Research On The Elastic Wave Characteristics Of Unsaturated Soil

In geotechnical engineering,ocean engineering,material science and acoustic etc,the wave problem in elastic porous materials is of great significance.Itinvolvesphysical,soilmechanics,fluidmechanics,thermodynamics and many other aspects.Since the Biot theory was carried out,the previous research was based on the two-phase medium materials,namely the saturated state when the porosity of the porous materials is filled with one kind of fluid.The practical engineering materials,however,especially natural materials are in unsaturated state,that is,the pore of the porous medium is filled with two or more fluids,for example,the backfill soil for building foundations and the oil layer containing natural gas,etc.Therefore,it is very important to study the wave characteristics of unsaturated soils.For such problems,there are different theories,for example,the extended Biot theory,the Theory of Porous Media and the mixture theory.Based on the Theory of Porous Media,this paper establishes a series of control equations about skeleton displacement,pore water pressure and pore gas pressure as unknowns quantities.Based on this,the fluctuation characteristics of unsaturated soils are studied.First,based on the Theory of Porous Media,considering the compressibility of the solid skeleton,the viscosity of the fluid and other factors,using the balance equations of mass and momentum of solids and fluids,a new kind of unsaturated soil control equations was established by introducing the V-G model and the effective stress represented by the suction stress.In Laplace domain,for unsaturated porous medium,wave velocity and attenuation expressions of three types of P waves and one type of S wave was carried out by the curl and divergence calculations.According to the physical properties of Massilon sandstone,numerical result was obtained.Compared with known experimental results,the correctness of result was proved,and analyzing the effects of saturation,frequency,and suction stress on wave velocity and attenuation.Afterwards,based on the established control equations,in this paper,a set of ordinary differential equations is obtained by using Laplace transform and dimensionless method in one dimension.Using the exponential function to represent the displacement of the skeleton,pore water pressure,and pore gas pressure,combined with the non-homogeneous boundary conditions,in the Laplace domain,the dynamic response of the unsaturated column under surface loads is obtained.Using the numerical inverse Laplace transform,the non-dimensional solution in the time domain is obtained.Compared with the existing solutions,the validity of the method is verified.Then by changing the relative permeability coefficient,the existence of P₂ wave and P₃ wave in unsaturated soils is proved.Finally,the effects of shear modulus,porosity and compressibility constant of the solid skeleton on the dynamic response of the soil were analyzed.