Nonlinear numerical method for earthquake site response analysis II — case studies

This paper presents two numerical case studies of medium and strong motion events, namely Loma-Prieta 1989 and Hyogoken-Nambu (Kobe) 1995. These simulations were performed using CyberQuake model. The cyclic elastoplastic constitutive model is fully detailed in the companion paper. Through these case studies, we demonstrate the importance of using appropriate constitutive modelling when the part played by nonlinear phenomena is preponderant. The need to account for 3D kinematics (i.e. the three components of the input motion), is also demonstrated, even though a 1D geometry is considered, as the plastic coupling existing between components of motion during the earthquake, strongly affects the seismic soil response.     

Seismic Displacement of Gravity Walls by a Two-body Model

Gravity walls retaining dry soil are modeled as a system of two bodies: (a) the gravity wall that slides along the wall-foundation soil boundary and (b) the critical soil wedge in the soil behind the wall. The strength of the system is defined by both the frictional and the cohesional components of resistance. The angle of the prism of the critical soil wedge behind the wall is obtained using the limit equilibrium method. The model accounts for changes in the geometry of the backfill soil behind the wall by considering the displacements at the end of each time step under limit equilibrium. The model shows that the standard (single) block model is over-conservative for the extreme case of critical-to-applied-seismic acceleration ratios less than about 0.30, but works well for cases where this ratio ranges between 0.5 and 0.8. The model is applied to predict the seismic displacement of gravity walls (a) tested in the shaking-table and (b) studied numerically by elaborate elasto–plastic analyses.     

Non-linear site response simulations in Chang-Hwa region during the 1999 Chi–Chi earthquake, Taiwan

The destructive 1999 Chi–Chi earthquake (M_w 7.5) was the largest inland earthquake in Taiwan in the 20th century. Several observations witness the non-linear seismic soil response in sediments during the earthquake. In fact, large settlements as well as evidence of liquefaction attested by sand boils and unusual wet ground surface were observed at some sites. In this paper, we present a seismic response simulation performed with CyberQuake software on a site located within the Chang-Hwa Coastal Industrial Park during the 1999 Chi–Chi earthquake in Taiwan. A non-linear multi-kinematic dynamic constitutive model is implemented in the software. Computed NS, EW and UP ground accelerations obtained with this model under undrained and two-phase assumptions, are in good agreement with the corresponding accelerations recorded at seismic station TCU117, either for peak location, amplitudes or frequency content. In these simulations, liquefaction occurs between depths 1.3 and 11.3 m, which correspond to the observed range attested by in place penetration tests and other liquefaction analyses. Moreover, the computed shear wave velocity profile is very close to post-earthquake shear wave velocity profile derived from correlations with CPT and SPT data. Finally, it is shown that in non-linear computations, even though a 1D geometry is considered, it is necessary to take into account the three components of the input motion.     

A THERMO-VISCOPLASTIC CONSTITUTIVE MODEL FOR CLAYS

The effect of heat on clay behaviour is characterized by non-linearity and irreversibility. Due to the complex influence of temperature, thermomechanical factors have to be taken into account for the numerical simulation of the behaviour of such materials. A cyclic thermo-viscoplastic model is developed for this purpose. It includes thermal hardening and the evolution of yield surfaces with temperature. From the physical point of view, it is built on the basis of available experimental results for a temperature range in which no phase change occurs. Conceptually, it is the generalization of an isothermal multimechanism cyclic model. A thermoplastic formulation of the model is also derived. The results obtained from numerical simulations compare well with experiments. © 1997 by John Wiley & Sons, Ltd.     

Thermodynamical approach for CamClay-family models with Roscoe-type dilatancy rules

The CamClay model has been extensively used in numerous research programmes for constitutive modelling in Soil Mechanics during the past quarter of a century. Several derivations of this model are now available and routinely used for numerical simulations in the geomechanical engineering field. However, to the authors' knowledge the thermodynamical basis of this model in its original form has never been established, at least in a modern thermodynamics framework. The thermodynamics principle proposed by Ziegler is very expedient for this purpose as the non-associated flow rule may be considered. This approach is applied to the CamClay model with the Roscoe dilatancy rule. A dissipation function and free energy are specified in terms of kinematic variables (i.e. state and internal variables), and the material response is derived entirely from these functions.     

Numerical simulation of liquefaction effects on seismic SSI

The present paper deals with the influence of soil non-linearity, introduced by soil liquefaction, on the soil–foundation–structure interaction phenomena. The objective is to reveal the beneficial or unfavourable effects of the non-linear SSI on both structural drift and settlement of a given structure. Factors such as the signal modification due to liquefaction, and ratios of fundamental frequencies of soil, structure and signal may play an important role on the damage of the structure. The importance of each of these factors is evaluated through a significant parametric study. A 2D coupled finite element modelling is carried out using an elastoplastic multi-mechanism model to represent the soil behaviour. This paper presents the research work we did in the framework of the European Community project NEMISREF (New methods of mitigation of seismic risk on existing foundations, GRDI-40457), to study possible retrofitting measures using GEFDYN computational tools.     

Numerical simulation of dynamic soil–structure interaction in shaking table testing

This paper provides an insight into the numerical simulation of soil–structure interaction (SSI) phenomena studied in a shaking table facility. The shaking table test is purposely designed to confirm the ability of the numerical substructure technique to simulate the SSI phenomenon. A model foundation–structure system with strong SSI potential is embedded in a dry bed of sand deposited within a purpose designed shaking-table soil container. The experimental system is subjected to a strong ground motion. The numerical simulation of the complete soil–foundation–structure system is conducted in the linear viscoelastic domain using the substructure approach. The matching of the experimental and numerical responses in both frequency and in time domain is satisfying. Many important aspects of SSI that are apparent in the experiment are captured by the numerical simulation. Furthermore, the numerical modelling is shown to be adequate for practical engineering design purposes.     

Quantification of soil non-linearity based on simulation

Recent earthquake studies have demonstrated that non-linear behavior of soft soil can be significant compared to other effects affecting seismic motion. Therefore, the question is to know when sediment non-linearity is a first-order effect and when it is not. In this study, we propose a method for quantifying non-linear effects based on simulations. An elasto-plastic model is used to simulate the behavior of four materials (sands and clays). For each computation, the non-linearity is quantified by the use of a ‘non-linear parameter’ and compared to four non-linearity indicators. These computations suggest that the efficiency of an indicator depends on the nature of the soil underlying the recorder and that the most efficient indicator should be based on the high frequencies content rather than on the resonant frequency changes.     

Elastoplastic constitutive modelling of soil–structure interfaces under monotonic and cyclic loading

This paper is dedicated to the non-linear numerical modelling of the soil–structure interface. Thus, in a first part, after the presentation of the constitutive model, the soil–structure interface interaction is treated in terms of direct shear test simulations. A strategy for the interface model parameters’ identification is also presented. This strategy is linked to the similitude of soil–structure interface behavior and the soil behavior, regarding the interface surface roughness. In a second part, the performance of the numerical simulations are verified numerically against published results for soil–structure experimental shear tests. Finally, as an application, interface stress paths are studied in axially loaded pile–soil systems and load transfer mechanisms are identified.