1. Nonlinear Site Effects: laboratory and field data observations and numerical modeling Luis Fabián Bonilla Institut de Radioprotection et de Sûreté Nucléaire, France

2. Presentation Outline Empirical evidence of nonlinear site effects Some models of nonlinear site response Examples

3. Loose sand => licuefaction -Lowpass filtering -Deamplification Dense sand => cyclic mobility - High frequency peaks - Amplification Port Island, Kobe / Kushiro Port

4. Nonlinear Effects: TTRH02 Station (Japan) Site amplification is different for strong ground motion

5. PGA distribution (Kik-net) (M7, 26 Mai 2003)

6. EPRI modulus reduction and damping curves

7. Velacs Project, 1992 (pore pressure effects)

8. How is the transfer function affected? Deamplification: the damping increases (pay attention) Increase of the signal duration (long period waves arrive later) 1.The shear modulus is computed as G= 2 2.The fundamental frequency of the soil is f 0 = /(4H) 3.If G changes, so does : if G(-) ---> (-) ---> f 0 (-)

9. Numerical solutions Why? There is no analytical solution Finite differences, spectral elements, finite elements methods, etc. Boundary conditions: Surface: free surface effect Bedrock: elastic boundary conditions (transmitted waves) or rigid boundary conditions (complete reflection)

10. Some models of nonlinear site response

11. The equivalent linear model (1972) G- frequency dependent (Assimaki and Kausel, 2002)

12. Iwan-Mroz Model (1967) – Plasticity Theory G max G1G1 G2G2 GnGn Shear Strain Shear Modulus (G) G max G1G1 G2G2 GnGn Shear Strain Shear Stress Reconstruction of backbone from the modulus reduction curve Backbone

13. Multi-spring Model (1) 2D plane strain model Each spring obeys the hyperbolic model Hysteresis follows the generalized Masing rules Capability to model anisotropic consolidation conditions Plasticity theory and phenomenological description of hysteresis

14. Pore pressure excess is correlated to shear work Model space has five parameters to take into account dilatancy Plastic parameters are angle of internal friction, and angle of phase transition Elastic parameters are thickness, Q, density, P and S wave speeds Multi-spring Model (2)

15. Examples

16. The M7.8 Kushiro-Oki 1993 event Dense sand deposit, first studied by Iai et al (1995) V s30 = 284 m/s

17. Results Pore pressure analysis may be needed if soil is saturated Input Trad. EqL Improved EqL Iwan-Mroz Multispring

18. 2D linear and nonlinear response of the Grenoble basin Linear Nonlinear

19. Perspectives The choice of rheology is important in the modeling of nonlinear site response. A desirable rheology should have the lower number of parameters that realistically model observed data. The Iwan-Mroz represents better the nonlinear soil behavior with the same data as the Eq. Linear method. However, better soil characterization is needed when having saturated medium (triaxial and centrifuge modeling). Luca Lenti, LPCP-IRSN postdoc, has developed a 3D elasto- plastic model following Iwan (1967). Only G/Gmax data are needed. We need to study which numerical integration scheme (FDM, FEM, SEM, etc.) is suitable to handle material nonlinearity. How are we going to combine all these numerical efforts? SUGGESTIONS?