1. Liquefaction Analysis For a Single Piled Foundation By Dr. Lu Chihwei Moh and Associates, Inc. Date: 11/3/2003

2. Back ground During earthquake Structural damage Pile foundationUpper structure Large bending moments Inertia momentKinematic moment Liquefaction Pile U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

3. U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

4. U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

5. U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

6. Guidelines for Foundation Design in Japan (2001) Before Liquefaction ー Upper Structure After Liquefaction ー Upper Structure and Ground Deformation Flow Failure ー Ground Deformation due to Lateral Flow U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

7. Damage to piles Damage on upper structure Earthquake Progressive damage Waves de-amplified Occurrence of liquefaction Displacement Liquefied layer Unliquefied layer Lateral flow of ground Large displacement Before Liquefaction Illustration of the interaction between soils and a pile foundation U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

8. Key points Nonlinear behavior of soils (A cyclic elasto-plastic model for sand and a cyclic elasto-viscoplastic model for clay) Nonlinear behavior of piles (Axial Force Dependent Model) 3-Dimensional liquefaction analysis A series of calculations on a single-pile foundation installed in a 2-layer ground (sand layer+clay layer) U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

9. M-  relation (Conventional way) Axial force on M-  relation has to be neglected. U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

10. Axial force (kN) The pile used in the simulation M-  relation of the pile Dead load of the pile head in single pile foundation is 1250KN and in the group pile foundation is 1753 KN =68131 kN Buckling k U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

11. Sand layer Clay layer Dense, Loose & Medium dense sand, Reclaimed soil Two-Layer ground A cyclic elasto-plastic model (Oka, 1999) based on a nonlinear kinematic hardening rule A cyclic elasto-viscoplastic model (Oka, 1992) based on a nonlinear kinematic hardening rule Clay layer Sand layer U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

12. Constitutive law of sands based on finite deformation theory Cyclic Elasto-plastic constitutive model by Oka et al.(1992, 1999) Ⅰ Non-linear kinematic hardening rule Ⅱ Non-associated flow rule Ⅲ Overconsolidation boundary surface Ⅳ Generalized flow rule Ⅴ Consideration of strain dependency of shear stiffness U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

13. The soils used in the simulation U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

14. Liquefaction strength curves of different sandy soils Dr=50% Toyoura Sand: N=20, Stress Ratio=0.13 (Oka 2001) U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

15. The Governing Equation Based on Biot’s soil-water coupling theory u-p formulation Momentum equation Continuity equation Constitutive equation Definition of effective stress : Density of total phase : Nominal stress tensor : Acceleration vector : Body force vector : Density of fluid phase : Unit weight of water : Coefficient of permeability : Pore water pressure U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

16. Discretization of Governing Equations Space discretization Time discretization u-p formulation FEM Newmark’s β method U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

17. U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

18. Shaking direction x y z o Input wave U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

19. Effective Stress Decreasing Ratio (a) At the center of sand soil(b) At the center of clay layer Liquefaction takes place completely Sand Clay Excess Pore Water Pressure Ratio Effective Stress Decreasing Ratio Excess Pore Water Pressure Ratio U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

20. Acceleration responses ( a) Top of the pier ( b) Ground surface Loose sand Medium sand and reclaimed soil Sand Clay Top of pier Surface U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

21. Displacement responses ( a) Top of the pier ( b) Ground surface Loose sand Medium sand and reclaimed soil Sand Clay Top of pier Surface U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

22. (a) At pile heads ( b) Lower segment (b7) Bending moments Loose sand Medium sand and reclaimed soil Sand Clay Pile head b7 U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

23. Distributions of sectional forces at the time when the maximum bending moment occurred at the bottom of pier Bending moment (kN*m) Shear force (kN) U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

24. Distributions of sectional forces of the end of seismic event (t=10 sec) Shear force (kN) Bending moment (kN*m) U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

25. Loose sand Medium dense sand Distributions of sectional forces a: At the time when maximum bending moment occurs at the bottom of the pier b:At the largest displacement occurred at the ground surface c:At the largest moment occurred at the low segment d: At the end of simulation Bending moment (kN*m) Shear force (kN) U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

26. Reclaimed soils case Dense sand case Distributions of sectional forces a: At the time when maximum bending moment occurs at the bottom of the pier b:At the largest displacement occurred at the ground surface c:At the largest moment occurred at the low segment d:At the end of simulation e:At the time maximum acceleration occurred at the ground surface Bending moment (kN*m) Shear force (kN) U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

27. Conclusions U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 Lu Chihwei

28. U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003 In engineering practice: 1.How to feed back soil springs for structural design? 2.The ground line for design of superstructure shall be lowered when ground liquefies. 3.The damping of waves on the ground surface due to liquefaction 4.Sectional force at the interface --- Relative stiffness between 2 layers--- How to apply them? 5.The damage due to lateral spread Lu Chihwei

29. Thank you very much for your attention Dr. Lu Chihwei Moh and Associates, Inc. U.S.-Taiwan Workshop on Soil Liquefaction, 11/3/2003