Research On Solving Methods, Characteristics And Applications Of Layered Soil Site's Natural Frequency

The natural frequency of soil layers is one of the most important dynamic characteristics of site soils. It's indicated by large numbers of observation data that much seismic disasters is caused by the resonance vibration between structures and ground, so, in order to effectively estimate and prevent this kind of seismic disasters, the natural frequencies of engineering structures should keep away from that of the ground. In this dissertation, engineering sites are regarded as horizontally layered soils on half space, and the solving methods, characteristics and engineering applications are studied deeply and systematically. On the basis of these researches, the natural frequency and its influencing factors of horizontal soil layers on half space are analyzed.The mass matrix, stiffness matrix, damping matrix, establishment of vibration equations and the solving of natural frequency and mode shapes of the shear mass point system method based on clump mass matrix(clump mass method) are explained firstly, based on it, another kind of shear mass point system method based on consistent mass matrix(consistent mass method) is developed. Through introducing semi-infinite element to simulate the half apace, a kind of improved consistent mass method is developed and the influence of the half space elasticity is analyzed by it. Then, the solving precision and its influencing factors of shear mass point system methods and the influence of delaminating strategy on the convergence speed of consistent mass method are analyzed. At the same time, the differences of two kinds of shear mass point system methods are compared. Finally, the influencing factors and their characteristics of the natural frequency of horizontally layered sites on half space are analyzed with shear mass point system methods and a problem about the computing depth selecting of sites' natural frequencies is put forward and discussed briefly.Based on the horizontal vibration differential equations of straight beam and its mode shape function solution, the natural vibration differential equation of vertical shear cantilever model on rigid half space is solved and the analytic solutions with transcendental equation form of single layer and double, three layers on half space are obtained. At the same time, the recurrence solution which applicable for random multi-layer is deduced. Then, considering the elasticity of half pace, that is, take the reaction between half space and the soil layers on it considered, the spring-shear beam model is developed and the analytic solutions of single layer and double, three layers and random multi-layer on half space are obtained. Through introducing complex material parameters, the analytic solutions with damping are gained. Finally, the influence of the elasticity of half space on sites' natural frequencies and the solving precision of wave velocity method and consistent mass method are analyzed by spring-shear beam model solutions.On the basis of plane body wave motion equations, dividing to in-plane(P-SV) and anti-plane(SH) problems, the conversion matrixes of state vectors between soil layer's top and under sides are deduced, and based on these, dynamic stiffness matrixes of soil layers and half space can also be gained separately. By assembling dynamic stiffness matrixes of all soil layers and half space, system vibration equation can be get, which is expressed with integral dynamic stiffness matrix, and hence natural frequency and vibration mode for thewhole system can be solved. Then, taking pure shear vibration in horizontal direction into considerations, solutions are deduced under the condition of wave injecting vertically, and taking contrast with solutions get by shear beam methods, accuracy of shear beam methods and rationality of using spring - shear beam model to consider half space elasticity are analyzed. Lastly, according to introducing complex material parameters, solutions with damping are obtained. Then through calculation cases, damping influences of soil layers and half space on natural frequency are studied.On the assumption that Rayleigh wave is the main energy in microtremors caused by environmental vibrations, the relation between the reflecting depth of microtremors and the computing depth of site's natural frequency is analyzed and relations between Rayleigh wavelength and computing depth for different models with different site's conditions are obtained. On the basis of these, characteristics and influent factors of them are summarized.