Seismic Response Analysis Of Partially Saturated Soil Site Based On Random Field

The random vibration has been one of research hotspots in the field of soil dynamics and is also a fundamental issue in the research works of geotechnical engineering and earthquake engineering and geophysics,etc.The three main factors that affect the ground motion response and response spectrum are the source characteristics,seismic wave propagation and site conditions.In the analysis of dynamic response of soil,many scholars usually care about magnitude and epicentral distance but the results of seismic damage investigation and theoretical analysis show that the soil characteristics of the site have great influence on the seismic damage,so we pay more and more attention on the dynamic characteristics and soil structure of soil in the seismic response analysis.In engineering seismology and geotechnical earthquake engineering,the dynamic characteristics of soil usually refer to soil shear modulus,mass density,damping ratio and shear wave velocity,which are three necessary calculation parameters in seismic safety evaluation of engineering sites.In practical engineering,most of the soil we see is the saturated soil,therefore,the research of the complex P and SV waves not only have great theoretical significance on the propagation of partially saturated soils,but also have extremely important practical significance on our production and life.In this paper,the propagation characteristics and dynamic response of SH wave and the complex P and SV waves in partially saturated soils are studied on the basis of soil dynamics and random vibration theory.Firstly,the related theories of partially saturated soils are expounded where a simplified model of partially saturated soil is considered as a three-phase medium and the most important factors in the study of soil dynamics,such as shear modulus,mass density,damping ratio and saturation,are focused on,which not only takes the dynamic characteristics of the gas in the partially saturated soil into account,but also considers the influence of the gas compression on the compressibility of the fluid and the wave propagation in the partially saturated porous media.Then the random vibration theory,wave theory and random seismic model in the paper are introduced in detail.Secondly,based on random vibration and wave theory and the Tajimi-Kanai spectrum model,a seismic model with a given magnitude and epicenter distance is used to simulate the seismic motion.For the random variation of soil properties such as shear modulus,mass density,damping ratio and saturation of partially saturated soils,we analyse the random dynamic response of the partially saturated soil site by using Rosenblueth point estimate method when the seismic wave such as SH wave or the complex P and SV waves a input and we obtain these digital features including the amplified power spectral density function,the acceleration power spectrum density,the mean value and the standard deviation and so on,respectively.In a numerical example,considering a clay ground,the digital features such as the amplified power spectral density function,the acceleration power spectral density,the mean value and the standard deviation are analyzed for the random variation of soil properties and the different incident angles.The results show that the random variation of partially saturated soils properties and incident angles have great influence on the site amplification effect.Lastly,according to an analytical method presented by Amina Sadouki that evaluates the response of ground motion along with random variation of inhomogeneous elastic soil characterizes,we analyse the effect of the change of depth on dimensionless average distance and the shear stress.when partially saturated soils characteristics which are mass density and shear modulus are random variable.Integro-differential equations are solved by using the Laplace transform method and we obtain that effects of random change of the soil properties on distributions of the dimensionless mean displacement and stress with depth.In a numerical example,a clay ground is also considered,we obtain the curves that the effects of their random change on the dimensionless mean displacement and stress with depth distribution when mass density and shear modulus of partially saturated soil characteristics change randomly.Through the analysis of the graph,we obtain the influence of random variation of soil properties on the dimensionless mean displacement and stress.