Mathematical Modeling of Shear Stress and Direct Shear Test for Compressible Soil: Case of Soil Bordering the Wouri River

This paper focuses on the development of the mathematical model of shear stress by direct shear test for compressible soil of the littoral region, which will be a great tool in the hand of geotechnical engineers. The most common use of a shear test is to determine the shear strength which is the maximum shear stress that a material can withstand before the failure occurs. This parameter is useful in many engineering designs such as foundations, roads and retaining walls. We carried out an experimental laboratory test of ten samples of undisturbed soil taken at different points of the border of Wouri river of Cameroon. The samples were collected at different depths and a direct shear test was conducted. The investigations have been performed under constant vertical stresses and constant sample volume with the aim to determine the frictional angle and the cohesion of the compressible soil which are so important to establish the conditions of buildings stability. Special care was taken to derive loading conditions actually existing in the ground and to duplicate them in the laboratory. Given that the buildings constructed in this area are subjected to settlement, landslide, and punch break or shear failure, the cohesion and the frictional angle are determined through the rupture line after assessed the mean values of the shear stress for the considered ten samples. The bearing capacity of the soil, which is the fundamental soil parameter, was calculated. From the laboratory experimental results, the least squared method was used to derive an approximated mathematical model of the shearing stress. Many optimizations methods were then considered to reach the best adjustment.