Large-scale 3-D Simulations of Spontaneous Rupture and Wave Propagation in Complex, Nonlinear Media

Roten, D.1, Olsen, K.B.2, Day, S.M.2, Dalguer, L.A.1 and Fäh, D.1

1 Swiss Seismological Service / ETH Zürich2 San Diego State University

Annual Meeting of the Seismological Society of America17-19 April, Salt Lake City, UT

Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT

Introduction

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• Advances in computer codes and increases in computational resources enable numerical prediction of ground motions at increasingly higher frequencies, e.g.:- M8 up to 2 Hz (Cui et al., 2010)- Chino Hills EQ up to 5 Hz

• Nonlinear behavior of soft soils should be taken into account when predicting ground motions at frequencies above ~1 Hz

• Nonlinear material behavior may also occur in the damage zone around the fault (on- and off-fault plasticity; e.g. Andrews (2005), Ma (2008).

3Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT

Implementation of damage rheology in AWP-ODC

Non-associative Drucker-Prager plasticity with yielding in shear (based on guidelines from SCEC/USGS Spontaneous Rupture Code Verification Project):

4Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT

Implementation of damage rheology in AWP-ODC

Return map algorithm:

Time-dependent relaxation (Andrews, 2005):

5Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT

• Staggering of grid requires interpolation of missing elements in stress tensor and initial stresses from adjacent nodes

• Optimization that reduces number of interpolations results in significantly reduced computational cost

Material model CPU time per iteration Normalized CPU time

Elastic 0.18 s 100%

Elastoplastic 0.68 s 378%

Elastoplastic optimized 0.29 s 161%

Computational aspects

6Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT

Verification against SCEC/USGS TPV13

• Spontaneous rupture on a planar, dipping fault (approximated by vertical fault in AWP-ODC)

c = 5 Mpa

tan(φ) = 0.85

Tv = 0 s

7Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT

Convergence test (vertical strike-slip fault)

8Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT

ShakeOut Earthquake Scenario

• Based on kinematic source description (Graves et al., 2008)• visco-elastic medium

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ShakeOut Earthquake Scenario with Plasticity

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Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT

QuickTime™ and aMotion JPEG OpenDML decompressor

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Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT 11

ShakeOut Earthquake Scenario with Plasticity

Visco-elasto-plasticVisco-elastic

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Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT

ShakeOut Earthquake Scenario with PlasticityFinal Principal Plastic Strain η at surface

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Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT

ShakeOut Earthquake Scenario with PlasticityFinal Principal Plastic Strain η at z = 600 m

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Annual Meeting of the Seismological Society of America, April 17-19 2013, Salt Lake City, UT

Conclusions

• We have implemented damage rheology based on the Drucker-Prager yield condition into the highly scalable 3D finite difference code AWP-ODC

• The method has been validated against four finite element codes in the framework of the SCEC/USGS Spontaneous Rupture Code Verification Project

• Computational cost of modeling plasticity amounts to an additional ~60% of the CPU time required for an elastic simulation

• We simulate the ShakeOut-K earthquake scenario for a visco-elasto-plastic material, assuming that cohesions range from ~50 kPa in low-velocity sediments near the surface to several MPa at depth

• Our results suggest that long-period (< 2 s) ground motion in the Los Angles area, amplified by a wave guide of interconnected sedimentary basins, could be significantly reduced as compared to visco-elastic solutions

• Improved calibration of additional parameters (cohesion C and friction angle ϕ is required to reliably predict off-fault plasticity and nonlinear behavior of near-surface deposits