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0 ThALYIS DF TRENCH DRAIN SYSTEMS
LI')RASH ?CINDATIONS
A Soecial Research Problem
Presented to
The FacultY of the School of Civil EngineeringGeorgia institute of Technology
Chris M. Willis
August 1989
-IN
GEORGIA INSTITUTE OF TECHNOLOGYA UNIT OF THE UNIVERSITY SYSTEM OF GEORGIA
SCHOOL OF CIVIL ENGINEERING
* ATLANTA, GEORGIA 30332
89 9 14 065
ANALYSIS OF TRENCH DRAIN SYSTEMS
BENEATH FOUNDATIONS
A Special Research Problem
Presented to
The Faculty of the School of Civil EngineeringGeorgia Institute of Technology
by
Chris M. Willis
In Partial Fulfillment
of the Requirements for the Degree of
Master of Science in Civil Engineering
Approved:
Dr. Richard D. Barksdale/Date
TABLE OF CONTENTS
pageACKNOWLEDGEMENTS iiABSTRACT iiiLIST OF FIGURES iv
Chapter1 TRENCH DRAIN SYSTEM 1
I. IntroductionII. Purpose of the Study
2 PREPARATIONS FOR THE ANALYSIS 5I. IntroductionII. Dimensional AnalysisIII. Radius of InfluenceIV. Using Aral Seepage ProgramV. Evaluation
3 INPUT AND OUTPUT OF THE TRENCH DRAINEVALUATION 32I. IntroductionII. Problem GeometryIII. Using and numbering conventionIV. Conduct of studyV. Summary
4 ANALYSIS OF TRENCH DRAIN DEWATERING 63I. IntroductionII. ResultsIII. Results of Predictive FormulasIV. Prediction of Trench Drain PerformanceV. Comparison of Trench Drain with Blanket
DrainVI. Conclusions
5 CONCLUSIONS 92I. IntroductionII. Trench Drain System AnalysisIII. Predictive MethodIV. Cost ComparisonV. Evaluation
REFERENCES 96
APPENDICESA SUMMARY OF PROGRAM COMPUTER RUNS A-1B SAMPLE INPUT AND OUTPUT B-1C DESCRIPTION OF COMPUTER PROCEDURES C-1D SPREADSHEET AND DATA FILE DISKS D-1E ARBITRARY SELECTION OF RADIUS E-1
i
ACKNOWLEDGEMENTS
The author would like to express gratitude to all
who contributed to this special research problem. Many
thanks goes to Dr. Richard D. Barksdale, my advisor, whose
guidance and interest greatly instilled encouragement.
I would like to thank Dr. Mutusfa Aral for his guidance
and instruction in tahe firite element model study zAfor
allowing me the use of his model. Additionally I would
like to thank Dr. Robert C. Backus along with Dr.
Barksdale and Dr. Aral for the instruction and guidance
in the geotechnical and hydraulics courses which made this
study possible.
Special gratitude is expressed to the U. S. Navy
Civil Engineer Corps for sponsoring my studies and for
the opportunity to attend this school.
Finally, I would like to express my special thanks
to my wife, Pat and my -)n-, for their patience,
encouragement and support. The.-s is the support which
makes everything possible and worthwhile.
ii
ABSTRACT
This study is an analysis of the performance
characteristics of a trench drain system used for
foundation dewatering. By the uses of a finite element
analysis program the trench drain system performance will
be modeled.
Through the use of dimensional analysis techniques
the results of the system modeling will be used to prepare
a means of predicting the system performance for a wide
range of variables.
As an economic concern the trench drain system will
be compared with the common blanket drain. This
comparison will provide information necessary for the
selection of the method most economical for the
application.
The trench drain characteristics of primary concern
are the total system flow and the maximum free surface
height of the water between trenches. The determination
of the radius of drawdown for the system is a vital
element of the prediction process and is a major portion
of the study.
iii
LIST OF FIGURES
2-1 Determination of radius of influence 162-2 Determination of radius of influence 172-3 Determination of radius of influence 182-4 Determination of radius of influence 192-5 Determination of radius of influence 202-6 Determination of radius of influence 212-7 Determination of radius of influence 222-8 Determination of radius of influence 232-9 Determination of radius of influence 242-10 Determination of radius of influence 252-11 Determination of radius of influence 262-12 Determination of radius of influence 27
3-1 Underdrain System in Half Space 343-2 Typical application of trench drain 343-3 Typical cross section of trench drain 353-4 Variables of Trench Drain Analysis 363-5 Example Mesh Used 373-6 Free surface between trenches 453-7 Free surface between trenches 463-8 Free surface between trenches 473-9 Free surface between trenches 483-10 Finding the Max. Free Surface 503-11 Finding the Max. Free Surface 503-12 Finding the Max. Free Surface 503-13 Finding the Max. Free Surface 503-14 Finding the Max. Free Surface 503-15 Finding the Max. Free Surface 503-16 Finding the Max. Free Surface 503-17 Finding the Max. Free Surface 503-18 Finding the Max. Free Surface 503-19 Finding the Max. Free Surface 503-20 Finding the Max. Free Surface 503-21 Finding the Max. Free Surface 50
4-1 Predicting the radius of influence 714-2 Predicting the radius of influence 724-3 Predicting the radius of influence 734-4 Finding the radius for example 4-1 754-5 Flow from a dimensionless product 784-6 Max Free Surface from dimensionless prod. 794-7 Flow with permeability 814-8 Max Free Surface with permeability 824-9 Flow for a three drain system 844-10 Max Free Surface for a three drain sys. 854-11 Spacing ecconomy for trench drains 90
iv
CHAPTER 1
TRENCH DRAIN SYSTEM
I. Introduction:
Shallow foundations are susceptible to damage and
leakage from the hydraulic forces of groundwater. The
pressure of water will damage walls, pass into the
structure through cracks and holes and contribute to the
deterioration of metal, wood and concrete structural
members. A structure will not satisfactorily full fill
the intention of the owner if water gathers in the
basement or garage of the building. A great deal of
effort is expended by builders, owners and designers
attempting to prevent water from infiltrating a foundation
or collecting behind the walls. The most simple solution,
as well as the most effective and economical is to
properly design the foundation so that water is not
present to penetrate the structure.
For a shallow foundation positioned at a moderate
depth below a water table the foundation trench drain
system is an alternative to expensive water resistent
methods of construction. The foundation trench drain
system is an application of a very old technique. A
trench filled with highly permeable granular material
collects water from surrounding, less permeable soil and
carries it by gravity flow and slope to a sump or outfall,
where the water can be removed or wasted. Today the flow
is usually in slotted pipes within the granular trench.
Since the water can be removed from the highly permeable
soil more quickly then it can exit the less permeable soil
a difference in elevation of the water levels of the two
soils is created. This gradient serves to provide
continued flow as long as the gradient exists.
The gravity flow method is obviously very easy to
implement and generally inexpensive. It does not always
work well to dewater or drain a site sufficient to
accomplish construction. It is usually not effective to
attempt dewatering by gravity flow when (Powers, pg.236):
a. Soil is a loose granular deposit without
plastic fines.
b. The soil has a high permeability.
c. There is a proximate source of large
recharge to the water table such as a lake or
river.
d. The aquifer is artesian or bounded under a
positive head by an impermeable upper surface.
e. The depth to be dewatered is large so that
there will be a high gradient between the water
table and the base of the foundation.
If the soil to be dewatered does not have the
limiting conditions gravity dewatering still might not be
2
advisable. The tendency of a soil to hold water is
called storage. All soils will retain water by capillary
tension while the apparent water table level is drawn
down. A soil with a high storage have a surprisingly
large amount of water held above the water free
surface(Powers, pg.114). Removal of the held water may
require energy in the form of pumping.
For this study the trench drain system for
dewatering beneath a foundation will be evaluated. The
evaluation will be done assuming that construction of the
foundation is complete and construction dewatering has
lowered the free water surface to below the design final
elevation. The trench drain system will maintain the
free water surface at the final elevation and not in
contact with the foundation.
II. Purpose of the Study:
In this study the characteristics of a trench drain
system will be evaluated with the use of the Aral Seepage
Program, a finite element analysis program. Under a
range of normal variables a trench drain system will be
evaluated to determine; (a)the output flow of the system
under the different configurations, (b)the range to which
drawdown of the water table can be expected and (c)the
maximum rise of the free water surface between the
trenches.
3
The results of the finite element analysis will be
grouped under dimensional analysis to provide a model for
prediction of the characteristics. The predictive method
will be effective within the range of variables
considered.
Finally a cost analysis of the trench drain system
as compared to a blanket drain system. With this
information a designer will be able to effectively select
the most cost efficient solution to the problem
considered if the choice is between the trench drain and
the blanket drain system.
4
CHAPTER 2
PREPARATIONS FOR THE ANALYSIS
I. Introduction:
In preparation for collecting data to analyze the
dewatering capacity of a trench drain system planning was
necessary to facilitate the assimilation of results.
Dimensional analysis, used in presenting the results of
this study is briefly reviewed in this chapter.
As with all numeric seepage calculations the area to
be dewatered is of critical importance. The size of the
cone of depression or the radius of influence is the
single most difficult parameter to establish. Many rules
of thumb, observations and formulas exist from which the
radius of influence is determined in practice. To predict
the rate of flow and water table drawdown the radius of
influence must be determined. The evaluation of the
radius of influence for use with the Aral Seepage Program
is reviewed in this chapter.
The Aral Seepage Program, a finite element analysis,
used in evaluating the trench drain system of this study
was detailed by an earlier study (Pirtle, Appendix A).
In preparing for runs of this program several items were
noted which amplify the instructions of the user's manual.
5
Il. Dimensional Analysis:
In this study the modeling of a large trench drain
system used, for dewatering beneath a foundation, was done
using a finite element analysis program. There are an
infinite number of geometries and conditions for such a
system and it is not practical to run the program for
each combination of dimensions and properties. The goal,
to provide a detailed summary of the expected results for
any single group of conditions from the results of a few
models, requires a range of variables covering normal
values. Results cannot be specific to a few
configurations of the system.
Dimensional analysis is a systematic grouping of
variables into a dimensionless product. The product can
represent a very small model of the system or a full size
application. The trends and results predicted from a
collation of the dimensionless numbers will be true for
any combination of variables. From a dimensionless number
the quantity of flow or free surface elevation between
trenches can be evaluated for an infinite number of
conditions.
In arriving at the dimensionless numbers for use in
evaluation, the variables must be identified and cataloged
by dimensions (Langhaar, Chap 3). The variables are then
grouped into dimensionless products. The results of this
6
study of trench drain systems is presented in terms of
dimensionless products. From inspection and
experimentation the dimensionless numbers which provide
the most insight are used in evaluating the models.
* The variables in the study of dewatering a foundation
by use of trench drains are listed:
-radius of influence (L), units of length
* -hydraulic conductivity, horizontal (ch), units
of length/time
-hydraulic conductivity, vertical (k), units of
* length/time
-trench spacing, (S), units of length
-trench width, (d), units of length
* -free head above trench bottom, (h), units of
length
-aquifer thickness, (h+H), units of length
* -number of trench drains, (N), no units
-slope of aquifer, (p), no unit
For this study only four trench drains were
• considered so no range of variables will be available
from which to reasonably predict the characteristics of
systems with other then four drains. The affect of other
* than four drains will not be considered. With a
di,,._sioaless product, later studies may determine a
ct..lation between a four trench system and other
* conf.', srations.
7
The aquifer slope will often be zero or near zero.
A multiple of zero will reduce any dimensionless number
to zero so the slope will also not be used in the
dimensional analysis. Slope is a critical variable and
the influence of aquifer slope will be shown by
individual results and trends. For intermediate results
interpolation between of the considered slopes will be
necessary.
The width of drainage trenches considered for this
study was restricted to one value. The trench width
varies in practice and a value of 1.5 feet provides the
minimum space necessary for placement of drainage pipe
and granular backfill. If it is more necessary to make
the trenches wider, the amount of dewatering will
increase (Pirtle, Chap 4) and there will be less
hydraulic rise in the water table between trenches. A
* wider trench is a more conservative approach and the
variable for width of trench drains is included as a
dimensional consideration.
Hydraulic conductivities, vertical and horizontal,
are the only variables with other then a length dimension.
This complicated the forming of dimensionless products.
* The vertical and horizontal conductivities had to be in
the product, which left five variables, all with a single
length dimension. There are five combinations to form a
dimensionless product, each with six alternative
8
arrangements. This study was done with the vertical
conductivity (k) equal to the horizontal conductivity
(kh) so the combinations for experimentation are:
L,d,S,h L,d,S,(H+h) L,d,h,(H+h) (1)
L,S,h,(H+h) S,d,h,(H+h)
Each grouping has six different arrangements,
yielding thirty possible dimensionless products. The
results of the model runs were prepared in the
dimensionless form. The products were compared and the
arrangement which provided an insight into a relationship
to total flow and the maximum free surface was selected
for use. In this case the final product is:
Ld/h(h+H) (2)
The variable not included in the product was the
trench spacing. In Chapter 4 trench spacing is considered
in evaluating the total flow and the maximum free surface
between trenches.
III. Radius of Influence:
The distance over which the water level is lowered
by dewatering is commonly referred to as the radius of
influence. The radius of influence is the distance from
the point or line of water removal to a point where the
water table is not affected by the dewatering operation.
9
Obviously any model of dewatering or pumping operations
is dependent on the radius of influence.
The radius of influence can be accurately determined
in the field by a pumping test. A pumping test, using a
fully penetrating well in an unbounded aquifer not in
contact with a body of water, will provide a measured
output and drawdown at known radii. The drawdown when
plotted against the log of time will allow for the
calculation of the effective conductivity of the soil.
Under the Dupuit assumptions mathematical models
((a)Powers, pg 100) can project a drawdown for various
distances and pump outputs. Calculation of the radius of
influence is also available with this method. F or a
trench drain system the pumping test method has several
problems. The trench drain is a method of open pumping
or gravity flow and will have a significantly lower output
then would a pumped well. By its nature the trench drain
system is longitudinally aligned and would not be modeled
by a well with accuracy. The trench drain does not fully
penetrate the aquifer and will offer a different output
than a fully penetrating well (Leonards, pg 270).
It is not unusual for the radius of influence to vary
greatly, often differing by an order of three to four
magnitudes ((a)Powers, pg 108). The radius of influence
is affected by every variable of the system. In general
the radius will increase with time and as the drawdown is
10
increasing. For pervious soils the radius of influence
is greater then for a soil of less hydraulic conductivity
(Leonards, pg 261). In the evaluation of a trench drain
system, after construction of the foundation, the
* dewatering has reached a steady state condition. The
affects of time and initial drawdown will not be
considered in this study.
* Normally the radius of influence is selected based
on knowledge of the area and experience with design of
dewatering systems. Several formulas exist to calculate
* the radius of influence, usually considering the hydraulic
conductivity, thickness of aquifer, free head above point
of lowest drawdown and adjustment factors. Several
* formulas are listed below:
Means of Calculating the Radius of Influence
1. Q = (.73+.27(H-h 0 )/H) (kx/2L) (H2-h 2 )
* Gravity flow to a partially penetrating slot
(Leonards, pg. 271) with Q=total flow,
H=aquifer thickness, h0=elevation of water in
* trench, x=length of trench, k= permeability and
L=radius of influence. Use consistent units.
2. L = 3.8h
• Highway subdrainage design (Moulton, pg 60)
with h=drawdown in water level in feet,
L=radius of influence in feet.
11
3. R0=3hk1/2
Radius of influence as a function of drawdown
((a)Powers, pg. 109 after Sichart) with
R0=radius of influence, h=drawdown. Use
consistent units.
4. Q/x = K(H'-h2)/L
Water table flow from a line source to a
drainage trench ((a)Powers, pg. 100). Q/x is
the total flow per unit length of trench, k is
permeability, H = thickness of aquifer,
h= trench elevation, L = radius of influence.
Use consistent units.
5. G = SYLq/KH2
* Predictive Analysis of Groundwater Inflows into
Excavations (Freeze, pg. 494).
G=a dimensionless discharge, S Y= specific yield,
* normally .01 to .3 (Freeze, pg. 61),
K= hydraulic conductivity, H = aquifer
thickness, q= rate of flow per unit length of
*trench, L= radius of influence. Use consistent
units.
These formulas and others will predict a radius of
* influence for the characteristics of the problem. The
prediction of a radius of influence for the foundation
trench drain system is discussed in Chapter 4.
12
The radius of influence is an input value in the
Aral Seepage Program. The program will calculate a
quantity of flow and a water level free surface for a
given radius of influence. The formulas from above and
several others offer severe limitations to predicting the
radius of influence. The formulas are not specifically
for a trench drain system and to various degrees do not
account for variations in horizontal and vertical
permeability, partial penetration of the aquifer and
gravity flow.
Water is produced from an unconfined aquifer by
three mechanisms: (1) expansion of the water under
reduced fluid pressures, (2) compaction of the aquifer
under increased effective stress and (3) dewatering of
the unconfined aquifer (Freeze, pg 324). In a gravity
flow trench system water is not removed from the aquifer
but, is carried away after it enters the trench (or
leaves the aquifer). The water will leave the aquifer at
a rate consistent with the Darcy principal, Q = kiA.
Once steady state is attained the area, A becomes
constant and so too is the flow. The amount of drawdown
over the distance from trench to original water level
(radius of influence) is the hydraulic gradient, i. The
permeability is a property of the soil and is assumed to
remain constant. The gradient in a steady state gravity
flow system can only change with a rising (infiltration)
13
or lowering (depleted) water table. To change the
gradient in a stationary water table an outside action
must take place to change the fluid pressures or to
physically remove water from the aquifer. Pumping would
be a means of changing the gradient and hence the radius
of influence and outflow of the system.
The theoretically correct radius of influence for
ideal conditions was determined by running each trench
drain configuration at a series of different radii. The
resultant total flow of the system were plotted against
the trial radii of influence. Total flow is the
cumulative outflow from all four trenches. Figures 2-1
through 2-12 are the results of the runs. The above
discussion shows the radius of influence to be at the
distance where no further drawdown occurs. The trial
radii greater then the true radius of influence yields a
result at the true free surface. Lesser trial radii
results in a forced solution with a larger gradient and
higher flow. For this study the radius of influence was
selected from the figures 2-1 through 2-12 as the
distance where flow became constant.
Establishing the distance where total flow remained
relatively constant required a uniform criterion to
define unchanging flow. Arbitrarily, unchanging total
flow was defined as 10% change over a 100 foot change in
radius. This definition was selected after compAr4csn of
14
the results across the thirty six different
configurations of the problem as studied. For this
problem, assuming a trench length of 200 feet the 10%
change criterion is less then .05 gpm total flow.
The radius of influence is an extremely variable
value, subject to interpretation and fine measurement.
An accuracy of fifty feet was established as a reasonable
estimation for the correct radius of influlencP.
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IV. Using Aral Seepage Program:
The Aral Seepage Program, a finite element model
program was used in the evaluation of drainage
characteristics of trench drain systems. An excellent
program user's manual is included in an earlier study
(Pirtle, Appendix A). Used for confined and unconfined
flow problems of axisymetric or two dimensional seepage,
the program is available at Georgia Institute of
Technology, Department of Civil Engineering.
The user inputs the problem geometry, soil
characteristics and position of ground water. By
equilibrium solutions to the discrete grid elements the
program adjusts the initially assumed free surface
through several iterations until the level of accuracy is
* satisfied. When completed a solution is presented to the
defined problem, including total seepage flow through
seepage faces and the steady state free water surface.
* The referenced user's manual includes detailed
sample input for an unconfined seepage problem. The
evaluated trench drain system is of the same nature and
Sso input was extremely similar. Appendix B of this study
is a copy of an input data file for a run of the Aral
Seepage Program for a trench drain. Figure 3-5 of Chapter
* 3 will provide node and element numbers as used.
28
Comments on the Aral Seepage Program User's Manual:
1. The user's manual does not provide guidance in
setting the model sensitivity on the Title and Type
Problem Card (card FERR). This card sets the degree of
accuracy which will discontinue iterations of the free
surface calculations. A precise number is not as
important as maintaining a minimum number of iterations
* during the run. Recommended accuracy will be a value
such that a minimum of three iterations are completed in
the free surface calculations. The necessary value of
* sensitivity will become evident after several runs.
2. The control card input for NNPC, total number of
corner nodal points, makes it clear that intermediate
* nodes will be generated between the listed corner nodes.
What is not clear is that it is recommended that a line
of elements several rows below the free water surface,
* should be defined as corner nodes. This establishment of
an unmoving row close to the free surface reduces the
iteration time. Iterations occur between the intermediate
* nodes and the free water surface. Figure 3-5 is a sample
of the finite element mesh used in this study.
The Free Surface Nodal Cards include the top and
* bottom corner nodes of the "movable zone" described
above. Sixteen corner nodes, or eight sets of free
surface and base, are allowed for each card.
29
3. General program notes not included in the user's
manual:
-The current version of the Aral Seepage
Program is limited to thirty columns of
elements.
-The total number of seepage faces with
Dirichlet boundaries is not necessarily one
less then the total number of Dirichlet
Boundary faces. In the trench drain problem
six boundary faces exist with only four
drainage faces. In a problem done by symmetry
there would be one less seepage face then the
number of Dirichlet boundaries.
4. The output from the Aral Seepage Program is
extremely straight forward with only one area of
confusion. Appendix B of this study includes a copy of
a printout result from the study. Under the "New
coordinates of the Free Surface Line" there are several
iterations of free surface corner nodal points and the x
and y coordinates. The last iteration is the free
surface calculated within the desired accuracy. A plot
of the listed x and y coordinates is a cross section of
the free water level. The maximum free surface elevation
between trenches is the maximum value between any of the
four trench drains. In Chapter 3 the selection of this
value is reviewed. The last page of the output contains
30
the total seepage flow. The area of confusion ccmes from
the presence of seepage output between trenches, across
element faces not defined as seepage faces. Those output
figures are not correct. Using the nodal address numbers
from the bottom of the trench (Fig. 3-5) the actual
seepage output at each trench can be obtained. To find
the total flow the sum of trench flows is calculated
manually as the listed total flow reflects the imaginary
outflow between trench faces.
V. Evaluation:
In the analysis of the trench drain system
dimensionless products will be used to prepare
presentations of the affect of the many changing
variables upon which the solution is dependent. The key
variable is the radius of influence which will be
determined by solving each model for several different
radii and selecting the correct value by interpolation.
Finally in the future use of the Aral Seepage Program
several notes can be used to augment the existing user's
manual.
31
CHAPTER 3
INPUT AND OUTPUT OF THE TRENCH DRAIN EVALUATION
I. Introduction:
The evaluation of different variables in a foundation
trench drain involves a significant amount of input and
output data. It is extremely important that methodical
presentation and collection of data be practiced. This
chapter details the system, under which all variables were
considered. The approach used insured that the entire
range under consideration was evaluated.
II. Problem Geometry:
In evaluating the dewater.ig trench drain systems the
geometry must established. Among the many variables in such
an evaluation are the vertical and horizontal hydraulic
conductivities of the soil, number of trenches in the system
and width of the trench. To simplify the problem the above
variables were held constant in thiz study.
Other variables in an evaluation are spacing between
drains, thickness of the aquifer, free head above drains and
slope of the aquifer. These factors were varied in this study
over ranges sufficient to determine the characteristics of the
system under as normally used.
Confined flow was not considered in this study and each
case was for a water table aquifer. A confined aquifer cannot
be dewatered effectively with an open pumping or sump method
32
((a)Powers, pg 114). A significant assumption of phraetic
flow, included in the finite element analysis, provides the
radius of influence of drawdown.
A primary concern in dewatering a water table aquifer is
the storage depletion ((c)Powers, pg.3). This study concerns
trench drains under steady state conditions following
construction. In steady state, the storage has been depleted
and will not contribute additional flow.
The previous study (Pirtle) was conducted under symmetry
as a half space problem with no slope. The finite element
method in a half space works very well until a sloping aquifer
is considered. Use of symmetry permits evaluating one half
of the problem, doubling the results accurately models the
0 full problem. To do this with a sloping aquifer models a
perched water table. Figures 3-1 and 3-2 represents one half
of a system under symmetry and a full system respectively.
For this study the affects of a sloping aquifer were
essential, and a full width model was required. Figure 3-3
is a representation of the cross section of the sloping
aquifer. In the full width model the free water surface both
upstream and downstream of the foundation trench drain must
be evaluated. Figure 3-4 is a cross section of the problem
with the assigned variable names.
In the model four trench drains were selected. Although
this models a relatively small foundation it should yield
results which may be used conservatively for larger
33
SSUMP
• -< . COLLECTOR
TRENCH DRAINS . IVA OI
Fig. 3-1 Underdrain System in Half Space
(after Pirtle)
BUILDING
TRENCH DRAINS
Fig. 3-2 Typical application of Trench Drain
(after Pirtle)
34
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foundations. Generally in a sloping aquifer the majority of
* dewatering and the maximum free surface between trenches occur
due to the outboard drain. For a sloping aquifer this model
will closely model even a large foundation as most of the
* removed water is into the upstream trench. The number of
drains might be a prime area for future study.
The width of the drainage trenches were held at one and
* one half feet wide. While the earlier study (Pirtle, Chap 4)
showed total flow to vary with drain width, it is reasonable
to select a single, typical value. The use of 1.5 feet is
* based on the approximate width of a normal backhoe bucket.
The horizontal hydraulic conductivity (permeability, k.)
was selected as a constant 0.2 ft2/day/ft which is, 7 x 10 5
* cm/sec. This is the normal permeability of a silty sand
((b)Cedergren, pg 34), common to the Atlanta area.
For the vertical hydraulic conductivity (l) the same
0.2 ft2/day/ft was used. While a reasonable value, it does
not reflect the normal condition of a greater horizontal
hydraulic conductivity, which may be greater than the vertical
* by a multiple of three to ten times ((a)Powers, pg.92). It
would be an excellent study to evaluate the affects of
anisotropy in the trench drain system.
* The primary area of concern in this study were the
affects of a sloping aquifer. To consider a complete range,
three slopes considered. Initially 0%, 7% and 15% slopes were
* selected. The aquifer thickness remains the same through the
38
area of consideration with a uniform aquifer base and water
table slope. Once the study was begun it became apparent that
the 15% slope was too severe. The study was modified with 7%
the maximum slope considered and additional data was collected
for a 3.5% slope.
Trench drain spacing was evaluated using 15 feet, 25 feet
and 35 feet. For the assumed four drain system this allows
consideration of a foundation from 60 to 120 feet wide. In
actual practice the trench drains are excavated between the
column lines so normal spacing is that of the column spacing.
The results for a model with trench spacing of 25 and 35 feet
are most likely to be used.
An assumption for this study was that the aquifer remain
if constant thickness across the entire area of water table
depression. For some models this area is 1000 feet across.
It is certainly not a normal soil condition for the aquifer
to be so uniform. In general the area of depression is
significantly smaller then the above value. Assuming uniform
thickness for distances of 300 and 400 feet is reasonable.
To separate the affects of free head from thickness of
aquifer the later was considered as two components. The first
component was thickness below the drain or trench elevation
(H) and the second was free head above drain (h). The sum of
the two components is the total aquifer thickness.
To bracket normal conditions in the evaluation of trench
drains a maximum aquifer thickness of 80 feet was used. While
39
arbitrary this value is reasonable in an aquifer at the
* surface. The minimum aquifer thickness used was 30 feet.
Certainly smaller aquifers exist at the ground surface but,
a trench drain would probably not be as effective as a cutoff
* wall in protecting the foundation for such a shallow depth.
The last variable considered in the study was the free
head of aquifer above the bottom of the trench drain. As
* described above the free head is a component of the aquifer
thickness. Free head was held at a maximum of 20 feet. As
the free head increases the amount of water removed must also
* increase. Under an open draining trench system the radius of
influence is much larger and interference with other
structures is a problem. As a free head of 20 feet is
* approached alternative dewatering methods may have to be
considered.
The minimum free head considered was ten feet. This
* value was selected arbitrarily. The foundation trench system
would work very well for a smaller free head. In retrospect
the minimum head considered should have been five feet. Less
* free head and the necessary trench depth would be so small
that a blanket drain would be more economical. A comparison
of the two drain systems will be undertaken on an economics
* basis in Chapter 4.
40
III. Naming and numbering convention:
As a shorthand means of identifying the variables (Figure
3-4) of this study each is named as follows:
Radius of influence, L
Total flow, q
Aquifer slope, p
Trench spacing, S
Trench elevation, H
Free head above trench, h
Maximum free surface height, F
Hydraulic conductivity (vertical), k,
Hydraulic conductivity (horizontal), kh
As described in Chapter 2 the determination of an
accurate radius of influence involved four to six trial runs
of a model. The result was 36 geometries and over 200
computer runs. In order to identify the geometry of each
trial the data files and resultants were named from a file
convention. An alpha-numeric name of six characters, with
41
each one have several values was used. The files were named
* and the data sorted as follows:
A12345.dat, where the .dat is a conventional suffix
of the operating system
* First Character (A)
Vertical hydraulic conductivity, k,
A = 0.2 ft2/day/ft
* Second Character (1)
Aquifer slope, g
0=0%
• 3-3.5%
7=7%
9 =15%
Third Character (2)
Radius of influence, L
3 = 100 ft
S5 = 200 ft
8 = 400 ft
9 = 500 ft
S0= 700 ft
Fourth Character (3)
Trench spacing, S
* 3 = 15 ft
5 = 25 ft
7 = 35 ft
42
Fifth Character (4)
Trench elevation, H
2 = 20 ft
6 = 60 ft
Sixth Character (5)
Free head, h
1 = 10 ft
2 = 20 ft
The above convention is used in this study in names of
data files. If a collection of data is gathered so that each
group has a constant trench elevation, H and free head, h the
data groups will be referenced by AxxxHh. In this example if
the H = 20 feet and h = 10 feet the data group will be Axxx2l.
The data files used in this study are included in Appendix D.
IV. Conduct of study:
The primary output of the finite element analysis used
in this study were the total drainage outfall per lineal foot
of trench drain system and the maximum free surface of
groundwater between trench drains. As detailed in Chapter 2
the study first had to determine the radius of influence for
each condition. From Figure 3-5 the elements of the finite
element grid between can be observed. The width between
trenches was divided into five spans. So at four nodes the
iterative determination of the FEA program predicted an
43
ultimate final elevation. This was determined for every trial
radius, L and the maximum node elevation observed was
recorded. Figures 3-6 through 3-9 are profiles, in the trench
area, of the represented free surface for several trial runs.
It was expected that the maximum free surface (F) would
occur near the center of the trench spacing (S). In order to
obtain an accurate maximum free surface, the nodes between
drains were not evenly spaced. Instead, the distance between
nodes were greater near the trenches. For each run the
maximum free surface selected was that of the maximum nodal
elevation. This is obviously not accurate in all cases. An
interpreted maximum fret surface (F) would increase many of
the values used but, would not reduce any value. The
* anticipated difference in magnitude of maximum free surface
(F) does not exceed 0.01 feet or 0.1 inch. This potential
error is not significant.
* A review of the maximum free surface value for the many
different finite element analysis runs revealed that the
maximum free surface (F) always occurred between the outer
* most trench and the second trench. In an aquifer with no
slope the conditions surrounding the outer trench were the
same for both sides. On a sloping aquifer the maximum free
* surface (F) was at the upstream side of the trench drain
system.
With the maximum free surface available for every
* geometry of problem and every trial radius c-' influence there
44
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theoretically correct radius of influence. Fortunately from
Figures 3-10 through 3-21 it is obvious that the maximum free
surface varies with trial radius of influence in a consistent
manner. As the theoretically correct radius of influence (L)
is known from Chapter 2, the maximum free surface can be
scaled from Figures 3-10 through 3-21. By convention the
interpolation of data to evaluate the radius of influence used
only values which were multiples of 50 feet.
The definition of a theoretically correct radius of
influence at the distance of unchanging total flow defines
the radius from the known phraetic nature of the problem.
The unchanging flow also quantifies the total flow expected
from the system. For this problem total flow was done per
unit of width, making this a two dimensional problem.
The '.tal flow, the maximum free surface and the radius
of influence for each geometry of problem are now available.
Analysis of trench drain systems were done with this data.
49
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V. Summary:
In summary there were three slopes considered, three
spacings between drains, two elevations of trench and two free
heads above the trench. That is thirty six geometries of
* problem, all considered under one horizontal and vertical
hydraulic conductivity. While the physical dimensions of this
problem are adequate to cover the majority of cases under
which trench drains would be utilized, the single values of
k leave room for further evaluation. With the use of
dimensional analysis this study might serve to allow
* extrapolation of results for different hydraulic
conductivities but, validation by further modeling is
recommended.
62
CHAPTER 4
ANALYSIS OF TRENCH DRAIN DEWATERING
I. Introduction:
Modeling a foundation trench drain system with the
a finite element analysis provides a myriad of results
for many different conditions. For the analysis to be of
use it must be presented so that future systems of trench
drains can have capacities and limitations predicted from
the results. This chapter is the presentation of results
tor use in prediction and selection of a trench drain
system.
II. Results:
Chapter 3 details the input and output of this trench
drain analysis. In Appendix A, Table A-1 summarizes the
different variables and trench drain systems evaluated.
From the data collected the total flow of a trench drain
system with four drains in an isotropic soil can be
determined for a range of design characteristics which are
reasonable minimums and maximums. From this output
information trends can be identified for the response to
each variable.
The radius of influence was found from the measures
described in Chapter 2. For each of the thirty six
evaluated geometries of trench drain system four tc six
63
computer models were run, each with a different trial
radius of influence. Figures 2-1 through 2-12 show the
results of these trials. As expected each trial of a
lesser radius of influence predicted a greater total flow
from the trench drain system. As the trial radius
approaches the theoretically correct radius of influence
the quantity of flow becomes unchanging and models the
* gravity flow condition accurately.
The spacing of trenches does not change the total
flow of the trench drain system in a consistent pattern.
The flow changed with other variables so that the single
affects of spacing on flow is indistinguishable.
It is obvious that spacing directly influences the
* magnitude of the maximum free surface between trenches.
On Table A-1 every combination of slope, trench elevation
and free head has increasing maximum free surface with
increasing spacing. This is consistent with expectations.
Greater spacing decreases the influence of adjacent
trenches. Figures 3-6 through 3-9 show that the maximum
free surface in a sloping aquifer is strongly influenced
by the upstream trench. The influence is even more
strongly exhibited with increasing space. A larger
* spacing of trenches further isolates the upstream trench
from drawdown influence from the inboard trenches.
In all cases the radius of influence decreased with
increased aquifer slope. With greater slope, spacing of
64
the trenches exhibited the affect of decreasing the radius
of influence. The dominant factor was the slope. The
radius of influence was unchanging with spacing when the
slope was zero.
Total flow did increase with the increasing slope of
aquifer but, the magnitude of the change varied with the
other variables so that a single affect from slope cannot
be determined.
The maximum free surface increased consistently with
the aquifer slope. The maximum free surface increased by
50%, for each 3.5% incremental change of slope, in every
geometry considered.
Impact of different free heads above the trench was
quite consistent and was normally coupled with the
elevation of the trench. For constant elevation of trench
the radius of influence increased with free head. In a
similar manner the total flow increased with free head,
with the magnitude of change impacted by the variables
considered. The maximum free surface also showed a
significant increase with free head when the elevation of
the trench is constant.
For a constant free head with changing elevation of
trench the same trends in radius of influence, total flow
and maximum free surface can be seen. The magnitude of
the change is not as great and the greater influence of
free head can be inferred.
65
In this study only one drain width was considered
and so the individual impact of a changing width cannot
be determined. Only one vertical and horizontal hydraulic
conductivity combination was studied and all studies were
done on a four trench system so the affects of these
single variables cannot be reported.
The many results of this study show the necessity
for a form of dimensional analysis in evaluating a model
affected by many variables. Some trends can be predicted
from a couple of variables but, a complete prediction of
performance or trend is not possible without a dimensional
analysis.
III. Results of Predictive Formulas:
It is not surprising that no single numeric method
exists for the evaluation of a trench drain system of four
drains, in a sloping aquifer. This study attempts to
provide that solution but, do other, existing solutions
serve the need? In Chapter 2 several formulas were
referenced in the discussion of determining a radius of
influence. In this section several formulas are
evaluated. The formulas below are presented with the
7ariables used in this study rather then as presented in
the source. A comparison of the results for the below
methods with the results of the finite element analysis
are in Table 4-1.
66
a.) Qp= (.73 + .27(h/(h+H)) Kx((h+H) -h')/L
Qp=total flow, h=free head, H=trench elevation, x=trench
length, K= permeability, L= radius of influence (use
consistent units)
The above formula (Leonards, pg 273) has the
advantages of being for a partially penetrating slot in
an unconfined aquifer. The disadvantages are that it has
no provisions for a sloped aquifer, multiple trenches,
trench width or means for calculating the maximum free
surface. The radius of influence is a value of input to
this formula.
b.) Figures 36, 61, 68 and 69 (Moulton)
The referenced charts offer allowances for sloping
aquifer, two drains, partial penetration of the aquifer
and a means of calculating a maximum free surface between
drains. Some disadvantages of the methods are the lack
of trench width, no allowance for more then two drains and
a half space solution to the zero slope portion. The
radius of influence is an input variable to solution. As
listed in Chapter 3 the recommended radius of influence
is 3.8*h. This value yields a maximum radius of influence
of 76 feet for this study. This value was much less then
used throughout the study and yielded results far greater
then predicted from the finite element analysis. In Table
67
4-1 the radius of influence used was that from the finite
element analysis which yielded results much closer to
those of the other calculations.
c.) Q/x = K((H+h)' - h')/L ((a)Powers, pg 100)
Q= total flow, x= trench length, K= permeability,
H= trench elevation, h= free head, L= radius of influence
( Use consistent units)
This method is a traditional trench solution. It
does not make allowance for partial penetration of the
aquifer, multiple trenches, trench width or aquifer slope.
d.) G = SyLq/KH2 and figures 18(b) and (c)
(Freeze, pg 261) G= dimensionless product, Sy= Specific
Yield, L= radius of influence, q= total flow per unit
width, K= permeability, H= aquifer thickness (use
consistent units)
This solution is for a partially penetrating trench.
Once again this method makes no provision for multiple
trenches, trench width, sloping aquifer. In addition the
Specific Yield is used adding another variable, this one
normally varying between .01 and .3 (Freeze, pg 61).
Each of the above methods have several disadvantages
and were not developed for use in the evaluation of a
trench drain system. Assuming that the finite element
analysis is the most accurate of the means of evaluation
tried it is obvious in Table 4-1 that no single formula
68
TABLE 4-1 Summary of Predictive MethodsSummary
A B Cn
Slope 0 3.5 3.5 7Spacing (Ut) 35 15 35 25Trench El (Ut) 60 20 60 20Free Head (Ut) 10 20 20 10
(Mansur, pg 273)total flow (ftA2/day) 0.5 0.46 0.81 0.55
(Moulton, pg 120 & 130)total flow (ftA2/day) 0.49 0.22 0.73 0.42
(Powers, pg 100)total flow (ftA2/day) 0.66 0.53 1.02 0.66
(Freeze, pg 261)total flow (ftA2/day) 5.88 0.64 5.12 2
Aral Seepage Programtotal flow (ftA2/day) 0.14 0.19 0.25Radius of Influ (it) 500 500 500 150
Trial Radius 200'Total Flow (ft 2/day) .3 .45 .54 .26
0
69
approximates the solution to the problem very closely.
Of the evaluated methods the Moulton method, using the
radius of influence as determined by the finite element
analysis was the most accurate. It is worth noting that
with no other means of selecting a radius of influence the
value determined in this study was used for each method.
This approximation would certainly affect the results.
Appendix E is a discussion of the affect of arbitrary
selection of radius on total flow and free surface height.
IV. Prediction of Trench Drain Performance:
The prediction of total flow and maximum free surface
is possible through the use of results presented in a
dimensionless form. As a trial some runs were done to
explore the affects of anisotropy and number of trenches.
These results are discussed below.
Any prediction of flow characteristics requires an
evaluation of the radius of influence. Figures 4-1
through 4-3 are useful for predicting the radius of
influence from the trench elevation, free head, slope of
aquifer and the trench spacing. These figures are only
appropriate for an isotropic condition in a four trench
system with a trench width of 1.5'. Use of the figures
will frequently require several interpolations.
70
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(J) C., 73
To use figures 4-1 through 4-3 the following example
will be useful.
Example 4-1: Find the radius of influence for a four
trench system with trench width of 1.5' and K/Kh =
* 1 with K = .2 ft/day. The trench elevation is 40
feet, the free head is 15 feet, the trench spacing
is 30 feet and the aquifer slope is 4%.
* a. Figure 4-4 is annotated from
Figure 4-2. Follow this figure
through the following steps.
* b. At slope = 4% on Figure 4-2
interpolate between the lines labeled
20/10 and 20/20 as well as between
* 60/10 and 60/20. These are the
points for trench elevations of 20
and 60 feet with a free head of 15
* feet. The radii of influence for
these two points are 330 feet and 456
feet.
* c. Again at slope = 4% interpolate
between the above two points to find
the radius of influence for a trench
elevation of 40 feet and a free head
of 15 feet with a spacing of 25 feet.
This radius of influence is 394 feet.
74
o
(D 4--
0 Q0
0N
I -C 0
CL)LL L.LA
:3 0--- 75
d. Follow the above procedure again
on Figure 4-3 to get a radius of
influence of 344 feet when spacing is
35 feet.
e. For a spacing of 30 feet
interpolate between the results of
steps c. and d. above to get a final
predicted radius of 369 feet.
As an alternate method a rough selection
of 350 or 400 feet will not make a significant
difference in the following calculation method.
As discussed in Chapter 2 the radius of
influence is an extremely variable value, often
approximated only within an order of magnitude.
One suggested method (Moulton, pg 66) has the
radius of influence estimated as 3.8 times the
free head. In this example that would predict
a radius of only 53 feet, one seventh of that
from this study but, within one order of
magnitude.
In Chapter 2 the derivation of the dimensionless
product used in this study was reviewed. The product
which best presented the behavior of total flow and
maximum free surface with the changing variables of the
problem geometry was:
76
Ld/h (h+H) (2)
Where L = radius of influence, d = trench width, h = free
head and H = trench elevation as shown on Figure 3-4.
Using consistent units for the variables yields a
dimensionless product.
Figures 4-5 and 4-6 are total flow and maximum free
surface, respectively against the dimensionless product
for the considered geometries. In both plots an
acceptable curve fit is possible. The points are aligned
with the largest aquifer slope to the left and the zero
sloped aquifer to the right. This observation is for
interest only as the dimensionless product provides
sufficient accuracy with the sloping aquifer influence
represented by the values of total flow, maximum free
surface a:- radius of influence. From the previous
example:
a. Calculate Ld/h(h+H). Fcr this problem
using the abo.e L = 369 feet,
Ld/h(h+H) = 369'*1.5'/15'(15'+40') = .671
b. From Figure 4-5 total flow q = .25 ft2/day
c. From Figure 4-6 maximum free surface
F = .9 ft
As a check of the accuracy of this method to predict
the output of the finite element analysis six sample runs
were conducted. The values of the variables and the
results of the finite element analysis are shown in Table
77
C
LL-V
10 0
_2 I-
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A-2. For this analysis three trial radii of influence
were used for each sample run. The theoretically correct
radius of influence, total flow and maximum free surface
were taken from plots similar to Figures 2-1 and 3-10.
* The determination of the theoretically correct
radius of influence is done under an arbitrary standard
to an accuracy of fifty feet. From Table A-2 the
prediction of total flow and maximum free surface agree
with the results of the finite element sample runs. This
is excellent accuracy in selecting the radius of
influence. This method is acceptable for an isotropic
soil with a four trench system.
Figures 4-5 and 4-6 were prepared assuming an
isotropic condition. As a matter of interest several
finite element runs were done modeling a four drain
system with various conditions of anisotropy. Normally
soils are anisotropic with K,/; between .1 and .33. The
results of these sample runs are shown on Figures 4-7 and
4-8, where the affects of differing hyiraulic
conductivity and anisotrophic soil are explored.
From Figure 4-7 it appears that different lines,
nearly parallel, exist for a four drp ,stems with the
line of largest total flow having the highest hydraulic
conductivity and the line of lowest flow with the lowest
hydraulic conductivity. The lines of differing
conductivity may converge to the left side of the plot.
80
C'14
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0~0 0
EE-
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0 CL 0
U- C1
CC
0 .0 0
CC
Q)iL. -0
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< -4-
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The degree of anisotropy appears to have no consistent
pattern.
Figure 4-8 shows the opposite influence. The degree
of anisotropy, represented by K,,/Kh, would have parallel
lines with decreasing maximum free surface as the degree
of anisotropy decreases. The lines of this plot may also
converge to the left as Ld/h(h+H) decreases.
Another area of interest is the affect of a
differing number of trench drains. As a means of
predicting the ultimate affect of systems with more or
less drains then the four evaluated. Figures 4-9 and
4-10 show the results of three runs of a three trench
system. While not conclusive it is likely that the line
for a three trench system is just below the four trench
line. With further study it might be possible to extend
the results of a four drain analysis based on the
paralleling trends of lines for the different trench
configurations.
83
INN0-
4-
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0* CL
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-cc
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CN
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* L.Z
0
85
This study has developed an effective method for
determining the total flow and maximum free height for a
trench drain system, knowing the geometry of the problem.
It appears probable that anisotropic conditions,
different hydraulic conductivities and trench systems
with other then four drains can be included into this
type of evaluation with some further research.
V. Comparison of Trench Drain with Blanket Drain:
An alternative to the trench drain system for
dewatering beneath a foundation is the blanket drain. A
blanket drain system is similar to the trench drain
system as it is a mass of open graded stone or gravel
isolated from the soil by a geosynthetic filter material
and has slotted collector pipes to carry water to a sump
for removal. It is different in geometry. The blanket
drain is a single rectangular cross section which
dewaters the surrounding soil to the depth of the bottom
of the section. The trench drain uses less gravel by
extending the dewatering depth down with narrow trenches
extending from a thin base of gravel across the bottom of
the foundation (Figure 3-4).
The blanket drain does an excellent job of
dewatering beneath a foundation and has the advantage of
easier construction. The biggest difference between the
two systems in a practical application is the cost. The
trench system requires more detailed labor and excavation
86
while the blanket drain requires more gravel. To do
a cost comparison of the two methods a standard
foundation size was necessary to determine the
excavation, placement and compaction productivity rates.
In this study a foundation of 100 feet by 200 feet was
used, only for the establishment of unit costs of labor.
The evaluation is aone based on a 3et slab elevation
and a predetermined base of trench or blanket drain.
That is the blanket drain will have to be thick enough to
dewater to the depth of the trench drain without lowering
the foundation. A basic cost to this evaluation was the
cost of gravel (#57 stone) which goes for $8.30/ton in
the Atlanta area. Labor costs used were $20/hr for an
equipment operator and $16/hr for a laborer (both rates
including overhead and fringes). Productivity values
came from the Means estimating guide for 1989. The cost
of equipment rentals were approximated from the sane
guide. The cost of the geosynthetic filter material was
estimated as $0.70/yd2 from discussions with suppliers and
engineers in the Atlanta area.
The cost data was input into a spreadsheet with a
variety of possible trench drain configurations. The
costs were calculateA for both the trench drain and an
equivalent blanket drain for several different systems
each with more drains. Table 4-2 is a copy of one such
trial. With the cost of gravel so much higher then the
87
filter material the ratio of trench drain cost to blanket
drain cost was less then one in all cases.
With a blanket drain at a shallow elevation the cost
comparison is more likely to recommend a blanket drain
system. Figure 4-11 is a summary of such a comparison.
To use a thickened blanket drain will sacrifice drawdown
capacity in exchange for some construction ease and cost
benefits. The decision will depend on the application.
88
TABLE 4-2
Trench and Blanket Drain Costs
Excavation unit costs Material costs (in place)Trench 0.4 $/cu.ft Geosyn 0.08 $/sq.ftBlanket 0.08 $/cu.ft Gravel Tr 0.45 $/cu.it
Gravel 81 0.9 $/cu.ft
per unit IngthSpacing Trench Trench Number ofTrench Blanket
Width Depth Trenches Total $ Total $
15 1.5 1 30 38.25 508.9615 1.5 4 30 153 1920.6415 2.5 1 30 63.75 540.7615 2.5 4 30 255 2040.6425 1.5 1 30 38.25 816.3625 1.5 4 30 153 3080.6425 2.5 1 30 . 848.16
25 2.5 4 30 255 3200.6435 1.5 1 30 38.25 1123.7635 1.5 4 30 153 4240.6435 2.5 1 30 63.75 1155.5635 2.5 4 30 255 4360.64
89
NN
0I c-uu
G))
900
VI. Conclusions:
* In this chapter a method for predicting the results
of a finite element analysis of a trench drain system for
isotropic soil and four drains is presented. A rough
• approximation has been made to show the possible impact
of anisotropy and different trench configurations.
Empirical data is not available to validate or modify the
• predictions of the Aral Seepage Program for a trench
drain system. Compared with other slot drain solutions
it appears that the finite element solution predicts
* lesser flows and is so less conservative.
The use of a trench drain system can be justified
economically over a blanket drain system in some
* configurations. The brief evaluation of this chapter
provides a simple comparison method for the relative cost
differences of the two systems.
91
CHAPTER 5
• CONCLUSIONS
I. Introduction:
• In this study the trench drain system was evaluated for thirty
six configurations using a finite element analysis program. The
results of the analysis were used under dimensional analysis to
* form a method of predicting the results of a similar analysis for
any configuration of a trench drain system within the limits of the
study. The final portion of the study was to evaluated the cost
* of a Lrench drain system as compared with the blanket drain system
for use in a drain beneath a foundation.
* II. Trench Drain System Analysis:
The results of the finite element analysis could not be
validated by test or field data nor, did the formulas available
show close agreement with the results of the analysis. It would
be useful if the actual outflow of a trench drain system were
* measured and the radius of influence of drawdown determined.
This study was limited to isotropic conditions and a four
drain system. The affect of other conditions was briefly explored
* but, a more complete study is necessary before the results are
extrapolated to conditions of many drains or variable soils.
Initial expectations are that results of Figures 4-7 through 4-10
* will be consistent with results of a more complete run of
92
variables. Whether more then four drains have significantly
different shape then the four and three drain curves will be most
important when the cost comparison of trench and blanket drains is
considered from Figure 4-11.
The one recurring constant in the reference material on
dewatering is the variable nature of the radius of influence. For
the narrow conditions evaluated in this study reasonable
estimations of the radius of influence are possible from Figures
4-1 through 4-3. The earlier recommendations of field observations
and computer modeling with other ranges of variables would expand
the information available for predicting the radius of influence.
The permeability used in this study, 0.2 ft/day is consistent
with the soil in the Atlanta area. If the trench drain system is
* to be used in a greatly more permeable soil the results may be
significantly different. It would not be recommended to use a
trench drain in a very porous sand or gravel just as an open sump
* is not satisfactory to dewater a site of that composition.
Establishing the upper and lower bounds of permeability for
practical use of trench drains is a most useful recommendation for
* further study.
III. Predictive Method:
* The predictive method using Figures 4-1 through 4-6 work well
in predicting the results of the finite element analysis. The
forms are easy to use and adapt readily to drain configurations
* within the range evaluated. The range of variables were selected
93
to match the conditions under which a trench drain system is
normally used. Extrapolation of the results beyond these values
may be of limited practicality and questionable accuracy.
The prediction of the maximum free surface at a low
dimensionless product (Ld/h(h+H)) should be treated with great
care. When the product is less then 0.5 the curve rises rapidly
and the maximum free surface exceeds 1.25 feet only in this range.
* The maximum free surface is of concern only when the water level
approaches the shallow blanket immediately beneath the slab,
approximately one foot for most trench systems. The curve for the
* maximum free surface was roughly aligned with the 7% slope values
at the left end and the 0% slope values on the right. For large
aquifer slopes the curve may approach vertical and might be
* sufficient reason to avoid the use of a trench drain system in such
an aquifer.
IV. Cost Comparison:
* If the necessary depth of dewatering is to the depth of the
trench drain system a blanket drain cannot compete on an economic
basis. If a very shallow level of dewatering is required beneath
* the foundation it would not be practical to install -tench drain
system. Trenches of under one foot depth would requ- individual
consideration. By the results of Figure 4-11 it is apparent that
* even sacrificing the depth of dewatering is not sufficient to turn
the advantage to blanket drains in all cases.
94
V. Evaluation:
The results of this study have satisfied the stated
intentions. Results and input were reviewed with care and show
consistent and reasonable trends. Appendix C is a brief
description of the method of compilation of data, preparation of
data files and execution of program commands. Also included in
Appendix D is a storage disk for an IBM compatible computer with
* the spreadsheets of results and the data files used.
95
REFERENCES
-Aral, M. M.; Sturm, T. W.; and Fulford, J. M., "Analysisof the Development of Shallow Groundwater Supplies byPumping From Ponds," School of Civil Engineering:Environmental Resources Center, Georgia Institute ofTechnology, ERC-02-81, 1981.
-Bear, Jacob, Hydraulics of Groundwater, McGraw-HillInternational Book Company, New York, 1979
-Bowen, R., Grounds Water, John Wiley & Sons, New York,N.Y. 1980
-(a)Cedergren, H. R., Drainage of Highway and AirfieldPavements, John Wiley & Sons, New York, N.Y. 1974
-(b)Cedergren, H. R., Seepage, Drainage and Flow Nets,John Wiley and Sons, Inc., New York, N.Y., 1977
-Freeze, R.A. and Cherry, J.A., Groundwater,Prentiss-Hall, Inc., N.J. 1979
-Harr, M. E., Groundwater and Seepage, McGraw-Hill BookCo., Inc., New York, N.Y., 1962
-Holtz, R.D. and Kovacs, W.D., An Introduction toGeotechnical Engineering, Prentice-Hall, Inc., New Jersey1981
-Jumikis, A.R., Thermal Geotechnics, Rutgers University* Press, N.J. 1977
-Lambe, T. W. and Whitman, R. V., Soil Mechanics, JohnWiley and Sons, 1969
-Langhaar, H.L., Dimensional Analysis and Theory of• Models, John Wiley & Sons, Inc., New York 1951
-Leonards, G. A., Foundation Engineering, Chap. 3, Mansur,C.I. and Kaufman, R.I., McGraw-Hill Book Co., New York,N.Y., 1962
• -Moretrench Corporation, Field Manual, MoretrenchWellpoint System, Moretrench Corporation 1967
-Moulton, L.K., Federal Highway Administration, HighwaySubdrainage Design, U.S. Dept. of Transportation, ReportNo. FHWA-TS-80-224, 1980
9
96
-Muskat, M., Flow of Homogenious Fluids Through PorousMedia, McGraw-Hill Book Co., New York, N.Y., 1937
-Department of the Navy, Naval Facilities EngineeringCommand, Soil Mechanics, Design Manual 7.1, Alexandria,Virginia, 1982
-Peck, R.B. and Hanson, W.E. and Thornburn, T.H.,Foundation Engineering, John Wiley & Sons, Inc., New York1974
-Perloff, W.H. and Baron, W., Soil Mechanics. Principlesand Applications The Ronald Press Company, New York 1976
* -Pirtle, G.N., "Underdrain Systems for Laige StructuresPlaced below Groundwater Table", School of CivilEngineering, Georgia Institute of Technology, Atlanta, GA1986
-(a)Powers, J.P., Construction 0ewaterinQ, John Wiley &* Sons, Inc., New York 1981
-(b)Powers, J.P. and Burnett, R.G., "Permeability and theField Pumping Test", Use of In Situ Tests in GeotechnicalEngineering, IN SITU 86, American Society of CivilEngineers 1986
-(c)Powers, J.P., Dewatering-Avoiding its Unwanted SideEffects, American Society of Civil Engineers, 1985
-Sowers, G. F., Introductory Soil Mechanics andFoundations, MacMillian Publishing Co., Inc., New York,
* 1979
-(a)Terzaghi, K., Theoretical Soil Mechanics, John Wiley& Sons, New York, 1943
-(b)Terzaghi, K. and Peck, R. B., Soil Mechanics in* Engineering Practice, Wiley, New York, N.Y., 1948
-Tripp, D.W. and Christian, J.T., "Evaluation of DeepPumping Tests", Journal of Geotechnical Engineering,Vol 115, No. 5, May 1989
• -Tschebotarioff, G.P., Soil Mechanics, Foundation andEarth Structures, McGraw-Hill, New York 1951
-Winterkorn, H.F. and Fang, H., Foundation EngineeringHandbook, Van Nostrand Reinhold, New York 1975-Wu, T.H., Soil Mechanics, Allyn & Bacon, Inc., New York
• 1966
97
APPENDIX A
0 SUMMARY OF PROGRAM COMPUTER RUNS
APPENDIX A
FINITE ELEMENT COMPUTER RUN SUMMARY
* TrecIh Free Radius of Total Max Free Number ofSpacing Elevation Head Influence Flow Surface Trials
Slope -015 20 10 400 0.11 0.18 615 20 20 550 0.2 0.33 615 60 10 500 0.17 0.35 615 60 20 600 0.29 0.615 625 20 10 400 0.1 0.204 525 20 20 550 0.17 0.35 525 60 10 500 0.15 0.429 525 60 20 600 0.27 0.763 535 20 10 400 0.09 0.227 535 20 20 550 0.15 0.38 535 60 10 500 0.14 0.475 535 60 20 600 0.25 0.853 5
Slope - 3.5/ 115 20 10 300 0.14 0.38 415 20 20 500 0.19 0.52 415 60 10 450 0.15 0.53 415 60 20 550 0.26 0.93 425 20 10 250 0.14 0.5 425 20 20 450 0.18 0.69 425 60 10 400 0.16 0.79 425 60 20 550 0.24 1.27 4
* 35 20 10 200 0.15 0.66 435 20 20 400 0.18 0.82 435 60 10 350 0.18 1.02 435 60 20 500 0.25 1.35 4
Slope15 20 10 200 0.23 0.6 515 20 20 350 0.3 0.82 515 60 10 300 0.23 0.819 5
* 15 60 20 500 0.29 1.016 525 20 10 150 0.27 0.85 525 20 20 250 0.32 1.17 525 60 10 200 0.28 1.27 525 60 20 450 0.31 1.4 535 20 10 100 0.28 1.14 535 20 20 200 0.33 1.432 535 60 10 150 0.33 1.69 5
* 35 60 20 400 0.34 1.85 5
Table A-I Summary of Finite Element Runs
0
9
APPEN~DIX A A-i
.a C; - 2 4
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C; C; a 40 42 40
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APPENDIX A A-2
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APENIXA -
APPENDIX B
SAMPLE INPUT AND OUTPUT
APPENDIX B
SAMPLE INPUT DATA FILE
"A35521"2,0.0000190,29,0,30,20,6,4,01,-190,6.65,17,-190,22.65,11 ,-190,36.65,018,-114,3.99,124,-114,19.99,128,-114,32.99,035,-43.7,1.5295,141 ,-43.7,17.5295,145,-43.7,29.5295,052,-19,0.665,158, -19,16.665,162,-19,27.665,069,0,0,17590,16,1
79,0,25,086,10,-0.35,192,10,16,1
* 96,10,20,0103,11.5,-0.4025,1109,11.5,16,1113,11.5,20,0120, 16.5,-0.5775,1126,16.5,16,1
* 130016.5,22,0137,23,-0.805,1143,23,16,1147,23,22,0154,25,-0.875,1160,25,16,1
* 164,25,22,0171,31.5,-1.1025,1177,31.5,16,1181,31.5,22,0188,36.5,-1.2775,1194,36.5,16,1198,36.5,20,0
205,38,-1.33,1211,38,16,1
215,38,20,0222,43,-1.505,1228,43,16,1
* 232,43,22,0239,49.5,-1.7325,1
245,49.5,16,1249,49.5,22,0256,51.5,-1.8025,126?,51 .5,16,1
* 266,51.5,22,0273,58,-2.03,1279,58,16,1283,58,22,0290,63,-2.205,1
APPENDIX B
296,63,16,1300,63,20,0307,64.5,-2.2t'ib,1313,64.5,16,1317,64.5,20,0324,69.5,-2.4325,1330,69.5,16,1334,69.5,22,0341,76,-2.66,1347,76,16,1351,76,22,0358,78,-2.73,1364,78,16,1368,78,22,0375,84.5,-2.9575,1381,84.5,16,1385,84.5,22,0392,89.5,-3.1325,1398,89.5,16,1402,89.5,20,0
* 409,91,-3.185,1415,91,16,1419,91 ,20,0426,101,-3.535,1432,101,15.65,1436,101,21.465,0443,120,-4.2,1449,120,14.985,1453,120,21.8,0460,144.7,-5.0645,1466,144.7,14.1205,1470,144.7,22.9355,0477,215,-7.525,1483,215, 11.66,1487,215,21.475,0494,291 ,-10.185,1500,291,9,1504,291 19.815,01,12,18,19,20,13,3,2,4,0.2,0.2,018,29,35,36,37,30,20,19,4,0.2,0.2,035,46,52,53,54,47,37,36,4,0.2,0.2,052,63,69,70,71,64,54,53,4,0.2,0.2,069,80,86,87,88,81,71,70,4,0.2,0.2,086,97,103,104,105,98,88,87,4,0.2,0.2,0103,114,120,121,122,115,105,104,4,0.2,0.2,0
* 120,131,137,138,.9,132,122,121 ,4,0.2,0.2,01379148,154,155,156,149,139,138,4,0.2,0.2,0154,165,171,172,173,166,156,155,4,0.2,0.2,0171,182,188,189,190183,173172,4,0.2,0.2,0188,199,205,206,207,200,190,189,4,0.2,0.2,0205,216,222,223,2249217,207,206,4,0.2,0.2,0
* 222,233,239,240,241234,224,223,4,0.2,0.2,0239,250,256,257,258,251,241,240,4,0.2,0.2,0256,267,273,274,275,268,258,257,4,0.2,0.2,0273,284,290,291,292,285,275,274,4,0.2,0.2,0
* APPENDIX B 2
290,3019307,308,309,302,2929291,4,0.2,0.2,0307,318,324,325,326,319,309,308,4,0 .2,0 .2,0324,335,341,342,343,336,326,325,410.2,0.2,03419,352 ,358, 3599,360 ,353, 343 ,342 ,4,O.2,0 .2,0~358,369,375,376,377,370 ,360 ,359,4,0 .2,0 .2,0375,386,392,393,394,387,377,376,4,0.2,0.2,0392,403,409,410,411,404,394,393,4,0.2,0.2,0409 ,4209,426,4279,4289,4219,411,9410 ,4 ,0 .2,0.2,0
* 426,437,443,444,445,438,428,427,4,0.2,0 .2,0443,454,460,461,462,455,445,444,490.2,0.2,0460 ,471 ,477, 478,9479 ,472, 462 ,461949,0.290 .2,0477, 488, 494, 495, 496, 489 ,479 ,478, 4,0.2 ,0.2,01,36.65,5,2,1
I 96,20,1,17,6198,2011,17,6I 300,201,s17,6402,20,1917,6494,19.815,5,2,11117,28,24,45,41962,58,79,75,96992,113,109,130,126
*1 147,143,164,160,181,177,198,194,215,211,232,228,249,245,266,262* 283,279,300,296,317,313,334,330,351,347,368,364,385,381 ,402,398
419,415,436,432,453,449,470,466,487,483,504,50017,34,51,68,85,102,119,136,153,170,187,204,221,238,255,272
1 289,306,323,340,357,374,391,408,425,442,459,476,49396,1917I 198,1,17
* 300t1917402,1,17"End of Problem'3,0.0001
APPENDIX B 3
* 769
SAMPLE OTPUT
CE504CW
Userid: CE504CWFile: CE504CW OUTPUT
0
%POOI 8001s Savc
RORGS 000106FILTE CE504CW OTU
CREATED 07/03/89 23:02:08PRINTED 07/03/89 23:02:23CLASS A
*FORMS XDDEVICE 600SEQUENCE 769
APPENDIX B
*~S~N SFER 009O,
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9E202ATED NODAL POINT DATA AND 1(9)-VI COOPDINATIS
NODE 2 I -10 0000 yi I 1.822Noon . -190.0000 VI 17 .187
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NODE 20 41 -114.0000 I. 1.8 J40
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NODE 28 4l -114.0000 VI 26.4800mODE 28 K. -114.0000 y. 2.1800
No0 28 45 "43.7000 Y 1.828880DE 37 41 *42.7000 VI I.8821NODE 28 4 -4.7000 VS 12.1862NODE 41 4 423.7000 V. 17,8218
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NODE 8 XI 11,OO00 VI .a82*MODE 88 II *!1.0000 ym 11.2117
mODE 88 4 -11.0000 y IN.8880
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* MOE 78 18 0.0000 VI 28.0000M ODE 88 41 10.0000 VI ".2800NDDE 84 41 t0 0000 ym 811000
NODE 82 45 10.0000 YI I1,0000NODE 84 X. 10.0000 Y 3110000
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MOE 112 OS . .. 0 s 2.000
MOOD 120 IS 11.00 I -. 87NODE 122 XI 11.8000 VS 4.1112NODE 124 XI 1818000 VS 10.4742NODE 128 X. 11.000 v 20.0000
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moo: Im I, 2mvoo ¥. ~o o
NOOE 11 1. 2;.0000 - 18.0000
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NODE 171 45 21.1000 V1 "1.1028
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2 ODE 177 49 1.000 yI 1.0000
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60 228 41 42.0000 VI 10,10NODE :2 XI 42.0000 VS 1E0000... .. .. .... ... .. .. ......."..... .. ...... .. .. ...'..".... ... .. .. ... ... ...' ' a t ... .... .. ... .. .. .. .. ... .. .. .. .. ..... .. .. .. ... .. .. .. .. ... .... .. .. ... .. .. .. .. ... .. .. .... ..... .. .. .. ... .. .. .. ..
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* ODE 248 45 4001000 VI 42200000............... WO d " I ...... . ... ''' 6 ......V ..... ''' + ...................................................... e t...I N........... i * S I, Wb s - - V ....... ......... ........... ......... ................. -- -- -... .... .......
MODE 248 45 .1.1000 yI •.12170 ODE 280 41 11,000 VS 10.0888
MO0 202 X. 61.9000 y 10.0000-NODE 24 - i 11.1000 Y• 1. .0000
-NODE 288 45 81.8000 VS 22.0000
-006 272 X .800000 y "2.0200NODE 278 48.0000 V. 2.8800
.If. " ........ ... i ......... ....................................................... .....................................NOoE 278 II 88.0000 I 18.0000mo0 281 41 88.0000 VI 8.000NODE 202 El 98,000 v 22.0000MODE 280 DI 1.0000 V. -2.00DODE 282 X. 82.0000 VS 2.8822NODE 238 II 82.0000 I 8382I7
SNOOE 288 45 82.0000 VI 11,0000
........... 2b...........1 3 y ................ .... ......... M l li ........... if' - 1.. .. . 4' ' 6 6 4 ......... v e I... . N+'' 6 ............................................................................ ............................. .. .. .... ...... ........................ . ..
-8008 200 45 82.0000 .D20.00003NODE 201 5 84.8000 V: -2.2:7:
NODE 208 Em 84.8000 VI 2.6282RNOe 211 I3 1 4.8000 VI 1.81 2
NODE 212 El 14.8000 VI 16.0000NOoE 210 N- 64.1000 Y. 18 0000NDE 217.II.14.1000 . V. 20 0000
NODE 32 41 88.8000 VI 2.7117NODE t2 XI 8.8000 Vs 6.600
INODE 220 45 68.8000 YI 18,0000
,MODM 222 41 88,I000 YI IN 00008O0 224 8• 88.8000 Vs 22.0000
NODE 241 XI 78 0000 Vt "2 80
--006s 311 X. 76 0000 V. 22 0000MOOt 34 6* 7.0000 Y. -2 73006004 240 Na O.0000 V. 3 1133MODE 262 I* 74.0000 7. I.7147
MCDI 264 I. 74.0000 VS 1•.00006001 266 Im 74.0000 Vs 11.0000
O 214 Na 7•:0000 2a 22 0000
MDD*.27* 3~~so ... 7ODt 37• a 44.6000 y •.6•04 I004D: 3 , 410*00 v, i*.0000
N ODE 362 •I 11 .I000 VS I• 0000
Of00 393 31- 69.6000 3.1326
404 364 05 8l.1000 Vl -3,2•40*444 214 I* 46.I000 V . 4.2+21
............................. N o+ " +e .......... i s ....... i • I4 6 . . .. . .. ...... - ..... 6 6 -6i ............................................................. .......... ............................. ....................................... ... . . . .. .
N ODE 2•I 0a 4•.4000 Vs 11.0000
6006 400 6i 6•.•000 Vi 11.0000
M 0 4•.1000 1, 20 0000MODE 40 5 1.0000 Va -3 1410
mODt 41? X. 11.0000 y 3.2100* 6006 413 15 41.0000 V: 6.4040
* ODE 111 05 61.0000 Vl 16.0000
................*+t"+' ..... ' .... '''+ +......Y .... ''6 6................................................................. ..*4.......:oo . s l1oo.....................
N ODE 11M 05 11.0000 VJ 20.0000
MODE 426 15 101.0000 V I 3.f31060DM 426 D* 101.0000 Vl 2.6600
* MODE 430 05 101.0000 Vl I.2•i0
MODE 422 Xe 101.0000 y 11.6100... o 434 X. 101 .0000 V. 1I.•I7
* OO• 426 OS 101.0000 Vu 21.4110
S " . ..... . . :00............................ .........MODE 446 05 120.0000 YV 2.160N MODE 447 IS 120.0000 Va 4.6400mOot 446 XS 120,0000 V. 14.2150MODE 41 120.0000 V 18.2121WO60 413 X- 120.0000 V 21.8000
* OOS 460 15 144.7000 V# -1.01
MODE 462 5X 144.7000 Y 1.3301
MDEl 411 5X 144.7000 V. 14'1201ODE 4 .4 .5 144.7000 V. 19.280NOE 470 X 144.7000 V. 22.4311N ODE 77 05 211.0000 Ve -7.1210
406 474 IS 2110000 VS 1.1300* ODE 411 a 211.0000 V# 1.2610
MODE 463 05 211.0000 VS 11.+600. . . ... . ... .. . . . . . . . . . . . . . . ..MODE X 216.0000 VS 21.47 0NODE 4it Ia 2 a.0000 v .I0.110MODE 446 IS 21.0000 V. -3.7:00MODE 466 1 V11.0000 V 2.6010NODE 100 61 211.0000 VS •.0000
*0E 602 Il 2111000 ya 14.407
OD 604 Ia 261.0000 s 1.!60...................... ~ ~ ~ ~~ k U .+ p +. 6 .. + + . y + +-. o ..... .......... ............. ................................................. .............................................................. ...................... ............
......... 114 ...0... . ... ... .. ... ... ............
MI•MER OF ELEMENTS ....... 141
ILE. NO. MODAL POINTS
I 1 12 1 19 20 13 2 2 .200006*00 .200009-00 0.
2 3 13 20 21 22 14 6 4 .200001*00 .200006*00 0.
3 6 14 22 23 24 16 7 4 .200009-00 .200006*00 0.4 7 II 24 36 26 11 1 : .200001*00 .200006*00 0.1 6 16 26 27 217 11 10 .20000600 .200006*00 0.
6 14 26 36 34 37 30 20 I1 .200006400 .200001*00 0.20 30 37 34 36 31 22 21 .200002-00 .20006*0 0.2 31 34 40 41 32 2 23 .200009*00 2000OleO 0.
24 32 41 42 43 33 26 26 .2000040 .200001130 0.
10 26 33 43 44 4$ 34 21 27 .2O0OOE*00 2000OleO 0.
II 3s 44 63 63 4 47 27 3 .20060 .20040 0.
..... .............I"....4.k... ....... S'* 1A4 . 44 ... . U ...................13 3 41 7 46 41 40 .. 200001*001 41 4 14 66 10 60 442 .20000100 .200001400 0.1 43 10 60 l1 62 61 46 44 .200001400 .200006*00 0.,, 12 63 ,, 0 7,1 64 ,1 6 .20000,4o0 .2000o,.0o 0.17 14 64 71 72 73 I ! S ,.2000*O0 .200006:00 0.
so 6 64 73 76 76 I of 67 .200006*00 .200009-00 0.11. 46 . 76 77 67 40 66 020000100 .200001*00 0.
. . . d ......... .. 6 -. 1.... - - S, " ........ ................. . . '...... .. .21 So s0 so 4? !! II 71 70 .200003a00 .200001*0@ 0.22 71 61 I4 46 10 62 73 72 .200001+00 .200006f00 0.
23 73 42 60 I1 42 03 7S 74 .200006*00 .20000 -00 0.24 76 13 32 3 :4 4 77 71 .20000600 .200001*00 0.
26 77 64 64 41 66 46 76 74 .200003.00 .20000*00 0.
31 66 67 103 104 107 66 46 47 .0000100 .200001*00 0.27 44 II lO1 10 107 o4 30 .. .20000100 .200001*00 0.
............................... ...... . J"' 6 . . 10 0 ' if . ... . . . 6f. ........ ...... ................ . ......................
2M 62 100 10 110 111 101 44 63 .200006*00 .200006*00 020 4 101 III 112 113 102 44 84 .20000:-00 .20000100 031 103 114 120 12t 122 11. 10: 104 .200006*00 .200006400 0
32 111 11 122 123 124 II 107 106 .200006*00 .20000*00 0.
'3 107 11 124 121 124 11 01 104 .20000'*00 .20000100 0.24 106 117 126 127 126 114 111 110 .200001 00 .200006*00 031 Ill 11. 126 121 130 111 112 112 .200001*00 .20000:*00 0.
.. ...... ............. .... . .1146 ..... " .... "......i .. '.. 44 .2I 4 .. ..fi ..............:. " .......... - GOO.. ........ 6. ................................. .............27 122 132 136 140 141 12 124 123 .20000 *00 .20000*00 0.26 124 123 141 1 14143 134 121 126 .200006*00 .200002%00 0.34 121 124 143 144 D14 136 124 127 .200001*00 .200009*00 0.40 -24 121 141 146 117 136 130 12- .2oo66T*00 200006*00 0.41 :27 1421 164 166 114 14 13: 12 .200001*00 .2000030 0 O.42 136 141 16l 167 11: 10 141 140 .200006*00 .200006*00 0.42 141 160 1SO 11 110 11143 142 .200001*00 .200006*00 0.
.................. .. " ' " ." " . ' . 1". .......... .6*. 4 -0 0.. . 666' ..
4S 146 I12 142 163 114 113 141 146 .200001*00 .200001*00 0.I 114 111 171 172 173 111 116 161 .200006*00 .200006*00 0.
47 164 168 173 174 176 s 67 1:: 167 .200003*00 .200004*00 0.44 I64 '167 I1 176 177 164 110 166 0200000 .200001*'00 0.
44 110 146 I77 17176 111 162 161 200001.00 .200006*00 0.60 142 116 174140D 141 170 114 162 .200006*00 .200003*00 0.MI 171.142 1* 182 110 1*3 173.172 . 200001*00 .20000600 0.
42 $~2 6 0*9-00i, '....................................................................................2 176 144 1.2 1:2 164 ,, 7 176 .20003.00 .2o0o0.o0 0.64177? 146 114 111 164 146 174 76 200004*00 .200006*00 0.,
66 171 1 66 1 47 1; i 167 171 170 200006*00 .200001*00 0.
16 14*166l 206 206 207 200 lE0 III 200008*00 '.20000N*00 0.
S7 160 200 207 306 206 201 162 1*1 .200006*00 .200001*00 0.
1 142 201 306 210 211 202 164 163 .00500,*00 .20000*00 0
It 104 202 211 212 2 202 144 its 200001*00 .200001*00 0............ ......... . I ' '61' 1'li . .i I. .....................0 1..66 00...... .. .
6? 201 214 222 2 24 27 20? 204 200001.00 .200001*00 0.
62 307 21' 224 221 226 21* 204 204 .200006*00 .200006*00 062 204 216 22t 227 226 214 211 210 200002*00 .200006*00 0.14 il1 211226• 226 230 220 212 2 200006*00 .20000E*00 0.
66• 213 220 220 221 232 21 218 214 .200006*00 .200001*00 0.
66• 222 223 23 240 2:1 224 221 22 .200006*00 .20000.*00 0..7 7 2 26000 2 00 0
ii 236 260 266 ;47 296 2S1 241 240 20000900 200O01*OO 0.12 241 2 1 2 6 241 210 2:2 243 242 .200001100 .20006*00 0.72 242 212 2 2 24 244 200006.00 200001*00 0.7 241 212 262 212 284 214 247 246 .2000O1*OO .2OOOO|*OO 0.76 247 24 264 7;: 266 266 240 246 .200001*00 .200002*00 0.76 266 267 272 274 276 21 26& 24 7 .2000001 0 20000*00 O.?7 21S 266.271.274 277 26 260.216 .20000*0 0 .20000*00 0.
76 262 270 276 240 261 271 264 263 .200001*00 a 200006O0 0.60 264 271 261 262 262 272 27S 211 .20000*00 .200006*00 0.I1 272 264 210 2a 22 21 271 274 .20000*00 .2000000 062 271 261 262 262 264 266 277 276 .200001*00 .2O000*00 0.63 277 246 264 265 266 267 276 276 .200006*00 .200006*00 0.
64 271 247 266 267 216 266 244 240 .200001*00 .200001*00 0.. ........... . ..I 261 2 2D_ 211 200 261 26222 20000100 .. 200006*00 0.
2 1 % 2 1, .2066.0 :o616............ 2ON~o........... . .................67 262 202 206 310 211 202 264 262 200006*00 .20000l*00 0.66 264 202 211 212 213 204 266 261 .200006*00 .200006e00 0.66 265 304 313 214 311 206 266 21 .2000000 .2000O0e00 0.60 216 201 2ll 216 217 206 200 266 .20OOO|*OO .200OO|*OO 0.
120 216 224 32 226 211 206 206 .2000*00 .200006*00 0.62 206 211 32 227 226 220 311 ;10 .2OO*O0 .20006*00 062 211 220 226 226230 221 2132.12 .20000 00 .2000a00 0
4 .* 2 0 '" 1 -33 -11 .... 6;"' "" .. . 6o oo.66 ... .............................. .............................................66 211 322 222 ;2 34 :2 317 216 .20000*00 .200001*00 0.66 224 226 261 242 242 226 26 221 .2|000.00 .20000*00 0.
0731325 44 24 3431 2 33 28 # 2OOeO 2O~ O67 326 336 342 344 34 237 32 227 .200001100 .200006*00 0.
66 220 226 247 246 246 22 322 221 .20000Oo .200006*00 O.100 232 232 246 210 211 340 234 322 .200006*00 .20006*00 0.1tO 341 312 21 216 360 313 243 342 .200006*00 200 0 0 .0414.. II16-t Sd . .. C.. "2 4 ........ 1664466 ............. o.......................
102 246 264 262 J62 264 26. 247 246 .2000600 200006*00 0.104 247 21 264 266 2i466 266 246 4 .200006*00 .200006*00 0
10 324 316 266 267 66 37 211 310 .200009-00 .20000e*00 O
1065 26 6 7 7 7 7 6 200* 00 2O0006*0 0.107 30 270 -77 276 276 271 262 261 .200006*00 .200006*00 0.104 262 271 271 260 21 272 264 262 .2000*009 .200006*00 0107 264 272 361 32 262 372 366 36 .20006*00 .20OO0*O.0
~1 10 1 1 .i R.4 ~ ~ 0~111 271 Ill 21232 34 237 377 32 .20000:00 .20000*00 0.112 277 267 264 266 266 266 276 276 .200006*00 .200006*00 0.112 273 266 266 267 266 266 211 230 3200001*0 .20000*00 0:14 311 316 316 266 400 60 2-2 262 .200001:00 .20000*00 .
31 3 30 400 401 402 21 266 264 .20000100 .20006*0O 0.116 262 402 606 410 411 404 214 262 .200001*00 .20000*00 0117 264 404 411 412 412 401 266.261 .20000*00 .20000600 0.
.................... C... ....0 -ifI... -t . ..~1 0. * 6 i 2W1i9 .... .:20000 6 ..... 2".00001.00..b67........ .---------... --II 26 406 4 41416 417 407 400 326 .200006*00 .20000 00 0.120 400 407 417 41: 416 404 402 401 .200001*00 .2O000*00 0.121 406 420 426 427 426 421 II1 410 .20 006*00 .2O000*00 0.122 411 421 426 426 420 42 12 1 1.20OO00 .20000;200 0.122 412 422 420 422 422 411 614 .200006*00 .20000*00 0124 411 422 422 422 4 424 41 .20000*00 20000*0 0.126 41T 424 424 426 4)6 426 •'9 414 .200001?00 .20000.00 0.
127 426 426 44S 446 447 436 420 426 .200001*00 .200001*00 0.126 420 426 447 446 446 440 422 421 .200001*00 .200006*00 0.126 622 440 446 410 411 441 424 422 .200006*00 .200006*00 0.120 434 441 411 412 412 442 42 421 .2000000 .200001*00 0.121 442 464 460 411 462 411 446 464 .200001*00 .200006*00 0.
122 441 411 4 2 4 A2 464 416 447 446 .200006*00 .200006200 0.123 447 416 464 466 4 417 44 446 .200001*00 .200006*00 0.
124 449 417 466 467 466 466 411 410 .200006*00 .200006*00 0.121 411 416 466 466 410 41: 412 412 .200001*00 .200006*00 0.126 460 471 477 47 476 472 462 461 .200001*00 .200006*00 0.127 412 472 476 660 4&1 472 464 462 .200006*00 .200002600 0.126 464 472 461 462 462 474 466 466 .200006*00 .20000100 0.I12 466 474 462 464 41 471 466 467 .20000.00 .200001*00 0.140 466 471 461 466 467 476 470 466 .200001*00 .200006*00 0.
141 477 466 464 461 466 466 476 476 .20000600 .200006*00 0.142 471 466 461 6:7 416 460 461 460 .200006*00 .20000*00 0.
... .................... f4 .aa . . 04 .. . . .................................................. ...........................145 41 462 102 602 S04 42 467 486 .200006*00 .20000R*00 0.
DIRICHL7 BOUNOARY CONITION 0ATA060065 I6IP6CTIVE O[RICIIL6T IOUNOARY COUDITIOMS
7: I 2 6.1100 23..0021- 4 2.100
2100................. ................ !i '. .t b0 ..................................................................................................................................................................................................
*7: 6 26.6600 26.6600
11I- t0 26.6100 24 6100O
* 1*2 20.0000 20.0000
.412-•02 20.0000 20.0000
0 .17623 2.000 2000.21-24 0:0000 20:.0000:
........ fo12o 66- .. 6. 6 .................................................................321-20 20.002000
34"406 20.0000 20.0000.41-41 20.0000 20.0000
.49:-461 11.1110 1 1110.466-417 11,1110 11.6110
.10-601 11.1110 11.1110
.604-602 16.1110 11.110• 0
MODAL POINTS ON FREE SUIFACI
11 17 26 24 41 91 62 46 76 S1 66 102 112 i 1 130 12 147. 12 164 170
('6~ 12 W66 .66 yf A .............211 267 368 274 261 261 402 406 41 42S 426 442 412 46 470 4716 467 462 104 0
LEIPASII PACE NODAL P01NT 0ATAO9IOUTIO N OF06 UMIERI FREE SURFPAGE LIC
* 11"112
"' 146 ....... ....... ...1.6666 ...... .......................................................... .. ...........................................................
1101.470 V 144.70 Y I I I.6 26661462 *120 0000 V * 1: .4.6606.426 6 * 101.0000 *v 20 0024m6oog41 2 I OIII00 * 20O160'602 .66.6000 Y* , 20.00006606.266 6 * 64 6000 7 * 20.02115006.266 I 76? 0000 * 20 017
0' O]*O 62i30000 0' 20 0000
* :O::: 2¥: 20:0a72
0001-2416 x I 000 1 20 1411
0001.22 I * 42.000 0 2O.14TV6006'2IS 0 * 260000 • S 20.00006001116 0 I 26 00 O 5 20 0000
6006'l64 6 * 25 0000 • * 20.4467
M O O v6 4 7 v 2 2 .0 0 0 0 Y * 20 .1 62
6006*l]O 0 * . 6OOO 0 . 20.2;•6'
NODs13 0 * 11.6000 y 20.0000
6006' 6 0 * 1020000 2 0.:0000
6006' 62 0 1.00 V* 22.4669i ~ ~ ~ ....... '1 . 6 oo •: o
M65116 4 06 V 444....... wa........... .......... ............................. ..................... ........ .....6006' 25 0 * "114.0000 • I 21 0207
6006. 11 0 * -I60.0000 • 26].6600
ITEM * 2
........... w .o ~ " 2 ... . e .P e .s Y t .. ! ....................................................................................................................................................................... .... ..... .....
:000W:4400IA?6 P 6P66 UPAILIS001 467 0 * 21.00000 1 19.616*B 60065470 0 ' 144.7000 • 06I.6624
WI I noe462 0 1200000 1 • .1 .6610
6006'41, 0 * 101.0000 Y 20.0000
NO01i402 0 IlOODO 1 * 20.0000N006'402 0 8466000 V 20.0000
005 0 .46000 1 20.22.. ~ts 6 -I...... ..... .60000 .....-....to o6*.............................................
600'236I 0 I 76 0000 V * 20.01266005.224 0 * 6161000 1 : 20.0..2
OO317 0 S 64 1000 • 20.0000NOD1NTO • 62.0000 Y I 20.0000006.262 0160000 1 I 20.1106600.2:6 * 61.6000 • * 20.1401D249 0 46SOOO V I 20.760
........ . 42.................................0.................. ....................... ....................................
60D6216 0 826..0000 1 * 20.00006006.166 0 26.1000 0 ; 20.00006006.11 0 201000 0• 20.38131ODO184 I * 21.0000 0 1 20.1404
666*' 1 . 6 . 0.00 ......0... 200 0 .. .. . .. .. . .. .. . .. .
600'1476 0 * 0.0000 1 20.6220
4OO 1 S R -47000 Y4 .1 • 26.52060-11 •. .0011 OO V3 20.0NIN
6006. iI 0 e10.0000 1 36.6100• 122:: 21 66 * 2470 • .0
NEW C000INAT$ OF THE PRE SURPACE LIME
NOO453 021-.OOOO 1 11.:1;260065470 0 144.7000 0 5 10.6262
6006.462 0 5 120.0000 V I 06.6602
6006546 1: :,oo 10.00 20.00
600'416 0 * 01.0000 1 20.0000N00 302 x a 4.00 1 20.000000E6524 x 54.5000 1 20.02
6E34 x * 74.0000 I 20.0006006l11 0 76.8O000 0 20.0142
mo006'224 0 * 1.000: v 20.0665NODE ]] V.0000 1 20.1001
6006.20 0 2000 1 0700: :166.6 •, .. . . ......oo ° ... .. .... :60065242 0 * 64.0000 y ' 20.1158
* 6006266 0 6 1.000 0 * 20.1077
"6 . 1 . 66.. ... ' ........................... .............. ................................................. .............60065222 0 5 42.0000 Y 5 20.1624
:00::216 . 34.0000 0 1 20.000060011164 2 * 26.5000 V 5 20.0000
NO1112•30.6000 • a 20.2137600Ell4 x 21.0000 Y 20.42
6006'147 0 5 22.0000 0 ' 20.1784
0 6 .:916Y. . . . .6 6 ............... .......... .............. .............. ........... ...........---- ..........................6006 1 6 ' 10.000 0 2 20.00006001M 75 6 9 0.0000 I I 2O.646O
600' 62 0 : 0.0000 1 22.7617S006: 6 1 36.00 0S 2.7917
600o. 25 0 ' "14.0000 1 3..226006'1:I1 . 60.00 I .... 00
...................... lt " ....... 1 ................................................................................................................................................... ................................................................................. ... .
NEW COODINATES OP TH6 FREI SURIACI LIME
6006.447 0 * 21.0000 • # 1.4446N0061470 0 * 044 7000 • t 01.6626
ooI462 X 120.0000 1 . 19.1012.6i 162 . . . ....... ....... ................................................................................................ ..................................... ................. 60061410 0 * 61.OOOO I I 20.0000
60640 ' 6.6000 V 5 20.0000•60065266 0 * 54.6000 • 5 20.02216D0l'3NI • I 7I.0000 • I 20.01
600l5250 0 * 76.0000 V 5 20.0142
60051224 0 * 66.6000 IY 20.05660D0]17 0 5 64.000 .• a 20.0000
*669.266.... 6 w .. i 41 6664 ....... ..i.... ...66...6....6.... .......6006.262 6 64I0000 V o 20.11NO00g266 6 61.1000 V I 20.$67700I';4 x * 46.100OO 1 20.1760
2 00 20
w--~ ~ ~~3::0 IV: : '' ' ooo ¥•]~o"m 0 + l A ........... w ' .... . 6 6 ..... ...+ " ....... 'I + .. ................................................................................................................................................... ........ ... ........ ............ A
.00.0] 0 7 11 0000 * 20.0000
60061011 0 * 26.600 9 2 0.0000ROOK. ti: I 26000 P s 20.2427
*661.to 6 ~ v 1 26.6630.6 0
600OR020 0 s 0.0000 0 21.1100 ' j0 0 6 0 1 2 I ' 1" 1 0 O O O 0 I 2 . 0 0 0
NODE* 1 6 5 "0 0000 • 20.0000
60060 76 • * "10.0000 0 * 21.10060011 42 0 5 :;:0:00 01 270
60061~~~ 46. 0 -2 00 V5 1 60 I S C, 0I C * C0 100 4 .37346001
O00 X COMOINA6 I I C6o6OfNlua W-0066T716L X'-VLOCIVO 0-VILOC0IT TOTAL VOIL. Pall. COI .
*11 ;0000 17:7 26: 16000 -1560 .1 40 ;.::..-06 .190.000 1 .02 265S0 -.-1240*-01 71TI801, .13401-0:
7~ ~ ~ ~ X -930- 000 2 10 2010 .20-1 -13soc-02 :12400.11
.I .1 0000.... ... 6.. 6100 - -2121 1 j ................. 1 1 0*~S l ...~ 100 ....... .64 .. .....-0 ... *80 42
1: :112.0000 21 32200 34.039 -. 14069-01 .64141-023 .14011-01
17 :112 000 2400 27-.010 -. 26-1 .81-02 12111-0_8 114.0000 2.6100o 21.211 -.14671-01 .1174.10 1466210
Is. .- 114 600 :.6l17 3t.2110 - 14681-01 .1711-_2 14181.01........ ;0.4.100, ... . ........ . 1 I.. ....... 21 6 .......... ... -o . ....... 01 .... ... ..21 11.000 1160 a122 0 46-1 .400 1710
22 -11400 1417 21.22 481 7060 1710
2 - 114.00006 il.22 31.2122 - 146SE:01 .7171E-02 .1474-01
21 140000 2260 1.2144 .;'1-1 8312 1710
26 114.0 0 25.671: 21.2260 -:14711-01 18110 . 741-0127 -114.0000 26.1124 21 .33P7 -. 14122-01 .12711-03 .147SE-01
26 -78.8100 2.7568 26 :.174 -1610 1110 1660
1 -78.8100 1.4284 28.131 -. 19829-01 111729-02 ;61022 -7.60 14 711 628-.111'T-01 .122102 .112-
24 -7.8100 24.1082 2 4.6:04 -. 11141-0 :.10101 .1641-011 -143,7000 I.1255. . 21. 7439 .16961-01 ..........5211-02 .16601-01
37 -42.7000 1.66 21.712 ,11-1 .7210 a1110
28 .37000 1.122 21 771&3: 6110 .;21:3O .610
21 -27000 12.19:2 25782 165-01 692S21-03 ISS71-0140 -43 700,5 14:628 21:7160 1 11101 12002 .6-
41, -43.7000 9711 2 .60a - '1101 .1091E-02 .1 110.2 -4.00 19.6119 21..21. :.1.110 ;;326::02 .11 -042 . 4 7.000 21,9344 21::......... . 11411-01 124 -2 ;:61:-o,44 w4j..7000 22 7766. . .18.a Z44*i*i4Kl. . . .i8-o . . . 41 - ..................
41 -2.700 21.16 21.890 -. 16441-1 .27-2 141046 -2.2100.o 0.07 267027 -:.;7010.0,10 .101
47 -31.25so0 64206 247216 -. 70010 .71221-02 .1702E-014 -3:5500 11.1:3; 24.764 -. 1 '0 -0' 152;2:-03 ;70:::-01
46 -2.20 17.0 72 24 7725 .1:7*001 .12-0 ,170 1
10 -21.3100 20.551 24 715 -.16:179-01 127T102 .702101111 3260 I.1 2 4226 -. 611 .14229-02 .70-1
............. .. 00 .. 16..... 80 . 3 1 .40 A .17801 t0~ ,112s -1 0000 got217 22....... .1-468 . 1748 601 . .6...0.....1-0
16 31.0 .3310 22.3 :.71-0 71-:03 110
67 -1.000 1.61 22.1114 -,.17:6-0:184-0:.76:0II 15.0000 16.66610 22.7014 -1 7421-01 .1271-02 .174Sol.01
so -1.00 1.4256 22. 71114 -14-0 .12201-02 .174110
......... ........ .. . ............ ......j..... * 8-o.............88-.79S :1 0 ........ 0 1e
812 !7,00 11 2.7318 -. 172:1-01 .2721-02 .;73;1:0;62 16000 2712 22.7.10 -7160; 1210 1210
62 -16000 .22 22.6146 - .17061e-0 .1602 .70-164 -3100 5.1616 22.87 -. 120Q .21111-0 .1310
1 11.000 5-.5682 2:2.6,2.2 -.7,a1T01 -2.2:1-0: 1711051 3.00 33.2S 22S114 -1&41E.-0! .72.201-2 .660
:6 ::,Sole 151682.8720 -. 1611131-01 .10722-02 .1 610
66 6600 22.60 22.80 .81-1 '280 1610
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.... it . . ........ .... 2 0 01 . . .. .0o ............ 010.7I t.. . 20 .0........... :2 12 -03 ........... ..441 I10.,000 17.111 20.0018 :.2071-03 " 13 2!-04 .2071-0344 1 110.1000 20.0007 20 0018 .111s-03 ".70711-01 111102443 120 0000 -4 2000 9.19112 "2311E-03 100l101 .23186-03444 120 0000 -1,002S I 113 -.2311e03" 1104-01 .23211802441 20.0000 2 1110 11 1114 -.2206-02 .21218-01 .23016-0248 20 0000 S122 !1.1114 - .2021-02 "I11-123020-032447 I20000 .. 1l00 11 114 -. 22041-03 .&1]11"-0 22148-02448lil.........20 000O....... ,117............. i1612 ....... 21O0'O0 ......... ; t i........22808-0 ......... ....... ..4 120..... 14.1.10 111112 ".22108-0. .170-01"O 22101"02880 20 0000 1 S.211 1113 ".22188-03 - 11 'E 221"02
:1? 20 0000 74:,1 21111 "22018"02 1400-01 2201t'03T312 120 0000 II 7267 12 4113 "2231-03 " 16228*0S 2226-03
1 461 20.0000 11.1812 11.4113 .23411-03 .2221-0 .e411-02
8012. 100 -4082 16.1770 22786-02 . 7213 1 2277-02416 22 2100 1 7628 1.6772 *.2271"-02 47278-08 .22728-02
414 -..... 13222:000. . . 2 .. .... 1 77 2 3 4 2 02234 s tI............ I 6 9 1 sill . -7 *8 4'o* -i6.... 2*,4t it8-01 -........... ............ .....417 132.00 4.1828 16.1774 -.22401-03 .7031-0 I .22488-03414 22.2100 17.2611 6.6774 -. 224002 1137 0 .2248.-03416 132.2100 11 774 11,1774 -. 22408-02 - 21808-08 .22401-03410 14' 7000 -1.0141 I1131 -,221011O 78828-01 .1 7219-03411 14.7000 -,1.70 11.122 -. 22111-0. 11611-0l +22206-024612 44.7000 1,3301 II33 .22116"02 .86701"06 .22206-02482 14.7000 4 1280 1.11 -.42211"0. .410"1 .22211-03
464 144.7000 776 8.1641 .22224-02 3701*OI .22221-0]461 44 7000 10.6220 I.83 -.222;1-0l .2731"-01 .2232-02446 144.7000 4,1201 II4621 ".2:2..-0 .20741-01 .2224I-02487 144.7000 18,613 4.161 -. 22241-0 .11442-06 .222:1-034 14 4.7000 17.0120 1 6i61 -. 22249-03 12666-I01 .2224I-03481 144 7000 6 1024 6 4283 " .22268-02 ]22848-08 .22]1-"02170 1447000 11821 I ". .6 -:229 .03 16741"08 .222-03
471 71.100 -6.2144 6.8248 ".21211-02 .72473-08 .21221-02
472 171.8100 21002 11.1211 .313,2 .21231-02472 71.4800 64662 6.6282 -. 21246-02 .2228-01 .212.1.*0.4 3 . , :4 : . 4.4 8: k1. . . . .i* l 61 ............. ._1: 1242- ;.................... ............ 4 '+........... ++i'li0+ ............ ' ili ~ l ...............ll ''i i+............ :-: :' I i ; ' ........ : lf il ............... l1114.1t~ ...2 .............. ...... ........................
.... 178.100 1.10.. 11.1214 ".2124-03 .11441"O .2121-"O67 3 7,..,00 ,..,2 ,,,32,4 -2124,-02 .42 00 .2,1, 0211.0000 -7 1210 11.;4 -. 20201-0 .7171-01 20311-02
47 1.OO -4.2271 I.8I4I -. 2021 - 02 .1117101 .20]O1"O476 211.0000 100 1.81 " .20286-02 .I001OO 20211-02
440O 211.0000 2.0671 iII847 - .20281"02 142271"01 230281-021218 00OO 1.2 110 1.2027 60 2 ? 1 1'. 2 71 3
482 211.0000 11.6400 11 8884 ".20211-02 22746-01 .2022-02
484 211.0000 12.7172 16.Si88 -. 20266-02 .1i186*01 .20266-0341 214.000O 7144 11.SIN: 7 .2026-2 .121-G01 .20276-03
411 211. 0000 1731217 11 .84 II ."2 021[*02 163111"01 .230218-02447 211.0000 II 1184 4.884II .2021- 02 .222311"08 20288-02444Iti 212.O0000 II.1 4 ...107 -. 16206-02 11201"O1 116-102
446 262 000 "2 46001 II1 - .16281"02 41411-01 6261"02.4 1 ....... 0...... .. l
.................. ............... . Ii .sii ... .... .. 4 0 . . . :1 I ........ .. --46 . . . . . . . . . . . . . . . .
461 212 0000 0.2200 11.4111 ". 111-0"O . 121108 . 11421 "0O
662 212.0000 1.0810 I+II02 *.11441"02 .10411-06 .18441"02412 212.0000 118116 441112 -. 21404-03 1171-09 .20102
11 21I.00OO "10 1410 11.1110 "11211"02 11311"01 .1211"03493 21 0000 11 171 11.8110 -. 14228- .20221"14 .1428-02414 211 0000 -27600 6.4110 ?71841602 .. 220-01 I2211-03447 2110000 -. 021 : :.3110 : 3.14481-02 "I.8 I8 14 848i-02
444 . 26 666Oo 6946.. .:.20244~...-.42WO
46i 2$1.000 1.8026 16 1110 -. IIII4-03 "414261I 1llll-O100 261.0000 60000 118110 - 1 611.0. .40276-08 .1..1"0.. 101 211 0000 11.7024 :: :180 l84"02 01 01 2 2 I .0 0 0 0 1 4 0 7 8 I l . IO - 8 6 0- 0 2 .: 2 1 1 -O 1 I 1 8 1 1 8 0 2
102 211.0000 17 111 11.10 1044N1- *3 1 0 . 11111-03804 211 0000 1I1110 1.1110 "11871-0 111"6 11171-02
....... l 4
8i V4+. 8ti-8 14 Uy8't.6 ftt. j kfLt .......................................................................................................................... . ......
44I1
8 66 NI 11] 86 I~l L * .810101 08 I 1100018O1 00 * . 104111,OO + ~ / r + k' '
:141 -I1Cll4OI . 101 0'*00
IEI * I 112 66 1141 816. ¥81 * 411101"O1 01 I 210001.02 00 S .1141111"0
I .... iI I 1 I l .. . M l * ll .....i~ i +I +;' . ill 0 1 . ..... .. ........ . ..bl 6 .... .....O ."' .'.".i..
"
... ' ' -
............ .... .......... ...... .. .. .
TOTAL OIICOIC 1 * 1212761
W IS 1 .ii 1 *000L 1184-f lsa I 4000413 7o
68 * 216 62 * 200 0 8 881 * .12s01-01 l 210003-02 00 * ,3160000
7°.0,,... 2... Is Alt,. .•990 .1 10.. ....1 V p d "Va l f " d * 10 U 0 o l N ItL f ...... ... k i + 4.. ... ...... .. . .......... .... . .. ...- .... .... .. ... ...... ................ . . . . ........ .... .. ... .... . .
we 9 200 61 . 217 &WE 861 6 1101-02 01 * 1OOO6.01 00 * 107101+00
TOTAL 01]"C6101 * 1 ..1...01 ... 3
65 402 6f * 411 ;Vt VdL . .1721]E-02 01 i I1000I*001 0 * IA04 6-02,
70TL OISC"AIG * 176466.01
6nd If P,@010I-
APPENDIX C
DISCRIPTION OF COMPUTER PROCEDURES
APPENDIX C
APPENDIX C
Using a Personal Computer in Runningthe Aral Seepage Program
I. Introduction:
The Aral Seepage Program is located on the Georgia
Institute of Technology main frame computer in the Cyber B
area. To run many runs of the program it is very
convenient to prepare and edit the data files on a
personal computer, using an editor or word processor. A
brief description of the method for this particular
program follows. A user should get instruction and
information for use of the Cyber B from the Office of
Computer Services, Rich Building, Georgia Institute ot
Technology.
II. Preparing the Data Files:
Using the Aral Seepage Program User's Manual (Pirtle,
Appendix A) draw and label the mesh for the problem to be
run. An example is Figure 3-5 of this study, but a
working copy of the mesh should be large enough for easy
referral and use. With the mesh and a complete list of
problem characteristics a data file can be prepared, from
the user's manual instructions.
In this study the number of nodes and basic shape of
the mesh was to be unchanged for all of the runs. To
APPENDIX C 1
simplify preparing the data files a spreadsheet was
prepared. Changing the dimensions or hydraulic
conductivities (vertical or horizontal) required one entry
and the spreadsheet adjusted the node positions from
simple formulas. The complexity of the spreadsheet is
entirely dependent on the problem considered and the skill
of the user with a spreadsheet program. Any of the
commercially available programs will work satisfactorily.
If the study will involve several different mesh
arrangements and/or only a few runs the data file can more
easily be prepared on an editor by typing it in, if the
editor is set to create an ASCII file.
An ASCII file is a file of the characters as entered.
Word processing programs and spreadsheet programs have
hidden command codes which control the programs so that
the features are executed. Features are the calculation
of values in a spreadsheet or the margins, justification
and format of a word processor.
Most spreadsheet programs have a function or
ancillary utility program for conversion of the
spreadsheet to a values separated by commas ASCII format.
With that utility the spreadsheet no longer will do
calculations or have the simple column alignment.
In this study the programs available provided an
ASCII file with all values separated by commas. The file
did have commas to separate what had been empty cells
APPENDIX C 2
within the spreadsheet. Other programs may not have that
result. To delete the commas a word processor was used.
A program which allows editing an ASCII file is necessary
for this operation. If a word processor is used in the
normal mode of edit command codes will be imbedded to set
margins and the file will not run properly on the Aral
Seepage Program.
III. Sending the Data File:
With a proper data file prepared running the Aral
* Seepage Program from a personal computer requires one
device and several clearances. An authorization to use
the Cyber B must be obtained, with a file ctorage area,
* a password and an identification code. This is explained
by manuals available at the Office of Computer Services.
Access to the Aral Seepage Program, named OWRCC must now
* be obtained from the School of Civil Engineering at the
Mason Building. The device needed is a MODEM for transfer
of data and commands to the Cyber B. The speed and
• manufacture of the MODEM is subject to the needs of the
user.
A communications program is necessary to use the
* MODEM and many such programs are available. Georgia Tech
offers students and faculty a program named COGITATE for
use in communicating. In this study a different program
* was used but, it had the KERMTT file transfer program and
APPENDIX C 3
this is necessary.
With the communications program call the GTNET system
and when a connection is made enter the GTNET command:
>> Connect *OCS CYBER B
A connection to this directory will be made and right to
access will be challenged:
Family CYBERB
Userid (input the assigned ID)
Password (input the selected password)
Access will be granted to the Cyber B area. To copy the
data file to your file for execution of the Aral Seepage
Program the program COGITATE has menu entries to execute.
If another communication program is used the KERMIT
protocol is necessary. The details of this description
are better left to someone else. In this study the
following procedure worked.
* \ KERMIT2
Control was now with the user's computer by use of KERMIT
commands. Executing the "Send" command of KERMIT and
* naming the data file to be downloaded successfully
transferred the file. The file name was changed as the
cyber will use the first eight alpha-numeric characters
* of the name and ignore any periods normally used to
separate suffixes in the MS-DOS environment. At the
completion of sending data files execute the KERMIT
* command to "Finish" and control will be re-established
APPENDIX C 4
with the Cyber.
IV. RunninQ the ProQram:
To run the program and receive a printed output from
* the laser printers in the Rich Building do the following:
\ OLD,OWRCC
\ GET,DATA (note:DATA is data file as
* named upon receipt by Cyber. To see names
answer \ with LF)
\ OWRCC,DATA,PRINT (note:PRINT is name
* selected for the output by user. If no print
is specified the output of the run will go to
the screen. With a MODEM this is a very long
* process and is not recommended.)
A short wait of less then a minute can normally be
expected here. If an error message is received the data
* file should be checked for errors in concept and tried
again. If a transfer error is suspected send the file a
second time.
• \ SAVE,PRINT (note:SAVE only if a copy of
the output is desired for the holding on Cyber)
APPENDIX C 5
\ PRINT? (note:A hard copy of the
program output will be received in the Rich
Building if the output file name PRINT is input
at the first query and all other entries are
allowed to default by responding with the
"ENTER" or "RETURN" key. The last query asks
for the USERID and responding with the ID has
* it printed on the cover of the hard copy for
easier identification.
There are several other printer locations and many
options one can exercise in printing the results. For
more information consult the advisors in the Rich
Building.
* To exit from the Cyber:
\ LOGOUT
>> LOGOUT
* V. Caution:
This appendix is not a replacement for the user's
manuals of the programs used, nor for the instructions
* and guidance of the Office of Computer Services. It is
a quick and easy guide of a procedure that has been
successful in running programs on the Aral Seepage
* Program.
APPENDIX C 6
As stressed above many different programs will do
the functions of the above procedure. For information
the following were used:
Spreadsheet: SuperCalc 3
Editor: WordStar 4.0
Communications: ProComm 2.1
It would be an advantage if the output file from the
Aral Seepage Program could be captured and downloaded
from the Cyber. This was attempted with KERMIT once but,
was discontinued after twenty minutes of transfer with a
1200 Baud MODEM.
A
APPENDIX C 7
0
APPENDIX D
SPREADSHEET AND DATA FILE DISKS
A
APPENDIX D
APPENDIX E
ARBITRARY SELECTION OF RADIUS
APPENDIX E
APPENDIX E
Arbitrary Selection of Radius
In this study the radius of influence was determined
as the distance at which no more then a 10% decrease in
total flow over a 100 foot change in trial radii occurs.
This arbitrary selection is certainly open to discussion.
It is very common for less restrictive criteria to be used
in the definition of radius of influence of drawdown.
Figures E-1 and E-2 are cross section drawings of
the free water surface in the trench area if the radius
of influence had been selected at lower values based on
some different arbitrary standard. Obviously the free
surface reaches the upper blanket and possibly the
foundation. The formulas used in Chapter 4 were based on
field data of seepage and the field interpretation of the
radius of influence, under some standard determination.
If the selection of radius of influence for this
study had been based on a different criteria the
predictive forms and dimensionless products would have
been changed. Using a standard of 0.1 ft3/day/ft, maximum
change in trial radii of influence, Criteria A, results
in Figures E-3 and E-4. These figures are the
dimensionless product for a different standard of radius
of influence. The new standard is on average 0.07
ft3/day/ft less restrictive and predict the radii of
APPENDIX E 1
TABLE E-1
SUMMARY OF DATA, CRITERIA A RADIUS DETERMINATION
SIope SD Hr h Li' Q" F'(ft) f t 2*--/ d ay (ft)
U 15 ) I0 250 0. 18 0.28]25 C) i '71 C C "CS1) 250 .15 0.31
:5-= 10 250 0. 15 '0. 6
C 15 2) 20 400 0.25 0.4U 2 2C 20 400 0. 0.45
i5 60 1 (. 22 J.45
0 25 b) 1 - o. 21 0.65C -5 60 10 o . 75
0 15 6 20 450 0.5 0.760 25 60-?-' 45 o ). 91.
35 60 4.) 1.C515 20 10 200 0.2 0.48
5 25 20 I0i C) o.7... 5 35 210
3 5 15 2 20 400 0.25 C..625 20250 0.25 0. 95
.- 20 20 300 C.25 0.987.5 15 60 10 300 .21 C.65
10 150 C).24 1.1
5 10 150 o..5 1.4-.5 15 60 20 45C 0.32 0.92.-5 25 60 2 425 0.3 1.27
5 5 60 2C) 4C)( 0.3 1.55
7 15 2C 10 1o C.. 0. 81
7 25 20 1C)7 35 ) 1 0
7 15 22 20 225 C. 38 0.987 25 20 2 . 175 . 9 1.25
7 .5 2C) 20 125 o. 39 1.857 15 60 10 15C.) f. - 1.C)5
* 7 25 60 1C) 75 0. 8 1.87 35 60 10 lo 0 .4 2.17 15 6) 20 350. ).8 1.217 25 o0 2:) 700:) C.-9 1.87 -5 60 20 225 -.41 2.42
* APPENDIX E 2
Table E-l. The new curves of dimensionless products in
Figures E-3 and E-4 show the less restrictive curves to
be nearly unchanged.
As a further check a second standard, Criteria B was
developed. This standard is defined as a total flow
increase of 75% from the total flow at a trial radius of
700 feet. The scatter plot of the dimensionless product
versus total flow and maximum free surface is shown by
Figures E-5 and E-6 for Criteria A and Criteria B. Table
E-7 summarizes the results of Criteria B.
Figures E-7 and E-8 show the final curves for total
flow and the maximum free surface against the dimension-
less product for all considered standards. The curves
* are little changed. The use of one composit curve would
suffice in predicting total flow and maximum free surface
for any standard of radii determination.
* An incorrect radius of influence will under predict
the flow and maximum free surface if too high. A con-
servative approach would be to reduce the radius of
* influence as predicted from Figures 4-1,2 and 3. The
amount of adjustment would require additional field data
from a trench drain system.
APPENDIX E 3
0-))
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LLJ(0
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of L .3LiLi
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APPENDIX Een4
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APPNDI En
TABLE E-2
SUMMAr,Y OF DATA, CRITERIA S RADIUS DETERMINATION
Slope Sp Hr h Li : F'
(ft) f t" -' ay (ft)U 152¢1025.12. .
,25 0 1. 0 4U -25 0. 21
015 2): 20 400 '.2 K.' 4 -
I 2) 4(K4(-)_.7 46.. 02 .2 ].
0j 1 6 !, 4,9.44
2 = o O 1 0 - 4 2 5 '' iS8') . '
U 3; 6U 1 U 4U ): '- i S .';15 6 24C( .4IS
60 20 175 .T 1 )50 35oO 2 4A (.. :3 I.15
5 15 0 10 200 . 19 0. 48:.1520I¢ i0 1 )' 19 C) -
. 15 20 20 -5 u. 28 0.75-- -C C C' C. .5 1. 5
-C C (- - C-1.983.." 0 20 T300 -'5 09
•.515 bcO I C) '22 5 .26 c .8.5 6 ( 0 225 C. - 1 .85
-.5 35 60 10 100 U.26 1.54-) o. 37 1.05
515 6040...
560 20 375 '. 75 1.5
3.5.= 60 20 25i7 15 20c: 10
* 7 25 20 107 20 10
7 15 2C) 2 1-75 . 45
7 "" 1. 5-a 2 2): 10i0x ) --
7 15 60 10 125 .,5 1.3
7 25 6 1-5
7 35 60 10
7 15 .20 300 . 45 1.4
7 Z5 -0 20 . 49 1.957 5 6C, 20 150 U.56
APPENDIX E
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APPENDIX E7
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APPENDIX E9
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APPENDIX E 11
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APPENDIX E 12
