Investigation On Dynamic Response Of Unsaturated Soils And Foundation

Studies on dynamic response of subgrade and foundation relate to many subjects, such as mathematics, mechanics and geotechnical engineering etc. It not only has great academic values on development of elastic dynamics, but also is applied widely in fields such as building engineering, hydraulic engineering, road engineering and dynamic machine foundation, etc. In former studies on this subject, soils were taken majorly as one-phase or two-phrase media (saturated soils). In present study, dynamic governing equations for unsaturated soils are established by taking soils as three-phase porous media, and considering the viscous and inertial coupling between pore fluids and soil skeleton. Based on which, we systematically study the steady state and transient dynamic response of unsaturated half space under surface loads, and analyze the vertical vibration of rigid and elastic circular plate on unsaturated soils. The major works and achievements are as follow:1)After analyzing and comparing the existed dynamic models for unsaturated porous media, a group of practical wave equations for unsaturated soils are established in present. Major improvements include: 1. V-G model for SWCC(soil-water characteristic curve ) is adopted and relative permeability of pore fluids is deduced based on Mualem theory, which make the equations established can be degenerated exactly to the classical Biot's wave equations for saturated soils. 2. the influence of saturation on dynamic shear modulus is considered and a formula to calculate dynamic shear modulus of unsaturated clay with arbitary saturation is raised. Solving wave equations, dispersive equations of body waves propagation are obtained, which indicate that there are three compressive waves and one shear wave in unsaturated soils. Numerical analysis is performed to study the propogation characteristic of body waves in unsaturated soils. Influences of some parameters on waves velocity and attenuation are examined.2)Lamb's problem for unsaturated half-space under vertical surface point load is analyzed. With the help of Hankel transform, solving wave equations in cylindrical coordinates, general solutions of displacement, stress and pore fluids pressure are obtained. Thus the integral solutions are gotten both in the case of drained surface and in the case of undrained surface excited by vertical concentrated harmonic resources. Numerical results indicate that displacement amplitude of ground surface increases with saturation when soils are in the state of funicular saturation. While soils approach completely saturated, with saturation rising, displacement amplitude decreases. And permeability, drainage conditions have significant influence on displacement only when saturation is very high. 3)Analysis about the steady state dynamic response of unsaturated half-space is also performed in Cartesian coordinate. By introducing displacement function, decoupling the wave equations, and then converting partial differential equations into constant differential equations with the help of double Fourier transform, the solutions of steady state dynamic response of unsaturated soils under arbitary distributed loads are presented.4)The work is extented to axisymmetrical and non-axisymmetrical steady state dynamic response of layered unsaturated soils. In the case of axisymmetrical problem, wave equations are transformed into a group of state equations in cylindrical coordinates by introducing a group of state vectors, then solutions are obtained with the help of Hankel transform. In the case of non-axisymmetrical problem, wave equations are transformed into a group of state equations in the Cartesian coordinates by introducing a group of state vectors, then solutions are obtained by means of double Fourier transform. Numerical results indicate that displacement of ground surface is influenced mainly by stratum in critical depth. The critical depth is about 10 times of side length or diameter of the area which loads exerted on. The relative position of soft and hard strata has significant influence on displacement, which is relatively small when hard stratum lies close to ground surface.5)Transient dynamic response of unsaturated half-space under vertical surface loads is presented in time domain. Using Laplace-Hankel transfer to decouple the partial differential equations of unsaturated soils, the integral solutions of displacement for axisymmetrical problem are obtained. Numerical examples show vividly the propagation process of waves in unsaturated half-space. The results indicate that, with saturation rising, the speed of shear wave decreases obviously, and the vertical and radial displacement amplitude increases significantly at the same time when soils are in the state of funicular saturation.6)Vertical vibration of rigid circular plate and elastic circular thin plate on unsaturated subgrade are invesgated. By using Hankel transform technology, the relations between surface displacement and stress are obtained firstly. Considering mixed boundary value conditions, the dual integral equations for vertical vibration of rigid circular plate and elastic thin circular thin plate on unsaturated subgrade are established. Then by means of Abel transform, the dual integral equations are transformed into Fredholm integral equation of the second kind, which can be solved easily by numerical methods. At last, the semi-analytical solutions for vertical vibration of rigid circular plate and elastic thin circular thin plates are obtained. Numerical results indicate that saturation has significant influence on vibration of plate. In general cases, with saturation increasing, the stiffness of subgrade decreases, and the damping increases. But when soils approaches completely saturated, the change is just on the contrary, furthermore, a slight change of saturation will make significant influence on vibration amplitude of plate.