Kelvin半无限体内部作用竖向力时的解答与应用

选择Kelvin模型描述土体的粘弹性本构关系,利用半空间体内部受竖向集中力的Mindlin弹性解,根据粘弹性理论中的准静态弹性-弹粘性对应原理,推导了竖向力作用在Kelvin粘弹性半无限土体内部的理论解。通过对应力和位移解答进行Laplace逆变换,给出了应力与位移的时域解。作为解答的应用,建立了Kelvin粘弹性半无限体内部矩形面积上作用有三角形分布、均匀分布荷载时的粘弹性沉降计算公式。为了便于计算与工程应用,根据粘弹性理论解编制了计算程序。结果验证和实例分析表明,文中理论解是正确的,研究结果为工程应用提供了理论依据。

Viscoelastic solutions and application of kelvin semi-infinite solid subjected to vertical force

Based on half-space Mindlin solution and correspondence principle in viscoelastic theory,the viscoelastic solutions of the Kelvin semi-infinite soil subjected to vertical force are derived by the Laplace transform.The solutions in time domain are established by inverse Laplace transform.By means of viscoelastic solution of vertical displacement,the settlement formulas for the center and corner point of a flexible rectangular foundation made by homogeneous distributing load on rectangular area beneath the surface of ground are systematically inferred.A computer program is compiled based on the developed solutions.Finally,the Kelvin viscoelastic solutions are confirmed by reducing to the elasic solutions.An example is given by making use of the presented method.The calculation results show that the new theory is feasible and applicable.The solution of this paper is of some significance both to engineering practice and to the calculation of total settlement of pile foundation.