Innovative scheme for evaluation of soil induced stresses using a customized two-point Gauss formula

Abstract

This paper presents a systematic procedure in which the variation in induced stresses in soil layers is effectively dealt with using only two sublayers. A customized two-point Gauss quadrature formula was derived to evaluate induced stresses such that the weight factors for the derived formula were set equal to those of the two-point Gauss-Legendre formula. However, the base points were obtained by dividing the compressible layer into two sublayers whose thicknesses were determined such that their middle points are the base points for the derived formula. The thickness of the two sublayers was expressed in terms of a factor called the sublayering ratio. Expressions for this ratio were derived for different types of loads and loaded areas, and its values were presented in a series of normalized, non-dimensional charts. Numerical examples were included to illustrate the use of the developed charts for obtaining the value of the sublayering ratio, and the application of the derived formula in settlement computations.