半无限平面问题的相对位移

A study of relative displacements in semi-infinite plane

通过Flamant和Melan的解析解答、Mindlin解答的积分蜕化公式以及有限元数值分析计算结果,展示了在半无限平面问题中线荷载作用方向位移解答的不确定性。线荷载作用方向没有绝对位移,只有相对位移,但相对位移会随着与位移约束参考点距离的增大而增大,或随着线荷载在垂直于半平面方向分布长度的增大而增大,不具收敛性。这意味着,在解析和数值分析中,纯粹的半平面问题的位移解答具有多值性,因此,将岩土工程问题作为半空间问题进行分析是必要的。

By using the analytical Flamant and Melan solutions, the integral formulae derived from Mindlin＇s equations, solutions in semi-infinite plane are derived to calculate displacements and compare with computed results from the finite element method. It is found that the calculated displacements are indeterminate in the line loading direction, where no absolute displacements but only relative displacements can be obtained. However, the calculated relative displacements increase with an increasing in the distance away from the reference point of displacement constraint; and they also increase with an increasing length of line load distribution normal to the half-plane, leading to non-convergence. This means the derived displacement solutions of pure half-plane problems are multivalued. Thus, it is necessary to analyze geotechnical problems using the half-space assumption.