Solutions for Displacement and Stress in Strain-Softening Surrounding Rock Incorporating the Effects of Hydraulic–Mechanical Coupling and Rockbolts Effectiveness

This study focuses on the stress and displacement of a circular opening that is excavated in a strain-softening rock mass incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness. It follows the generalized Hoek–Brown failure criterion. Moreover, an improved numerical approach and stepwise procedure are proposed. This approach considers the deterioration of the strength, deformation, and dilation angle and the variation of elastic strain in the plastic region considering the effect of the hydraulic–mechanical coupling and the rockbolts effectiveness. The presented solutions were validated by FLAC results. Several examples are conducted to demonstrate the validity and accuracy of the proposed solution through MATLAB programming. Parametric studies are also conducted to highlight the influences of hydraulic–mechanical coupling and rockbolts effectiveness on stress and displacement. Results show that stress and displacement, incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness, are between those when hydraulic–mechanical coupling or rockbolts effectiveness is considered separately. However, this theory needs more verification from practical engineering.     

考虑轴向力和渗透力时圆形隧道广义Hoek-Brown解

为了研究渗透水压力和轴向应力共同作用时隧道围岩的应力和位移变化趋势,将圆形隧道简化为轴对称模型,假定渗透场以渗透体积力作用在原应力场,以围岩开挖断面为假定平面,引入垂直于该平面的轴向应力。基于广义Hoek-Brown强度准则和非关联流动法则,推导出考虑轴向应力和渗透场共同作用时弹-脆-塑性围岩的应力和位移非线性解,采用数值算例分析了轴向应力和渗透力共同作用时隧道围岩塑性区应力场和位移场的分布规律。计算结果表明：与无渗透水压力作用下的模型相比,渗透力作用使得围岩塑性区各点位移增大,并且内外水头差越大,位移增大越明显。当轴向应力为中主应力时,围岩塑性区半径和塑性区各点应力增大,轴向应力为大主应力和小主应力时,围岩塑性区半径和塑性区应力变化较小。因此,渗透力的存在不利于隧道围岩的稳定性,并且轴向应力的大小对于富水地区隧道围岩的应力和位移分布具有较大影响。在施工设计时考虑渗透力以及轴向应力的共同影响对于保证隧道围岩稳定性具有重要意义。     

Generalized Hoek-Brown solution of circular tunnel considering effects of axial stress and seepage forceEI北大核心CSCD

This paper studies the joint effect of seepage force and axial stress on the stress and displacement of circular tunnel. The circular tunnel is simplified as an axisymmetric model and the seepage field is simplified as volumetric force in the stress field. The excavation cross-section of surrounding rock is assumed as a plane as well, and an axial stress perpendicular to the plane is further introduced. Nonlinear solutions for the stress and displacement of circular tunnel are deduced considering the joint effect of axial stress and seepage force, based on the generalized Hoek-Brown failure criterion and the non-associated flow rule in elastic-brittle-plastic rock mass. Numerical simulations are also employed to analyze the distribution of stress field and displacement field in plastic zone of a circular tunnel under the joint effect of axial stress and seepage force. The calculated results show that the displacement in plastic zone increases significantly with the gradient increment of the seepage pressure, compared with the situation without seepage force. The radius and stress of surrounding rock in plastic zone increase when axial stress is the intermediate principal stress, while the radius and stress have less change when axial stress is the major or minor principal stress. It can be concluded that the seepage force has negative effects on the stability of circular tunnel, and the axial stress significantly influences the stress and displacement of the circular tunnel, especially in water-rich areas. Therefore, it is necessary to consider the joint effects of axial stress and seepage force to ensure the stability of circular tunnel in water-rich area.     

高水位隧道堵水限排围岩与支护相互作用分析

为了保护环境并尽可能降低衬砌结构所受的水压力,提出高水位山岭隧道应采取“以堵为主,限量排放”,即“堵水限排”的防排水设计原则。但对于堵水限排情况下衬砌结构的设计,目前尚没有规范可依,这是目前隧道设计施工亟待解决的问题。在隧道力学和渗流力学的基础上进行理论分析,研究渗流应力耦合作用下围岩的力学特性,利用特征曲线法分析了不同排放量下围岩与支护的相互作用,并与数值方法计算结果进行对比。计算结果表明：不同排水量下围岩特性曲线不同,支护阻力也不同,不同排水条件下围岩有效切向应力和有效径向应力的变化很明显,排水对围岩应力以及支护体系受力的影响是不容忽视的。另外,传统隧道设计方法在全排水时完全不考虑水的作用是不安全的。所得结论可为堵水限排衬砌结构设计提供理论依据。     

Elasto‐plastic seepage‐induced stresses due to tunneling

When tunneling is carried out beneath the groundwater table, hydraulic boundary is altered, resulting in seepage entering into the tunnel. The development of flow into the tunnel induces seepage stresses in the ground and the lining is subjected to additional loads. This can often cause fine particles to move, which clog the filter resulting in the long‐term hydraulic deterioration of the drainage system. However, the effect of seepage force is generally not considered in the analysis of tunnel. While several elastic solutions have been proposed by assuming seepage in an elastic medium, stress solutions have not been considered for the seepage force in a porous elasto‐plastic medium. This paper documents a study that investigates the stress behavior, caused by seepage, of a tunnel in an elasto‐plastic ground and its effects on the tunnel and ground. New elasto‐plastic solutions that adopt the Mohr–Coulomb failure criterion are proposed for a circular tunnel under radial flow conditions. A simple solution based on the hydraulic gradient obtained from a numerical parametric study is also proposed for practical use. It should be noted that the simple equation is useful for acquiring additional insight into a problem on a tunnel under drainage, because only a minimal computational effort is needed and considerable economic benefits can be gained by using it in the preliminary stage of tunnel design. The proposed equations were partly validated by numerical analysis, and their applicability is illustrated and discussed using an example problem. Comments on the tunnel analysis are also provided. Copyright © 2010 John Wiley & Sons, Ltd.     

软岩洞室最优支护的广义SMP准则解与对比研究

现有洞室最优支护设计均基于Mohr-Coulomb（简称M-C）准则,不能真实反映岩石强度的中间主应力效应以及围岩的三向不等应力状态。基于广义SMP准则和稳定蠕变J3准则,考虑中间主应力对岩石强度的提高作用,建立了软岩洞室最优支护力与围岩允许最大位移的理论解答。洞室最优支护解答对M-C准则、外接圆Drucker-Prager（简称D-P）准则均具有很好的拓展性,且工程实例验证了其正确性。研究结果表明：3种强度准则结果间的差异实际反映的是对中间主应力效应的不同考虑,M-C准则和外接圆D-P准则对应的结果是两个极端情况,推荐选用广义SMP准则解答;岩石长期强度是洞室最优支护设计的关键参数,围岩凝聚力与内摩擦角的影响亦很显著,应合理测定岩石的强度参数并充分考虑变异性。     

Elastic Solution for Deep Tunnels. Application to Excavation Damage Zone and Rockbolt Support

Summary  A new formulation is presented for deep circular tunnels in rock with cylindrical anisotropy. The formulation is an exact solution since it satisfies equilibrium, strain compatibility, and the anisotropic constitutive model. Complete solutions have been found for two scenarios: tunnel with excavation damage zone, and tunnel with rockbolt support. The solution is based on the assumption of a deep, circular tunnel in a medium with two homogeneous zones: an inner zone surrounding the tunnel, which is either isotropic or anisotropic, and an outer zone, for the remainder of the medium, which is isotropic. Plane strain conditions, elastic response of rock, rockbolts and support, and simultaneous excavation and support installation are also assumed. For tunnels surrounded by an excavation damage zone with reduced rock properties, the tangential stresses and the radial deformations at the tunnel wall are very sensitive to both the magnitude of stiffness reduction of the damaged rock and the size of the damaged zone. The effect of the rockbolts on the rock is approximated by treating the rockbolt-rock composite as a material with cylindrical anisotropy with stiffnesses related to the properties of the rock and rockbolts, and spacing of the rockbolts. Comparisons between the analytical solution and a numerical method show small differences and provide confidence in the approach suggested.     

考虑围岩蠕变全过程与扩容的深埋隧洞非线性位移解

深埋隧洞围岩变形是一个复杂的非线性力学问题,其中岩石的蠕变全过程和扩容是两个重要的影响因素。引入扩容角考虑塑性体积变化的影响,推导Hoek-Brown屈服准则下考虑与不考虑洞周面力的深埋隧洞围岩非线性应力解。借助可描述蠕变全过程行为的河海模型,获得了围岩黏弹塑性区蠕变位移表达式。针对不同NVPB蠕变参数和不同材料参数m值情况,讨论分析了洞周面力与扩容角对隧洞洞壁蠕变位移的影响规律。结果表明：在高地应力作用下,采用非线性蠕变模型描述深埋隧洞围岩蠕变问题可获得蠕变全过程曲线;扩容角增大或洞周面力和材料参数m值减小时,相同时刻隧洞洞壁蠕变位移增大,对围岩长期稳定不利。研究结论对深埋隧洞围岩临崩预报具有一定指导意义。     

A new closed-form solution for circular openings modeled by the Unified Strength Theory and radius-dependent Young’s modulus

A new closed-form solution is presented for the stress and displacement distribution surrounding circular openings with finite external radii that are subject to uniform internal and external pressures under plane strain conditions. The specific solution for a deep circular tunnel in an infinite rock mass is also provided. It is assumed that the rock mass is elastic–brittle–plastic and governed by the Unified Strength Theory (UST). In the plastic zone, the radius-dependent Young’s modulus (RDM) model and a non-associated linear flow rule were adopted to establish the radial displacement solution. The new closed-form solution obtained in this paper is a series of results rather than one specific solution; hence, it is suitable for a wide range of rock masses and engineering structures. The traditional solutions, which are based on the Mohr–Coulomb failure criterion and the Generalized Twin Shear Stress yield criterion, can be categorized as special cases of this proposed solution. This new solution agrees reasonably well with the results of a borehole collapse test, a secondary development numerical simulation and an additional closed-form solution using the generalized non-linear Hoek–Brown failure criterion. Parametric studies were conducted to investigate the effects of intermediate principal stress, RDM and dilatancy on the results. It is shown herein that the effects of intermediate principal stress and dilatancy are significant; the RDM model is recommended as the optimum approach for calculating radial displacement and support pressure.     

斜坡下考虑支护效应浅埋隧道力学响应的时效解答

针对岩质或黄土浅埋隧道,考虑岩土体黏弹性流变特性和支护效应,给出斜坡下进行隧道施工时的全域时效解答。根据一般黏弹性问题求解方法,采用复变函数方法、Laplace变换、黏弹性叠加关系,用随时间和空间变化支护力体现管片支护效应,导出适用于任意黏弹性模型岩体、任意时刻施加支护的应力与位移。解答与相同模型有限元结果一致,根据解答分析了广义Kelvin黏弹性模型岩体中浅埋隧道开挖时侧压力系数、斜坡倾角、埋深对稳定地表沉陷大小和范围、洞周时效位移、应力的影响,给出可按深埋问题处理时的埋深范围。解答可用于岩质和黄土隧道初步设计中,并为隧道与地下结构相互作用分析两阶段法提供自由位移场。     

岩石弹塑性应力-渗流-损伤耦合模型研究(Ⅰ):模型建立及其数值求解程序

在地下水渗流场、应力场、损伤场的耦合作用下更易造成隧道围岩坍塌或涌水等灾害。首先,将围岩材料视作各向同性连续介质,基于Drucker-Prager准则建立岩石弹塑性损伤本构模型,采用完全隐式返回映射算法实现弹塑性损伤本构方程的数值求解。其次,以上述研究为基础根据岩石处于弹塑性状态时渗透系数动态演化公式,建立岩石弹塑性应力-渗流-损伤耦合模型,并给出三场耦合情况下的数值求解迭代方法。针对耦合模型中涉及参数较多且不易测定的问题,基于差异进化算法原理建立智能反分析方法,对耦合模型中的损伤参数进行反演。最后,利用C++语言编制相应的岩石弹塑性应力-渗流-损伤耦合程序和参数反演程序,利用所编程序进行以下计算:(1)对智能反分析程序的性能、正确性进行分析,对比不同差异策略、交叉因子、变异因子的反演精度和收敛速度。(2)分别采用弹性模型和弹塑性损伤模型进行隧道围岩位移场、应力场的计算。(3)不考虑力学作用的情况下进行孔隙水压力、渗流量的计算。(4)采用所建耦合模型计算得到隧道围岩应力场、渗流场以及损伤场的相互影响规律。研究结果表明,基于差异进化算法的智能反分析程序能够较好地解决耦合模型中损伤参数不易确定的难题,为实际工程中获得不易测定的计算参数提供了有效的方法,同时所建立的耦合模型通过应力、渗流和损伤的相互作用更能够真实地反映出岩石材料的宏观破坏现象,所编计算程序能够模拟地下水渗流场、应力场、损伤场之间的耦合特性,为受地下水影响严重的工程建设提供了方法,研究结论为后期对实际隧道工程进行耦合计算奠定基础。     

Analytical and Numerical Study of the Mechanics of Rockbolt Reinforcement around Tunnels in Rock Masses

Summary  This paper addresses the problem of quantifying the mechanical contribution of rockbolts installed systematically around tunnels excavated in rock masses. The mechanical contribution referred to here is that of increased stress confinement and decreased tunnel convergences as compared with corresponding stresses and displacements obtained for non-reinforced tunnels. The problem is treated analytically first by presenting a closed-form solution for stress and displacement distributions around a circular tunnel excavated in elastic material and reinforced by grouted or anchored rockbolts. The analytical solution assumes that rockbolts are regularly spaced around the tunnel and that axi-symmetry conditions of geometry and loading apply. The results obtained with the closed-form solution are shown to be equivalent to the results of the same problem solved with traditional numerical methods. Based on the analytical and numerical results and by introducing dimensionless ratios that allow to quantify the increase of radial stresses and the decrease of radial displacements in the reinforced region of the tunnel, the paper shows that reinforcement can have a significant mechanical effect (i.e., increasing the confinement and decreasing the convergences) in tunnels excavated in rock masses of poor to very poor quality. The paper analyzes then the mechanical contribution of rockbolt reinforcement when the rock mass is assumed to behave elasto-plastically. For this case, it is shown that rockbolt reinforcement can also have a critical effect in controlling the extent of the plastic failure zone and the convergences of the tunnel. Correspondence: C. Carranza-Torres, Department of Civil Engineering, University of Minnesota, Duluth Campus, 1305 Ordean Court, Duluth, USA     

水-力耦合作用下三趾马红土围岩变形特征研究

以地下水位线以下的石楼隧道典型三趾马红土围岩段为例,通过现场监测对三趾马红土围岩的体积含水量、孔隙水压力、围岩应力（土压力）、拱顶沉降与水平收敛进行了分析。在此基础上,通过原位大剪试验获得了可靠的围岩抗剪强度参数,并建立了隧道三维有限元数值模型,分别对考虑水-力耦合效应、不考虑水-力耦合效应的三趾马红土围岩变形规律进行了探讨,分析了孔隙水压力随着隧道开挖的变化和三趾马红土围岩位移场、应力场受水-力耦合效应的影响程度,并提出了围岩破坏变形机制。结果表明:（1）实测拱顶下沉大于围岩水平变形,围岩应力可分为增长期（ < 20d）、调整期（20~60d）、稳定期（>60d）3个阶段,且整体应力水平较高,下台阶含水量大于上台阶,孔隙水压力经历了由负变正的过程。（2）现场剪切试验所测围岩的黏聚力为64.0kPa,内摩擦角为27.7°。（3）数值分析表明,隧道开挖后孔隙水压力场变化十分明显,这是由地下水流速场的改变引起的,水力坡降在衬砌面附近最为明显,渗透动水压力导致土体产生一定的渗透变形;考虑水-力耦合后围岩剪应力、最大剪应变、拱顶沉降、水平收敛、底板隆起均较大。（4）受开挖及支护的影响,地下水产生渗流并依次经过拱顶、边墙,最终汇集于隧底;受开挖、地下水渗流的影响,围岩节理裂隙进一步扩张,成为地下水良好的运移通道;围岩的有效应力随着孔隙水压力的减小而增大,围岩的力学强度在土体趋于饱和状态时骤降,反过来,高有效应力、低围岩强度以及贯通性节理裂隙三者共同改变着地下水渗流场的状态。（5）为保障围岩整体稳定性,建议及时排出隧道底部积水并施做仰拱。     

Coupling Rheological Behavior of Rock Mass Supported with Rockbolts Based on the Point Load Model

Rockbolts can be regarded as a permanent support structure for underground engineering. However, the coupled rheological mechanism between rockbolts and rock mass remain poorly understood. In this research, the rock mass supported with discretely mechanically or frictionally coupled rockbolts with the point load model was investigated. At first, the elastic solutions of the coupling model were solved. Subsequently, the viscoelastic analytical solutions were acquired by applying the Laplace inverse transforms. Finally, the effect of viscosity coefficients and supporting parameters on the coupling model rheological behavior were explored. The results indicated that the angle of rockbolts support has a greater influence on the radial stress and tangential stress of the rock mass in the elastic state, but has little influence on the rheological state. Moreover, the roof, the interface between the left wall and right wall should be supported strengthen; the viscosity coefficient has little influence on the radial stress and tangential stress in the rheological state and has a negative correlation with the radial displacement. In order to limit the displacement in the rheological state of the rock mass, we choose the rockbolts with a large viscosity coefficient.

     

考虑渗流和剪胀的圆形巷道围岩广义SMP准则解

本文基于广义SMP准则,综合考虑中间主应力、孔隙水压力和围岩的剪胀特性,建立了巷道围岩的理想弹塑性模型。根据弹塑性理论,推导了渗流作用下的围岩应力场、位移场和塑性区半径的统一解析解。结合具体算例对SMP准则计算得到的围岩应力分布和塑性区半径与Mohr-Coulomb（M-C）准则进行了对比,并对孔隙水压力和围岩剪胀角等影响因素进行了分析。研究结果表明:SMP准则计算得到的塑性区半径小于M-C准则,说明M-C准则相较于SMP准则更为保守;孔隙水压力对巷道围岩的位移场具有很大的影响,表现为孔隙水压力越大,巷道洞壁附近围岩位移量越大,且围岩塑性区半径和弹塑性交界面处的峰值切向应力与孔隙水压力成正比;采用相关联流动法则会低估围岩的强度,不考虑剪胀则会低估围岩的实际变形。      

增湿条件下膨胀土隧道衬砌破坏数值分析

针对小河沟膨胀土隧道降雨增湿塌方现象,以围岩含水率分布变化引起膨胀应力场为主要研究内容,展开增湿对隧道支护结构的影响研究。首先,利用热传导热能量平衡方程与孔隙渗流连续方程数学描述相似性,推导出热传导膨胀模拟增湿膨胀的替代方程。然后,结合室内试验和文献资料,率定膨胀土膨胀力及渗流参数。最后,在正确考虑地质构造影响的基础上运用有限差分软件FLAC3D热-力耦合模块进行建模计算,分别对不同膨胀力模型的增湿过程进行仿真模拟,得出支护结构受力变形随含水率分布及膨胀力大小的变化规律。分析得到了对隧道支护结构造成不良影响的关键含水率和膨胀力值。研究成果可以有效指导膨胀性黄土隧道支护设计和变形控制。     

引水隧洞膨胀性围岩的稳定性分析

膨胀岩在实际工程中通常表现为围岩随时间的推移大量向洞室内塑性挤出或底板大量隆起,最终导致洞室支护和围岩产生裂损或破坏。山西万家寨引黄入晋工程南干线7号隧洞地层特点除砂岩与泥岩互层外,膨胀岩共有3～4层,且斜穿隧道。通过对隧洞开挖及支护过程应用考虑膨胀岩影响的粘弹塑性有限元进行分析,得出膨胀围岩对隧洞及支护结构的受力及稳定性的影响。建议在通水运行过程中密切监测其变形、应力应变、渗透压及外水压力的变化规律,以确保工程的安全运行。     

A new procedure for ground response curve (GRC) in strain-softening surrounding rock

A new procedure for the ground response curve (GRC) is investigated in strain-softening surrounding rock for a circular opening. The procedure started each step with a radius increment and the analytical solutions of stress and strain in each annulus were presented. The plastic region is divided into a finite number of concentric annuli, whose thickness is uniformly determined by a small radius increment. Combining the equilibrium equation and failure criterion, stress for each annulus can be obtained analytically. The displacement for each step can be calculated analytically through solving the differential equation by invoking flow rule and Hooke’s law. The strains for each annulus can be obtained by the strain-displacement relationship. In the successive manner, the distributions of stress and displacement can be found. It should be noted that the finial stress and displacement at radial direction are the internal support pressure and deformation at the excavation surface, respectively. By assuming different plastic radii (using a plastic radius increment), GRC, the evolution curve of plastic radii and internal support pressure can be obtained analytically. Some numerical and engineering examples are performed to demonstrate the validity of the proposed procedure. It is shown that the results of the proposed procedure at the tunnel crown are basically consistent with field measuring data. The influence of the annulus number, plastic radius increment and dilation on the accuracy of the proposed approach is investigated. Results show that the solutions are more accurate and the calculation efficiency is higher.     

断层破碎带隧道突水突泥灾变演化模型试验研究

为研究断层破碎带隧道开挖扰动作用下突水、突泥灾变演化过程,建立了三维地质模型试验系统,以江西永莲隧道F2断层突水、突泥灾害为例,通过大量的材料配比及物理力学性能参数测试,研制出适用于流-固耦合模型试验的新型断层及正常围岩相似材料,对隧道突水、突泥灾害进行研究。试验结果有效地揭示了无支护条件下断层破碎带隧道的洞周位移、渗流压力、应力-应变以及突出物质量等特征参数对时效性的响应规律。随着时间的增长,渗流压力整体呈上升趋势,越靠近开挖面其波动范围及幅度越大;突出物质量在发生突水、突泥灾害前出现短时减小后迅速增加;洞周围岩拱顶以竖向位移为主,而拱腰以水平位移为主;在相同相应力状态下,拱腰位置应变比拱顶位置大。将试验灾变特征与现场实际演化过程进行对比分析,两者结果较为吻合。该系统可广泛应用于其他地下工程的模型试验研究,其研究方法及结果对类似工程研究具有一定的指导和借鉴意义。     

深埋隧道锚杆支护作用的数值模拟与模型试验研究

以重庆至长沙公路共和隧道为研究对象,研制出环氧-硅橡胶的相似模型材料,在大型真三轴模型试验机上进行了隧道在毛洞和锚杆支护条件下的超载试验,采用应变测量技术对隧道关键部位的应变值和锚杆的应变值进行了测量,据此分析了围岩体在锚杆支护后的应力变化规律和锚杆的轴力变化规律。采用与模型试验相同的边界条件进行了隧道在锚杆支护条件下的数值模拟工作,对围岩体的塑性区、应力场和锚杆轴力随荷载的变化过程进行了研究。结果表明,两种手段反映的围岩体应力变化规律和锚杆轴力随荷载的变化规律是一致的