Despite the advantages of combined vertical, moment, and horizontal (VMH) failure envelopes, serviceability was not adequately considered in previous studies, leading to the introduction of serviceability-based "design envelopes" in current research, as a complement to conventional failure envelopes. This study employs three-dimensional finite element analysis to develop design and failure envelopes for square raft and cubic embedded block foundations under VMH loading. The numerical investigation, validated against well-documented benchmarks, uses the Hardening Soil model with small-strain stiffness (HSS). The envelopes were developed using probe tests associated with the dominant system parameters: breadth (2.5 to 25 m), embedment depth to breadth ratio (1, 2, and 3), and c-ϕ subsoil relative density (loose, medium, and dense). The results demonstrate that serviceability limits often govern foundation design, since the design envelopes are significantly smaller than the associated failure envelopes. Embedment depth is identified as a significant parameter that influences the transition from base-bearing to three-dimensional resistance mechanisms and enhances moment and horizontal capacities. The study examines the relationship among foundation geometry, embedment ratio, and subsoil strength in shaping failure and design envelopes. Multivariate regression analysis was used to derive mathematical equations for ellipsoidal failure and design envelopes. Overall, the findings challenge the traditional safety-factor paradigm and highlight the need for displacement-based design methodologies in modern foundation systems.
Ebrahimipour et al. (Thu,) studied this question.