Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural...Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural frequencies of soil deposit, nor simulate a damping of frequency independence. This research develops a new discrete model for onedimensional viscoelastic response analysis of layered soil deposit based on the mode equivalence method. The new discrete model is a one-dimensional equivalent multi-degree-of-freedom（MDOF） system characterized by a series of concentrated masses, springs and dashpots with a special configuration. The dynamic response of the equivalent MDOF system is analytically derived and the physical parameters are formulated in terms of modal properties. The equivalent MDOF system is verified through a comparison of amplification functions with the available theoretical solutions. The appropriate number of degrees of freedom（DOFs） in the equivalent MDOF system is estimated. A comparative study of the equivalent MDOF system with the existing discrete models is performed. It is shown that the proposed equivalent MDOF system can exactly present the natural frequencies and the hysteretic damping of soil deposits and provide more accurate results with fewer DOFs.展开更多
Wave-induced flow is observed as the domi- nated factor for P wave propagation at seismic frequencies. This mechanism has a mesoscopic scale nature. The inhomogeneous unsaturated patches are regarded larger than the p...Wave-induced flow is observed as the domi- nated factor for P wave propagation at seismic frequencies. This mechanism has a mesoscopic scale nature. The inhomogeneous unsaturated patches are regarded larger than the pore size, but smaller than the wavelength. Surface wave, e.g., Rayleigh wave, which propagates along the free surface, generated by the interfering of body waves is also affected by the mesoscopic loss mechanisms. Recent studies have reported that the effect of the wave-induced flow in wave propagation shows a relaxation behavior. Viscoelastic equivalent relaxation function associated with the wave mode can describe the kinetic nature of the attenuation. In this paper, the equivalent viscoelastic relaxation functions are extended to take into account the free surface for the Rayleigh surface wave propagation inpatchy saturated poroelastic media. Numerical results for the frequency-dependent velocity and attenuation and the time-dependent dynamical responses for the equivalent Rayleigh surface wave propagation along an interface between vacuum and patchy saturated porous media are reported in the low-frequency range （0.1-1,000 Hz）. The results show that the dispersion and attenuation and kinetic characteristics of the mesoscopic loss effect for the surface wave can be effectively represented in the equivalent vis- coelastic media. The simulation of surface wave propaga- tion within mesoscopic patches requires solving Blot＇s differential equations in very small grid spaces, involving the conversion of the fast P wave energy diffusion into the Blot slow wave. This procedure requires a very large amount of computer consumption. An efficient equivalent approach for this patchy saturated poroelastic media shows a more convenient way to solve the single phase visco- elastic differential equations.展开更多
基金National Natural Science Foundation of China(51208296&51478343)Shanghai Committee of Science and Technology(13231200503)+2 种基金Fundamental Research Funds for the Central Universities(2013KJ095&101201438)Shanghai Educational Development Foundation(13CG17)National Key Technology R&D Program(2012BAK24B04)
文摘Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural frequencies of soil deposit, nor simulate a damping of frequency independence. This research develops a new discrete model for onedimensional viscoelastic response analysis of layered soil deposit based on the mode equivalence method. The new discrete model is a one-dimensional equivalent multi-degree-of-freedom（MDOF） system characterized by a series of concentrated masses, springs and dashpots with a special configuration. The dynamic response of the equivalent MDOF system is analytically derived and the physical parameters are formulated in terms of modal properties. The equivalent MDOF system is verified through a comparison of amplification functions with the available theoretical solutions. The appropriate number of degrees of freedom（DOFs） in the equivalent MDOF system is estimated. A comparative study of the equivalent MDOF system with the existing discrete models is performed. It is shown that the proposed equivalent MDOF system can exactly present the natural frequencies and the hysteretic damping of soil deposits and provide more accurate results with fewer DOFs.
基金support by the Natural Basic Research Program of China (the ‘‘973 Project’’,Grant No. 2013CB733303)the National Natural Science Foundation of China (Grant Nos. 41304077, 40974079)+1 种基金Postdoctoral Science Foundation of China (Grant No. 2013M531744)Key Laboratory of Geospace Environment and Geodesy (Grant Nos. 12-02-03)
文摘Wave-induced flow is observed as the domi- nated factor for P wave propagation at seismic frequencies. This mechanism has a mesoscopic scale nature. The inhomogeneous unsaturated patches are regarded larger than the pore size, but smaller than the wavelength. Surface wave, e.g., Rayleigh wave, which propagates along the free surface, generated by the interfering of body waves is also affected by the mesoscopic loss mechanisms. Recent studies have reported that the effect of the wave-induced flow in wave propagation shows a relaxation behavior. Viscoelastic equivalent relaxation function associated with the wave mode can describe the kinetic nature of the attenuation. In this paper, the equivalent viscoelastic relaxation functions are extended to take into account the free surface for the Rayleigh surface wave propagation inpatchy saturated poroelastic media. Numerical results for the frequency-dependent velocity and attenuation and the time-dependent dynamical responses for the equivalent Rayleigh surface wave propagation along an interface between vacuum and patchy saturated porous media are reported in the low-frequency range （0.1-1,000 Hz）. The results show that the dispersion and attenuation and kinetic characteristics of the mesoscopic loss effect for the surface wave can be effectively represented in the equivalent vis- coelastic media. The simulation of surface wave propaga- tion within mesoscopic patches requires solving Blot＇s differential equations in very small grid spaces, involving the conversion of the fast P wave energy diffusion into the Blot slow wave. This procedure requires a very large amount of computer consumption. An efficient equivalent approach for this patchy saturated poroelastic media shows a more convenient way to solve the single phase visco- elastic differential equations.
