横观各向同性层状地基上埋置刚性条带基础动力刚度矩阵求解

提出了求解横观各向同性层状地基埋置刚性条带基础动力刚度矩阵的精确算法。算法利用空间变换方法求解得到了横观各向同性层状地基表面或内部任意点的动力位移响应,针对开挖基础求解开挖区域内节点群的动力柔度矩阵,最后利用容积算法求解埋置刚性条带基础动力刚度矩阵。此算法采用精细积分算法求解频率–波数域内层状地基的动力柔度系数,对层状地基的层数和厚度均没有任何限制。此外,算法基于维数较小的矩阵(2×2)运算,数值计算稳定,求解效率较高,数值算例验证了所提算法的精确性及对横观各向同性多层地基的广泛适用性。

Solution of dynamic stiffness matrix for rigid strip foundations embedded in layered transversely isotropic soil

A precise algorithm is proposed to evaluate the dynamic stiffness matrix of the rigid strip foundation embedded in layered transversely isotropic soil. The space transformation method is used to obtain the dynamic displacement response of arbitrary nodes at the surface or in the layered transversely isotropic soil. Then the dynamic flexibility matrix of the nodes in the excavation scope is established. Finally the flexible volume method is introduced to evaluate the dynamic stiffness matrix of the rigid strip foundation. The proposed method solves the dynamic flexibility coefficients of the layered soil in the frequency-wave number domain by using the precise integration method, and there is no limit to the number and thickness of layers. In addition, the computation is based on the matrix algebra with small dimension, and the computation is always stable with high efficiency. Numerical examples demonstrate the accuracy and the wide applicability of the proposed method to the layered transversely isotropic soil.