Dynamic Response Of Twin Closely-spaced Tunnels To Earthquake Waves

Many metropolises in China have devoted into metro construction recently to release the city transportation pressure, and thus raising some underground cavity groups composed of twin cavities. Similarly, twin circular tunnels were also widely used in highway and railway projects to step over mountains. Most of these underground structures were constructed in earthquake region and the stability analysis to ensure their safety during earthquake is remarked by great engineering significance. There used to be a general understanding that the underground structures should sustain seldom damage by earthquake than the ground structures. However, the intensive damage of underground structures experienced in1995Kobe earthquake reminded researchers that more attentions should be paid to the dynamic response analysis of underground structures.According to the wave theory, the essential issue of the earthquake dynamic response of underground tunnels is the scattering of the seismic waves. In the earthquake process, local topography condition has large influence on the seismic wave propagation. The origin of this influence is the reflection, refraction and the scattering of seismic waves induced by the field, and the specific manifestation of this influence is the amplification and narrowing effect of the stratum on the seismic wave propagation, which is the cause of the regionalization of the damage distribution. When the underground structure comprises of several cavities, the mutual disturbance of the wave fields of multiple cavities will increase the complexity of the scattering of seismic waves of multiple cavities during earthquake. In routine study, dynamic stress concentration is always used to be an important index to evaluate the stability of underground structure subjected to earthquake. Hence, this work devoted into the investigation of the distributions of dynamic stress concentration factors for twin closely-spaced circular tunnels in earthquake.Herein the scattering issues of the deep buried twin circular tunnels by stable incident P, SV and SH waves were analyzed by employing the plane elastic complex variable theory and conformal mapping as follows:(1)The Holmholtz equation of stable condition was established by introducing the displacement potential function and was solved by using the separation of variables. Furthermore, the stress and strain expressions of the surrounding medium for the single circular deep buried tunnel subjected to the stable incident P, SV and SH waves, respectively.(2)The scattering expression with undetermined coefficients of the single circular deep buried tunnel subjected to the stable incident P, SV and SH waves were derived respectively in plane coordinate system. Superposition principle was applied to superimpose the incident wave and the scattered wave and achieve the total wave field expressions with undetermined coefficients of the single circular deep buried tunnel subjected to the stable incident P, SV and SH waves, respectively.(3)The initial computing region Γ was mapped to a circular ring region Ω by using the conformal mapping function. Thus the local coordinate system of two single circular tunnels in initial calculation model was transformed into the complex plane coordinate system. The wave field expression and the complex variable function expressions for the displacement and stress can be solved by conversing into the global coordinate system.(4)Unknown coefficients in wave field expressions can be determined by using the corresponding stress boundary condition in the mapped region and thus the equations be solved. Due to the fact that the wave potential function is a infinite series, the convergence of the series is herein assessed by studying the variance of dynamic stress concentration factor against the series.(5)Parametric study was conducted finally. Given the incident angles of incident wave as y=0°and y=90°, the influence of the space of twin circular tunnels and the dimensionless frequency variance on the dynamic stress concentration factor on the cavity walls was discussed, when the twin circular tunnels were subjected to the stable incident P, SV and SH waves, respectively. The difference of the distribution of the dynamic stress concentration factor was examined when twin circular tunnels were changed into a single circular tunnel.