The Influence Of Circular Lining Tunnel On Sub-Ground Motions Along The Line For Incident Plane SH Wave

With the development of urbanization construction,land resources are becoming increasingly scarce,and the development and utilization of underground space is deepening.The construction of the underground structure destroyed the local integrity of the soil and changed the dynamic characteristics of the original site,thus affecting the seismic safety of nearby ground and underground engineering structures.Therefore,it is of great significance for seismic design of structures along underground structures to deeply and systematically analyze the variation of seismic ground motion along underground structures with depth.At present,most of the research results only analyze the influence of the underground tunnel on the surface movement when SH wave incident,but there are few studies on the dynamic response of the soil around the underground tunnel in a certain depth range.Therefore,on the basis of predecessors,taking the influence of underground tunnels on the surrounding ground motion as the research object,based on elastic wave theory,using wave function expansion method and mirror image principle,the scattering problem of single circular lining tunnel and double circular lining tunnel with arbitrary angle in elastic half space when plane SH wave incident is analyzed,and the analytical solutions for the displacement of the field near a single circular lining tunnel and a double circular lining tunnel with arbitrary angle are obtained.The specific solution process is as follows: Firstly,the coordinate transformation is carried out of each wave potential function for convenience calculation.The general form of Graf addition formula and the modified Graf addition formula are applied in the coordinate transformation,and the transformed wave potential function is brought into the boundary condition;then,combining with the basic equation of elastic dynamics,a set of infinite order linear equations is obtained by theoretical derivation.The equations are solved by truncation,and the displacement fields in each coordinate system are obtained and the amplitude of the subsurface displacement around single and double circular lining tunnels is obtained;Finally,a numerical example is used to analyze the influence of the underground circular tunnel on the surrounding ground motion of the SH wave incident in the elastic half space.The variation of SH incident angle,incident frequency,tunnel burial depth and lining stiffness with depth is investigated.The results show that the underground tunnel has a significant effect on the ground motion along the tunnel.This study not only provides theoretical guidance for the seismic response of underground circular lining tunnel to the surrounding ground,but also provides theoretical basis for quantitative evaluation of seismic safety of underground tunnel to underground buildings along the line.