Mathematical Analysis for the Evaluation of Settlement and Load-Bearing Capacity of a Soil Base Adjacent to an Excavation Pit

Abstract

The present paper states and provides an analytical solution for the problem of evaluating the settlement and load-bearing capacity of weighty soil layers of limited thickness resting upon incompressible soil bases and an excavation pit wall upon exposure of the foundation to a distributed load in the vicinity of a wall. The authors develop a method for determining the stressed state component in the reduced engineering problem based on the Ribere–Faylon trigonometric series and for accounting for the nonlinear deformation properties of soils, building on the analytical dependencies of S.S. Grigoryan and S.P. Timoshenko. In order to determine the relationship between stress and strain, the Hencky’s physical equation systems were used. They factor in the impact of average stresses σm on the shear modulus of elasticity G (σm) and volumetric modulus of elasticity K (σm). The obtained solutions make it possible to assess the deformation of soil bases and the load-bearing capacity with respect to nonlinear properties in a way that accurately corresponds to the actual performance of subsoils exposed to loading. The theoretical results are followed by numerical experiments to prove their validity.

A Mathematical Analysis of the Stress Statement of the Soil Basis under Complex Loading near the Retaining Wall

“…In earlier works [32,34], authors have analyzed the effect of a distributed load q = const on an area with a width of b = 2a, located at distance d from the edge of a rectangular retaining wall on a soil foundation resting on an incompressible base. This paper offers the statement of and a solution to the problem of the simultaneous application of two distributed loads with different values of intensity (q 1 и q 2 ) and different or similar widths (b 1 и b 2 ), at a distance d from the retaining wall.…”

“…The components of the stress statement of the soil basis outside the enclosing structure are calculated using the method of Z.G. Ter-Martirosyan [7,8,33,34] and are applied to the Ribiere-Fileon trigonometric series in the following manner:…”

Mathematical Computations of Long-Term Settlement and Bearing Capacity of Soil Bases and Foundations near Vertical Excavation Pits

“…Ter-Martirosyan [24][25][26], A.Z. Ter-Martirosyan [1,26,27], as well as foreign scientists, including L. Shukle [28] and others [29][30][31][32][33][34] contributed greatly to the study of deformations of clay soils and their influence on projected changes in the stress-strain state of soil bases. Most of these researchers focused on developing the theory of creep and making new rheological models.…”

“…Ter-Martirosyan to solve the boundary problem with a distributed loading [1]. Mathematical formulas for the settlement and load-bearing capacity of a soil base adjacent to an excavation pit were also developed, taking into account the elastoplastic properties of the soil [26].…”