Displacement control is critical to the design of retaining walls, especially in urban areas, to avoid any potential damage to adjacent structures during excavations. In this study, model tests are first conducted to investigate the stress and deformation mechanisms of an embedded cantilevered retaining (ECR) wall during excavations. The development of the wall top displacement and the active and passive earth pressures acting on the ECR walls during excavations are studied. Upon the experimental observations, a displacement-dependent earth pressure coefficient is proposed to derive an analytical solution to predict both the active and passive earth pressure acting on the ECR wall (pile), where the displacement value and displacement mode of the ECR wall (pile) are taken into account. Comparisons between the model predictions and test results are carried out. A good agreement is observed, which shows the validity of the proposed solution. Based on the proposed solution, a displacement-controlled method for the design of ECR walls (piles) that takes into account the location of the rotation point is proposed. Parametric studies are conducted to demonstrate the impact of deformation control and excavation depth on the design parameters of ECR walls (piles).

Soil arching is significantly influenced by relative density, while its mechanisms have barely been analyzed. A series of DEM numerical simulations of the classical trapdoor test were carried out to investigate the multi-scale mechanisms of arching development and degradation in granular materials with different relative density. For analysis, the granular assembly was divided into three zones according to the particle vertical displacement normalized by the trapdoor displacement δ. The results show that before the maximum arching state (corresponding to the minimum arching ratio), contact forces between particles in a specific zone (where the vertical displacement of particles is larger than 0.1δ but less than 0.9δ) increase rapidly and robust arched force chains with large particle contact forces are generated. The variation in contact forces and force chains becomes more obvious as the sample porosity decreases. As a result, soil arching generated in a denser particle assembly is stronger, and the minimum value of the arching ratio is increased with the sample porosity. After the maximum arching state, the force chains in this zone are degenerated gradually, leading to a decrease in particle contact forces in microscale and an increase in the arching ratio in macroscale. The recovery of the arching ratio after the minimum value is also more significant in simulations with a larger relative density, as the degeneration of contact force chains is more obvious in denser samples. These results indicate the importance of contact force chain stabilities in specific zones for improving soil arching in engineering practice.

Conventional methods for designing retaining structures are not applicable to asymmetric excavation or deformation-based designs. This study proposes a quadruple-line displacement-dependent earth pressure coefficient model. Based on the proposed model, an analytical solution was developed to facilitate the deformation-based design of the asymmetric length of retaining walls propped at the crest. Furthermore, the effects of the soil internal friction angle, strut stiffness, excavation asymmetry level, and deformation control value on the embedment ratio (R_e) of retaining walls were investigated. The results showed that R_e determined by the classical equivalent-beam method is unsafe due to its basis on the ultimate-state earth pressure theory. The R_e value of the shallower side exhibited greater sensitivity to asymmetric excavation than that of the deeper side. The retaining structure’s required R_e decreased with an increase in the excavation asymmetry level. The required R_e on either side of the retaining structure decreased as the deformation control values increased. The controlled deformation had a more obvious effect on the R_e value of the retaining structure on the deeper side. The proposed method can be used for the deformation-based design of asymmetric wall lengths of retaining structures propped at the crest, considering the different excavation depths on both sides.