Research On Dynamic Response For Underground Cavity Subjected To Anti-plane Impact Load

The brakes, the vehicle collision and accidental explosion occur frequently in underground traffic roads such as vehicles tunnels and subway tunnels. When these situations occur the impact load exerted on the cavity is not only radial, tangential impact load along the cavity can not be ignored. It is necessary to evaluate its safety performance because the influence of the tangential impact on the structure and the soil is also great. So far the theory of dynamic response for underground cavity under radial impact loads has developed sophisticatedly at home and abroad. However, the study on anti-plane dynamic response is reported less. Therefore the study on the dynamic response of a cylindrical cavity subjected to an axial impact load is not only of profound theoretical significance, but also of great practical value in the actual project based on elastodynamics and wave propagation theory.In this paper the material of the soil is assumed to be homogeneous, isotropic and linearly elastic. The external impact load excited on cylindrical cavity is simplified to uniform sudden load along the axial direction. Based on wave propagation theory, the dynamic response of an elastic soil body containing a cylindrical cavity subjected to the anti-plane load is studied including steady-state response and transient response. The main research contents and conclusions are as follows:First of all, assuming that the wave source function is harmonic, the steady dynamic response of an elastic full space containing a cylindrical cavity subjected to the axial impact load is solved using analytical methods. The soil stress-time curve and displacement-time curve and the decay curve with wave propagation distance are drawn. And then on the base of the theory of the full space, according to the image method, the dynamic response of the soil half-space is obtained, The calculation results show that, the stress and displacement of the soil are axially symmetric, the farther the wave is from the source, the smaller the stress and the displacement are, and the stress and the displacement are just functions of the radial distance from the axis in full space. In half space, the stress and displacement and the complexity of spatial variations along the circumference increase with the increasing of the frequency of the wave source, and the position of maximum displacement and maximum stress moves away from the ground surface. The bigger the depth is, the smaller the stress and displacement are, and the less the spatial variation with angle of stress and displacement is.Secondly, the transient response to sudden anti-plane shock load of an infinite soil body containing a cylindrical cavity is studied. Using Laplace transform method, the frequency domain solutions are obtained. Using Laplace inverse transform combining with contour integral, the general analytical expressions of the soil displacement and stress are obtained in the time domain, respectively. And the calculation results are compared with those from numerical inversion proposed by Durbin and the static results, one observes good agreement between analytical and numerical inversion results, which lending the further support to the method presented. Durbin’s method is applicable to this paper. Finally the stress and displacement variation with time is analyzed, the conclusions are gained:after the wave arrival the stress and the displacement at this point increase abruptly, then reduce and tend to the static value gradually at last.Then, taking into account the ground surface, the transient response of an elastic soil body half-space containing a cylindrical cavity subjected to the axial impact load is investigated. Then infinite space solutions are translated into solutions for the elastic half-space using image method. Using integral transform method, the stress and displacement are obtained in the frequency domain. And the numerical solutions of the problem are presented by the numerical inversion proposed by Durbin. Thus the displacement and stress distribution of the soil in half-space are gained. The propagation of elastic waves, the variation of the stress and displacement with respect to the time, angle, the radial distance and depth of the cavity are presented.After that, taking into account the lining, using the integral transform frequency solutions of the lining and soil of the displacement and stress are obtained. The dynamic response in time domain of the lining and the soil using the numerical inverse Laplace transform proposed by Durbin is attained. Displacement-time curves and stress-time curves are drawn on the outer boundary of the lining and a point in the soil. The influence of the relative shear modulus and relative thickness of the lining on the response is analyzed. The results show that, lining and soil media the relative shear modulus, the displacement and stress of the lining and the soil decrease with the increasing of the relative shear modulus and relative thickness.Finally, based on transient response in full space containing a cylindrical cavity with lining subjected to the axial impact load, by means of image method, frequency solutions of the lining and soil of the displacement and stress are obtained respectively. Then using numerical inverse transform, the transient response of the lining and the soil subjected to impact load in the time domain is obtained. Displacement-time curves, stress-time curves and polar plots are drawn in half space. The influence of the depth, the relative shear modulus and relative thickness of the lining on the response is discussed.