Gravity‐driven groundwater flow and slope failure potential: 1. Elastic Effective‐Stress Model

Abstract

Hilly or mountainous topography influences gravity‐driven groundwater flow and the consequent distribution of effective stress in shallow subsurface environments. Effective stress, in turn, influences the potential for slope failure. To evaluate these influences, we formulate a two‐dimensional, steady state, poroelastic model. The governing equations incorporate groundwater effects as body forces, and they demonstrate that spatially uniform pore pressure changes do not influence effective stresses. We implement the model using two finite element codes. As an illustrative case, we calculate the groundwater flow field, total body force field, and effective stress field in a straight, homogeneous hillslope. The total body force and effective stress fields show that groundwater flow can influence shear stresses as well as effective normal stresses. In most parts of the hillslope, groundwater flow significantly increases the Coulomb failure potential Φ, which we define as the ratio of maximum shear stress to mean effective normal stress. Groundwater flow also shifts the locus of greatest failure potential toward the slope toe. However, the effects of groundwater flow on failure potential are less pronounced than might be anticipated on the basis of a simpler, one‐dimensional, limit equilibrium analysis. This is a consequence of continuity, compatibility, and boundary constraints on the two‐dimensional flow and stress fields, and it points to important differences between our elastic continuum model and limit equilibrium models commonly used to assess slope stability.