饱和层状地基条形基础动刚度的精细积分算法

采用基于积分变换、对偶方程和精细积分的算法求解饱和多层地基条形基础的动刚度问题。利用Fourier积分变换得到Biot多孔饱和介质波动方程在频域-波数域内的常微分方程，引入广义对偶变量，对二阶常微分波动方程进行降阶处理；针对地表自由排水和封闭排水边界条件，给出了适于精细积分算法的矩阵表达；对控制方程采用精细积分解答，得到波数域内的格林函数，对结果进行逆Fourier积分变换，得到空间域的力和位移关系；施加边界条件，最终得到刚性条形基础的动刚度的解答。通过与文献已有结果进行对比，验证了精细积分算法的准确性。最后计算两组算例，分别分析了表面薄层的孔隙率、渗透力阻尼系数对条形基础动刚度的影响。

PRECISE INTEGRATION METHOD FOR DYNAMIC STIFFNESS OF STRIP FOUNDATION ON SATURATED POROELASTIC SOIL

An approach based on integral transformation, dual form of wave motion equation and precise integration method (PIM) is presented to evaluate the dynamic stiffness of strip foundation resting on soils that are fluid-filled poroelastic. The two-phase behavior of the porous medium is represented according to Biot's theory. Fourier integral transform is used with respect to the x-co-ordinate, and the wave equations are reduced to ordinary ones. Considering the different contact conditions between the soil and foundation which are pervious or impervious, the PIM solution in the wave-number domain of the problems is achieved. With the aid of Inverse Fourier transforms of Green's function in the wave-number domain, the relationship between force and displacement in the physical domain is obtained. Finally, a numerical example is calculated to show that the proposed PIM can provide accurate results for solutions of dynamic stiffness of strip foundation. Besides, the technique can be applied to the computation of two groups of examples to analyze the influence of the porosity and seepage force.