Active and passive critical slip fields for cohesionless soils and calculation of lateral earth pressures

Abstract

A new method of solving earth pressure problems is proposed in this paper within the framework of the limit equilibrium approach. The concept of the critical slip field (CSF) is postulated: the active critical slip field (ACSF) in the active case, and the passive critical slip field (PCSF) in the passive case. Based on the principle of extremum thrust force (which is theoretically consistent with the principle of optimality) in conjunction with the method of slices, a numerical procedure is presented for the determination of such fields and consequently the distribution of earth pressures on retaining walls. For simplicity at this stage, the backfill material is assumed to be a homogeneous cohesionless soil with sloping ground surface carrying uniform and vertical surcharge, while the retaining wall is allowed to be battered, and the strength of the soil may be either fully or partially mobilised. Compared with the rigorous method (i.e. the method of characteristics), the proposed method is simple in principle and easily implemented in a computer program. However, it is more accurate than other approximate techniques and agrees well with available closed-form solutions. A number of examples of ACSF and PCSF are given in this paper, and the validity and efficiency of the proposed method are demonstrated. In addition, it is easy to extend this numerical procedure to obtain more general ACSF and PCSF accommodating non-homogeneous c, ϕ soils subject to complicated loading conditions.