地盤シミュレーションの高度化研究. 国立研究開発法人防災科学技術研究所 兵庫耐震工学研究センター Pal Mahendra Kumar

Transcription

1 地盤シミュレーションの高度化研究 国立研究開発法人防災科学技術研究所 兵庫耐震工学研究センター Pal Mahendra Kumar

2 目次 1. Introduction 2. Problem statement 3. Results so far 3.1 Generation of analysis model Eigen value analysis Elastic analysis 3.2 Elasto-plastic analysis Parameter identification Discussion of simulation result 3.3 Incorporation of soil container mass in analysis model Modeling of soil-container Discussion of simulation results 4. Summary and future plan 2

3 はじめに Damage to under-ground structures during strong earthquake Pictures of damage Schematic diagram Damage to Daikai subway station during 1995 Great Hanshin Earthquake 1. Yamato et al, damage to Daikai subway station of Kobe rapid transit system and estimation of its reason during 1995Hyogoken-Nanbu earthquake, 土木学会論文集 No. 537/1-35, ,

4 E-Defense shake table test on soil underground specimen About experiment: To comprehend a better understanding the soil-structure interaction a large-scale shake table test [2] was conducted at E-Defense in February 2012 Experiment specimen Objectives Drawing Reproduction of experimental results Study of laminar soil container modeling CAD model Analysis model [2] Yohsuke K., Manabu N., Ikuo T. and Susumu Y.: Dynamic behaviour of underground structure in E-Defense shaking experiment, Soil Dyn. And Earth. Engrg., 82, pp ,

5 これまでの成果 3.1 Generation of analysis model 3.2 Elasto-plastic analysis 3.3 Incorporation of soil container mass in analysis model

6 Material properties Mechanical properties Density (g/cm 3 ) Young s modulus (MPa) Poison s ratio Aluminum Acrylic Plastic Dry Sand Dry Sand Cement mixed soil Cement mixed soil Cases considered for analysis Vertical shaft and cutand-cover tunnel Shield tunnel Lower layer of soil strata Upper layer of soil-strata Remark Case 1 Aluminum Alumunium Cement mixed soil 1 Dry Sand 1 Before experiment Case 2 Aluminum Acrylic Plastic Cement mixed soil 2 Dry Sand 2 After experiment 6

7 Analysis models Non-Conformity mesh model Conformity mesh model Structural component: Hexahedral element Soil : Tetrahedral element Interface: using Multi-Point Constraints (MPC) Structural component: Tetrahedral element Soil : Tetrahedral element Interface: adaptive mesh refinement 7

8 Analysis Model Scale of analysis Computational demand* Mesh model Elements Nodes Dofs Non-conformity 1,539, ,959 1,562,877 Mesh model Average Computation time for each time step (min.) Average number of CG iterations per time step Conformity 9,863,072 5,312,922 15,938,766 Non-conformity Conformity Eigen value analysis Model 1 st Mode 2 nd Mode 3 rd Mode 4 th Mode Free MPC on top MPC on top model Full MPC model Modeling laminar soil container Full MPC Experiment *The analysis is completed on Supercomputer of NIED by using flat MPI. Analysis is performed using 128 cores of SGI Altix4700 (CPU: dual core Intel Itanium processor 1.66 GHz). 8

9 Acceleration (cm/s 2 ) Displacement (mm) Acceleration (cm/s 2 ) Displacement (mm) Time history against 50% JR Takatori experiment experiment_filtered full MPC MPC on top free x-direction, neighbor of container wall Time (s) x-direction, center of the container Time (s) y-direction, neighbor of container wall Time (s) y-direction, center of the container Time (s) Acceleration response Displacement response Neighbor of ring Center of specimen MPC on top has relatively better agreement with experimental results in compare with other two models namely, Free model and Full MPC model. Therefore, MPC on Top model has been chosen as appropriate analysis model. 9

10 Exponential Contractancy (EC) model Normal yield surface F = MD ln p p 0 + MD η E Where, M is critical state parameter, D is dilatancy factor, η η E is parameter controlling the shape of yield surface. η = M η E 3Τ2 1Τp s 1Τp 0 s 0 Where, p and s are the hydrostatic pressure and deviatoric stress tensor, respectively. 0 q 正規降伏曲面 F 下負荷面 σ v R R F σ v Critical state line 上負荷面 σ ҧ v 1 R F p OCR = തσ v σ v R = σ v ഥσ v, R = σ v ഥσ v R R = σ v തσ v σ v തσ v = σ v σ v The sub-loading surface shall satisfy the following conditions Sub-loading surface is in similar shape as the normal yield surface. The current stress-point is always on sub-loading surface. Along with expansion of sub-loading surface, the normal yield surface also expands and thereby plastic deformation occurs. R = 1: the sub-loading surface coincides with normal yield surface [3] Ohno, S., Iizuka, A. and Ohta H..:Two categories of constitutive model derived from non-linear description of soil contractancy, J ofam (JSCE), 9, pp ,

11 deviatric stress (kpa) deviatric stress (kpa) Parameter identification deviatric stress (kpa) deviatric stress (kpa) 25 mm 100 mm Experiment specimen mm 800 Analysis model テストNo. ρ(g/cm 3 ) w(%) e S r (%) D r (%) B 値 テストNo. 試験装置 排水条件 拘束圧 002 スマート三軸試験 排水 157kPa 003 スマート三軸試験 排水 200kPa 004 従来の三軸試験 排水 50kPa 005 従来の三軸試験 排水 100kPa 006 従来の三軸試験 排水 200kPa Yield stress is fixed axial strain (%) axial strain (%) 実験値 m=5.0 a=0.3 m=5.0 a=5.0 m=5.0 a=50 m=1.0 a=0.3 m=1.0 a=5.0 m=1.0 a=50 m=0.3 a=0.3 m=0.3 a=5.0 m=0.3 a= Yield stress is fitting parameter axial strain (%) OCR=10 is fitting parameter 実験値 m=5.0 m= axial strain (%) 実験値 OCR=10, 拘束圧 200kPa m=5.0 a=0.3 m=5.0 a=5.0 m=5.0 a=50 スマート三軸試験装置 m=1.0 (Nakayama,E., a=0.3 Kobayashi,I, Iizuka,A. and Ohta,H.: Chapter 22 Development of a Portable Triaxial Testing Apparatus-Smart Triaxial, Geotechnical Predictions and Practice in Dealing m=1.0 with Geohazards, a=5.0 Chu, Jian, Wardani, Sri P.R., Iizuka, Atsushi (Eds.), Geotechnical, Geological and Earthquake Engineering Series,,Vol. 25, Springer,

12 Material parameters Elasto-plastic parameters Initial conditions S.No. Parameter name Value S.No. Parameter name Value 1 Dilatancy (D) Initial void ratio e Critical stress ratio (M) Swelling index κ Irreversible ratio Λ Coefficient of earth pressure K i Over-consolidation ratio (OCR) 10 4 Normal Yield stress σ v(kpa) Yield surface shape parameter η E Initial vertical stress σ v (kpa) 20 Evolution parameter S.No. Parameter name Value 1 Sub-loading surface parameter (m a ) Super-loading surface parameter (a = m a /D) Super-loading parameter (b, c) Similarity ratio for sub-loading (R 0 = 1/OCR) Similarity ratio for super-loading (R ) 0.9 OCR = തσ v σ v R = σ v, R = σ v ഥσ v ഥσ v R R = σ v തσ v σ v തσ v = σ v σ v Here, σ v, σ v and തσ v are the stress on subloading, normal yield surface, and super-loading surface. 12

13 Displacement time history on top surface Simulation Experiment Experiment_Filtered Neighbor of ring y Center of specimen x Neighbor of ring Displacement response Center of specimen 13

14 Displacement time history on top surface Simulation Experiment Experiment_Filtered Neighbor of ring y Center of specimen x Neighbor of ring Center of specimen Neighbor of ring Displacement response Center of specimen 14

15 Acceleration time history on top surface Simulation Experiment X-direction X-direction Neighbor of ring y Center of specimen x Y-direction Y-direction Neighbor of ring Acceleration response Center of specimen 15

16 Displacement time history Simulation Experiment mm mm Location 25.8 mm 20 mm Location of Disp. sensor 16

17 Rubber Slider Laminar rings S. No Ite ms Position Laminar soil container modeling Weigh t (ton) No of rings Weight (ton) Top Middle Upper Lower Total Bottom SA SB SC Water resistance 0.50 Slippage Total weight (1+2+3): 43.7 Constrained condition ( 拘束条件 ) r 1 t r 0 t R θ 0 t. r 1 0 r 0 0 = 0 θ 1 t θ 0 t = 0 Here, r i t, θ i t are position and rotation vector of i th node at t th time step, respectively. R(θ) is rotation tensor corresponding to rotation vector θ Rigid bar(s) y x Node(s) with lumped mass Graphical representation of laminar ring modeling S. No Position Weight/ring (ton) No of rings Weight (ton) Total (ton) 1 Top Middle Bottom Note: Additional weight of rubbers and slider is equally distributed to all laminar rings. The value of contribution is equal to (2.05/37)= Laminar rings with lumped mass at nodes 17

18 Displacement time history on top surface Experiment Simulation without mass of container Experiment with soil container mass Neighbor of ring y Center of specimen x Neighbor of ring Displacement response Center of specimen 18

19 Acceleration time history on top surface Experiment Simulation without mass of container Experiment with soil container mass X-direction X-direction Neighbor of ring y Center of specimen x Y-direction Y-direction Neighbor of ring Acceleration response Center of specimen 19

20 Displacement time history mm Simulation Experiment Simulation with container mass mm Location 25.8 mm 20 mm Location of Disp. sensor 20

21 Effective Stress path p q Graph e ln(p ) Graph Displacement on surface top Input wave in x-dir 21

22 今後の構想 22

23 Summary and future work Acceleration time history results have good agreement with experimental results Except the residual deformation, displacement time history results also show reasonable agreement with experimental results. Incorporation of mass of laminar soil container may be essential to reproduce the residual deformation. Effective stress-path and e-ln(p) graph suggest that Soil in the vicinity of soil-strata interface is failing Plasticity is inadequately modeled Re-simulation by lowering the value of OCR is planned for next work in the to-do list with an aim to increase the plasticity [23]

24 Thank you for listening 24