Numerical and theoretical research on stress distribution in the loosening zone of the trapdoor problem

Abstract

Summary The traditional theory of soil arching effect was developed on the assumption that stress distribution in the loosening zone is uniform. However, because of the deflection of principal stress' direction, the stress distribution in the loosening zone is actually ununiform. For the evaluation of principal stress axis deflection and stress redistribution, a discrete element method numerical model of trapdoor problem is established for the simulation of soil arching effect. Based on the numerical results, an arc shape of major principal stress trajectory and uniform horizontal stress distribution at the same depth of the loosening zone are adopted. An analytical model is raised to estimate the average loosening earth pressure acting on the trapdoor and stress distribution in the loosening zone at a limit state. In addition, comparison studies are carried out between the predictions of the proposed solutions and discrete element method numerical results as well as available model test results, thereby validating the accuracy of the proposed theoretical model. Both numerical and theoretical results indicate that the vertical stress distribution in the loosening zone is obviously ununiform. The load acting in the middle of loosening zone is transferred toward two sides so that the vertical stress distribution in loosening zone is concave.

A new isotropic hyper-elasticity model for enhancing the rate of convergence of Mohr-Coulomb-like constitutive models and application to shallow foundations and trapdoors

“…For the active trapdoor problem, FEM results are slightly smaller than the upper bound solution until the H/B ratio is lower than 2.5, whereas for larger values FEM results lay in the range between the lower and upper bound solutions (although they are closer to the upper bound). Moreover, failure mechanism are consistent with those evaluated by Garcia & Bray and Liang & Xu [9,15] with discrete element methods (DEM) using the commercial PFC code, and load-displacement curves obtained from FEM simulations (not reported here for the sake of conciseness) are consistent with those obtained from experiments [3,10] on reduced scale models tested in laboratory.…”

“…Most of their simulations were performed with a non-null cohesion intercept and in all results a non-associated flow rule is considered, with a null dilatation or an angle of dilatancy much smaller than the friction angle. Active and passive trapdoor problems were investigated also recently by other authors [4,3,34,10,9,35,15] by means of numerical and experimental models.…”

Earth Pressure of the Trapdoor Problem Using Three-Dimensional Discrete Element Method

“…Lai et al [1] pointed out that soil arching effect is the key to the load transfer of high pile embankment. Liang et al [2] pointed out that it is the main reason why the earth pressure on the shield tunnel far less than its theoretical value. Jiao et al [3] considered soil arching effects on the distribution of earth pressure on rigid retaining walls and reported that it also affects the active earth pressure acting on the rigid retaining wall.…”

“…In theoretical studies, Liang et al [2] proposed an analytical model to estimate the average loosening earth pressure acting on the trapdoor and the stress distribution in the loose area under the limit state. Based on the experimental observation, Liang et al [21] proposed an analytical solution considering the deflection of the principal stress axis to predict the minimum and residual value of the loose earth pressure acting on the top of the trapdoor.…”