Research On Dynamic Responses Of Orthotropic Foundation Under Moving Loads

In the construction of expressway and other traffic facilities,the deformation and stability of subgrade and pavement have become the main technical problems of engineering quality control.Accurate grasp of the dynamic characteristics of soil and the dynamic response of subgrade and pavement structure under moving load have important theoretical and practical value for traffic engineering,civil engineering and earthquake engineering.In this paper,orthotropic elastic half space model is employed.The dynamic responses of orthotropic foundation and the interaction of orthotropic subgrade-pavement(plate)are systematically studied with displacement component as the basic unknown quantity subjected to the harmonic moving loads in rectangular coordinate system.The calculation model of plane strain problem of multilayered orthotropic foundation is then established.The dynamic responses at arbitrary depth of multilayered foundation are derived by means of the transfer matrix method.The main work and research results are as follows:(1)A mechanical model for plane strain dynamic problems of orthotropic soil foundation under arbitrary dynamic loads is established.The dynamic partial differential equations of plane strain problem are drawn for orthotropic medium under rectangular coordinate system.The initial and boundary conditions are introduced.The integral forms of the dynamic responses of orthotropic half-space medium are derived by using Laplace-Fourier integral transform and inverse transform method.Based on the theoretical solutions,the corresponding calculation programs are compiled.Degenerate solution shows that the method was reasonable and feasible.As demonstrated with numerical examples,the dynamic characteristics of soil can be described more accurately by considering the orthogonal anisotropy of soil.(2)A mechanical model for three dimensional dynamic problems of orthotropic soil foundation is established.Generally,the vehicle load function can be expanded by Fourier series to the sum of several harmonic loads.A three dimensional vibration equation of orthotropic soil under moving harmonic loads is derived by introducing a moving coordinate system.Based on the initial conditions and boundary conditions,the integral solutions of the steady state dynamic responses are obtained by using the double Fourier transform and inverse transform method.The influence of soil and load parameters on the soil vibration are investigated by numerical analysis.The results from the calculating examples show that the influence of speed is complex.It is necessary to be divided into different velocity intervals to discuss the influence on dynamic response of the foundtion.The surface vertical displacement and vertical stress of 1m depth decrease as load resonant frequency increases.The vertical normal stress at the center of load decreases sharply with the increase of depth.(3)Based on the Kirchhoff thin plate theory and elastodynamics theory,the Kirchhoff small deformation infinite elastic thin plate is adopted to simulate the pavement,and the orthotropic elastic half space is used to simulate subgrade.The mechanical analysis model and the dynamic differential equations of the infinite elastic plate on orthotropic foundation under moving harmonic loads are established under the rectangular coordinate system.The initial conditions and boundary conditions are introduced so that the integral forms of plate deflection and the contact stress between the plate and the foundation under moving loads are derived by means of the coordinate transformation and the Fourier integral transform.By means of numerical analysis,studies are conducted to investigate the effect of parameters such as the soil orthotropic parameters,the load parameters,and the board parameters on dynamic response of subgrade and the plate.The numerical results show that the dynamic response of subgrade and pavement interaction can be described more accurately by considering the orthogonal anisotropy of soil.Increasing plate elastic modulus or plate thickness is a better measure to reduce plate deformation,contact stress.It is unnecessary to measure the density of slabs accurately in the general range of concrete density.It is essential to divide different velocity zones to consider the dynamic response of subgrade and pavement.With the increase of load harmonic frequency,the maximum value of plate displacement decreases,and the maximum contact stress increases.(4)Based on the dynamic equation of plane strain problem of single-layer orthotropic foundation under moving harmonic load,the transfer matrix of single-layer orthotropic foundation is deduced through Fourier transform and the introduction of state vector.The calculation model of layered orthotropic foundation is then established under rectangular coordinate system.Combining the contact condition and the continuous condition between layers,the analytic expressions of the displacements and stresses at arbitrary depth in plane strain problem of multilayered orthotropic foundation are obtained by means of the transfer matrix method.According to the theoretical solutions,the corresponding calculation programs are compiled to study the influence of soil layered characteristics and orthotropic properties on soil deformation.The results indicate that neglecting the layered characteristics of soil and orthogonal anisotropy of upper soil cannot accurately describe the dynamic characteristics of foundation.The research results provide some theoretical and technical support for the design and destruction mechanism of subgrade engineering and pavement engineering for transportation facilities,such as expressway.