Cavity Expansion in Cohesive-Frictional Soils with Limited Dilation

The problem of cavity expansion from zero radius has no characteristic length and therefore possesses a similarity solution, in which the cavity pressure remains constant and the continuing deformation is geometrically self-similar. In this case, the incremental velocity approach first used by Hill (1950) to analyze cavity expansion in Tresca materials can be extended to derive a solution for limiting pressure of cavity expansion in other types of material. In this article, a rigorous semi-analytical solution is derived, following Hill's incremental velocity method, for the expansion of cavities from zero initial radius in cohesive-frictional soils with limited dilation. In particular, the radius of the elastic-plastic interface c is used in this article as the time scale and the solution for the limit pressure has been presented. Solutions are evaluated for a number of cases representative of a range of cohesive-frictional and dilatant soils. A comparison is also made between the solutions presented here and previous solutions for cohesive-frictional soils that have unlimited (on-going) plastic dilation. In particular, the influence of limited plastic dilation on the cavity limit pressure is identified and discussed.

Calculation of active earth pressure on retaining walls with line surcharge effect and presentation of design diagrams in cohesive – frictional soils

In this study, a formulation and models have been proposed to calculate the active earth pressure on the wall and to determine the angle of failure wedge with line surcharge effect and taking into account the soil cohesion. The proposed method has the advantage of taking into account soil parameters such as cohesion, the angle of friction between the soil and the wall, the surcharge effect in the elasto-plastic environment, and the range that determines the critical surcharge. This paper presents dimensionless diagrams for different soil specifications and surcharges. According to these diagrams, it is easy to determine the distribution of excess pressure caused by surcharge, the distribution of the total active earth pressure on the wall, the angle of the failure wedge as well as the minimum and maximum active coefficient of the pressure with respect to surcharge distance. Furthermore, all soil parameters, surcharge and the results have been addressed. In general, the results indicated that increasing the angle of internal friction of the soil and cohesion would result to a nonlinear reduction in the active earth pressure coefficient, contrary to the line surcharge, which increases the active earth pressure of the soil and ultimately increases the active earth pressure coefficient. In this research, a diagram has been presented that expresses the surface that the active earth pressure coefficient changes with respect to the surcharge distance. The lower limit of each graph expresses the minimum active earth pressure coefficient (kas (min)) at the minimum surcharge distance, whereas the upper limit indicates the maximum active earth pressure coefficient (kas (max)) at the maximum surcharge distance from the wall. Comparison of the results of the proposed method with previous methods, codes and numerical software shows that in general, the proposed method is able to simplify the analysis of walls with surcharge effect in cohesive-frictional soils. In addition to the formulation and diagrams, a computer program in MATLAB software has been written. Using the results of these codes, the pressure on the wall with the linear surcharge effect, angle of failure wedge and pressure distribution on the wall in the cohesive-frictional soils can be calculated for all scenarios.