Experimental Validation of Modified Barton’s Model for Rock Fractures

Among the constitutive models for rock fractures developed over the years, Barton’s empirical model has been widely used. Although Barton’s failure criterion predicts peak shear strength of rock fractures with acceptable precision, it has some limitations in estimating the peak shear displacement, post-peak shear strength, dilation, and surface degradation. The first author modified Barton’s original model in order to address these limitations. In this study, the modified Barton’s model (the peak shear displacement, the shear stress–displacement curve, and the dilation displacement) is validated by conducting a series of direct shear tests.     

Empirical Formula of Shear Strength of Rock Fractures Based on 3D Morphology Parameters

The prime objective of this work is to provide a reference to predict the peak shear strength of rock fractures. The paper studied some shear properties of rock fractures and proposed an empirical formula for the peak shear strength of rock fractures based on 3D morphology parameters. The rock fractures were induced in cylindrical sandstone and marble specimens by means of indirect tension. A rock direct shear apparatus (RDS-200) was adopted to conduct direct shear tests on five groups of rock fractures under different levels of normal load. Before the direct shear test, 3D morphology parameters of rock fracture surfaces were obtained using a 3D optical scanner. By analyses of direct shear test data, the relationships between peak shear strength, peak shear displacement, peak dilatancy angle, residual friction coefficient and peak normal stress were found. According to the evolution trends of peak shear strength and peak dilatancy angle along with the normal stress, an empirical formula was proposed to predict the peak shear strength of rock fractures in both sliding and cutting failure modes considering the 3D morphology parameters of rock fracture surfaces. The empirical formula could be commonly used for different types (sandstone and marble) and grain sizes (powder-grained, fine-grained, medium-grained and coarse-grained) of rock fractures.     

Hydraulic Characteristics of Rough Fractures in Linear Flow under Normal and Shear Load

Summary A hydro-mechanical testing system, which is capable of measuring both the flow rates and the normal and shear displacement of a rock fracture, was built to investigate the hydraulic behaviour of rough tension fractures. Laboratory hydraulic tests in linear flow were conducted on rough rock fractures, artificially created using a splitter under various normal and shear loading. Prior to the tests, aperture distributions were determined by measuring the topography of upper and lower fracture surfaces using a laser profilometer. Experimental variograms of the initial aperture distributions were classified into four groups of geostatistical model, though the overall experimental variograms could be well fitted to the exponential model. The permeability of the rough rock fractures decayed exponentially with respect to the normal stress increase up to 5 MPa. Hydraulic behaviours during monotonic shear loading were significantly affected by the dilation occurring until the shear stress reached the peak strength. With the further dilation, the permeability of the rough fracture specimens increased more. However, beyond shear displacement of about 7 to 8 mm, permeability gradually reached a maximum threshold value. The combined effects of both asperity degradation and gouge production, which prohibited the subsequent enlargement of mean fracture aperture, mainly caused this phenomenon. Permeability changes during cyclic shear loading showed somewhat irregular variations, especially after the first shear loading cycle, due to the complex interaction from asperity degradations and production of gouge materials. The relation between hydraulic and mechanical apertures was analyzed to investigate the valid range of mechanical apertures to be applied to the cubic law. Received June 12, 2001; accepted February 26, 2002 Published online September 2, 2002     

峰前循环剪切作用下岩石节理剪切力学特性

微震、工程爆破等低应力循环剪切荷载作用对节理岩体工程失稳破坏具有重要影响。为研究峰前循环剪切加卸载作用下岩石节理剪切力学特性,采用RDS-200型岩石节理剪切试验系统对人工劈裂黄砂岩节理进行了峰前循环剪切下的直剪试验。通过与未进行峰前循环剪切加卸载时岩石节理力学参数预测值对比,得到峰前循环剪切加卸载作用对峰前剪切刚度、峰值剪切强度、峰值剪切位移与残余剪切强度的影响。结果表明：（1）峰前循环剪切加卸载后,当法向应力为2 MPa时,岩石节理峰前剪切刚度增大,当法向应力为4～10 MPa时,岩石节理峰前剪切刚度在循环剪切应力幅值范围内增大,在超出循环剪切应力幅值时减小;（2）峰前循环剪切加卸载后,峰值剪切强度降低了10%～20%,降低百分比随法向应力增大整体呈对数函数增大;峰值剪切位移增加了2%～40%,增加百分比随法向应力增大整体呈对数函数减小;（3）峰前循环剪切加卸载后,岩石节理残余剪切强度无明显变化,峰值剪切强度与残余剪切强度差值减小,峰后剪切应力做功损失百分比降低。     

Applicability of existing models to predict the behavior of replicas of natural fractures of welded tuff under different boundary conditions

Assessing the shear behavior of intact rock and rock fractures is an important issue in the design of a potential nuclear waste repository at Yucca Mountain, Nevada. Cyclic direct shear experiments were conducted on replicas of three natural fractures and a laboratory-developed tensile fracture of welded tuff. The tests were carried out under constant normal loads or constant normal stiffnesses with different initial normal load levels. Each test consisted of five cycles of forward and reverse shear motion. In this paper, the results of the constant normal load shear experiments are analyzed using several constitutive models proposed in the rock mechanics literature for joint shear strength, dilatancy, and joint surface damage. It is shown that some of the existing models have limitations. New constitutive models are proposed and are included in a mathematical analysis tool that can be used to predict joint behavior under various boundary conditions. © Rapid Science Ltd. 1998     

A Bonded Particle Model Simulation of Shear Strength and Asperity Degradation for Rough Rock Fractures

Different failure modes during fracture shearing have been introduced including normal dilation or sliding, asperity cut-off and degradation. Attempts have been made to study these mechanisms using analytical, experimental and numerical methods. However, the majority of the existing models simplify the problem, which leads to unrealistic results. With this in mind, the aim of this paper is to simulate the mechanical behaviour of synthetic and rock fracture profiles during direct shear tests by using the two-dimensional particle flow computer code PFC2D. Correlations between the simulated peak shear strength and the fracture roughness parameter D _R1 recently proposed by Rasouli and Harrison (2010) are developed. Shear test simulations are carried out with PFC2D and the effects of the geometrical features as well as the model micro-properties on the fracture shear behaviour are studied. The shear strength and asperity degradation processes of synthetic profiles including triangular, sinusoidal and randomly generated profiles are analysed. Different failure modes including asperity sliding, cut-off, and asperity degradation are explicitly observed and compared with the available models. The D _R1 parameter is applied to the analysis of synthetic and rock fracture profiles. Accordingly, correlations are developed between D _R1 and the peak shear strength obtained from simulations and by using analytical solutions. The results are shown to be in good agreement with the basic understanding of rock fracture shear behaviour and asperity contact degradation.     

Experimental study on damage failure mechanical characteristics and crack evolution of water-bearing surrounding rock

Water plays an important role in the mechanical properties of roadway surrounding rocks and poses a great threat to their stability. To study the damage and failure characteristics, and the fracture development laws of surrounding rock, a uniaxial compression test for prefabricated fractures in water-bearing surrounding rock was carried out. Results indicate that water-bearing prefabricated fracture specimens are in better development condition after failure. In water-bearing specimens, the propagation direction is more complex. There are more secondary fissures, and the fracture strength is significantly lower than in dry specimens. When immersed in water, the interior structure of surrounding rock is weakened and softened; thus, the intensity is reduced, and the development and propagation of fractures is promoted. For larger angles of the prefabricated fractures, the compression failure of surrounding rock changes into shear failure. As the angles approach 90°, the shear failure again prevails. Therefore, the strength of the surrounding rock firstly decreases and then increases. A new ultimate stress strength model is developed for fractures caused by shear slip failure in water-bearing surrounding rock. The model results are consistent with the experimental results, and the validity of the model is verified. These results are helpful for deeply understanding the failure process of water-bearing surrounding rock with prefabricated fractures. The proposed model could be used for the evaluation of water-bearing surrounding rock stability in coal mines, as well as dynamic risk monitoring.     

Flow–stress coupled permeability tensor for fractured rock masses

In this paper a new analytical model is proposed to determine the permeability tensor for fractured rock masses based on the superposition principle of liquid dissipation energy. This model relies on the geometrical characteristics of rock fractures and the corresponding fracture network, and demonstrates the coupling effect between fluid flow and stress/deformation. This model empirically considers the effect of pre‐peak shear dilation and shear contraction on the hydraulic behavior of rock fractures and can be used to determine the applicability of the continuum approach to hydro‐mechanical coupling analysis. Results of numerical analysis presented in this paper show that the new model can effectively describe the permeability of fractured rock masses, and can be applied to the coupling analysis of seepage and stress fields. Copyright © 2008 John Wiley & Sons, Ltd.     

岩石裂纹损伤及围压对剪切破坏影响研究

岩石内部细观裂纹的存在,对压缩作用下岩石剪切断裂的宏观现象有着重要的影响。然而,能够通过解析解阐释细观裂纹几何特性、围压等影响因素对压缩作用下剪切断裂面角度变化趋势的研究很少。基于Ashby模型中提出的裂纹尖端应力强度因子,提出了一种改进的考虑裂纹角度影响的应力强度因子表达式。利用该改进的应力强度因子表达式,推出了一个可以预测岩石峰值强度的裂纹扩展、应变与应力之间的本构关系。结合本构关系的峰值强度与摩尔-库仑失效准则,得到了岩石损伤与内摩擦角、黏聚力、剪切强度及失效断裂面角度之间的理论关系;讨论了围压、裂纹尺寸、角度及摩擦系数对岩石宏观剪切断裂面角度的影响,通过试验结果验证了模型合理性。结果表明：随着损伤增大,内摩擦角、黏聚力及剪切强度不断减小;随着围压增大、摩擦系数增大和初始裂纹尺寸减小,剪切断裂面角度不断增大;随着裂纹角度增大,剪切断裂纹面角度先减小后增大。     

龙滩水电站泥板岩剪切流变力学特性研究

利用岩石剪切流变仪,对龙滩水电站泥板岩进行了剪切流变试验,分析了泥板岩剪切位移随时间的变化规律,探讨了不同应力状态下剪切流变速率的变化趋势,讨论了岩石剪切强度随时间的变化规律。将非线性流变元件(NRC模型)与西原模型串联起来,建立了新的能够描述加速流变特性的岩石非线性流变模型。采用泥板岩剪切流变试验曲线,对建立的黏弹塑性剪切流变模型进行了辨识,获得了岩石黏弹塑性剪切流变模型的材料参数,流变模型与试验结果的比较显示所建模型的正确性与合理性。     

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.     

Study of rock joints under cyclic loading conditions

Summary A conceptual model for the behaviour of rock joints during cyclic shear and under constant normal stresses was proposed according to results from shear tests with 50 concrete replicas of rock joints. The shear strength and deformability of joint samples were found to be both anisotropic and stress dependent. Based on these experimental results, a two-dimensional constitutive model was developed for rock joints undergoing monotonic or cyclic loading sequences. The joint model was formulated in the framework of non-associated plasticity, coupled with empirical relations representing the surface roughness degradation, appearance of peak and residual shear stresses, different rates of dilatancy and contraction, variable normal stiffness with normal deformation, and dependence of shear strength and deformability on the normal stress. The second law of thermodynamics was represented by an inequality and used to restrict the values of some of the material parameters in the joint model. The new joint model was implemented into a two-dimensional Distinct Element Method Code, UDEC, and its predictions agreed well with some well-known test results.     

改进的Maksimovic峰值剪切强度准则的试验验证

Maksimovic峰值剪切强度准则形式简洁,参数的物理含义明确,但由于反映节理粗糙程度的特征量“粗糙度角 ”须由试验值确定,因此不可用于估算岩石节理的峰值剪切强度。改进的Maksimovic峰值剪切强度准则在继承原准则优点的基础上,采用定量化的三维形貌参数表示节理的“粗糙度角 ”。采用岩石节理的直剪切试验数据对改进的Maksimovic峰值剪切强度准则进行了试验验证,计算值与试验值具有很好的相关性,表明可以采用该准则估算岩石节理的峰值剪切强度。     

地震作用下结构面劣化特征及高位危岩体动力失稳机制

地震是高位危岩体失稳崩塌主要诱因之一,而结构面强度与变形特性对高位危岩体稳定性起关键控制性作用.为研究地震作用下高位危岩体动力失稳机制,基于数值试验研究结构面震动劣化效应,并利用极限平衡法对高位危岩体动力稳定性进行研究.研究结果表明,结构面的峰值抗剪强度随着循环剪切次数的增加而减小,且减小幅度愈来愈小,最终趋于稳定值;随着起伏角度增大而增大,且增大幅度随着循环剪切次数的增加而减小;并在同一起伏角度下,随着循环剪切幅值的增大而减小.最后,基于回归分析法建立结构面震动劣化数学模型,并提出一种考虑结构面震动劣化的高位危岩体动力稳定性分析方法.其研究成果有助于丰富高位危岩体动力稳定性方面的基础理论研究,具有重要的理论意义和工程参考价值.      

节理峰值剪切位移及其影响因素分析

根据Barton-Bandis节理峰值剪切强度准则,分析了节理峰值剪切位移与法向应力之间的变化关系,并以此为基础总结了Barton峰值剪切位移公式的不足。通过室内直剪试验验证了节理粗糙度与法向应力是影响结构面峰值剪切位移的两个主要因素。试验结果表明,峰值剪切位移与节理粗糙度成反变化关系,与法向应力成正变化关系。建立了考虑节理粗糙度与法向应力的节理峰值剪切位移计算新公式。克服了Barton经验公式只考虑节理粗糙度,而不考虑法向应力作用的局限。新公式能很好地拟合试验数据,表明其合理性。     

砂土-格栅筋土界面特性的本构模型研究

基于砂土与土工格栅、土工织物界面的室内大型直剪试验,分析了两种不同界面的力学性能。试验结果表明,峰值、残余剪切应力与界面剪胀性曲线存在一定的联系,即峰值强度通常会发生在界面相对减缩过程结束和残余剪切强度发生在界面的相对剪胀过程结束。加载过程中由于土工合成材料的逐步磨损、褶皱或者断裂导致了筋土界面强度出现较为明显的强度软化现象,在界面抗剪强度的研究中不可忽略。在试验基础上提出一种能够描述筋土界面力学性能的组合本构模型,该模型包含4个关系式：(1) 峰值、残余强度包络线;(2) 强度峰值前的双曲线模型;(3) 强度峰值后的位移软化模型;(4) 反映剪胀特性的界面剪胀模型。该组合模型的预测结果与直剪试验结果吻合较好,表明所用模型是合理的。     

Physical explanation for the displacement-length relationship of faults using a post-yield fracture mechanics model

A plane strain model for a fault is presented that takes into account the inelastic deformation involved in fault growth. The model requires that the stresses at the tip of the fault never exceed the shear strength of the surrounding rock. This is achieved by taking into account a zone, around the perimeter of the fault surface, where the fault is not well developed, and in which sliding involves frictional work in excess of that required for sliding on the fully developed fault. The displacement profiles predicted by the fault model taper out gradually towards the tip of the fault and compare well with observed displacement profiles on faults. Using this model it is found that both (1) the shape of the displacement profile, and (2) the ratio of maximum displacement to fault length are a function of the shear strength of the rock in which the fault forms. For the case of a fault loaded by a constant remote stress, the displacement is linearly related to the length of the fault and the constant of proportionality depends on the shear strength of the surrounding rock normalized by its shear modulus. Using data from faults in different tectonic regions and rock types, the in situ strength of intact rock surrounding a fault is calculated to be on the order of 100 MPa (or a few kilobars). These estimates exceed, by perhaps a factor of 10, the strength of a well developed fault and thus provide an upper bound for the shear strength of the crust. It is also shown that the work required to propagate a fault scales with fault length. This result can explain the observation that the fracture energy calculated for earthquake ruptures and natural faults are several orders of magnitude greater than that for fractures in laboratory experiments.     

基于方向性粗糙度参数的节理峰值抗剪强度理论模型

节理裂隙控制着岩石工程的剪切滑移稳定性。现有的节理峰值抗剪强度模型多为经验模型,且较少考虑粗糙节理峰值抗剪强度的采样点距效应及各向异性。采用3D打印技术制备了5组吻合的粗糙光敏树脂节理模具,利用水泥砂浆复制了25组相同壁面强度的人工粗糙节理,开展了5种法向应力水平下节理直剪试验。基于改进的接触面积比-视倾角门槛值关系,建立了仅含一个方向性粗糙度参数的三维粗糙节理峰值抗剪强度理论模型。该理论模型除粗糙度参数外无需拟合其他参数。对比分析发现,新模型比文献中的经验模型预测精度更高。新模型预测效果受采样点距影响较小,且能有效地反映节理峰值抗剪强度的各向异性。     

Underestimation of roughness in rough rock joints

Numerous studies have been made to improve Barton's shear strength model for the quantification of rock joints. However, in these previous studies, the roughness and shear strength of the rock joint have been underestimated especially for relatively high undulated profiles (joint roughness coefficient (JRC) >14). The main factors of roughness underestimation in rough rock joints are investigated for the proper quantification of rock joint roughness. The aliasing effect and the roughness characteristics are analyzed by using artificial joint profiles and natural rock joint profiles. A 3D camera scanner is adopted to verify the main source of underestimation when using conventional measurement methods. Shear strength tests are carried out by using two types of shear apparatus to study the roughness mobilization characteristics, which may also affect the roughness underestimation. The results of joint roughness assessment, such as aliasing and undulation of waviness, show that the roughness can be underestimated in relatively rough joint profiles (JRC>14). At least two components of roughness parameters are needed to properly represent the joint roughness, for example, the amplitude and the inclination angle of joint asperity. Roughness mobilization is affected by both the normal stress and the asperity scale. Copyright © 2008 John Wiley & Sons, Ltd.     

宜巴高速岩堆不同密实度大型直剪强度特性

岩堆是指陡峻山坡上,岩体崩坍物质经重力搬运,在山坡坡脚或平缓山坡上堆积的松散堆积体。拟建的宜巴高速公路线路方案穿越多处大型岩堆体,且地质条件复杂,各处岩堆体的密实程度各不相同。不同密实程度的岩堆体的强度和稳定性差异很大,对项目建设造成极大不利。为此进行了相同含水量不同密实度的岩堆体大型直剪强度特性实验,结果表明:岩堆体含水量、密度均存在很大的不均匀性,岩堆充填和胶结物含水量5% ~7%,平均含水量为6.5%,干密度最大值2.246gcm-3,平均天然密度为2.112g cm-3,平均干密度1.982g cm-3; 除干密度2.10gcm-3 试样在低垂直压力(50, 100, 200kPa)下分别出现剪切力峰值116.04, 154.7, 210.82kPa以外,其余各垂直压力下剪切力随水平剪切位移增大而增加,没有明显峰值,表现出明显的应变硬化特征; 岩堆体直剪强度指标c和随着其干密度的增加而增加,相同含水量下一般岩堆体越密实,其抗剪强度越高; 原始级配不同干密度下,随着岩堆体密实度增加,其抗剪强度对密实度的敏感性大幅度下降。