基于弹性半空间Green函数的明置条形基础阻抗解答

Impedance Functions of a Surface-Supported Strip Foundation Based on Elastic Half-Space Green Functions

基于弹性半空间理论,在Lamb解的基础上推导了非轴对称的简谐线激振荷载及条形均布激振荷载作用下的地基Green函数。然后将明置条形基础与地基的接触面分割成若干个条形单元,根据刚体位移所决定的各单元位移,运用上述Green函数求解各单元的接触力,将所求得的力叠加即为地基阻抗函数。通过分段积分法及Cauchy主值积分对涉及的多值广义积分进行数值处理,计算了明置条形基础的垂直阻抗,观察了其收敛性,亦计算了其水平和回转动柔度,并与半解析半数值的薄层法的结果进行了比较,表现出很好的一致性。最后通过算例讨论了土体泊松比对明置条形基础阻抗的影响。

Non-axisymmetric Green functions of the elastic half-space under harmonic line load and uni- form load with infinite length were derived based on the Lamb＇s solution. The interface between the foun- dation and the supporting medium was divided into a number of strip elements. A piecewise integration method was used to calculate the multi-value improper integral. The impedance function was solved by adding the contact forces on each strip, based on the fact that the displacement of the rigid foundation de- termines that of each elements. The vertical impedance of a surface-supported strip foundation was calcu- lated and its convergence was observed. The horizon and rotational impedances were compared with those obtained from the thin layer method （TLM）. Agreements between the present results and the TLM re- sults were observed. Finally, the effect of Poisson＇s ratio on impedance functions was discussed in detail.