Accurate determination of active earth pressure distribution on rigid retaining wall including the magnitude and height of application of its resultant is of immense importance for designing the earth retaining structures. In this paper, an analytical solution based on the soil arching effect is presented. According to Mohr’s stress circle, a new relationship between active earth pressure and normal stress on failure surface at any depth from backfill surface is obtained. By analysing parabolic arch of minor principal stresses, a new coefficient of active lateral earth pressure is proposed. The problems that the vertical static equilibrium equation of differential flat element considering soil arching effect is not reasonable are analysed. Then, based on the limit equilibrium of differential flat element, new formulas relevant to the distribution of active earth pressure, the magnitude and height of application of its resultant are derived. The effects of backfill internal friction angle, wall–soil friction angle, wall height, surcharge load and backfill unit weight on those formulas are investigated in detail. In addition, the comparisons of the predictions by proposed equations with available test data as well as existing solutions are carried out, which implies adequate accuracy of the proposed solutions for all ratios of wall–soil friction angle to internal friction angle.

When a retaining wall is built near a building or a mountain, the backfill width is often limited. It limits the use of the classical theoretical formula based on the assumption of an infinitely large half-space. Finite-element analysis shows that when the retaining wall movement is translational, one to three slip surfaces will develop from the wall heel, and eventually develop to the surface along the soil–wall or soil–rock interface. An effective model for calculating the active earth pressure of narrow granular backfill against the wall under translational mode is established by taking into account the inclination angle of the rock face and the friction angles of the soil–wall and soil–rock interfaces. The active earth pressure under the failure mechanisms of one to three slip surfaces are given by using the limit equilibrium method and the whole analysis method of sliding wedge. The coefficient of active earth pressures is as low as 0.5–0.7 times the Coulomb solution and the location ($h_0/H$ ) of the resultant of active earth pressures ranges from 0.34 to 0.44. The influence of different parameters on the number of slip surfaces was also studied by parametric analysis.

In engineering constructions, the backfill behind retaining walls is usually narrow, and its boundary conditions are asymmetric due to the space limitation. When the retaining wall rotates about the bottom, the direction of the principal stress also rotates due to the granular properties of soil and the multiple interfaces friction. Such phenomenon is more significant in narrow backfill, however, there are few studies about this. The finite element method analysis is able to demonstrate how the failure mode of narrow backfill and the rotation of principal stress are affected by the backfill geometry and interfaces friction. Theoretical analysis is employed here to calculate the principal stress rotation angle and lateral pressure coefficient of the interface element. Similarly, active earth pressure of narrow cohesionless backfill against inclined rigid walls rotating about the bottom, considering principal stress rotation and uniform load on the ground, is derived by differential element limit equilibrium, which, upon comparison with methods used in previous studies, is suitable for the asymmetric inclined boundaries and improves the scope and accuracy of calculation. Parametric studies herein show that increasing the new structure inclination and decreasing its friction will reduce the interference in the existing structure.

The aim of this study is to investigate the coupling effects of re-excavation and hydraulic uplift on base instability of pit-in-pit (PIP) braced excavations. The numerical model of PIP braced excavation in Shanghai soft clay overlying a confined aquifer was established by upper-bound finite element limit analysis (UBFELA) method. The effects of the sensitive design parameters (i.e., the artesian pressure, thickness and undrained shear strength of the aquitard and excavation width of inner pit) on failure mechanisms and upper-bound safety factor (FS) against hydraulic uplift were analyzed. The results show that the value of FS increases with an increase in the thickness and undrained shear strength of the aquitard, but decreases with increasing the artesian pressure and excavation width of inner pit. The failure modes can be typically classified into three categories: circular slip surface in outer pit (M1), hydraulic uplift combined with circular slip surface in entire PIP system (M2), and basal hydraulic uplift in inner pit (M3); then the corresponding critical artesian pressure is determined. Finally, the average value of critical artesian pressure used to distinguish the three types of failure modes is recommended as the design value against hydraulic uplift in the PIP system, and validity is verified by the comparison with the current design methods. The proposed stability design by UBFELA contributes to ensure the serviceability and performance of PIP system.

Reinforcement solutions can ensure that low geosynthetic-reinforced (LGR) embankments progressively subside instead of suddenly failing due to void collapse, which provides an early warning to allow surface refilling to be carried out. This study investigates the characteristics of the bearing capacity and failure modes of the LGR embankments overlying voids using large-deformation finite-element analysis and normalization method. The system as a whole has six distinct failure modes: the trapdoor, sidewall, combination of roof and sidewall, rotational roof, combination of roof and single sidewall, and slope failure modes. Five types of slip lines exist for the LGR embankment: the vertical, trapezoid, double-cambered, partial-vaulted, and vaulted slip lines. This study also presents the effects of influencing parameters (e.g., rupture strength of the reinforcement, location and size of the void, and height and shear strength parameters of embankment fills) on the ultimate bearing capacity of the system. Design charts are obtained to determine the required soil properties and evaluate the characteristics of the bearing capacity of the system.