1 Parallel Computing for Seismic Geotechnical Applications Jinchi Lu 1 , Ahmed Elgamal 2* , Kincho H. Law 3 , and Zhaohui Yang 1 1 University of California, San Diego, Department of Structural Engineering, La Jolla, CA 92093-0085 2* Corresponding author, University of California, San Diego, Department of Structural Engineering, SERF Building Rm 345, Mail Code 0085, La Jolla, CA 92093-0085; PH (858)822-1075; FAX (858)534-1310; email: elgamal@ucsd.edu 3 Stanford University, Department of Civil and Environmental Engineering, Stanford, CA 94305-4020 Abstract Parallel computing is gradually becoming a main stream tool in geotechnical simulations. The need for high fidelity and for modeling of fairly large 3-dimensional (3D) spatial configurations is motivating this direction of research. A new program ParCYCLIC for seismic geotechnical applications has been developed. Salient characteristics of the employed parallel sparse solver will be presented. Using this code, simulations of seismically-induced liquefaction, lateral-spreading, and countermeasures will be presented and discussed. Introduction Large-scale finite element (FE) simulations of earthquake-induced liquefaction effects often require a lengthy execution time. Utilization of parallel computers, which combine the resources of multiple processing and memory units, can potentially reduce the execution time significantly and allow simulations of large and complex models that may not fit into a single processing unit. Parallel computing is gradually becoming a main stream tool in geotechnical simulations. Bielak et al (2000) modeled earthquake ground motion in large sedimentary basins using a 3D parallel linear finite element program with an explicit integration procedure. They noted that the implementation of an implicit time integration approach is challenging on distributed memory computers, requiring significant global information exchange (Bielak et al. 2000). Yang (2002) developed a parallel finite element algorithm, i.e. Plastic Domain Decomposition (PDD), and attempted to achieve dynamic load balancing by using an adaptive partitioning-repartitioning scheme. The research reported herein focuses on the development of a state-of-the-art nonlinear parallel finite element code (implicit time integration method employed) for earthquake ground response and liquefaction simulation. The parallel code, ParCYCLIC, is implemented based on a serial program CYCLIC, which is a nonlinear finite element program developed to analyze liquefaction-induced seismic response (Parra 1996; Yang and Elgamal 2002). Finite Element Formulation In CYCLIC and ParCYCLIC, the saturated soil system is modeled as a two-phase material. A simplified numerical formulation of this theory (Chan 1988), known as u-p formulation (in which displacement of the soil skeleton u, and pore pressure p, are the primary unknowns), was implemented in a 3D Finite Element program CYCLIC (Parra 1996; Yang 2000; Yang and Elgamal 2002). The u-p formulation is defined by (Chan 1988): 1) the equation of motion for the solid-fluid mixture, and 2) the equation of mass conservation for the fluid phase that incorporates equation of motion for the fluid phase and Darcy's law. These two governing equations are expressed in the following finite element matrix form (Chan 1988): 0 f Qp d  B U M s  T =  +  +  & & (1a) 0 f Hp p S U Q p T =  + + & & (1b) where M is the total mass matrix, U the displacement vector, B the strain-displacement matrix,   the effective stress tensor, Q the discrete gradient operator coupling the solid and fluid phases, p the pore pressure vector, S the compressibility matrix, and H the permeability matrix. The vectors s f and p f represent the effects of body forces and prescribed boundary conditions for the solid-fluid mixture and the fluid phase, respectively. Equations 1a and 1b