Probabilistic Models for Structure’s Average and

Shideh Dashti, Ph.D.Associate Professor

Geotechnical Engineering and Geomechanics

University of Colorado Boulder

Probabilistic Models for Structure’s Average and

Differential Settlement on Liquefiable Ground

Acknowledgements

National Science Foundation (NSF

Grants 145431 &1362696 &

1134968)

Department of Education (DoE

Award P200A150042)

Janus Supercomputer at CU

Boulder (NSF Grant CNS-0821794)

Graduate Students: Z. Bullock &

Z. Karimi

Collaborators: Profs. A. Liel, K.

Porter, K. Franke, and B. Bradley

3

I. Research Motivation and Methodology

II. Collection of Data on Building Performance

III. Selection of Optimum IMs and Key Predictors

IV. Semi-Empirical Probabilistic Procedure

V. Conclusions and Ongoing Work

Excessive total and differential settlement of shallow-founded buildings in prior earthquakes

EE

RI S

pe

cia

l E

art

hq

ua

ke

Re

po

rt 2

011

Consequences of liquefaction on shallow-founded structures

Bo

ula

ng

er

19

99

Bearing failure of a building in the 1999 Kocaeli earthquake

Consequences of liquefaction on shallow-founded structures

Bra

y e

t a

l. 2

00

4

Dr = 60% FSl = 0.6

Dr = 40% FSl = 0.4

Dr = 90% FSl = 2.5

Non-liquefiable

Post-liquefaction volumetric strain, εv

Facto

r of

safe

ty f

or

liq

uef

act

ion

, F

s

State of practice: evaluate settlements in the free-field

d = ∑(ev)(Dh)

Ish

iha

ra a

nd

Yo

sh

imin

e 1

99

2

Building Width / Thickness of

Liquefied Soil

Fo

un

dati

on

Sett

lem

en

t /

Th

ickn

ess o

f L

iqu

efi

ed

So

il

Liu

and D

obry

1997

0.0 4

0.2

2

0.4

d = ∑(ev)(Dh)

Dr = 60% FSl = 0.6

Dr = 40% FSl = 0.4

Dr = 90% FSl = 2.5

Non-liquefiable

Alternative procedures adjust free-field settlement based on limited empirical data

Building Width / Thickness of

Liquefied Soil

Fo

un

dati

on

Sett

lem

en

t /

Th

ickn

ess o

f L

iqu

efi

ed

So

il

Liu

and D

obry

1997

0.0 4

0.2

2

0.4

As they ignore:

• Soil-structure interaction

• Key mechanisms of deformation

• Total uncertainty

The existing predictive models for settlement & tilt are inadequate

Permanent deformations

Liquefaction “triggering”

Post-liquefaction strength

Consequences on structures

Engineered mitigation (if necessary)

Se

ed

et

al. 2

00

3


Implications:

• characterizing the severity of the hazard and need for remediation

• evaluating performance of mitigation techniques, accounting for uncertainty

Permanent deformations

Liquefaction “triggering”

Post-liquefaction strength

Consequences on structures

Engineered mitigation (if necessary)

Se

ed

et

al. 2

00

3


Performance-based engineering procedures depend on choice of intensity measures

• A strong IM correlates best with demand parameter(s), with minimum uncertainty

• Uncertainty around estimating IM propagates forward, often governing total uncertainty

• It is not clear if prior procedures employed the most optimum IM

Cumulative absolute velocity, CAV (cm/s)

Sett

lem

ent,

S(m

m)

Ka

rim

i, D

ash

ti e

t a

l. 2

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8 -

SD

EE

observationalexperimentalnumericalstatistical

Research on response of shallow-founded structures on liquefiable soils

Integrated Approach to Evaluating Building Performance

Bray et al. 2004

Olarte et al. 2017; 2018

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 10 100 1000Pro

bab

ility

of

exce

ed

ance

Settlement, S (mm)

Exceedance probability curve

Bu

llock e

t a

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01

8

Adjusted residual

Freq

uen

cy

Methodologically Integrated Approach

3






Collecting Case History Observations

Case history database insightful but not sufficient for developing empirical procedures

Bray et al. 2014

Bertalot et al. 2013

Earthquake Source Cases

1964 Niigata Yoshimi and Tokimatsu 1977 15

1990 Luzon Acacio et al. 2001 17

1999 Kocaeli Bray and Sancio 2009 3

1999 Kocaeli and Düzce Unutmaz and Cetin 2010 27

2010 Chile Bertalot et al. 2013 21

2011 Christchurch Bray et al. 2014 4

Total 87

Bullock, Dashti et al. 2018 – Geotechnique

Centrifuge Modeling

Centrifuge experiments inspired by case history observations

CIE

ST, U

niv

ers

ity o

f C

olo

rad

o B

ou

lde

r

Centrifuge experiments inspired by case history observations

Variables studied in experiments:

1. Soil layering and properties

2. Structure type and properties

3. Ground motion properties

Da

sh

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0a

,b –

AS

CE

JG

GE

Response of structures different from free-field soil

-50

0

50

100

150

200

250

300

350

400

450

500

550

0 5 10 15 20 25 30 35 40

-50

0

50

100

150

200

250

300

350

400

450

500

550

A; T3-30

C; T3-50-SILT

C; T3-30

Free Field; T3-30

B; T3-50-SILT

Free Field; T3-50-SILT

A; T3-50-SILT

B; T3-30

-50

0

50

100

150

0 5 10 15 20 25 30 35 40

-50

0

50

100

150

ru = 1.0

T3-30

T3-50-SILT

-0.6

0.0

0.6

0 5 10 15 20 25 30 35 40

Time (sec)

Input Accel.

Excess P

ore

Pre

ssu

re (

kP

a)

Accele

rati

on

(g)

Vert

ical D

isp

lacem

en

t (m

m)

Structure

“Free-Field”

• Structures settled more

than free-field

• Magnitude of settlement

related to motion

intensity and rate of

energy buildupS

ett

lem

en

t (m

m)

Du

(kP

a)

Acc.

(g)

Structures:

Free-Field Soil :

• Partial Drainage (εp-DR)

• Sedimentation (εp-SED)

• Consolidation (εp-CON)

These deformations are not the same under

the structure and in the free-field.

1. Volumetric deformations

Primary deformation mechanisms identified near structures

Da

sh

ti, B

ray e

t a

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01

0a

,b –

AS

CE

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• Partial Bearing Capacity Failure (εq-BC)

• SSI-Induced Building Ratcheting (εq-SSI)

2. Deviatoric deformations

These are not considered in the empirical procedures.

Primary deformation mechanisms identified near structures

3. Soil ejecta (εq-Ejecta)

Da

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Numerical Modeling of Centrifuge Tests

Numerical simulations with the PDMY02 constitutive model in OpenSees

• 3D fully-coupled SSI

analyses

• 20-8 node brickUP

elements

• Constant K over time

Elg

am

alet al. 2

002

Soil model calibration performed withelement tests

CSS Test

Aru

lmo

lie

t a

l. 1

99

7 a

nd

NC

EE

R 1

99

7

Numerical simulations captured peak excess pore pressures

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Nu

me

rica

l Pe

ak r

u

Experimental Peak ru

Free-Field

Under foundation center

Under foundation edge

STKO: Petracca, Camata, et al. (2017)

Acc

. (g)

Time (s)

Numerical simulations did not capture free-field volumetric settlements

Sett

lem

en

t (m

m)

Sett

lem

en

t (m

m)

Acc

. (g)

Time (s)

Numerical simulations captured settlement of structures on relatively thin liquefiable layers

Numerical simulations predicted structure’s permanent settlement and tilt well

Ka

rim

ia

nd

Da

sh

ti 2

01

6 –

JG

GE

Numerical simulation captured structure’s flexible base response

Frequency (Hz)

0 1 2 3 4 50

5

10

15Structure A

Experiment

Simulation

Fixed base

Tra

nsf

er F

un

ctio

n (

a mass

/ a

fou

nd

ati

on )

simulation

0 1 2 3 4 50

5

10

15Structure A

Experiment

Simulation

Fixed base

Tra

nsf

er

Functi

on (

a mas

s / a

fou

nd

atio

n )

simulationa mass

a foundation

• Centrifuge test layout

• Linear SDOF structures

• Concrete mat foundation

• Elastic bedrock (Vs,rock)

Df

Heff

Numerical model used to evaluate influence of different parameters

Ka

rim

ie

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Input Parameter, IP Range of IP

Fix-Based Fundamental Frequency, fo 0.5 to 4 Hz

Building Height, H 1.7 to 14.0 m

Oscillating Mass, M 5 to 2,472 ton

Foundation Bearing Pressure, q 30 to 220 kPa

Foundation Contact Area, A 30 to 340 m2

Foundation Aspect Ratio, L/B 1 to 10

Foundation Embedment Depth, Df 2 to 5 m

Liquefiable Layer Relative Density, Dr 30 to 85%

Liquefiable Layer Thickness, HL 3 to 24 m

Presence of Multiple Liquefiable LayersVarious thickness and

embedment depth

Depth to Liquefiable Layer, DL 2 to 8 m

Low-permeability Silt Cap 0.5 m thick

Initial Site Period 0.25 to 1.2 s

Structure and soil input parameters were varied

Total: 421 models

Soil

Fou

nd

atio

nSt

ruct

ure

Ka

rim

ie

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8 –

SD

EE

Major characteristics Range

Gro

un

d M

oti

on

Moment Magnitude, MW 4.9 to 9.0

Distance to Rupture, Rrup 0 to 367 km

Peak Ground Acceleration, PGA 0 to 1.1 g

Cumulative Absolute Velocity, CAV 10 to 6,400 cm/s

Significant Duration, D5-95 2.2 to 112.1 s

No. Records from Crustal Events 112

No. Records from Subduction Events 38

Ground motion suite covered broad range of intensity levels

421 models under 150 ground motions = 63,150 total analyses

Magnitude, Mw

Fre

qu

en

cy in

Dat

ase

t

Distance to Rupture, R

150 Motions:

3






Numerical Result

Regression

• Efficiency

• Predictability

• Sufficiency Standard deviation around regression

Ka

rim

i a

nd

Da

sh

ti 2

01

7 –

EQ

Sp

ectr

a

Optimum intensity measures (IMs) identified for predicting settlement and tilt

Slope, c

• Efficiency

Availability of and uncertainty inexisting attenuation relations

• Predictability

• Sufficiency

Optimum intensity measures (IMs) identified for predicting settlement and tilt

Bu

llock e

t a

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9 –

EQ

Sp

ectr

a

Location and analysis type for optimum intensity measures (IMs) evaluated from different analyses

3D Nonlinear Dynamic Analysis1D Equivalent Linear Analysis

Bullock, Dashti et al. 2019 – EQ Spectra

Bu

llock, D

ash

ti e

al. 2

01

9 –

EQ

Sp

ectr

a

Efficiency

Suff

icie

ncy

on

mag

nit

ud

e

Outcropping and within rock, evolutionary IMs consistently better than surface motions

GMPEs developed for rock motion intensity and all tectonic environments

CA

V (

cm/s

)

Distance to Rupture (km)

Northridge (Mw 6.69) Loma Prieta (Mw 6.93) Chi Chi (Mw 7.62)• CAV found to be

more predictable

• Std. dev. 1.4 to 2.0

times smaller

• CAV selected as

optimum IM for

settlement and tilt Bu

llock e

t a

l. 2

01

7 –

BS

SA

Parametric study results used for sensitivity analysis

• Parameters varied one at a

time to isolate their effects

• Co-varied with relative

density and pressure

• Related parameters

manually separated (e.g.,

mass and pressure)

Ka

rim

i e

t a

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8 –

SD

EE

Set

tlem

ent,

S (

mm

)

• Soil relative density an important parameter



• Soil thickness was influential up to 8m.




• Depth to top susceptible layer below foundation very influential


Set

tlem

ent,

S (

mm

)




• Foundation contact pressure influential up to a threshold


Set

tlem

ent,

S (

mm

)




• Foundation contact pressure and area influential up to a threshold

Ka

rim

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0 50 100 150 200 250 300 350 400 450

Liquefiable layer thickness, H_L (m)

Crust thickness, D_L (m)

Presence of multiple liquefiable layers

Presence of impermeable silt cap

Structure plan dimensions ratio, L/B

Relative density, D_r (%)

Bearing pressure, q (kPa)

Foundation embedment depth, D_f (m)

Structure mass, M (kg)

Foundation contact area, A (m2)

Structure height, H (m)

Bedrock shear wave velocity, V_S (m/s)

Initial site period, T_s_o (s)

Structure period, T_s_t (s)

Settlement (mm)

Tornado diagram used to evaluate sensitivity of settlement

Top susceptible layer thickness, H1 (m)

Depth to top susceptible layer, D1 (m)

Presence of multiple susceptible layers

Presence of low permeability cap

Foundation bearing pressure, q (kPa)

Foundation embedment depth, Df (m)

Structure mass, Mst (kg)

Foundation width, B (m)

Effective structure height, heff (m)

Initial site period, Tso (s)

Bedrock shear wave velocity, VS (m/s)

Structure period, Tst (s)

Relative density, Dr (%)

Foundation length-to-width ratio, L/B

Ka

rim

i e

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SD

EE

3






Developing probabilistic models for settlement

Probabilistic model first developed based on numerical database

Bu

llock, D

ash

ti e

t a

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01

8 –

Ge

ote

ch

niq

ue

Base model regressed using numerical results and shape of sensitivity analyses

Bu

llock e

t a

l. 2

01

8 –

Ge

ote

ch

niq

ue

The functional form implicitly reduces the influence of deep & dense layers

• Model not sensitive to definition of

“liquefiable”

• Depends on susceptibility criteria

(e.g., Bray&Sancio 2004)

• Influence of dense layers is reduced

• Influence of deep layers is reduced

Model captures trends in the numerical data well

Model developed to predict probability of “insignificant” settlement

• Threshold set at 1 centimeter of settlement

• Model has AUC of the receiver operating curve = 0.93

1.00 is perfect; 0.50 is random guessing

Validation of Probabilistic Model with Case Histories

Base model performs poorly on case histories – empirical adjustment needed

• Continuum model cannot capture certain deformation modes:

-Sedimentation

-Ejecta

• Real world ground motion is multidirectional

• Site conditions can be highly heterogeneous (stronger effect on tilt)

• A latent-variable correction (through cross validation) added to the model

Model residuals are unbiased on all input parameters after adjustment

Log-normal distribution characterizes total model uncertainty

• Log-normal most

appropriate for modeling

(total) uncertainty

• Using lognormal

distribution predicts larger

settlements at tails but

smaller around median

Model extrapolates well to structures with other types of shallow foundation

• Same distribution fits all

residuals

• No clear bias in residuals

• Not enough data to rigorously

validate

• Average settlement may be

relatively insensitive to shallow

foundation type

• Note: this does not apply to

foundation tilt

Observed Settlement, S: mm

Pre

dic

ted

Set

tlem

ent,

Sad

j: m

m

Semi-empirical model for foundation permanent tilt developed similarly

• Relation between input parameters and tilt less apparent

• A machine learning technique called “the lasso” used to identify the functional form

Bu

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Adjustment for tilt based on centrifuge data & case histories

• Centrifuge results include: inertial effects

and possible ejecta

• Case histories include: inertial effects,

heterogeneity, ejecta, and complex

shaking

Bu

llock e

t a

l. 2

01

8b

–A

SC

E J

GG

E

ln 𝜃𝑟𝑠𝑒

= ln 𝜃𝑟 𝑛𝑢𝑚 + 𝛾0 + 𝛾1 ln ℎ𝑒𝑓𝑓 + 𝜅0 + 𝜅1𝐹𝐿𝑃𝐶 + 𝜅2𝐷𝑆,𝑇+ 𝜅3max 𝐻𝑆 1.0𝐵 + 𝜅4 Τ𝑁𝑁𝑆,1.0𝐵 𝑁𝑆,1.0𝐵 + 𝜀𝑟𝑠𝑒

Spreadsheets prepared for estimation of IM, foundation settlement, tilt, and uncertainty

Building construction type Reinforced concrete selection required

Number of stories 3

Building height, h (m) leave blank if using number of stories as proxy

Building or foundation width, B (m) 9

Building or foundation length, L (m) 15

Building mass, Mst (kg) 628377.75

Foundation bearing pressure, q (kPa) 45.66

Building height, h (m) 10.23 all other parameters must be known or estimated

INPUTS

PARAMETERS FOR MODEL


Magnitude (M W) 8.1

Distance to rupture (R rup , km) 80

Focal depth (H , km) 40

Tectonic environment Subduction

Rupture mechanism Interface

Foundation width, B (m) 9

Foundation length, L (m) 15

Foundation embedment depth, Df (m) 2

Foundation bearing pressure, q (kPa) 45.6621165

Building height, h (m) 10.23

Building mass, Mst (kg) 628377.75

INPUTS

Earthquake Scenario Details

Building and Foundation Details


Low permeability cap present above top susceptible layer? Yes

Non-susceptible crust thickness 3

Maximum continuous thickness of susceptible material in top B 6

Number of susceptible layers in top B 1

Number of non-susceptible layers in top B 2

Soil profile testing method SPT

N1,60 of layer 1 12

Thickness of layer 1, HS,1 (m) 3

Depth from bottom of foundation to center of layer 1, DS,1 (m) 2.5

N1,60 of layer 2 9



N1,60 of layer 3 19



N1,60 of layer 4 0


Depth from bottom of foundation to center of layer 4, DS,4 (m) 0

Soil Profile Details

Susceptible Layer Geometry and Density


Bullock, Dashti et al. 2019 – ASCE JGGE


Median value of cumulative absolute velocity, CAV (cm/s) 580.53

16th percentile of settlement, S (mm) 65.63

Median value of settlement, S (mm) 128.86


Lognormal standard deviation for settlement, σln 0.67

OUTPUTS (SETTLEMENT)

Median value of pk. Incr. grnd. velocity, Vgi (cm/s) 15.45

16th percentile of residual tilt, θr (deg) 0.33

Median value of residual tilt, θr (deg) 0.57


Lognormal standard deviation for residual tilt, σln 0.55

OUTPUTS (RESIDUAL TILT - SEMIEMPIRICAL MODEL)


Bullock, Dashti et al. 2019 – ASCE JGGE


Median value of cumulative absolute velocity, CAV (cm/s) 580.53


Median value of settlement, S (mm) 128.86


Lognormal standard deviation for settlement, σln 0.67

OUTPUTS (SETTLEMENT)

Median value of pk. Incr. grnd. velocity, Vgi (cm/s) 15.45


Median value of residual tilt, θr (deg) 0.57


Lognormal standard deviation for residual tilt, σln 0.55

OUTPUTS (RESIDUAL TILT - SEMIEMPIRICAL MODEL)

3






Conclusions: the new models are significant improvements to the status quo

• First probabilistic procedures accounting for the presence and 3D properties

of the structure, foundation, SSI, layering, and all mechanisms of

deformation

• 421 models, 150 ground motions → 63,150 3D SSI analyses

• Validated with centrifuge and adjusted with case histories to include all

mechanisms of deformation

• Not dependent on liquefaction triggering analyses, only susceptibility

• Fully probabilistic to fit within a PBD framework, for all tectonic

environments

Connecting the models to liquefaction mapping will enable rapid regional risk estimation

• Developing models for ru and time histories of settlement and tilt

• Connecting the models to proxies that can be mapped with various levels of information, such as LPI or LSN or P[Liq]

• Practitioners can then generate rapid estimates of the liquefaction risk at the community- or portfolio-level

77

Ma

ure

r e

t a

l. 2

01

4

Building scale

Regional scale

Hayward Baker (2004)

CU CIEST Lab 2016

Paramasivam et al. (2018, 2019);

Olarte et al. (2017; 2018a,b);

Ramirez et al. (2018); Kirkwood &

Dashti (2018a,b,2019)

Performance-based design of mitigation techniques to improve performance of system holistically

Bray et al. (2004)Kirkwood and Dashti (2018a,b; 2019)

Performance-based design of mitigation techniques to improve performance of system holistically

Related (recent) publications

Bullock, Dashti, Liel, and Porter (2019). Intensity Measure Evaluation for Predicting Consequences of Liquefaction for Shallow-Founded Structures. Earthquake Spectra.

Bullock, Karimi, Dashti, Porter, Liel, & Franke (2019). Probabilistic Models for the Residual and Peak Transient Tilt of Mat-Founded Structures on Liquefiable Soils. ASCE JGGE.

Bullock, Karimi, Dashti, Porter, Liel, & Franke (2018). A Physics-Informed Semi-Empirical Probabilistic Model for the Settlement of Shallow-Founded Structures on Liquefiable Ground. Géotechnique.

Karimi, Dashti, Bullock, Porter, & Liel (2018). Key Predictors of Structure Settlement on Liquefiable Ground: A Numerical Parametric Study. Soil Dynamics and Earthquake Engineering.

Bullock, Dashti, Liel, Porter, Karimi, & Bradley (2017). Ground Motion Prediction Equations for Arias Intensity, Cumulative Absolute Velocity, and Peak Incremental Ground Velocity for Rock Sites in Different Tectonic Environments. Bulletin of the Seismological Society of America.

Karimi & Dashti, (2017). Ground Motion Intensity Measures to Evaluate II: the Performance of Shallow-Founded Structures on Liquefiable Ground. Earthquake Spectra.

Karimi & Dashti (2016). Seismic Performance of Shallow-Founded Structures on Liquefiable Ground: Validation of Numerical Simulations Using Centrifuge Experiments. ASCE JGGE.

Karimi & Dashti (2015). Numerical and Centrifuge Modeling of Seismic Soil-Foundation-Structure Interaction on Liquefiable Ground. ASCE JGGE.

Thank you…

Documents

Probabilistic Models for Structure’s Average and