700 Mode 11399.9996Standard Deviation 21448.04963 Standard Deviation 21377.4302 Standard Deviation 23878.54684Sample Variance 460018833 Sample Variance 456994521.8 Sample Variance 570184999.2Kurtosis -0.664903412 Kurtosis -0.588149668 Kurtosis -0.886393787Skewness 0.400653996 Skewness 0.47779941 Skewness 0.30788879Range 98933.37236 Range 98727.84014 Range 99288.7588Minimum 1062.49964 Minimum 1192.01386 Minimum 707.5792Maximum 99995.872 Maximum 99919.854 Maximum 99996.338Sum 416407681.4 Sum 397922001.7 Sum 440403256.8Count 9261 Count 9261 Count 9261
148
Table E-4. 17th Street Bridge SGS (20feet). A B
PSF PSF
Mean 45407.11477 Mean 44728.03485Standard Error 235.5262499 Standard Error 231.9539298Median 41856.568 Median 41280.174Mode 48900.002 Mode 48900.002Standard Deviation 22665.65424 Standard Deviation 22321.87526Sample Variance 513731882.1 Sample Variance 498266115Kurtosis -0.732519328 Kurtosis -0.718776057Skewness 0.383255739 Skewness 0.39948428Range 99920.77422 Range 99567.77814Minimum 60.007784 Minimum 414.47586Maximum 99980.782 Maximum 99982.254Sum 420515289.9 Sum 414226330.7Count 9261 Count 9261
C DPSF PSF
Mean 42210.90062 Mean 43657.61793Standard Error 222.0514785 Standard Error 225.6671411Median 39094.814 Median 39968.552Mode 49700 Mode 49700Standard Deviation 21368.92187 Standard Deviation 21716.87187Sample Variance 456630822.1 Sample Variance 471622524Kurtosis -0.546710456 Kurtosis -0.656686698Skewness 0.494754071 Skewness 0.442924124Range 99843.95339 Range 99635.08658Minimum 84.734612 Minimum 222.54142Maximum 99928.688 Maximum 99857.628Sum 390915150.6 Sum 404313199.7Count 9261 Count 9261
149
Table E-4. Continued. F G
PSF PSF
Mean 41916.56315 Mean 42862.22371Standard Error 215.7209468 Standard Error 214.3914192Median 39004.65 Median 39756.89Mode 41800 Mode 38500Standard Deviation 20759.70892 Standard Deviation 20631.76305Sample Variance 430965514.3 Sample Variance 425669646.5Kurtosis -0.571675821 Kurtosis -0.597299848Skewness 0.480379812 Skewness 0.420685131Range 99964.77187 Range 99763.42888Minimum 10.554133 Minimum 18.545119Maximum 99975.326 Maximum 99781.974Sum 388189291.3 Sum 396947053.7Count 9261 Count 9261
H IPSF PSF
Mean 45380.61602 Mean 41610.78171Standard Error 235.732166 Standard Error 222.7657464Median 41800 Median 38575.492Mode 38500 Mode 32200Standard Deviation 22685.47038 Standard Deviation 21437.6588Sample Variance 514630566.5 Sample Variance 459573214.6Kurtosis -0.716214975 Kurtosis -0.524411823Skewness 0.415227363 Skewness 0.521869386Range 99922.89606 Range 99693.49401Minimum 65.887942 Minimum 158.311992Maximum 99988.784 Maximum 99851.806Sum 420269885 Sum 385357449.4Count 9261 Count 9261
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APPENDIX F FLAC3D PROGRAMMING MODELS
Table F-1. FLAC Results. 1 (feet)
Cap
.15(ton) Bias A 200 1.175 0.007300506B 240 0.979167 0.012186026C 235 1 0.008020456D 220 1.068182 0.000456898E 210 1.119048 0.000869697F 200 1.175 0.007300506G 285 0.824561 0.070222666H 250 0.94 0.022367296I 225 1.044444 0.002035143J 265 0.886792 0.041113462K 235 1 0.008020456L 230 1.021739 0.004599263
LL 185 1.27027 0.032657286M 235 1 0.008020456N 190 1.236842 0.021692902Ñ 230 1.021739 0.004599263O 190 1.236842 0.021692902P 190 1.236842 0.021692902R 200 1.175 0.007300506S 235 1 0.008020456T 215 1.093023 1.20149E-05U 235 1 0.008020456V 240 0.979167 0.012186026W 200 1.175 0.007300506X 187.5 1.253333 0.026822687Y 195 1.205128 0.013356703Z 200 1.175 0.007300506
AA 190 1.236842 0.021692902BB 220 1.068182 0.000456898
Determinis 235 Mean 1.089557 0.407317752 Standar 0.120611204 COV 0.110698
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Table F-1. Continued. 5 (feet)
Cap
.15(ton) Bias A 235 1 0.01099541B 185 1.27027 0.027360888C 220 1.068182 0.001345216D 215 1.093023 0.000140085E 215 1.093023 0.000140085F 190 1.236842 0.01741954G 230 1.021739 0.006908913H 195 1.205128 0.010053913I 285 0.824561 0.078566743J 225 1.044444 0.003649919K 175 1.342857 0.056643116L 240 0.979167 0.015798563
LL 240 0.979167 0.015798563M 295 0.79661 0.095017342N 215 1.093023 0.000140085Ñ 200 1.175 0.00491976O 190 1.236842 0.01741954P 190 1.236842 0.01741954Q 265 0.886792 0.047553019R 190 1.236842 0.01741954S 250 0.94 0.02717849T 230 1.021739 0.006908913U 190 1.236842 0.01741954V 235 1 0.01099541W 240 0.979167 0.015798563X 225 1.044444 0.003649919Y 175 1.342857 0.056643116Z 200 1.175 0.00491976
AA 245 0.959184 0.021221301BB 200 1.175 0.00491976CC 190 1.236842 0.01741954DD 150 1.566667 0.213266321EE 280 0.839286 0.07052917FF 220 1.068182 0.001345216GG 260 0.903846 0.040406164HH 180 1.305556 0.040279107II 180 1.305556 0.040279107JJ 230 1.021739 0.006908913KK 300 0.783333 0.103378754MM 160 1.46875 0.13241666
Determinis 225 Mean 1.104859 1.280593501 Standar 0.181206321 COV 0.164009
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Table F-1. Continued
12 (feet)
Cap
.15(ton) Bias A 260 0.903846 0.01190932B 250 0.94 0.0154095C 240 0.979167 0.00721962D 270 0.87037 0.03754473E 250 0.94 0.0154095F 215 1.093023 0.00083453G 200 1.175 0.01229105H 250 0.94 0.0154095I 280 0.839286 0.0505572J 200 1.175 0.01229105K 235 1 0.0041133L 265 0.886792 0.03145038
LL 310 0.758065 0.09367914M 260 0.903846 0.02569251N 190 1.236842 0.02982774Ñ 200 1.175 0.01229105O 285 0.824561 0.05739551P 205 1.146341 0.0067579Q 225 1.044444 0.00038772R 210 1.119048 0.0030154S 280 0.839286 0.0505572T 240 0.979167 0.00721962U 285 0.824561 0.05739551V 200 1.175 0.01229105W 200 1.175 0.01229105X 285 0.824561 0.05739551Y 330 0.712121 0.12391371Z 210 1.119048 0.0030154
AA 225 1.044444 0.00038772BB 195 1.205128 0.01987908CC 250 0.94 0.0154095DD 200 1.175 0.01229105EE 230 1.021739 0.00179741FF 225 1.044444 0.00038772GG 260 0.903846 0.02569251HH 270 0.87037 0.03754473II 185 1.27027 0.04249175JJ 190 1.236842 0.02982774KK 300 0.783333 0.07884958MM 165 1.424242 0.12967736
Determinis 235 Mean 1.012976 1.16180183 Standar 0.17259719 COV 0.170386
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Table F-2
1 (feet) End Bearing .15(ton) Mean 218.362069Standard Error 4.689030312Median 220Mode 200Standard Deviation 25.25120102Sample Variance 637.6231527Kurtosis 0.124369761Skewness 0.651972746Range 100Minimum 185Maximum 285Sum 6332.5Count 29
5 (feet) End Bearing .15(ton) Mean 218.375Standard Error 5.727205375Median 217.5Mode 190Standard Deviation 36.22202723Sample Variance 1312.035256
Kurtosis -
0.226714365Skewness 0.449655743Range 150Minimum 150Maximum 300Sum 8735Count 40
12 (feet) End Bearing .15(ton) Mean 238.125Standard Error 6.175031Median 237.5Mode 200Standard Deviation 39.05433Sample Variance 1525.24Kurtosis -0.63762Skewness 0.310262Range 165Minimum 165Maximum 330Sum 9525Count 40
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TYPICAL FLAC3D EXAMPLE ;------------------------------------------------- ; Vertically loaded pile ;------------------------------------------------- model mohr prop bulk 8.86E+06 shear 6.10E+06 fric 15 coh 71980.51 range group 1 prop bulk 8.70E+06 shear 5.99E+06 fric 15 coh 70372.78 range group 2 prop bulk 8.00E+06 shear 5.51E+06 fric 15 coh 63234.3 range group 3 prop bulk 8.39E+06 shear 5.78E+06 fric 20 coh 67204.36 range group 7998 prop bulk 7.94E+06 shear 5.47E+06 fric 20 coh 62625.79 range group 7999 prop bulk 7.48E+06 shear 5.15E+06 fric 20 coh 57934.44 range group 8000 ini dens 4.4 range group 1 ini dens 4.4 range group 2 ini dens 4.4 range group 3 . ini dens 3.1 range group 7998 ini dens 3.1 range group 7999 ini dens 3.1 range group 8000 ; gen zone brick p0 (13.5,13.5,20) p1 (16.5,13.5,20) p2 (13.5,16.5,20) p3 (13.5,13.5,40)& p4 (16.5,16.5,20) p5 (13.5,16.5,40) p6 (16.5,13.5,40) p7 (16.5,16.5,40)& size 2 2 20 gen zone brick p0 (13.5,13.5,40) p1 (16.5,13.5,40) p2 (13.5,16.5,40) p3 (13.5,13.5,40.1)& p4 (16.5,16.5,40) p5 (13.5,16.5,40.1) p6 (16.5,13.5,40.1) p7 (16.5,16.5,40.1)& size 2 2 1 group pile range x=13.5 16.5 y=13.5 16.5 z=20 40.1 save pile_geom.sav ; model elas range group pile prop bulk 6.50E+06 shear 3.00E+06 range group pile interface 1 prop kn 1.8e7 ks 1.8e7 fric 5 coh 30000 ; ini dens 3.1 range group pile model null range z 39.9 40.15 ; fix z range z -.1 .1 fix x range x -.1 .1 fix x range x 29.9 30.1 fix y range y -.1 .1 fix y range y 29.9 30.1
155
set grav 0 0 -32.18 ini szz 0. grad 0 0 100 range z 0 40 ini sxx 0. grad 0 0 50 range z 0 40 ini syy 0. grad 0 0 50 range z 0 40 ; hist unbal ; solve rat 1.0e-5 save pile0.sav ; model elas range group pile prop bulk 3.10E+08 shear 2.54E+08 range group pile ini dens 4.9 range group pile call find_add.fis solve rat 1.e-5 save pile1.sav ; ini state 0 ini xdis 0 ydis 0 zdis 0 ; ; monitor vertical loading at pile cap def zs_top ad = top_head zftot = 0.0 loop while ad # null gp_pnt = mem(ad+1) zf = gp_zfunbal(gp_pnt) zftot = zftot + zf ad = mem(ad) endloop zs_top = zftot / 9 end fix z range z 40.05 40.15 group pile ; def ramp while_stepping if step < ncut then udapp = float(step) * udmax / float(ncut) else udapp = udmax endif ad = top_head loop while ad # null gp_pnt = mem(ad+1) gp_zvel(gp_pnt) = udapp ad = mem(ad)
156
endloop end ; hist gp zdis 15,15,40 hist gp zvel 15,15,40 hist zs_top hist zone szz 15,15,39.9 hist zone szz 15,15,20 ; set mech damp comb set udmax = -1e-4 ncut 15000 step 112500 plot create history plot add hist 4 vs -2 save pile2.sav
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APPENDIX G UNIT COST DATA
158
159
LIST OF REFERENCES
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Fenton, G.A. (1999). “Estimation for Stochastic Soil Models.” ASCE Journal of Geotechnical and Geoenvironmental Engineering, 125 (6), 470-485.
Fenton, G.A. (2002). “Probabilistic Foundation Settlement on a Spatially Random Soil.” ASCE Journal of Geotechnical and Geoenvironmental Engineering, 128 (5), 381-390.
Fenton, G.A. and Griffiths, D.V. (2003). “Bearing Capacity of Spatially Random c-φ Soils.” Canadian Geotechnical Journal, 40(1), 54-65.
(Jing 2003).
Kulhawy, F.H., Spry M.J. and Grigoriu, M.D. (1988). “Reliability-Based Foundation Design for Transmission Line Structures.” EPRI Vol. 1. Geotechnical Site Characterization Strategy.
Kulhawy, F.H., Filippas O.B. and Grigoriu, M.D. (1988). “Reliability-Based Foundation Design for Transmission Line Structures.” EPRI Vol. 3. Uncertainties in Soil Property Measurement.
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Mark, C., McWilliams, L., Pappas, D. and Rusnak, J. (2004). “Spatial Trends in Rock Strength-Can They be Determined from Coreholes?” National Institute for Occupational Safety and Health.
McVey, M. and Ellis, E. (2003). “Static and Dynamic Field Testing of Drilled Shafts.” Florida Department of Transportation No. 99052794.
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National Highway Institute (1998). “Load and Resistance Factor Design (LRFD) for Highway Bridge Substructures.” NHI Course No. 13068, Volume 2.
Nowak, A.S. and Collins, K.R. (2000). “Reliability of Structures.” Chapter 8 Design Codes.
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Phoon, K. K., Kulhawy, F. H. and Grigoriu, M. D. (2003). “Development of a Reliability-Based Design Framework for Transmission Line Structure Foundations.” Journal of Geotechnical and Geoenvironmental Engineering, 798-806.
Phoon, K.K. and Kulhawy, F.H. (2002). “Observations on Geotechnical Reliability-Based Design Development in North America.” Foundation Design Codes and Soil Investigation in View of International Harmonization and Performance, 31-48.
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BIOGRAPHICAL SKETCH
Johanna Otero was born in Monteria, Colombia, to Maria Isabel Sanchez and Rafael Otero.
She graduated from Colegio la Sagrada Familia High School in Monteria Colombia in December
1992. She received his Bachelor of Science in civil engineering in the fall of 1998 from the
University EAFIT, Medellin Colombia..
After graduation as an Engineer, she worked on the transportation area on Pereira
Colombia for almost four years.
Johanna continued her education by entering graduate school to pursue a Master of
Engineering in the Construction Management Group of the Civil and Coastal Engineering
Department at the University of Florida in the fall 2003. She received his Master of Engineering
in the fall of 2004. Currently, she is pursuing a Doctorate of Philosophy at the same institution.
