Incremental Iterative Calculation Method for Stress and Deformation of Retaining Structures under Asymmetric Excavation - JIN Ya-bing, YU Peng, GE Fan, FU Xu-dong (长江科学院院报)
[Objectives] Numerous engineering practices and studies on foundation pits have shown that the bending moment and horizontal displacement of the support structure on the deep excavation side of asymmetric excavation foundation pits are significantly greater than those on the shallow excavation side, which is notably different from the situation where the support structures on both sides of symmetric excavation foundation pits deform inward uniformly. When using the current standard’s support fixed point adjustment coefficient method for calculation, there are shortcomings such as a wide range of values for the fixed point adjustment coefficient λ and difficulty in quantification, as well as significant discrepancies between the calculated results and actual conditions when asymmetric excavation causes the absence of displacement fixed points on the internal supports. [Methods] The hyperbolic model of earth pressure versus horizontal displacement (p-y) of the retaining structure was adopted. It was assumed that the curvature of the p-y curves for active and passive deformation at y = 0 are the same and calculated using the m-method, i.e., K0a = K0p = K0 = mz·z. Calculation methods for active earth pressure, passive earth pressure, and net earth pressure on the retaining structure were proposed. Considering the excavation and support construction process of the foundation pit, the increment of earth pressure load on the retaining structure caused by excavation was first calculated, and then the increments of internal force and displacement were solved using the incremental method. An incremental iterative calculation procedure for the stress and deformation of the foundation pit retaining structure was established. Based on this incremental iterative calculation procedure and according to the force balance conditions and deformation compatibility at the left and right ends of the internal support retaining structure, a calculation method for the stress and deformation of internal support retaining structures under asymmetric excavation of foundation pits was proposed and numerically implemented on the MATLAB platform, overcoming the difficulty of quantifying the fixed point adjustment coefficient λ in current normative calculation methods. [Results] Calculation results of engineering cases showed that the horizontal displacement curves of the diaphragm walls on the deep and shallow excavation sides obtained by the incremental iterative calculation method were generally consistent with the distribution of the measured curves. The maximum horizontal displacement of the support structure on the deep excavation side was 23.15 mm, while the measured value was 25.83 mm, with a difference of 10.4%. The calculated maximum horizontal displacement of the support structure on the shallow excavation side was 8.75 mm, while the measured value was 8.99 mm, with a difference of only 2.67%. The maximum horizontal displacement of the support structure on the deep excavation side calculated by the traditional elastic fulcrum method was only 12.93 mm, differing from the measured value by 49.67%, thus underestimating the horizontal displacement of the deep excavation side. The maximum bending moments of the diaphragm walls on the deep and shallow excavation sides obtained by this method were 451.24 kN·m/m and 228.95 kN·m/m, respectively, differing by 49.3%. The axial force of the internal support obtained by this method was 204.56 kN/m, which lies between the internal support axial forces calculated by the traditional elastic fulcrum method for the deep and shallow excavation sides, avoiding the waste caused by designing solely based on the deep excavation side. [Conclusions] The study shows that the traditional elastic fulcrum method tends to overestimate the support stiffness and underestimate the horizontal displacement on the deep excavation side. The incremental iterative calculation method satisfies the force balance conditions and deformation compatibility at both ends of the internal supports. The horizontal displacement curves of the diaphragm walls on both sides obtained by this method are basically consistent with the distribution patterns and values of the measured engineering curves. It overcomes the difficulty of quantifying the fixed point adjustment coefficient λ in current normative calculation methods and can serve as a reference for the design and calculation of similar foundation pits.