数值流形方法的阻尼、收敛准则以及开挖模拟

Damping,convergence criterion and excavation simulation algorithm for numerical manifold method

数值流形方法采用动态松弛法求解准静力学问题,能量耗散机制不清楚。通过引入黏性和自适应两种阻尼吸收系统产生的动能,基于最小势能原理建立了考虑阻尼力影响的总体平衡方程。提出了模拟岩体分期开挖的数值流形方法,将开挖面视为特殊的不连续面,根据开挖时序设置开挖面上接触点的状态,以达到模拟分步开挖的目的,给出了相应的迭代计算格式,并定义了位移和加速度收敛准则用以判断计算过程中系统是否达到新的平衡状态。数值算例结果表明,改进后的数值流形方法具有良好的收敛性能,其计算结果与解析解以及离散元是吻合的。

The dynamic relaxation algorithm is used to solve quasi-static problems in numerical manifold method（NMM）.However,the mechanism of energy dissipation of NMM is unclear.In this paper,the viscous-type and self-adaptive dampings are adopted to absorb the kinetic energy caused by the oscillation of system.The equilibrium equations containing damping term are derived by minimizing the total potential energy.A new algorithm for simulation of sequential excavation in rock masses is proposed.The excavation faces are considered as the special kind of discontinuity,and the phased excavation process is simulated through setting contact states of excavation faces according to excavation sequences.The convergence criterion including displacement and acceleration criteria are defined to determine whether the system reaches new equilibrium or not.The numerical results show that the improved NMM has good convergence performance and that the results from NMM agree with those from UDEC and analytical solutions.