Abstract The vertical, rocking and horizontal vibrations of a rigid disk on multi-layered soils are studied by using a coupled approach of stiffness matrix method and “integral equation method”. Considering groundwater level, the layered soils consist of a number of dry layers and saturated layers, and a bedrock at the bottom. To allow the assembly of a global equation of this layered system, the stiffness matrices of the top and bottom saturated layers are modified to match those of adjacent dry layer and bedrock using drainage conditions. Together with the mixed boundary-value conditions at the disk plane, three disk-soil interaction problem, i.e., vertical, rocking and horizontal vibration cases, can be expressed as corresponding dual integral equations for solving. The correctness of the proposed method is verified by existing solutions with good convergence. Parametric studies illustrate the effects of groundwater level, permeability of saturated soil and the hydraulic condition at dry-saturated soil interface on dynamic compliance coefficients of rigid risk and pore pressure in saturated soil layer.

中文翻译：

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含地下水位的多层土壤上刚性圆盘的垂直-摇摆-水平振动

摘要 采用刚度矩阵法和“积分方程法”的耦合方法，研究了刚性圆盘在多层土上的垂直、摇摆和水平振动。考虑到地下水位，层状土壤由多个干层和饱和层组成，底部有基岩。为了组装这个分层系统的全局方程，顶部和底部饱和层的刚度矩阵被修改，以匹配相邻干燥层和使用排水条件的基岩的刚度矩阵。结合盘面混合边值条件，三个盘土相互作用问题，即垂直、摇摆和水平振动情况，可以表示为相应的对偶积分方程求解。现有解验证了所提方法的正确性，收敛性良好。参数研究说明了地下水位、饱和土壤渗透率和干饱和土壤界面的水力条件对饱和土层刚性风险和孔隙压力的动态柔顺系数的影响。