An Evaluation of Free Field Liquefaction Analysis Using OpenSees

1
An Evaluation of Free Field Liquefaction Analysis
Using OpenSees

• Lindsay Baynes
• Dept. of Civil and Environmental Engineering

2
Overview

• Constitutive model for liquefaction
• OpenSees framework and PDMY model
• PDMY parameter calibration using single element
  of undrained soil
• Free field analysis
• Evaluation of EDP uncertainty

3
Liquefaction

• Definition loss of strength due to the build up
  of excess pore pressures that occurs when loose,
  saturated sands with a tendency to contract upon
  deformation are subjected to dynamic excitation
• Susceptible soils loosely-deposited, saturated,
  shallow, uniform sands
• 2 types
• Flow liquefaction
• Cyclic mobility

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Cyclic Mobility
Cyclic mobility
Loading Begins
Increasing pore pressures, decreasing effective
stresses
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Constitutive Model for Liquefiable Soil

• Components
• Elastic linear-elastic and isotropic until
  yielding
• Yield criterion transition point between
  elastic and elasto-plastic behavior
• Post-yield behavior
• Flow rule rate of change
• of plastic strain beyond elastic limit
• Hardening rule translation and
• expansion of yield surface

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Constitutive Model Idealization of Liquefaction

• Post-yield behavior characterized by 4 phases
• Contraction within the PT surface (0-1)
• Perfectly-plastic shear strain on the PT surface
  (1-2) only at low effective confining stress
• Dilation during loading above the PT surface
  (2-3)
• Contraction during unloading above the PT surface
  (3-4)

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OpenSees Framework

• Multi-purpose finite element platform

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PDMY Model

• PressureDependentMultiYield (PDMY) material used
  to model pressure-sensitive materials in OpenSees
• Coupled with FluidSolidPourous material to
  simulate saturated, undrained conditions
• Requires user-specification of 14 parameters
• 11 related to soil relative density
• Geotechnical parameters r, Gmax, Bmax, f, fPT
• Constitutive parameters c, d1, d2, l1, l2, l3
• 3 model constants

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Geotechnical PDMY Parameters
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Constitutive PDMY Parameters
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PDMY Model (cont.)

• Contraction parameter, c rate of shear-induced
  volume decrease (drained) or pore pressure
  buildup (undrained)
• Dilation parameters, d1, d2 rate of shear
  induced volume increase (drained) or pore
  pressure decrease (undrained)
• Liquefaction parameters, l1, l2, l3 effective
  confining pressure below which perfectly plastic
  behavior can occur, maximum amount of perfectly
  plastic shear strain that can be accumulated
  during each phase, maximum amount of biased
  perfectly plastic shear strain.

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PDMY Parameter Calibration

• Single element of undrained soil subjected to
  harmonic load
• Cyclic stress ratio and relative density varied
• Data compared to existing field and experimental
  data

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Single Element Analysis (0.24 CSR and 65 Dr)
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Single Element Analysis (0.24 CSR and 85 Dr)
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Relationship between CSR and NL

• Existing relationship based on
• Field relationship between density and CSRL
• Laboratory relationship between magnitude and NL

NL
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Relationship between CSR and NL (cont.)
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Relationship between ru and N/NL

• Existing relationship based on results of cyclic
  tests

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Relationship between ru and N/NL (cont.)
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Relationship between gmax and Dr

• Existing relationship based on shaking table tests

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Overview

• Constitutive model for liquefaction
• OpenSees framework and PDMY model
• PDMY parameter calibration using single element
  of undrained soil
• Free field analysis
• Evaluation of EDP uncertainty

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Free Field Analysis

• Site response analysis overview
• Testing scenario
• Undrained analysis and comparison to Cyclic
  Stress Method and WAVE results

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Site Response Analysis

• Energy waves emitted from rupture along fault
• Altered by rock and soil
• Recorded motions used in site response analysis
  must be convolved or deconvolved to account for
  alteration

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Input Motion

• Yerba Buena rock outcrop motion scaled to 0.1 g
• Applied to base of soil profile (not deconvolved)

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Soil Profile

• Free field idealized by 1-D soil profile
• 10 m loose sand ((N1)60 10, 20, 30)
• 40 m dense till ((N1)60 40)
• GWT at 2 m (undrained)
• OpenSees model
• 220 elements, fixed base nodes
• PDMY Material

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PDMY Parameter Values
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Undrained Comparison of OpenSees and Cyclic
Stress Method Results

• Cyclic Stress method
• Uses relationships based on lab and field data to
  predict factor of safety against liquefaction
• Compares estimated cyclic stress required to
  cause liquefaction to estimated cyclic stress
  induced by earthquake shaking

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Cyclic Stress Approach

• Cyclic stress required for liquefaction
• Use field data to estimate CSRL
• Apply MSF to adjust for magnitude
• Multiply by effective stress to compute tcyc,L

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Cyclic Stress Approach (cont.)

• Cyclic stress induced by earthquake
• Estimate based on peak surface acceleration,
  total vertical stress, and stress reduction
  factor
• tcyc 0.65 amax svo rd
• Factor of Safety
• Ratio of tcyc,L to tcyc
• Estimate excess pore
• pressure ratio over profile

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Comparison of Results ((N1)60 10)
Cyclic Stress Approach
OpenSees
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Comparison of Results ((N1)60 20)
Cyclic Stress Approach
OpenSees
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Comparison of Results ((N1)60 30)
Cyclic Stress Approach
OpenSees
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Undrained Comparison of OpenSees and WAVE Results

• WAVE
• Non-linear program
• Second order accurate finite difference method
• Bedrock vs 7500 m/s
• Motion not deconvolved

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Comparison of Results
WAVE
OpenSees
(N1)60
10
20
30
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WAVE
OpenSees
(N1)60
10
20
30
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Overview

• Constitutive model for liquefaction
• OpenSees framework and PDMY model
• PDMY parameter calibration using single element
  of undrained soil
• Free field analysis
• Evaluation of EDP uncertainty

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Evaluation of EDP Uncertainty

• Contribution of input (motion geotechnical)
  uncertainty to uncertainty in structural EDPs
• Characterize input uncertainty
• Evaluate EDP uncertainty using
• Tornado diagrams
• FOSM analysis
• Monte Carlo analysis

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Sources of Uncertainty

• Prediction of loading
• Input ground motion usually accounted for
  through DSHA or PSHA
• Prediction of capacity
• Soil characteristics focus on random soil
  variability (aleatory uncertainty)
• PDMY model

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Input Ground Motions

• Suites of 20 input ground motions for 2 hazard
  levels 72-yr and 475-yr return periods
• Rock outcrop motions
• Spectral acceleration scaled to common value at
  T 0.5 s

72-yr
475-yr
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PDMY Parameter Uncertainty
Range of values for varying relative density
and moisture condition
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Engineering Demand Parameters

• Analysis of 2 structural EDPs
• Dcyc normalized displacement range
  information about response to peak cycle
• NHE normalized hysteretic energy information
  about sustainability to several loading cycles
• SDOF structure defined by
• Natural period 0.5 s
• Height 244 cm
• Post-yield stiffness ratio 0.05
• Response modification factor, R 2, 5, 8

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General Procedure
Measure EDPs

• Site response analysis using OpenSees
• Same profile, (N1)60 10
• Input motion applied at base of profile
• Acceleration recorded at surface
• Structural analysis using SNAP
• Surface acceleration applied at base
• EDPs calculated

Surface acceleration
OpenSees site response
Input acceleration
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Tornado Diagram Analysis

• Identifies largest contributors to EDP
  uncertainty
• Procedure
• Base-case analysis performed for each input
  motion
• Analysis performed for each input motion with
  parameter Xj set to 16th percentile value (mean
  SD)
• Analysis performed for each input motion with
  parameter Xj set to 84th percentile value (mean
  SD)
• Arrange from highest to lowest swing
• No differentiation of parameters from layer to
  layer

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Tornado Diagrams (72-yr return period, R 5)
Dcyc
NHE
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Tornado Diagrams (475-yr return period, R 5)
Dcyc
NHE
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FOSM Analysis

• Determine contribution to EDP variance of each
  input parameter
• First order Taylor series approximation of
  input-output relationship used to arrive at
  expressions for output mean and variance
• Mean, standard deviation, correlation
  coefficients determined previously
• Partial derivatives determined by varying each
  input parameter
• Influence of parameters differentiated by layer
  (effect of dry layer 1 discounted)

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Relative Variance Contribution of Input
Parameters (Dcyc, 72-yr return period)
Layer 2
Layer 3
R 2
R 5
R 8
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Relative Variance Contribution of Input
Parameters (NHE, 72-yr return period)
Layer 2
Layer 3
R 2
R 5
R 8
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Relative Variance Contribution of Input
Parameters (Dcyc, 475-yr return period)
Layer 2
Layer 2
Layer 2
Layer 3
Layer 3
Layer 3
R 2
R 5
R 8
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Relative Variance Contribution of Input
Parameters (NHE, 475-yr return period)
Layer 2
Layer 3
R 2
R 5
R 8
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Summary of FOSM Results
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Monte Carlo Analysis

• Probability distribution of EDPs for each input
  motion
• Requires model execution for multiple cases of
  randomly-generated input variables
• Based on input parameter uncertainty and
  correlations
• More consideration of spatial variation
• More efficient LHS method used for generation of
  random parameter values

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Probability Distribution (Dcyc, R 5, 475-yr
return period)
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Probability Distribution (NHE, R 5, 475-yr
return period)
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Summary of Monte Carlo Results
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Summary

• Constitutive model for liquefaction
• OpenSees framework and PDMY model
• PDMY parameter calibration using single element
  of undrained soil
• Free field analysis
• Evaluation of EDP uncertainty

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Conclusions

• Program input can be simplified by relating PDMY
  parameters to Dr
• OpenSees effectively captures free field
  liquefaction behavior
• Uncertainty in input ground motion has a dominant
  effect on EDP uncertainty
• Contributions to EDP uncertainty from PDMY
  uncertainty vary with hazard level and structural
  characteristics
• OpenSees is a powerful tool that requires further
  study to improve characterization of contractive
  behavior