This paper provides a dynamic analysis of the response of a subsurface cylindrical tunnel to SH waves influenced by a neighboring semi-cylindrical hill and semi-cylindrical canyon in half-space using complex functions. For convenience in finding a solution, the half-space is divided into two parts and the scattered wave functions are constructed in both parts. Then the mixed boundary conditions are satisfied by moving coordinates. Finally, the problem is reduced to solving a set of infinite linear algebraic equations, for which the unknown coefficients are obtained by truncation of the infinite set of equations. The effects of the incident angles and frequencies of SH waves, as well as of the radius of the tunnel, hill, and canyon on the dynamic stress concentration of the tunnel are studied. The results show that the hill and canyon have a significant effect on the dynamic stress concentration of the tunnel.
To disclose the impacts of hysteretic energy (HE) demand on energy-based seismic design, this paper introduces the dimensionless parameter βEH to express the cumulative HE indirectly and establishes the βEH spectrum for energy-based seismic design. After analyzing numerous seismic responses of a single degree-of-freedom (SDOF) system, the author set up a simplified βEH spectral formula based on the genetic algorithm. Then, 750 ground motion records were selected according to Chinese site classification, and used to examine the effects of soil type and damping ratio on the βEH spectra. The results show that the soil type, site group and damping ratio have significant effects on the βEH spectra; the ductility ratio has an impact on the spectral value but not the spectral shape.
Based on the fundamental solution for a complete elastic space impacted by an out-plane harmonic linear source load, the Green's function is obtained, which is the fundamental solution of displacement field for an elastic half space with a semi-cylindrical hill under an out-plane harmonic linear source load at an arbitrary point basal body. According to the idea "division", the whole model is divided, Part I is a circular domain including the boundary of the hill, and all the rest can be considered as Part II. The disturbance impacted by the out-plane harmonic linear source load can be considered as the incident wave, and the corresponding wave function can be constructed in two domains respectively. Considering the conditions of common boundary, the Green's function suitable for the problem can be obtained. At last, the limitation of the Green's function solved in the paper is discussed.
Keywords: Green's function, semi-cylindrical hill, basal body J ka J ka kW C a J ka J ka z J k z J k z z r
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