A modified beam-spring model method and its application considering unloading effect during excavation

Beam-spring model method is a primary method for designing of retaining structures in actual excavation projects; it is based on foundation reaction coefficient method for calculating vertical elastic piles acted by horizontal loads. Unfortunately, the current method cannot consider the unloading effect on the soil lateral resistance coefficient and the soil deformation in the pit, so as to lead to underestimate the horizontal deformation of the retaining wall. The distribution of unloading stresses is deduced using the Mindlin solution. On the basis of previous experimental studies, the soil resistance coefficients considering the effect of excavation unloading under different ratios of unloading are derived. The development of deformation of retaining structures is divided into two stages: the first is the instantaneous unloading deformation of the soil in the pit; and the second is the deformation of retaining wall induced by the lateral earth pressure differences on the wall. Then a modified beam-spring model method is presented considering unloading stress paths and unloading deformations. Finally, the method is applied to two typical 3D numerical excavation cases. It is shown that the horizontal displacement of the wall calculated by the modified method is greater while the difference between the internal forces is quite small; the greater the excavation plane size is, the more obvious the differences between the deformation results are. The modified method can better reflect the effect of the size of the base plane on the deformation of the retaining structure.