Alain Pecker

MODELLING OF NONLINEAR DYNAMIC BEHAVIOUR OF A SHALLOW STRIP FOUNDATION WITH MACRO-ELEMENT

A new nonlinear soil-structure interaction macroelement is presented. It models the dynamic behaviour of a shallow strip foundation under seismic action. Based on sub-structured methods, it takes into account the dynamic elastic effect of the infinite far field, and the material and geometrical nonlinear behaviour produced in the near field of the foundation. Effects of soil yielding below the foundation as well as uplift at the interface are considered. Through the concept of macro-element, the overall elastic and plastic behaviour in the soil and at the interface is reduced to its action on the foundation. The macro-element consists of a non linear joint element, expressed in the three degrees of freedom of the strip foundation, reflecting the limited bearing capacity of the foundation. This model provides a practical and efficient tool to study the seismic response of a structure in interaction with the surrounding soil medium. Applications to a bridge pier show the potentialities of this kind of model.

EFFECTS OF SPATIAL VARIABILITY OF SOIL PROPERTIES ON SURFACE GROUND MOTION

The effects of spatial variability of soil properties on the behaviour of a cohesive and a cohesionless soil profile subjected to seismic excitation are analysed. The input data for the random fields are derived from existing, extensive soil investigations, and Monte Carlo simulation technique, combining digital generation of non-Gaussian stochastic vector fields with dynamic, equivalent linear and nonlinear finite element analyses, is used for this purpose. It is found that the variability of shear wave velocity has small effect on the ground surface response spectrum. The motion intensity and the variation of soil properties in the deterministic description of the profile considerably affect the standard deviation of the surface spectral acceleration, which is successively compared to the uncertainty introduced in attenuation relationships, used for the construction of hazard-consistent design spectra.

The role of non-linear dynamic soil-foundation interaction on the seismic response of structures

In this paper we provide an overview of recent research work that contributes to clarify the effects of non-linear dynamic interaction on the seismic response of soil-foundation-superstructure systems. Such work includes experimental results of seismically loaded structures on shallow foundations, theoretical advancements based on improved macro-element modeling of the soil-foundation system, examples of seismic design of bridge piers considering non-linear soil-foundation interaction effects, and numerical results of incremental non-linear dynamic analyses. The objective of this paper is to support the concept of a controlled share of ductility demand between the superstructure and the foundation as a key ingredient for a rational and integrated approach to seismic design of foundations and structures.

A METHODOLOGY FOR SEISMIC VULNERABILITY OF MASONRY ARCH BRIDGE WALLS

Notwithstanding its potentially high level, the seismic vulnerability of masonry arch bridges has yet to be completely perceived, possibly due to the relatively scarce damage evidence collected after recent earthquakes. The dearth of research studies on this topic is thus one of the main motivations behind the current endeavour, which aims at a better understanding of the dynamic interaction between the arch walls and the filling material of typical masonry arch bridges, and the consequent susceptibility of the latter to out-of-plane collapse mechanisms. Within this framework, a numerical model for the evaluation of the seismic out-of-plane capacity of bridge walls, including the effects of the infill material, is proposed. This methodology can be subdivided into three main components; computation of static earth pressure, evaluation of dynamic soil thrust, assessment of out-of-plane capacity of a masonry wall. In addition, a congruent and relatively simple procedure for the estimation of the seismic demand on the arch wall is described. Finally, a parametric study is carried out with a view to appraise the seismic vulnerability associated to typical masonry arch bridge typologies.

Soil inertia effects on the bearing capacity of rectangular foundations on cohesive soils

Two kinematic mechanisms are presented, which provide an upper bound of the ultimate bearing capacity of shallow rectangular foundations resting on cohesive soil, modeled by the Tresca strength criterion. The soil-foundation interface is described by the same criterion. The foundation is subjected to an inclined/eccentric load. The horizontal component of the body force in the soil is also taken into account to discuss the effects of the soil inertia on the bearing capacity. A multi-dimensional minimization algorithm allows one to find the geometric parameters corresponding to the best upper bound solutions for different load conditions. The shape effects are discussed and the solutions are compared both with previous theoretical upper bound solutions and with experimentally based formulas, in use in engineering geotechnical practice. Finally, the detrimental effects of the soil inertia on the ultimate bearing capacity of the foundation are analysed, as a function of the shape ratio and the design safety factor.

A KINEMATIC INTERACTION MODEL FOR A LARGE-DIAMETER SHAFT FOUNDATION: AN APPLICATION TO SEISMIC DEMAND ASSESSMENT OF A BRIDGE SUBJECT TO COUPLED SWAYING-ROCKING EXCITATION

The aim of this paper is to illustrate an analytical model for the assessment of kinematic interaction of large-diameter shaft foundations. The model is derived using recently obtained solutions of soil structure interaction problems of rigid walls and fixed base cylinders subjected to a dynamic excitation. The proposed model constitutes an extension to a deformable base of the elastodynamic solution of a rigid, fixed-base cylinder imbedded in a homogeneous or inhomogeneous soil stratum with different lateral boundary conditions. The analytical model has been validated by means of a finite elements code and it has been implemented in a consistent seismic soil-structure-interaction analysis procedure. An application of the model to a long, multi-span continuous prestressed concrete viaduct with tall piers has been carried out focusing on the importance of kinematic interaction. The main finding of the study is that the foundation input motion is characterised not only by a translational horizontal component which is usually of a reduced amplitude if compared with the free-field ground motion, but also by a rotational component that is responsible for a large seismic demand in the superstructure. The proposed model represents an effective tool to be used in the engineering practice to assess both the seismic actions induced by the ground shaking on the foundation system and the effective input motion of a superstructure founded on massive and large diameter shafts.

MAXIMUM GROUND SURFACE MOTION IN PROBABILISTIC SEISMIC HAZARD ANALYSES

The increasing use of Probabilistic Seismic Hazard Assessment for critical facilities leads to the consideration of earthquake scenarios with a probability of occurrence as low as 10−7 per year. For such low probabilities the computed ground accelerations, based on extrapolations of statistical ground-motion prediction relationships, may reach values as high as several gs, which poses tremendous difficulties for earthquake-resistant design. Obviously such large motions cannot exist at soil sites because, among other factors, the soil profile has a limited resistance capacity and cannot transmit unbounded motions. When failure is reached at any depth within the soil profile, the incident motion is filtered and no motion larger than the motion reached at that stage can be transmitted to the upper strata. The approach developed herein to estimate the maximum ground surface acceleration is based on an analytical solution to the wave equation in an inho-mogeneous soil profile; the assumed soil constitutive behaviour is of the elastic perfectly plastic type, and is completely defined by the maximum shear stress and the yield strain at any depth. When compared to parametric numerical site response analyses based on a sophisticated non-linear soil constitutive model the methodology gives reasonable predictions. Comparison with recorded strong motion records do not show any contradiction between prediction and observation.

A Dynamic Macro-Element for Performance-Based Design of Foundations

The work is concerned with the development of an original macro-element model for shallow foundations within the context of performance-based design of structures. The macroelement can be viewed as a link element placed at the base of the structure that reproduces in a simplified, yet coherent way the non-linear interaction phenomena arising at the soil-footing interface during dynamic excitation. As such, it offers an efficient prediction of the maximum and permanent displacements at the foundation level by identifying the non-linear mechanisms that produce them. These are: (a) the sliding mechanism along the soil-footing interface, (b) the irreversible soil behaviour mechanism and (c) the foundation uplift mechanism. These non-linear mechanisms are introduced within the macro-element model in a fully coupled way. In its present state of development the model can be used for strip and circular footings in purely cohesive or purely frictional soils.

Soil Structure Interaction

Usually in the seismic design of ordinary building, soil structure interaction is neglected and the dynamic response of the structure is evaluated under the assumption of a fixed based response. However during seismic loading the soil undergoes deformations which are imposed to the foundation, the question naturally arises of knowing if the motion in the vicinity of the structure is altered by the presence of the structure and how the structure response is modified by the compliance of the supporting soil. This interaction between the structure and the soil is named soil-structure interaction (SSI). The purpose of this chapter is to illustrate whether and under which conditions SSI is important and what are its consequences on the dynamic response of the structure.

Soil Behaviour under Cyclic Loading

Fundamental characteristics of soil behaviour during earthquakes are reviewed; field and laboratory evidences of non linearities and energy dissipation mechanisms are presented. Different kinds of soil constitutive models are discussed with special emphasis on the equivalent linear viscoelastic model commonly used in engineering practice.