Towards an error indicator-based h-adaptive refinement scheme in kinematic upper-bound limit analysis with the presence of seepage forces

This paper presents a new computational strategy for kinematic upper bound limit analysis in the presence of seepage forces with an improved mesh refinement scheme. In particular, the original adaptive refinement scheme is enhanced with a simple but efficient error-indicator of the nodal plastic dissipation for high-order elements. The proposed refinement criteria facilitate a precise quantitative evaluation of errors in the nodal plastic energy dissipation across each element and ensure that the rate of total refined element number gradually decreases with adaptive step. Adhering to two-dimensional steady state seepage condition, numerical details regarding the calculation of total water head distributions for the seepage field are provided. In a similar manner as treating the unit weight of the soil, the effects of seepage forces are incorporated as body forces in the upper bound formulation. Detailed numerical procedure of the proposed error indicator-based h-adaptive refinement scheme incorporating the inclusion of seepage forces is addressed and implemented in the in-house code. Several benchmark problems, including both homogeneous and non-homogeneous soils, are analyzed to evaluate the excellent performance of the proposed error indicator-based h-adaptive refinement scheme in upper-bound limit analysis and assess the influence of seepage forces on the stability of geostructures through comparison with that for dry condition.