Seismic Behaviour of Ground and Geotechnical Structures, Sco e Pinto (ed.) 1997 Balkerna, Rotterdam, ISBN 90 54 10 887 8

Analytical fonnulae for the seismic bearing capacity of shallow strip foundations

A.Pecker Godynamique et Structure, Bagneux, France

ABSTRACT: Following the observed foundation failures in Mexico City during the 1985 Michoacan earthquake, extensive studies have been carried out on the seismic bearing capacity of shallow foundations. These studies have thrown new light on the main factors affecting the seismic behavior of shallow foundations at failure and new analytical formulae have emerged to compute the seismic bearing capacity under pseudo-static conditions. These formulae account for the load inclination and eccentricity as well as for the inertia forces developed within the soil medium; they are valid for cohesive and dry cohesionless materials.

1 INTRODUCTION The evaluation of the seismic bearing capacity of foundations has not received much attention from the earthquake engineering community. If the cyclic behavior of foundations has been extensively studied,, with the development of impedance analyses in the last decade, their behavior at failure did not initiate much research. The major reason probably lies in the few observations of foundations failures during earthquakes (Auvinet and Mendoza, 1986; Romo and Auvinet, 1992; Pecker, 1994). This situation changed with the 1985 Michoacan Guerero earthquake and significant improvements in the foundation design have been obtained ever since. The object of this paper is to review the recent developments in the evaluation of the seismic bearing capacity of shallow foundations for which rational methods of analyses seem to emerge in the last feW years. These methods, based on lirnit analyses theories for the pseudo-static problem, have lent themselves to the derivation of analytical formulae which properly account for the load inclination and eccentricity of the forces acting on the foundation (inertia forces from the superstructure) and for the seismic forces developed within the soil medium by the passage of the seismic waves.

2. FACTORS AFFECTING THE BEARING CAPACITY OF SURFICIAL FOUNDATIONS

Many factors affect the seismic bearing capacity of foundations; knowledge and proper evaluation of these parameters are essential prerequisites for a correct evaluation of the foundation stability.

2.1 Pre-earthquake Conditions Observations of foundation behavior during the 1985 Michoacan-GuererO earthquake clearly evidenced that the initial static pressure and load eccentricity have pronounced effects on the seismic behavior of foundations. Foundations with low static safety factors (high contact pressures) or with significant load eccentricities behaved poorly whereas well-designed foundations appear not to have suffered significant damages.

2.2 Seismic loads

A key aspect of any soil-structure interaction problem and hence of bearing capacity evaluations is the calculation of the dynamic fOrces acting at the soil foundation interface. It must be recognized that the dynamic loads acting on the foundation have six components:

- a vertical force which, in most common situations, can be neglected since its magnitude is small with respect to the static permanent vertical load; - two shear forces (T) acting in two orthogonal, horizontal directons; these forces anse from the inertia forces developed in the structure by the shaking; they .induce an inclination with respect to the vertical of the force acting on the foundation; - two overturning moments around horizontal axes which are closely related to the inertia forces (T); they anse from the elevated position of the Center of gravity of the structure above the foundation level; these moments induce an eccentricity of the load acting on the foundation;

261