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既有理论针对土体与结构相互作用的地震响应研究一直集中在圆形隧洞截面,而就矩形隧洞的分析往往会增加动力计算的复杂性。基于拟静力法,采用复变函数理论和保角变换方法,推导获得远场剪切波作用下深埋矩形隧洞的地震响应解析解。该复变函数解答考虑了土体与隧洞间相互作用的剪应力和法向正应力,并针对保角转化函数引入修正系数,提高了在复平面转化时矩形隧洞截面表示函数的计算精度。结合数值模型验证解析方法的正确性,并对矩形隧洞归一化位移比和土体应力场变化进行参数分析。研究表明,通过引入修正系数,使得解析解精度得到一定提高,与数值模拟解答更为接近。矩形隧洞归一化位移比值随着隧洞衬砌与土体的相对刚度比值增大而减小,而随着截面尺寸比率的增大而增大。在矩形隧洞截面尺寸的比率和相对刚度比值一定的情况下,矩形隧洞的归一化位移比随着土体泊松比的减小而增大。当截面尺寸比率为1时(正方形隧洞),土体泊松比的变化对于隧洞归一化位移比值影响较小。矩形隧洞周围土体应力随着土体泊松比的增大而增大,随着土体弹性模量的增大而减小,而随着衬砌剪切模量的增大而减小。
The existing theory focuses on the seismic response of soil-structure interaction. The research on the rectangular tunnel always focuses on the complexity of dynamic calculation. Based on the quasi-static method, the complex seismic response theory and the conformal mapping method are used to derive the analytic solution to the seismic response of the deep buried rectangular tunnel under the action of the far-field shear wave. The complex function solution considers the shear stress and the normal normal stress of the interaction between the soil and the tunnel, and introduces the correction coefficient for the conformal transformation function to improve the calculation accuracy of the rectangular tunnel cross-section representation function in the complex plane transformation. The correctness of the analytical method is verified by numerical model. The normalized displacement ratio of rectangular tunnel and the change of soil stress field are analyzed. The research shows that by introducing the correction coefficient, the accuracy of the analytical solution is improved to some extent, which is closer to the numerical simulation solution. The normalized displacement ratio of rectangular tunnel decreases with the increase of the ratio of relative stiffness between tunnel lining and soil, and increases with the increase of sectional size ratio. Under the condition that the ratio of the rectangular cross-section size and the relative stiffness is constant, the normalized displacement ratio of rectangular tunnels increases with the decrease of Poisson’s ratio of soil. When the section size ratio is 1 (square tunnel), the change of Poisson’s ratio of soil has little effect on the normalized displacement ratio of tunnel. The stress of soil around rectangular tunnel increases with the increase of Poisson’s ratio of soil, decreases with the increase of elastic modulus of soil, and decreases with the increase of shear modulus of soil.