Shakedown Analysis of Unsaturated Soils Considering the Variation of Hydraulic States

Abstract

Long-term stability evaluation of unsaturated earth structures has always been one of the most important issues in geotechnical engineering. Most available methods are appropriate for calculating the maximum loads that the structures can resist when the hydraulic state is fixed, and the external loads are monotonically increased. In practical engineering, however, the hydraulic condition is ever changing, and so are the matric suction and the shearing strength of unsaturated soils. In this situation, the obtained minimized collapse loads can no longer be used as reference for the design criterion, which may greatly overestimate the stability of the structures. Classical shakedown analysis is a more appropriate method, which can only consider the variation of the loads but not the variation of hydraulic states. This paper presents a novel formulation for shakedown analysis of unsaturated soils considering both the variation of external loads and the variation of the shearing strength caused by drying–wetting cycles. By using the suction stress-based effective stress of unsaturated soils, the three-phased mixture is dealt with as a single-phased material. The suction-stress equivalent forces are established, and the variation of the hydraulic state is dealt with as the variation of equivalent forces. Numerical formulations are then developed by the combination of the finite-element method and the second-order cone programming. Some shakedown problems are solved, and the effect of hydraulic state variation on the shakedown limits of foundations, pavements, and slopes is studied in detail. It is shown that the neglection of moisture content variation would greatly overestimate the safety of earth structures, and the produced errors become more significant with the increase of the suction-stress increment and the decrease of the shearing strength. The shakedown limit reaches the smallest when both external loads and suction stress are varying. When the variation of equivalent forces is complicated, the loading domain can be approximated by a polyhedron using a uniform distribution of sampling points, and the shakedown factor of safety converges to the true value with the increase of the number of sampling points. Shakedown analysis is necessary in engineering designs when several wetting and drying cycles happen.