| The Falling Weight Deflectometer(FWD)is currently one of the most advanced non-destructive testing devices in the world,which is excessively applied to evaluate the structure capacity of pavements and back-calculate the modulus of pavement layers.Compared to the static loadings of classical EMLT(elastic multi-layer theory),FWD is more suitable to descript the dynamic characteristics of the practical vehicle loads on the pavement surface.Therefore,theoretical investigation on the dynamic response of layered pavement under FWD loading(both forward and back calculation)has been the focus of industry attention.In this paper,based on the orthogonal vector function system,a new method for solving the layered pavement problem is proposed to figure out the deflection value of the layered pavement under FWD load.The influence of related road factors on the road deflection value is analyzed by the analytical solution which is obtained from this paper.The main research contents are as follows:(1)Firstly,based on the governing equation,the Laplace transform is applied to suppress the time variable.The ordinary differential equations(ODE)of the governing equations in Laplace domain are derived by the cylindrical vector functions systems.On the basis of the facts that displacement and force duality at the upper and lower boundaries,a novel analytical method called dual variable and dual boundary(DVDB)for the ODE is proposed combined with dual variable and position method(DVP).(2)The accuracy and precision of Durbin method are validated by numerical examples,then Epsilon algorithm is introduced to accelerate the convergence speed of iterative item of Durbin method,which not only reduce the times of iterations but increase the calculation precision,finally by analyzing the average absolute error and the mean square error in the examples to determine the value of N in accelerated Durbin method,through inverse transformation of Laplace to obtain the time domain solution.(3)The numerical results of dynamic response of multi-layer pavement under the loading of FWD are compared and analyzed with the program written by FORTRAN language,and the accuracy and rationality of the deduced results are verified.The accuracy and applicability of the DVDB method are investigated by calculating the deflection values of complex pavement structures including ultra-thin layer,ultra-thick layer,discontinuous interface and viscoelastic model under FWD load.At the same time,the influence of the parameters of Burgers model are discussed,the influence of the transverse isotropy of material and elastic modulus of ultra-thin layer on pavement deflection value,and the dynamic response of discontinuous interface conditions. |
