地下厂房岩锚梁接触面非线性有限元模拟方法

Nonlinear Finite Element Simulation Method for Contact Face of Rock-anchored Beam and Surrounding Rock in Underground House

地下厂房岩锚梁接触面是岩锚梁整体结构薄弱环节,建立合理的接触面模拟方法是岩锚梁有限元数值分析的重要内容。针对地下厂房岩锚梁与围岩接触问题,分别构建模拟岩锚梁与围岩接触面非线性特征的有限元数学模型和力学模型。在Desai薄层单元基础上,推导岩锚梁接触面单元有限元数学模型,该数学模型形式简单,便于有限元计算;结合非线性弹性理论和弹塑性理论,提出岩锚梁接触面3维非线性力学模型,该力学模型能够模拟岩锚梁接触面弹性阶段的非线性现象和塑性阶段的损伤软化现象。针对岩锚梁接触面闭合、张开、剪切滑动等变形特征,提出考虑接触面黏结、开裂、滑移现象的分段式抗滑安全系数。详细论述了所提模型的有限元实现方法,并据此编写了有限元程序。将本文模型应用于某地下厂房岩锚梁有限元分析计算中,与接触面等效连续模型相比,所提模型计算得到的岩锚梁梁体应力稍小,荷载更多的是由长锚杆承担,梁体的整体变形量增加了2~3 mm,说明接触面的存在使得岩锚梁整体稳定性降低,岩锚梁接触面处的安全系数也稍小,局部出现拉裂损伤,与实际工程岩锚梁接触面开裂现象相吻合,说明所提模型能够合理反映岩锚梁接触面非线性接触特征。为地下厂房岩锚梁稳定分析提供了一种有效的有限元分析方法。

The contact face of rock-anchored beam in underground powerhouse is the weak part of the overall structure; it is thus an important content for finite element analysis of rock-anchored beam to establish reasonable contact face simulation method.For the contact problem of rock-anchored beam and surrounding rock of underground powerhouse,the mathematical and mechanical models were established to simulate the nonlinear characteristics of the contact surface of rock-anchored beam and surrounding rock.Based on the Desai thin-layer element,a mathematical form of contact element,which is simple and convenient for finite element calculation,was derived.By combining nonlinear elastic theory with elastic plasticity theory,a three-dimensional nonlinear mechanical model,which could simulate the nonlinear phenomena on elastic stage and damage softening phenomena on plastic stage of contact element,was proposed.In view of the deformation characteristics of contact elements such as closing,opening and shearing slip,a segmented safety factor,with considering the bonding,cracking and slip phenomena of contact face,was proposed.The finite element iteration method of the model was discussed in detail,and the finite element program was implemented accordingly.The proposed model was applied to the calculation of rock-anchored beam in an underground powerhouse.Compared with equivalent continuum model,the calculation results of the proposed model show that the stresses in rock-anchored beam are smaller,and the loads are mainly borne by long bolts.The overall deformation of the rock-anchored beam is increased by 2~3 mm,which means that the contact face decreases the overall stability of rock-anchored beam.The safety factor at the contact face is also slightly smaller and localized tensile damage occurs,which is consistent with the cracking of the contact face of rock-anchored beam in actual engineering.Therefore,the proposed model can reasonably reflect the nonlinear contact characteristics of the contact face,and it provides an effective finite element analysis method for the stability analysis of rock-anchored beam in Underground Powerhouse.