Tension Crack Modelling and its Influence on Active Earth Pressure in Numerical Limit Analysis

Abstract

The precise estimation of active earth pressure (AEP) in retaining walls supporting unsaturated backfills continues to be a major challenge in geotechnical engineering. Classical theories mostly consider dry or fully saturated soils, thus, neglecting the development of the tensile stress zones under partial saturation conditions [1], [2]. Such conditions eventually give rise to tension cracks, which further, alter the lateral stress field and thus, affecting the global stability of retaining structures [3]. Recent studies have emphasised that tension cracks in unsaturated backfills can extensively affect the magnitude and distribution of active earth pressure, especially when suction effects and discontinuities are studied [5], [6]. Examination of these discontinuities is critical in unsaturated soils, where crack propagation and matric suction simultaneously control the shear strength of the unsaturated soil [1], [2]. The present study incorporates lower bound finite element limit analysis (FELA) framework to examine the influence of tension crack density (n = number of cracks per length) on the active earth pressure coefficient (Ka) and the corresponding pressure distribution acting on retaining walls in unsaturated soils. The proposed framework has incorporated the Mohr-Coulomb yield criterion to capture the progressive failure and redistribution of stresses accurately [4]. Within this interpretation, prime geotechnical parameters including the cohesion intercept (c'), angle of internal friction (ϕ'), and bearing capacity factors (Nc and Nq) are analytically varied to evaluate their combined influence with crack density. The parametric study reveals that variations in crack density produce nonlinear changes in Ka, evolving from the interaction between tension discontinuity, suction and soil strength parameters. The presence of cracks, therefore, lowers stresses in the upper backfill and shifts the lateral pressure concentration toward the base of the wall, producing a non-linear pressure distribution. The current framework is further extended to evaluate the influence of geometrical orientation, particularly sloping backfills and wall inclination, upon the tension crack mechanism and resultant earth pressures. A backward-tilted wall or an upslope backfill increases confinement, restrains crack propagation, and thereby reduces magnitudes of active pressure. On the other hand, forward-tilted walls and downslope backfills promote deeper cracking and induce higher pressures near the toe [3]. These observations highlight the combined influence of suction, geometry and discontinuity behaviour on the lateral stress distribution in unsaturated backfills. Consequently, matric suction, tension crack density and geometrical configuration collectively govern the AEP response of retaining systems. The integration of these key factors into the design framework aids in realistic prediction of performance of the retaining wall under variable conditions. The proposed approach i.e., the lower bound FELA extends an efficient means to capture the combined effects of discontinuity, geometry and suction in the real field.