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目前对地下结构在竖向传播的水平剪切S波作用下的地震内力及变形已给出了拟静力法闭合解析解,但对P波竖向压缩作用下的有关解答仍待探讨。对此基于拟静力法,采用平面弹性力学复变函数理论,推导出无限远处作用地震P波压缩应力时方形深埋地下结构内力的解析解,以便初步抗震设计时采用。通过算例验证,应用复变函数方法求得的位移解析解数值较大,偏于安全。
At present, the closed-form analytical solutions of quasi-static method are given for the seismic internal forces and deformation under the horizontal shear S wave propagating vertically in the subsurface structure. However, the relevant solutions under the vertical compression of the P-wave are still to be discussed. Based on quasi-static method, the analytic solution of the internal force of square deep buried underground structure under P wave compressive stress at infinity is deduced by the theory of planar elastic mechanics complex function so as to be used in preliminary seismic design. Through the example verification, the displacement analytical solution obtained by using the complex function method is larger and safer.