Seismic Soil-Structure Interaction Analysis of the Kealakaha Stream - PowerPoint PPT Presentation

Seismic Soil-Structure Interaction Analysis of the Kealakaha Stream Bridge on Parallel Computers Seung Ha Lee and Si-Hwan Park Department of Civil and Environmental Engineering University of Hawaii at Manoa Sponsor: Maui High Performance Computing Center The 2005 Joint ASME/ASCE/SES Conference on Mechanics and Materials Baton Rouge, Louisiana June 1, 2005 – p.1

Outline Background and motivation of the study Parallel soil-structure interaction analysis framework The Squall system Numerical example Concluding remarks – p.2

Kealakaha Stream Bridge: Project Location Project location: Mamalahoa Highway over the Kealakaha stream, Island of Hawaii – p.3

Kealakaha Stream Bridge: Project Outline Existing bridge (scheduled for replacement): Six-span concrete bridge crossing the Kealakaha Stream. Seismically inadequate. New bridge: Three-span prestressed concrete bridge. Increased roadway width. Designed to withstand the anticipated seismic activity: Island of Hawaii is in Zone 4, the highest zone of seismic activity (1997 Uniform Building Code). – p.4

Kealakaha Stream Bridge: Layout – p.5

On-going Projects and Motivation of the Study Seismic Instrumentation of the Kealakaha Stream Bridge (FHWA and HDOT) Focuses on instrumentation and monitoring to provide better understanding of the bridge response to ground shaking. Soil Investigation and Soil-Structure Interaction Modeling of the Kealakaha Bridge (HDOT) Resulting computational model is beyond the capability of a single-CPU machine. Seismic Soil-Structure Interaction Analysis of the Kealakaha Stream Bridge on Parallel Computers (MHPCC) To develop a parallel computational framework for large-scale seismic soil-structure interaction analysis. To be used on commonly available clusters. – p.6

Ingredients of the Computational Framework Linearly elastic. Plane strain solid elements (soil) and frame elements (bridge): Not an exact model as far as interaction is concerned. Stepping stone for a 3-D model. Central difference method for time marching. Can avoid solving linear equations. Seismic excitation by effective seismic force (Bielak and Christiano 1984). Lysmer-Kuhlemeyer (1969) viscous absorbing boundary. – p.7

Explicit Time Marching Equations of motion: M ¨ u + C ˙ u + Ku = F Updating the solution (Bao et al. 1998): � 1 � � � 1 2 1 ∆ t 2 M + 2∆ t C d u n +1 = F n − K − ∆ t 2 M + 2∆ t C o u n � 1 � 1 ∆ t 2 M − 2∆ t C u n − 1 − C d : Diagonal part of C C o : Off-diagonal part of C C = C d + C o Matrix-vector multiplication is the most intensive part of the computation. – p.8

Structure of System Matrices Node k Two DOF’s per node Only 18 DOF’s are associated with the equilibrium equation for a DOF at Node k . → There are only 18 non-zero entries in each row of the system matrices M , C and K . – p.9

Parallel Sparse Matrix-Vector Multiplication Au = b : Process 1 : A 1 b 1 = A 1 u Process 2 : A 2 = A 2 u b 2 = u Process 3 : A 3 b 3 = A 3 u . . . . . . Process n : A n b n = A n u Parallel computational procedure (MPI-based): Broadcast u . Process i contains only the non-zero entries of A i (Compressed Sparse Row format) Compute A i u ≡ b i on each slave process. Send the result to the master process. – p.10

Squall System 2-node 32-processor Power3 (375 MHz) IBM SP system. Each node has 8 GB of shared memory. – p.11

Computational Model and Finite Element Mesh 100 m 100 m 55 m 110 m 55 m 100 m 100 m Layer 1 30 m ABC Layer 2 ABC 30 m Total field Scattered Scattered field field Layer 3 40 m Bedrock Layer 1 Layer 2 Layer 3 ρ (kg/m 3 ) 1500 2000 2500 c p (m/s) 1202 2082 3225 c s (m/s) 577 1000 1549 λ min (m) 23.1 40.0 62.0 Element size ( λ min / 8) 2.9 5.0 7.7 5376 solid / 56 frame elements ∆ t cr ≈ 2 × 10 − 5 s = ∆ t used. – p.12

Ground Acceleration Horizontal Ground Acceleration (g) 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 0 5 10 15 20 25 30 Time (s) April 2, 2000, Pahala Recording Station, Island of Hawaii M b = 4 . 9 T = 30 s and ∆ t = 2 × 10 − 5 s 1.5 million time steps. Takes about 4 hours and 30 minutes (16 processors). – p.13

Modeling the Unbounded Soil Horizontal displacement at the center of the bridge: 0.003 Horizontal Displacement (m) With ABC Without ABC 0.002 0.001 0 -0.001 -0.002 -0.003 0 5 10 15 20 25 30 Time (s) Including the viscous absorbing boundary condition does not lead to significant differences. Large buffer regions (with damping in the soil) are effective in modeling the unbounded soil. – p.14

Displacement Amplitude Contour U: 0 0.0006 0.0012 0.0018 0.0024 0.003 t = 6 . 74 s: t = 6 . 77 s: t = 6 . 81 s: t = 6 . 84 s: – p.15

Concluding Remarks Have established a computational framework for large-scale soil-structure interaction analysis. Future work: More efficient parallel computations 3D model Nonlinear constitutive laws for the bridge and soil More efficient and reliable modeling of unbounded domains – p.16