竖向荷载作用于半无限体内部时的粘弹性解

建筑物的持续沉降,特别是软土地区的建筑物基础沉降通常与地基土的流变性密切相关。考虑地基土的粘弹性特征,系统研究了空间半无限体内部作用集中力时的粘弹性解。研究假定半无限体为线性粘弹性介质,半无限体在内部集中力作用下的应力状态为三维应力状态,应力球张量和应变球张量之间符合弹性关系,而应力偏张量和应变偏张量之间符合Kevin固体粘弹性应力应变关系。利用半空间体内部受竖向集中力的Mindlin弹性解,根据准静态弹性-弹粘性对应原理,在相同荷载条件下,首先对弹性解进行Laplace变换,然后将弹性解中的物理参数用线性粘弹性理论中经过Laplace变换的物理参数来替代,最后再进行Laplace逆变换,求得位移、应力粘弹性解答。作为解答的应用,给出了粘弹性半无限空间体内部矩形面积上作用有竖向均布荷载、三角形分布荷载时的粘弹性沉降计算公式。解答的退化验证表明,该粘弹性解答是正确的,所得到的解答对工程实践具有一定的意义。

Viscoelastic Solutions of Semi-infinite Solid Subjected to Vertical Distribution Load

The long-term settlement of building is directly related to the viscoelasticity of soil,especially in soft clay region.However,the research on their viscoelastic analysis is quite limited.The viscoelastic solutions of semi-infinite soil subjected to vertical and(horizontal) force for stress and displacement are systematically studied,taking into account viscoelastic characteristics of soil.By means of half-space Mindlin's elastic solutions and correspondence principle between elasticity and viscoelasticity,the viscoelastic solutions of stress and displacement,subjected to suddenly applied vertical load and given elastic volume strain and the Kevin model distortion constitutive relations,were derived by the Laplace transform.The solutions in time domain is established by the inverse Laplace transform.Based on 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 were systematically presented.Finally,the viscoelastic solutions are confirmed by reducing to the elasic solutions.The study provides an effective method to the solution of some significance both to engineering practice and to the calculation of total settlement of pile foundation.