Analytical model for the design of grouted rock bolts

An analytical model which represents the behaviour of a reinforced rock mass near a circular underground opening in a homogeneous, uniform stress field has been developed. The theory adopts the concepts of elastoplasticity and considers a proper interaction mechanism between the ground and the grouted (or friction) bolts. It highlights the influence of the bolt pattern on the extent of the yield zone and tunnel deformation. A dimensionless parameter is introduced as a design tool which relates the tunnel convergence to the bolt spacing for a given bolt length. This publication contains the derivation of the analytical model and an illustration of the effect of bolts on the stress and displacement field near an opening. Its application to tunnel design is discussed briefly. The verification of the theory by laboratory simulation and field measurements will be presented, in detail, in a future publication.     

锚杆对围岩的加固效果和动载响应的数值分析

利用数值分析软件LS-DYNA3D程序,对锚杆对围岩的加固效果和动态力学性能进行了显示动力分析,比较了洞室围岩是否用锚杆加固时,爆炸波引起的岩体中垂直应力、拱顶位移以及锚杆本身轴向应变的变化特点。结果发现：同毛洞相比较,加固洞室围岩应力较大,拱顶位移较小;通过分析锚杆轴向应变-时程曲线,发现不同安装角的锚杆其轴向应变对动载的响应不同,拱部锚杆先受压后受拉,直墙部锚杆全受拉,两部位锚杆均产生轴向拉应变;将模拟的锚杆应变-时程曲线同模型试验的相应曲线进行了比较,两者一致性较好,其结果为动载作用下坑道围岩锚杆加固的布置方法提供了参考。     

A constitutive model for a laboratory rock joint with multi-scale asperity degradation

This paper presents a joint constitutive model that considers separately the mechanical contribution of waviness and unevenness of a joint to shear behaviour. The critical asperities for waviness and unevenness are determined from geometric properties in a lab-scale joint. The wear process is employed to model the degradation in dilation and strength during shear. From dimensional analysis, asperity degradation constants are developed using geometric parameters including asperity angle, wavelength, and amplitude as well as rock strength and stress. The applicability of the proposed model was assessed by performing direct shear tests on three joint roughness coefficient (JRC) profiles and providing its correlation with experimental results. Additionally, experimental data taken from literature were used to validate the model’s performance.     

节理峰值后归一化位移软化模型

切向荷载作用下贯通节理岩体峰值强度后的剪切应力、位移变形规律一般呈双曲线形式发展,即峰值后强度衰减速率逐步变小而趋于0,到达残余强度。直剪试验表明,非贯通节理岩体峰值后剪切应力、位移呈“S”型趋势发展,即强度衰减速率先是逐步增大,到达一定程度后逐步减少,最后趋于稳定达到残余强度值。贯通节理岩体峰值强度后的本构关系并不适合于描述该特征。提出一个新的非线性归一化位移软化本构模型,通过归一化剪切应力R与归一化剪切位移D的指数函数关系体现峰值后剪切应力、位移的发展趋势,即模型采用无量纲表达式。归一化剪切应力R是峰值后强度降? p-? 与峰值强度、残余强度差值? p-? r的比值;归一化位移D是峰值后剪切位移、峰值位移差值? -? p与残余位移、峰值位移差值? r -? p的比值。对含不同起伏角的非贯通节理岩体在常法向荷载条件下的直剪试验数据进行拟合分析,模型预测结果与实测值具有相当高的吻合度,验证了模型的正确性     

输电线路节理化岩体注浆锚杆基础抗拔力模型试验研究

针对输电线路注浆锚杆基础特点,根据相似理论设计了节理化岩体注浆锚杆基础抗拔模型试验,模型设计中考虑了岩石弹性模量、浆体弹性模量、节理迹长、节理倾角、锚杆埋深5个因素的变化,选择5因素4水平的正交试验方法进行了模型试验研究。结果表明,岩石弹性模量对注浆锚杆基础抗拔力的影响最大,其次为锚杆埋深、节理倾角、浆体弹性模量、节理迹长。试验过程中以剪切破坏和开裂破坏为主,并以此分析了注浆锚杆的传力机制,得出浆体与锚杆和岩体之间的黏结强度是控制试验结果的主要因素,影响着锚杆的极限抗拔力和破坏状态,在施工过程中应注意质量控制。     

Modeling strategy for jointed rock masses reinforced by rock bolts in tunneling practice

This paper deals with the modeling of jointed rock masses reinforced by rock bolts. It is well known that rock bolts are extremely effective in reinforcing jointed rocks. However, if a continuum approach is adopted for modeling jointed rock masses, it is often misleading to evaluate the effectiveness of the rock bolts by numerical analyses such as the finite element method. This may be due to the fact that since no more joints exist in the continuum, the effectiveness of the rock bolts in constraining the relative displacements along the joints cannot be evaluated properly. In order to investigate the reinforcement effect of rock bolts, physical model tests were performed in the laboratory. The test results revealed that jointed rock masses should be modeled as an equivalent continuum after the installation of rock bolts and that the mechanical parameters of the equivalent continuum should be evaluated by considering the reinforcement effect of the rock bolts. Therefore, the values of the mechanical parameters differ from place to place in accordance with the relation between joint orientation and rock bolt direction, even though joint systems are homogeneous. In conclusion, in the continuum approach for modeling jointed rock masses, it should be emphasized that rock bolts and jointed rock masses should not be modeled separately but should be modeled simultaneously by considering the reinforcement effect of the rock bolts in constraining joint movement. The modeling of shotcrete reinforced by steel ribs is also discussed in comparison to the modeling by rock bolts.     

A continuum model of layered rock masses with non-associative joint plasticity

Layered rock masses can be modelled either as standard, orthotropic continua if the layer bending can be neglected or as Cosserat continua if the influence of layer bending is essential. This paper presents a finite element smeared joint model based on the Cosserat theory. The layers are assumed to be elastic with equal thickness and equal mechanical properties. All the cosserat parameters are expressed through the elastic properties of layers, layer thickness and joint stiffness. Plastic-slip as well as tensile-opening of layer interface (joint) are accounted for in a manner similar to the conventional non-associative plasticity theory. As an application, the behaviour of an excavation in a layered rock mass is examined. The displacement and stress fields given by smeared joint models based on the Cosserat continuum and the conventional anisotropic continuum approaches are compared with those obtained from the discrete joint model. The conventional anisotropic continuum model is found to break-down completely when the effective shear modulus in the direction parallel to layering is low in comparison to the shear modulus of the intact layer, whereas the Cosserat model is found to be capable of accurately reproducing complex load–deflection patterns irrespective of the differences in shear moduli. © 1998 John Wiley & Sons, Ltd.     

注浆锚杆完整性检测方法研究

采用理论分析和实验室测试的方法对锚固锚杆和自由锚杆中的导波传播规律进行了研究,并在频率为20 kHz～ 3 MHz范围内对锚固锚杆和自由锚杆波的传播速度进行了测试,发现锚固锚杆内不同频率的导波传播速度对锚固介质具有不同的敏感性。低频率段（20～200 kHz）的导波传播速度对锚杆锚固质量较为敏感,自由锚杆和锚固锚杆中导波的传播速度相差较大,适合于检测锚杆的锚固质量。高频率段（1～3 MHz）的导波传播速度对锚杆锚固质量不敏感,导波的传播速度基本不变,适合于锚杆完整性检测。探索了利用高频段多频率导波检测锚固锚杆长度的方法。实验室检测结果显示,本检测方法具有很高的精度     

岩石锚杆锚固段荷载分布试验研究

岩石锚杆锚固段荷载分布规律是岩土锚固技术的关键问题之一。在拉拔试验锚杆杆体测点应变数值采集的基础上,利用复合幂函数和高斯函数对实测数据进行曲线拟合,获得了临界破坏状态下的锚固段轴力及剪应力分布情况。试验结果表明：岩石锚杆锚固段剪应力的分布集中在锚固段的前部;高斯函数可以较好地描述临界破坏状态下锚杆杆体的轴力分布;界面破坏出现在界面峰值抗剪强度远大于界面所能提供的黏结强度情况下。研究结果为锚杆的设计与计算提供了理论依据。     

The variogram method for a fractal model of a rock joint surface

The variogram method can be used to make a fractal model of a rock joint surface. However, it has been found that the range of lag satisfying the power law is very small, that is, less than about 10% of the profile length. The cause of this has been investigated mathematically. The main cause of this problem is due to the fact that the profile length is assumed infinite for the theory, but it is finite for the actual calculation. This discrepancy between the actual calculation and the theory yields a significant error and causes the problem when the lag is large. To confirm the validity of this conclusion, it has been demonstrated that the range of lag satisfying the power law increases with an increase in the profile length by applying the variogram method to profiles cut from a long profile. In addition, the range of lag was investigated mathematically and it has been clarified that the range of lag increases with an increase in the fractal dimension. These results suggest that the profile length, the sampling interval and the removal of the linear trend are items to which we must pay attention when we use the variogram method.     

A model for coupled mechanical and hydraulic behaviour of a rock joint

Constitutive laws for rock joints should be able to reproduce the fundamental mechanical behaviour of real joints, such as dilation under shear and strain softening due to surface asperity degradation. In this work, we extend the model of Plesha to include hydraulic behaviour. During shearing, the joint can experience dilation, leading to an initial increase in its permeability. Experiments have shown that the rate of increase of the permeability slows down as shearing proceeds, and, at later stages, the permeability could decrease again. The above behaviour is attributed to gouge production. The stress–strain relationship of the joint is formulated by appeal to classical theories of interface plasticity. It is shown that the parameters of the model can be estimated from the Barton–Bandis empirical coefficients; the Joint Roughness Coefficient (JRC) and the Joint Compresive strength (JSC). We further assume that gouge production is also related to the plastic work of the shear stresses, which enables the derivation of a relationship between the permeability of the joint and its mechanical aperture. The model is implemented in a finite element code (FRACON) developed by the authors for the simulation of the coupled thermal–hydraulic–mechanical behaviour of jointed rock masses. Typical laboratory experiments are simulated with the FRACON code in order to illustrate the trends predicted in the proposed model. © 1998 by John Wiley & Sons. Ltd.     

Three‐phase medium model for filled rock joint and interaction with stress waves

A three‐phase medium model is proposed in describing the dynamic property of filled rock joints and an analytical study on longitudinal wave transmission normally across a three‐phase rock joint is presented. Parameters in the three‐phase medium model were determined by a series of modified split Hopkinson pressure bar (SHPB) tests, where a sand or clay layer was used to represent an artificially filled rock joint. The effect of the unloading path on the transmitted wave was discussed by comparing the analytical and SHPB test results. The derived wave transmission coefficients across the filled joint agreed very well with those from the test results. Both the analytical and the test results showed that the wave transmission coefficients were affected by the mechanical properties of the fillings. Parametric studies with respect to the volume ratios of water and air in the three‐phase medium and the type of filling material have also been performed. Copyright © 2010 John Wiley & Sons, Ltd.     

考虑损伤阈值影响的岩石脆-延性转化统计损伤本构模型研究

普通岩石在三向受力状态下随着围压由低到高,会表现出由脆性向延性转化的特征.首先,在深入探讨岩石压缩变形机理与变形过程特征的基础上,并针对Lemaitre应变等价性理论的不足之处,基于能量理论建立了更符合实际情况的损伤模型;其次,从岩石并非一受力就会产生损伤这一客观事实出发,建立了能反映损伤阈值影响的岩石单元强度度量方法与损伤演化模型.最后,在上述模型基础之上,建立了可体现岩石在三轴试验中脆-延性转化特征的统计损伤本构模型及模型参数确定方法.     

层状岩体深埋长隧道锚杆支护优化设计

层状岩体是地下工程中经常遇到的一种岩体,力学性质具有明显的各向异性。选择合适的屈服准则和强度参数变化规律,结合各向异性弹性本构方程,获得横观各向同性弹塑性本构关系,利用该本构模型对共和隧道锚杆支护方案进行数值计算。首先考虑地应力、岩性的影响,从围岩的变形、破坏形式、塑性区及锚杆拉力的大小等方面改进、优化支护设计方案;其次从实际工程出发,考虑施工难度、工程造价等因素的影响,得到改进方案Ⅰ效果较理想,通过试验段现场监测确定改进方案I。本构模型对计算结果的影响很大,正确模型的计算结果可以为实际工程提供科学依据。     

软弱围岩隧道取消系统锚杆的现场试验研究

在软弱围岩隧道中,提出初期支护结构由钢架+喷射混凝土+钢筋网+锁脚锚杆+纵向连接筋组成,即取消系统锚杆用钢架联结处的锁脚锚杆代替。以包家山隧道为依托工程,采用现场试验的方法,选取2个试验段,进行锁脚锚杆取代系统锚杆后,有、无拱部锚杆的对比试验研究。对比试验的内容包括：隧道初期支护的净空收敛、围岩压力、钢架应力、喷射混凝土应力、锚杆轴力和纵向连接筋应力等。研究结果表明：2个试验段初期支护变形趋于稳定,结构受力安全,说明取消系统锚杆不影响初期支护结构的安全与稳定;拱部锚杆有受拉,也有受压,但受力都不大,最大拉应力仅为钢材极限强度的11.8%,其支护作用不明显;锁脚锚杆大部分受拉,最大值达到191 MPa,钢架支护作用明显,在支护体系中发挥着重要作用。取消系统锚杆减少了施工工序,降低了工程造价,缩短了工序循环时间,有利于及早封闭围岩以形成完整的支护结构。经济价值和社会效益显著。     

围岩作用下锚杆砂浆锈胀开裂过程分析

从砂浆锚杆锚固体自身的特点出发,借鉴钢筋混凝土结构锈胀开裂研究成果,对锚杆砂浆锈胀开裂过程进行了分析。考虑锚杆锈蚀体积膨胀过程,以填充系数表示砂浆开裂过程中锚杆锈蚀产物的损失,建立了锚杆锈蚀后砂浆内部位移模型,以弹性力学为基础,引入围岩参数影响系数概念,对锚杆锈蚀导致砂浆保护层开裂过程以及围岩参数对开裂过程的影响程度等进行了分析研究,并采用有限元分析方法对其进行了验证。理论分析结果表明,因锚杆锈蚀而导致的砂浆保护层开裂以及裂纹的扩展情况均与围岩特性密切相关,砂浆开裂后裂纹会经历一段稳定扩展过程,裂纹的最大稳定扩展半径随围岩参数影响系数的增加而增大,在合适的围岩参数条件下,裂纹可以一直稳定扩展致整个砂浆保护层外壁。有限元分析结论与理论结果一致。     

全长粘结式锚杆加固洞室抗爆性能试验研究

通过模型试验, 研究了在平面装药爆炸应力波的作用下,全长粘结式锚杆加固洞室抗爆性能。试验结果表明,通过分析自由场压力-时程曲线,证明试验数据可靠;经过加固的洞室拱顶位移峰值减少明显,当比例距离为5.23 cm/g1/2时,洞室发生破坏;在平面波的作用下,两个洞室洞壁各个位置都产生压应变,最大应变出现在拱脚处,随着比例距离减小,拱顶应变峰值先增加后减小,最大应变峰值越来越大;拱顶是加速度振动最激烈的地方,经过加固可以降低拱顶加速度,但效果不明显,在变形不大时底板加速度增加较大,必要时应该采取减震措施,经过加固洞室侧墙加速度普遍有不同程度减小,并且破坏越严重效果越明显,随着比例距离减小,拱顶和侧墙加速度越来越大,尤其当比例距离为5.23 cm/g1/2时,加速度急剧上升。     

Enriched finite element procedures for analyzing decoupled bolts installed in rock mass

Numerical procedures are developed to analyze interaction between fully grouted bolts and rock mass using ‘enriched finite element method (EFEM)’. A solid element intersected by a rock bolt along any arbitrary direction is termed as ‘enriched’ element. The nodes of an enriched element have additional degrees of freedom for determining displacements, stresses developed in the bolt rod. The stiffness of the enriched element is formulated based on properties of rock mass, bolt rod and grout, orientation of the bolt and borehole diameter. Decoupling at grout–bolt interface and elasto‐plastic behavior of rock mass have also been incorporated into the EFEM procedures. The results of this method are compared with analytical pull‐out test results presented by Li and Stillborg (Int. J. Rock Mech. Min. Sci. 1999; 36 :1013–1029). In addition, a numerical example of a bolted tunnel is provided to demonstrate the efficacy of the proposed method for practical applications. Copyright © 2010 John Wiley & Sons, Ltd.     

Implementation of displacement-dependent Barton-Bandis rock joint model into discontinuous deformation analysis

Discontinuous deformation analysis (DDA) has been widely applied in analyzing various rock engineering problems. As the joint strength play a vital role in the stability of jointed rock mass, this paper makes an attempt to implement the Barton-Bandis rock joint model into the DDA code to replace the original Mohr-Coulomb joint model. The developed Barton-Bandis joint model which is characterized by displacement-dependent shear strength is verified by experimental direct shear tests. An example of a block sliding on an inclined plane is used to demonstrate the capacity of the DDA-BB model in predicting the dynamic motion behavior of sliding blocks.