分数阶流变岩体中深埋圆形支护隧道力学分析

Mechanical Analysis for the Construction of Deeply Buried Circular Tunnels with Liner in Fractional Kelvin Viscoelastic Rock

为用更少的参数描述不同岩体的实际流变特性,引入分数阶Kelvin粘弹模型并对深埋圆形支护隧道的开挖过程进行力学分析.利用Laplace变换原理、分数阶微积分得到了衬砌支护力和洞口位移的时效解答,并对解答的正确性进行了验证.讨论了不同分数阶阶次下支护力、洞口位移及等效应力随时间变化的规律.分析结果表明,阶次较小的模型,洞口位移在短期内迅速增大,随后缓慢增长,在经历很长时间后仍在持续增长,且等效应力在相同时刻下更接近于0,更容易发生破坏,因此在工程中对阶次较小模型对应的岩体要关注其长时间后的蠕变位移和受力状态.

In order to describe the actual creep conditions of different types of rock mass,fractional Kelvin viscoelastic model is introduced to analyze the construction of deeply buried circular tunnels with liner.Using Laplace transform,fractional calculus and Simpson principle,the time-dependent solutions for pressures of liner,the hole displacements and the equivalent stresses are obtained and verified with FEM.Their evolutions under different derivative orders are discussed.The results show that under the case of small derivative order,the hole displacement increases quickly in a short time.Afterwards the increase rate becomes very slow,but is still increasing after a long time.And the equivalent stress is close to 0,which means the rock mass is prone to fail.In tunnel engineering,the long-term responses of the creep displacement and the stress of rock mass represented by the small derivative order model should receive more attention.