有初始原岩应力的弹粘塑性岩土介质中圆柱形孔扩张问题解析解

Analytic solution of the cylindrical cavity in elastic-viscoplastic materials with initial stresses

岩土体中一般都存在原岩应力,且大多岩土材料都具有弹性粘塑性性质。文章考虑有初始应力的情况下,求解弹粘塑性无限介质中长圆柱形孔受力扩张问题;将岩土介质视为弹粘塑性体,采用弗洛依登塔尔(Freudenthal)弹粘塑性本构方程,通过拉普拉斯变换和逆变换手段,得到孔周应力的弹粘塑性解析解以及粘塑性半径与时间的关系表达式;从解的结果来看,应力与时间相关,随时间变化,但最终趋于稳定;粘塑性区半径随时间增长也渐渐缩小,最后趋向稳定。

The problem about cylindric cavities in elastic-viscoplastic materials with initial stresses is studied. Rock or soil is regarded as elastic-viscoplastic materials which conform with the Freudenthal elastic-viscoplastic constitutive model,and by means of Laplace transform and Laplace reverse transform, the solutions of stresses and displacement are obtained. The results show that the stresses and radius of the visco-plastic zone are functions of past time. The stresses are related to time and vary with the changes of time, and gradually tend to a steady value. The radius of the visco-plastic zone reduces as the time increases and finally tends to a steady value.