一种块体–颗粒–杆件的耦合方法及其在隧道支护模拟中的应用

A block–particle–bar coupled algorithm to simulate tunnel excavation and support

为了模拟隧道开挖过程中边帮的失稳垮塌过程以及锚杆对隧道的支护过程,提出了一种基于罚弹簧的块体–颗粒–杆件的耦合方法.该耦合方法基于连续–非连续的数值模拟方法(CDEM),采用离散颗粒簇表征隧道周边松动圈以内的破碎岩体,采用块体单元表征松动圈以外的完整岩体,采用杆件单元描述锚杆及锚索等杆系类支护结构,采用插值耦合的方式实现杆件单元与离散颗粒及块体单元间力与位移的传递,从而实现高应力环境下隧道开挖失稳过程的模拟及支护效果的评价.颗粒与块体之间采用1根法向线性弹簧及2根切向线性弹簧进行耦合,法向弹簧引入拉伸断裂本构,切向弹簧引入Mohr–Coulomb脆性断裂本构.杆件与颗粒及杆件与块体之间的耦合模式基本一致,包含1根沿着杆件轴向的罚弹簧S_(gn)及1根垂直于杆件轴向的罚弹簧S_(gs),S_(gn)主要用于描述杆件与围岩之间的拉拔效应及推压效应,S_(gs)则主要用于描述杆件与围岩之间的侧向挤压效应.圆形盾构隧道弹性场分析、预应力锚杆加固矩形巷道模拟、全长连接锚杆对岩块的锚固作用分析、以及碎裂岩体中的隧道开挖支护效果分析等案例,证明了本文所述块体–颗粒–杆件耦合算法的准确性及合理性.

During tunnel excavation,the stress of the surrounding rock is redistributed,leading to a local stress concentration around the tunnel.In addition,blasting excavation and other factors lead to a strength reduction of rock mass around the tunnel and eventually form a relaxation fracture zone(loosening zone).If supporting measures are not adopted in time during tunnel excavation,the rock strength in the loosening zone will be further reduced and eventually lead to overall instability and collapse.To simulate the bolt/cable supporting effect on the loosening zone and surrounding intact rock,a block–particle–bar coupling algorithm based on penalty springs is proposed.This coupling algorithm is based on the continuum–discontinuum element method(CDEM).CDEM is a dynamic,explicit solution algorithm based on a generalized Lagrange system.A strict controlling equation is established by the Lagrange energy system,and an explicit iterative solution of the dynamic relaxation method is used to realize a unified description of continuous and discontinuous media.The progressive failure of a solid is analyzed through the fracture of the bond between the blocks or particles.Using CDEM,the entire process of the solid from continuous deformation to fracture and movement can be simulated.In the block–particle–bar coupled algorithm,discrete particle clusters are adopted to represent the broken rock mass inside the loosening zone around the tunnel,block elements are used to represent the intact rock mass outside the loosening region,and bar elements are introduced to describe the supporting structures,such as bolts and cables.A contact coupling mode is adopted between particles and blocks,one normal spring and two tangential springs are constructed,and brittle Mohr–Coulomb fracture constitutive law and tensile fracture constitutive law are introduced to represent contact behavior.To realize the transmission of force and displacement,the interpolation coupling approach is adopted between the elements of bars and the elements of discrete particles or blocks.In this coupling mode,penalty springs S_(gn)and S_(gs)along and perpendicular to the axis of the bar,respectively,are established.S_(gn)and S_(gs)are mainly used to describe the pulling and pushing effect and the lateral compression effect between the bar and the surrounding rock,respectively.The coupling algorithm described in this paper is adopted to simulate the elastic field of a circular shield tunnel,rectangular tunnel reinforced by prestressed rock bolts,reinforcement of full-anchored rock bolts on surrounding rock,and the tunnel support effect in a jointed rock mass.The results of the four numerical cases show the accuracy and rationality of the coupling algorithm.Using this proposed algorithm,the progressive failure process of rock tunnels under high ground stress and the supporting process by lining and bolt(cable)can be accurately simulated.