| Abstract: | Green's influence functions are derived for a linearly distributed load acting on part of a layered elastic halfplane on a line which is inclined to the horizontal. Using these Green's functions as fundamental solutions in the boundary-element method, the dynamic-stiffness matrices of the unbounded soil with excavation, of the excavated part and of the free field are calculated. The indirect boundary-element method using distributed loads and no offset leads to more accurate results than the weighted-residual technique and the direct boundary-element method. At the natural frequencies of the undamped excavated part built-in along the structure-soil interface, the spring coefficients associated with the dynamic-stiffness matrices of the excavated part and of the free field will become infinite. If the dynamic-stiffness matrix of the soil with excavation is calculated as the difference of that of the free field and that of the excavated part, the difference of two large numbers will arise in the vicinity of these frequencies. A consistent discretization must then be used. In particular, the dynamic-stiffness matrix of the embedded part cannot be determined by the finite-element method in this case. A parametric study is performed for the dynamic-stiffness matrix of the free field for a rectangular foundation embedded in a halfplane and in a layer built-in at its base; the aspect ratio and the damping of the soil are varied. |
