Some Applications Of The Theory Of Multiple Scattering Of Elastic Wave In Geotechnic Engineering

In an unbounded homogeneous medium, waves propagate without interruption at a constant speed and along a fixed path. But with the insertion of an obstacle in the medium, some secondary waves will be emitted from the obstacle, which is called scattering. Firstly, the amended Biot's model of saturated soils and the expansion method of wave functions were adopted, and the theoretical solutions of the scattering problem of an elastic cylindrical shell deeply embedded in saturated soils for incident fast compressional waves and shear waves were drawn out according to the continuous boundary conditions of stress and displacement between the cylindrical shell and around saturated soils. And the effect of dimensionless frequencies and shell thickness on the back-scattering spectra and dynamic stress concentration factors of two types of cylindrical shells with high and low rigidity are numerically computed and analyzed, which provides some theory foundation for the later study on the multiple scattering problems.According to the theory of multiple scattering, the potential functions of the scattering waves, diffracting waves and incident waves of the discontinuous barrier of a row of hollow or solid piles were expanded into the series of Fourier-Bessel functions with the expansion method of wave functions, then all the scattering waves of every piles were transferred to one same cylindrical coordinate, and the equations about the scattering and diffracting coefficients were finally obtained according the boundary conditions of each piles. By truncating the order of n to a finite number, the curves of the normalized displacements, which is the ratio of the sum displacement caused by the incident wave and scattering wave by the barriers at the place behind the barriers to the displacement caused by the only incident wave at the same with no barrier, and the transmissibility index for displacement changing with the pile distance were drawn, and the isolation effects of the three types of discontinuous barriers of rigid hollow pipe piles, elastic hollow pipe piles and solid piles were studied by analyzing the trend and distribution characteristic of the drawn curves.According to the solution results of the scattering of a row of discontinuous hollow pipe pipes, the circumferential curves of the DSCF (dynamic stress concentration factors) of the group circular linings deeply embedded in elastic or saturated soils were drawn, and the effects of the incident frequency and lining distance on the DSCF were analyzed. Adopt a large circular arc to approximate the half-space free surface of elastic soils, and the expansion method of wave functions and Graf's addition theorem, then the theoretical solution of the scattering of a half-space with two linings were obtained according the boundary conditions of the circular linings and the half-space, the circumferential curves of the DSCF of the two circular linings and displacements of thehalf-space surface were drawn, and finally the effects of the incident frequency and lining distance on the DSCF and displacements of the half-space surface were analyzed. Also adopt a large circular arc to approximate the half-space free surface of saturated soils, and the method of expansion of wave functions and Grafs addition theorem, then the theoretical solution of the scattering of a half-space with two unlined cavities were obtained according the boundary conditions of the two unlined cavities and the half-space when they are pervious and impervious, the circumferential curves of the DSCF of the two unlined cavities and displacements of the half-space surface for the two conditions of pervious and impervious were drawn, and finally the effects of the incident frequency and cavity distance on the DSCF and displacements of the half-space surface were analyzed.