A Modified B-Differentiable Equation Method for the Seismic Analysis of Arch Dams Considering the Initial Strength of Contraction Joints

For arch dams, the joint surface has a certain bond strength after grouting the contraction joints, which can withstand the arch-wise tensile stress to a certain extent and influence the stress distribution of the dam blocks on both sides. The seismic response analysis of arch dams needs to consider the influence of the initial tensile and shear strengths generated by the contraction joint grouting. Thus, a modified B-differentiable equation method is proposed by introducing the initial tensile strength and the initial shear strength of contraction joints the into traditional B-differentiable equation method. In the proposed method, the shear strength varies with the contraction joint opening. The modified B-differentiable equation method can still be solved by the B-differentiable damped Newton method with theoretical guarantee of convergence. Then, a seismic calculation model for the dam–reservoir–foundation system is developed based on the modified B-differentiable equation method, the Westergaard additional mass method, and multiple transmission boundary conditions. The influence of the initial tensile and shear strength of the contraction joints on the arch dam seismic response is discussed. The results show that the initial tensile and shear strength of the contraction joints have an influence on the opening and distribution range of the contraction joints and the maximum values of the principal tensile and compressive stress in the dam body. The initial tensile and compressive strength of the contraction joints should be considered when carrying out seismic response analysis of arch dams.