A narrow backfill zone is formed when retaining walls are built near existing stabilized structures (e.g., rock faces). In such circumstances, the classical passive earth pressure coefficient is no longer applicable, and a correction factor is required for the design. This paper aims to develop analytical solutions for estimating the passive earth pressure problem of narrow cohesive-frictional backfills behind retaining walls. The novel arched differential element method considers both effects of the horizontal shear stress in backfills and the soil arching, and it is employed to estimate the passive earth pressure distribution along with wall depth. The solutions are compared against those published experimental data, analytical approaches, and finite-element limit analysis solutions. The factors influencing the distribution of passive earth pressure are also undertaken using a series of parametric studies. To implement the derived solutions into a routine design, a modified practical design equation is presented following the standard Coulomb's solutions. This work provides a theoretical guideline for the initial design of retaining walls with narrow soils, and it should be of great interest to practitioners.

This study presents a hybrid framework to predict stability solutions of buried structures under active trapdoor conditions in natural clays with anisotropy and heterogeneity by combining physics-based and data-driven modeling. Finite-element limit analysis (FELA) with a newly developed anisotropic undrained shear (AUS) failure criterion is used to identify the underlying active failure mechanisms as well as to develop a numerical (physics-based) database of stability numbers for both planar and circular trapdoors. Practical considerations are given for natural clays to three linearly increasing shear strengths in compression, extension, and direct simple shear in the AUS material model. The obtained numerical solutions are compared and validated with published solutions in the literature. A multivariate adaptive regression splines (MARS) algorithm is further utilized to learn the numerical solutions to act as fast FELA data-driven surrogates for stability evaluation. The current MARS-based modeling provides both relative importance index and accurate design equations that can be used with confidence by practitioners.

Pit-in-pit (PIP) excavations in an aquifer–aquitard system likely undergo catastrophic failures under the hydraulic uplift, the associated undrained stability problem, however, has not been well analyzed in the past. To this end, a hypothetical model of PIP braced excavation in typical soil layers of Shanghai, China is developed using the finite element limit analysis (FELA) tool. The FELA solutions of safety factors (FSs) against hydraulic uplift are verified with the results from the finite element analysis with strength reduction technique (SRFEA) and existing design approaches. Subsequently, FELA is employed to identify the triggering and failure mechanisms of PIP braced excavations subjected to hydraulic uplift. A series of parametric studies considering the various geometric configurations of the PIP excavation, undrained shear strengths of aquitard, and artesian pressures are carried out. The sensitivities of relevant design parameters are further assessed using a multivariate adaptive regression splines (MARS) model that is capable of accurately capturing the nonlinear relationships between a set of input variables and output variables in multi-dimensions. A MARS-based design equation used for predicting FS is finally presented using the artificial dataset from FELA for practical design uses.