ANALYSIS OF ECCENTRICALLY OBLIQUELY LOADED SQUARE FOOTINGS FROM CONSTITUTIVE LAWS

Abstract

Shallow foundations are the common types of foundation designed for many important structures. In general, these foundations are subjected to a vertical load, moment and shear at the base, which induced the stresses and deformation in the supporting soil. Example of such structures, which foundations are subjected to eccentric-inclined load, are retaining walls, abutments, columns and portal frames. Bearing capacity and selltement are two main criteria for designing a footing foundation. Several theories and experimental methods have been propounded for computation of the above parameters separately. However, the best estimation of bearing capacity and settlement are possible only, if the pressure-settlement characteristics of the foundation-soil are known. Analytical Procedure for Square footing subjected to eccentric-inclined load resting on clay and sand. Pressure-settlement and pressure- tilt are essentially functions of the non- linear stress-strain relationships of soils. Constitutive laws defying such a behavior of soils have been adopted, in this study, to predict these relations. The procedure has been evolved for two types of soils, namely, cohesive soil (clay) and Cohesionless soil (sand). The whole footing area have been divided into a large number of small elementary areas so that load in each area may be considered as point load. The contact pressure distribution has been assumed as linear. While, the soil mass supporting the footing has been divided into numerous thin horizontal strips, up iii to a depth beyond which, the stresses become negligible. Various stress components due to each small area, at the middle of each strip along a vertical section have been evaluated using (Boussinesq's (1885) and Cerrutie (1988) equations. Normal and shear stress, however, have been obtained by superimposing same stress components due to all elementary areas. Then the principal stresses and their direction have been determined. The principal strains in the direction of the principal stress have been obtained using the non-linear constitutive laws. Then the strain in the vertical direction has been determined. Thus, the vertical settlement of each strip has been evaluated by multiplying the vertical strain by its thickness. The total settlement, along a vertical section, due to an eccentric-inclined load has been obtained as the summation of vertical settlements of all strips. The procedure has then been repeated to obtain settlements along various vertical sections. The maximum settlement, settlement of the point of load application and tilt of the rigid footing have been computed by equating both the area and distance of the centre of the settlement diagram of the flexible footing with the area and distance of the centre of the settlement diagram of the rigid footing. The whole procedure is then repeated for other values of loads, inclination (i) and eccentricity ratio (e/B).