probabilistic models for structure’s average and
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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
The existing predictive models for settlement & tilt are inadequate
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
The existing predictive models for settlement & tilt are inadequate
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
01
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
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
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
ti e
t a
l. 2
01
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
l. 2
01
0a
,b –
AS
CE
JG
GE
• 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
sh
ti, B
ray e
t a
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0a
,b –
AS
CE
JG
GE
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
t a
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8 –
SD
EE
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
t a
l. 2
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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
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
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
l. 2
01
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
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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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SD
EE
Set
tlem
ent,
S (
mm
)
• Soil relative density an important parameter
Parametric study results used for sensitivity analysis
• Soil relative density an important parameter
• Soil thickness was influential up to 8m.
Parametric study results used for sensitivity analysis
• Soil relative density an important parameter
• Soil thickness was influential up to 8m.
• Depth to top susceptible layer below foundation very influential
Parametric study results used for sensitivity analysis
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
• Foundation contact pressure influential up to a threshold
Parametric study results used for sensitivity analysis
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
• Foundation contact pressure and area influential up to a threshold
Ka
rim
i e
t a
l. 2
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8 –
SD
EE
Parametric study results used for sensitivity analysis
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
t a
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SD
EE
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
Developing probabilistic models for settlement
Probabilistic model first developed based on numerical database
Bu
llock, D
ash
ti e
t a
l. 2
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
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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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CE
JG
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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
Spreadsheets prepared for estimation of IM, foundation settlement, tilt, and uncertainty
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
Spreadsheets prepared for estimation of IM, foundation settlement, tilt, and uncertainty
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
Thickness of layer 2, HS,2 (m) 3
Depth from bottom of foundation to center of layer 2, DS,2 (m) 5.5
N1,60 of layer 3 19
Thickness of layer 3, HS,3 (m) 5
Depth from bottom of foundation to center of layer 3, DS,3 (m) 12.5
N1,60 of layer 4 0
Thickness of layer 4, HS,4 (m) 0
Depth from bottom of foundation to center of layer 4, DS,4 (m) 0
Soil Profile Details
Susceptible Layer Geometry and Density
Spreadsheets prepared for estimation of IM, foundation settlement, tilt, and uncertainty
Bullock, Dashti et al. 2019 – ASCE JGGE
Bullock, Dashti et al. 2018 – Geotechnique
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
84th percentile of settlement, S (mm) 252.98
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
84th percentile of residual tilt, θr (deg) 0.98
Lognormal standard deviation for residual tilt, σln 0.55
OUTPUTS (RESIDUAL TILT - SEMIEMPIRICAL MODEL)
Spreadsheets prepared for estimation of IM, foundation settlement, tilt, and uncertainty
Bullock, Dashti et al. 2019 – ASCE JGGE
Bullock, Dashti et al. 2018 – Geotechnique
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
84th percentile of settlement, S (mm) 252.98
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
84th percentile of residual tilt, θr (deg) 0.98
Lognormal standard deviation for residual tilt, σln 0.55
OUTPUTS (RESIDUAL TILT - SEMIEMPIRICAL MODEL)
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
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
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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…
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