广义Gibson饱和地基中刚性圆板的扭转柔度系数

考虑到地基在竖直方向上的非均匀性，结合扭转振动的特点，建立了简谐扭转动荷载作用时剪切模量随深度增大的广义Gibson饱和地基的动力方程，通过积分变换求解了动力方程。考虑到半空间地基表面处应力自由、埋置圆板所在平面为混合边界和无穷深度处为波的辐射边界等条件，得到了广义Gibson饱和地基中刚性圆板扭转振动时的对偶积分方程，通过合适的变换转化成了一个第2类Fredholm积分方程，求解了相应的动力响应问题。对比静扭距作用时的荷载-位移关系，给出了动力柔度系数和扭转角位移幅值的表达式，并把所研究的问题进行退化且与前人成果进行了对比。数值研究表明：当基础的埋置深度小于5倍基础半径时，广义Gibson饱和地基中埋置基础的扭转振动存在明显的边界层现象，且埋置深度越小，边界层现象越明显。

Torsional compliance coefficients of a rigid circular plate in generalized Gibson saturated soil

With considering the vertical heterogeneity of soil layers and the feature of torsional vibration, the dynamic motion equations of a generalized Gibson saturated soil are developed. Then the proposed equations are solved by using the integral transformation. Given the stress-free boundary condition at the top surface of the saturated half-space, the mixed boundary condition in the plane where the rigid circular plate is laid, and the wave radiation condition at the infinite depth, the dual integral equations are developed to depict the torsional vibration of a rigid circular plate embedded in a generalized Gibson saturated soil. By appropriate transformation, a Fredholm integral equation of the second kind is obtained; and the dynamic response of the soil is determined. The dynamic compliance coefficient and the torsional angular amplitude is formulated by comparing the relation between a static torque and angular displacement. The problem can be degenerated into a simple case, which is consistent with previous research results. Numerical studies indicate that there exists a boundary-layer phenomenon in the torsional vibration of a rigid circular plate in a generalized Gibson soil when the embedment depth is five-times smaller than the radius of the circular plate; in addition, the smaller embedment depth, the more pronounced the boundary-layer phenomenon is.