Safety factor of heave-resistant stability considering two- and three-dimensional size effects of foundation pits

A large number of project practices show that small-size foundation pits are more stable, which display obvious size effects. However, the methods recommended by the existing codes all assume that the excavation width and size do not affect the safety factor, resulting in a great waste of enclosure structure of small-size and narrow foundation pits. Currently, the safety factor calculated by the analytical method cannot scientifically and reasonably consider the three-dimensional size effect of foundation pits. In order to solve the problem, a new safety factor K_W is proposed, by which the problem of excavation bottom uplifting and instability is reduced to that of the expansion of the plastic zone due to unloading in the elastic half-space. The absolute value of the load caused by excavation isγ₁H. The enclosure structure of foundation pits leads to the extension of the plastic zone under the pit bottom downward when they fail. The ultimate state of the load will be reached when the fracture surface of the plastic zone passes through the toe of the enclosure structure. The additional stress caused by unloading can be calculated by the analytical solution of the elasticity. The limit load can be obtained by the additional stress plus the ground stress. Considering the overload qoutside the foundation pits, K_W is equal to p_u/(γ₁H+q). The new safety factor K_W can be adopted to analyze the impact of the excavation width on the stability of strip pits and the impact of the excavation size on the stability of rectangular pits and to calculate the safety factor at the different positions for the same foundation pit. An important method is proposed to decrease the embedded depth of enclosure structure taking the advantages of two-and three-dimensional size effects and spatial effect of foundation pits so that the new safety factor can be widely applied.