Review of a new shear-strength criterion for rock joints

Barton, N., 1973. Review of a new shear-strength criterion for rock joints. Eng. Geol., 7: 287–332.

The surface roughness of rock joints depends on their mode of origin, and on the mineralogy of the rock. Amongst the roughest joints will be those that formed in intrusive rocks in a tensile brittle manner, and amongst the smoothest the planar cleavage surface in slates. The range of friction angles exhibited by this spectrum will vary from about 75° or 80° down to 20° or 25°, the maximum values being very dependent on the normal stress, due to the strongly curved nature of the peak strength envelopes for rough unfilled joints.

Direct shear tests performed on model tension fractures have provided a very realistic picture of the behaviour of unfilled joints at the roughest end of the joint spectrum. The peak shear strength of rough—undulating joints such as tension surfaces can now be predicted with acceptable accuracy from a knowledge of only one parameter, namely the effective joint wall compressive strength or JCS value. For an unweathered joint this will be simply the unconfined compression strength of the unweathered rock. However in most cases joint walls will be weathered to some degree. Methods of estimating the strength of the weathered rock are discussed. The predicted values of shear strength compare favourably with experimental results reported in the literature, both for weathered and unweathered rough joints.

The shear strength of unfilled joints of intermediate roughness presents a problem since at present there is insufficient detailed reporting of test results. In an effort to remedy this situation, a simple roughness classification method has been devised which has a sliding scale of roughness. The curvature of the proposed strength envelopes reduces as the roughness coefficient reduces, and also varies with the strength of the weathered joint wall or unweathered rock, whichever is relevant. Values of the Coulomb parameters c and Φ fitted to the curves between the commonly used normal stress range of 5–20 kg/cm² appear to agree quite closely with experimental results.

The presence of water is found in practice to reduce the shear strength of rough unfilled joints but hardly to affect the strength of planar surfaces. This surprising experimental result is also predicted by the proposed criterion for peak strength. The shear strength depends on the compressive strength which is itself reduced by the presence of water. The sliding scale of roughness incorporates a reduced contribution from the compressive strength as the joint roughness reduces. Based on the same model, it is possible to draw an interesting analogy between the effects of weathering, saturation, time to failure, and scale, on the shear strength of non-planar joints. Increasing these parameters causes a reduction in the compressive strength of the rock, and hence a reduction in the peak shear strength. Rough—undulating joints are most affected and smooth—nearly planar joints least of all.     

斜入射线弹性节理应力波传播特征的数值模拟

依据弹性波理论,应力波斜入射线弹性节理时会发生波场分解。根据入射、透射及反射各波形的不同到时,运用离散元软件UDEC模拟应力波在含倾斜节理岩体中的传播并计算其透射、反射系数,并分析其波型转换规律。应力波斜入射单节理时,模拟得到的透射、反射系数随节理刚度、入射角度的变化规律,与已有的理论解是吻合的。应力波斜入射一组平行节理时,随着节理间距的增大,其同类波的透射系数Tpp、Tss先增大后减小,最后趋于稳定值;节理条数越多,Tpp、Tss越小。此外,不同条数的节理,透射系数达到最大值的临界节理间距值基本一致,但趋于稳定时的节理间距值随节理条数的增加而逐渐增大。     

地下洞室围岩脆性破坏时的应力特征研究

在高应力作用下,岩爆、钻孔崩落、片帮都是地下空间硬脆围岩中常见的破坏现象,这三类现象本质上均可归于完整岩体的脆性破坏,它们分别反映了高应力作用下完整岩体不同的破坏程度。通过对前人关于岩爆判据、钻孔崩落判据和片帮应力强度比判据研究成果的类比分析可知,这些脆性破坏现象在破坏时具备相同的应力背景条件。脆性破坏的应力条件可以用地下空间周边切向最大应力与岩石单轴抗压强度之比（ / ）或者工程区最大主应力与岩石单轴抗压强度之比（ / ）来描述,两种指标本质上反映了相同的应力背景条件。对于 / , / = 0.4 ± 0.1是发生脆性破坏的应力临界条件;对于 / , / = 0.15 ± 0.05是发生脆性破坏的应力临界条件。大量的工程实例和基于Hoek-Brown强度准则的力学分析也证明了这一背景条件的正确性。这里两种指标都取了一个范围,主要是由于不同的岩体分级、岩性和工程地质条件会对指标的界定产生较为显著的影响。     

不同地应力条件下双孔爆破的数值模拟

考虑岩石介质的非均匀性,把爆破过程视为爆炸应力波和爆生气体压力共同作用的结果,基于损伤力学理论建立了岩石爆破的力学模型,并对不同地应力条件下岩石双孔爆破裂纹演化规律进行了数值模拟,分析了不同侧压力系数和埋 深对裂纹扩展规律的影响。数值模拟结果表明：①爆炸应力波导致裂纹的萌生,爆生气体压力则会使裂纹进一步扩展和贯通; ②裂纹演化过程与地应力密切相关,裂纹扩展的主方向趋于最大地应力方向;③随着埋深增加和初始地应力增大,裂纹扩展半径和裂纹区面积减小,地应力对爆破致裂的抑制作用明显。     

节理对爆炸波传播影响的数值研究

采用加入无反射边界条件的DDA程序,研究了节理面对应力波传播的影响。结果表明,节理面能阻碍波的传播,有利于波的衰减,节理面越多,波的反射越强,而波的透射越弱。模拟了一个现场爆炸试验,研究爆炸产生的应力波在节理岩体中传播、衰减的规律,模拟结果与现场试验结果比较吻合。研究表明,DDA方法可以模拟节理面对应力波传播的阻碍作用,用它来模拟爆炸波在节理岩体中的传播是适用的。     

节理角度对预裂爆破成缝效果的影响研究

预裂爆破的现场实践表明,诸如节理、软弱夹层和断层等地质不连续面是影响预裂爆破效果的一个重要因素。运用LS-DYNA 3D程序研究了不同角度的节理对预裂爆破效果的影响。通过数值模拟发现,岩体中节理的存在对预裂爆破效果影响显著,其吸收应力波能量并阻碍应力波的传播,且影响预裂缝产状。研究结果表明,节理附近的预裂缝大多沿节理垂直方向开裂,逐渐与被破坏节理连接,节理夹角较小时,易形成锯齿状裂缝,且较难贯通。随着节理与炮孔连线夹角的增大,应力波在节理处的透射率越大,节理附近位置上的质点振速也越大,预裂缝更趋于平直且更易贯通。当节理垂直炮孔连线时透射率最大,所形成的预裂缝与炮孔连线基本重合,不会出现锯齿形裂缝,相对成缝效果最佳。     

古建筑风化石质构件力学参数的确定方法

针对目前常规确定岩石力学参数的方法只能得出岩块的整体强度,不能反映古建筑石质构件风化层内力学参数逐渐变化,无法很好地满足石质古建筑稳定性、耐久性研究的不足,提出了综合运用现场穿透波CT测试、表面回弹测试和室内试验确定风化石质构件力学参数的方法。方法的实施主要包括：通过现场穿透波CT测试,获得纵波波速在石质构件深度剖面上的分布;现场选取与欲研究的石质构件类似的岩石做室内力学试验和波速测试,得出力学参数与波速的统计关系;上述两者结合得出力学参数在石质构件深度剖面上的分布,在此基础上分析风化层内力学参数随深度的变化关系;对不同风化分区代表性石构件进行风化深度研究和表面回弹测试,得出构件表面强度比与风化深度的关系。以义乌宋代古月桥为例,对其方法进行了系统的介绍,并对古月桥承载条石风化层内力学参数随深度的变化关系以及表面强度与风化深度的关系进行了研究。研究表明：义乌宋代古月桥承载条石风化层内的抗压强度比、弹性模量比随深度呈负指数关系变化;表面强度比与风化深度呈2次多项式关系。     

Reliability analysis of the induced damage for single-hole rock blasting

Rock explosion has always been a complex problem because neither rock characteristics nor explosion waves could be accurately estimated. As such, this imposes a high uncertainty on deterministic methodologies available for damage prediction. In this paper, by defining two damage zones around the blast hole, including crushed and cracked zones, a first-order reliability analysis (FORM) was adopted to address this issue. For this purpose, FORM was used in a double-loop algorithm, where the inner loop was responsible for converging the FORM, and the outer loop was assigned to feed the inner loop with new cases. Using such nested-loop algorithm, the probability of exceedance was calculated for any desired damage zone radius. The maximum effect of the involved parameters on the failure probability induced around the blast hole was additionally studied using a parametric reliability analysis. The results showed that the radii for crushed and cracked zones are limited to 0.5 and 4.2?m, respectively, so that the probability of going beyond these limits is less than 1%. Moreover, the analyses of decoupled explosions showed that increasing the gap between the explosion charge and wall of the borehole could severely reduce the failure probability; however, the maximum effect of decoupling ratio occurs in the small range of radii between 0.3?mm and 2.35?m.     

Prediction of peak particle velocity and peak air pressure generated by buried explosion

Summary Three sets of different formulae expressed as functions of dynamic elastic constants of rock and some design parameters involved in a buried explosion are derived explicitly for the prediction of peak particle velocity (PPV) and peak air pressure (PAP). Separate equations are derived to estimate PPV and PAP for inside, outside, and at the boundary of the crater zone. The equations incorporate the physical parameters including (i) longitudinal wave velocity, (ii) shear wave velocity, (iii) density of rock, (iv) characteristic impedance of air, (v) detonation pressure of explosive, (vi) depth of hole, (vii) radius of hole, (viii) distance of the measuring transducer. Suggested equations are tested for a few hard and medium-hard rocks. Characteristic features and important conclusions are described.     

福建厦门地区中、新生代构造应力场研究

本文通过野外构造形变资料的研究,确定了厦门地区中生代的两期（侏罗纪、白垩纪）构造应力场及其主应力方向;利用最新一期共轭剪节理和震源机制解资料,确定了第四纪以来的构造应力场及其主应力方向。最大主压应力轴的优选方位分别为:侏罗纪SE138°,∠8°,白垩纪SW205,∠12°,第四纪以来NW312°,∠21°。 采用石英错密度法,估算了中生代古构造应力值,侏罗纪为88.5MPa,白垩纪为81.5MPa。利用岩石力学声发射技术,测定了现代构造应力大小,在标高为3——-151m（埋深为18——151m）的范围内,最大主压应力值为2.55——16.2MPa,最小主压应力值为1.1——10.1MPa。     

DEM–SPH simulation of rock blasting

A numerical model is proposed for the simulation of rock blasting. A bonded particle system is utilized to mimic the behavior of rock. The particles interact at the contact points through normal and shear springs to simulate rock elasticity. To withstand the deviatoric stresses, the particles are glued to each other. If the applied force exceeds the contact strength, local failure occurs and microcracks are developed in the synthetic rock. For simulation of gas flow, the smooth particle hydrodynamic method is implemented. The interaction of gas particles with the rock grains is assumed to follow a perfect plastic collision model in which the initial momentum of the colliding particles is preserved. A detailed examination of the interaction of gas with blast hole is investigated. It is shown that the proposed hybrid model is capable of simulating the induced shock waves in the gas together with wave propagation in the rock material. The model successfully mimics crack propagation in rock. In particular, the crushed zone around the borehole, radial cracks, and surface spalling are all captured successfully. The results of numerical analysis suggest that gas–rock interaction can, in fact, generate a few successive compressive waves in the rock specimen, causing further extension of radial cracks with time as the weaker secondary and tertiary waves interact with the crack tips.     

Critical review on shear strength models for soil-infilled joints

An infilled rock joint is likely to be the weakest plane in a rock mass. The presence of infill material within the joint significantly reduces the friction of the discontinuity boundaries (i.e. rock to rock contact of the joint walls). The thicker the infill, the smaller the shear strength of the rock joint. Once the infill reaches a critical thickness, the infill material governs the overall shear strength, and the joint walls (rock) play no significant role. Several models have been proposed to predict the peak shear strength of soil-infilled joints under both constant normal load (CNL) and constant normal stiffness (CNS) boundary conditions, taking into account the ratio of infill thickness (t) to the height of the joint wall asperity (a). CNS models provide a more realistic picture of the soil-infilled joint behaviour in the field. This paper presents a critical review on the existing mathematical models for predicting the shear strength of soil-infilled rock joint and verifies the normalised peak shear stress model with further laboratory investigations carried out on idealised saw-tooth rock joints at the University of Wollongong. Based on the prediction of the experimental data, the normalised peak shear stress model is slightly modified by the authors. A simplified approach for using this model in practice is presented and a new expression for prediction of dilatation at peak shear stress is suggested.     

Probabilistic analysis of crushed zone for rock blasting

Transmission of explosion waves through a rock medium causes a severe vibration that stimulates the mechanical behavior of rock mass. This stimulation imposes highly concentrated stresses on the ends of existing fine joints and depending on the toughness of the rock, causes them to propagate rapidly. Consequently, the propagation and joining of cracks form a crushed zone around the blast hole. Several studies are available in the literature to estimate the radius of crushed zone, deterministically. In this paper, however, a probabilistic approach has been adopted. This is because the initiation and propagation of cracks have a probabilistic nature, and neither the initial state of the rock nor the explosion load could be expressed in a fully deterministic way. Thus, after generating random values for involved parameters, including explosive density, detonation velocity, dynamic Young’s modulus, dynamic Poisson’s ratio, uniaxial compressive strength, and borehole radius, the Monte-Carlo sampling method was adopted to calculate the exceeding probability of the crushed zone radius from desired values. The results showed that the exceedance probability for the growth of cracks falls sharply by the increase in the crushed zone radius so that the probability of crushed zone radius longer than 0.5 m is less than one percent. The results of this study, compared to the deterministic models, provide advantages in that they are not only limited to a certain value for the crushed zone radius and show the probability of exceedance for any desired radius.     

空气间隔装药爆破机理研究

利用爆轰波理论分析了空气间隔装药炮孔内一维不定常激波的相互作用及其在炮孔堵头、孔底的反射过程,同时分析了孔内各点的压力随时间的变化过程,介绍了空气间隔装药爆破的机理及设计参数。基于此,认为应充分利用空气间隔爆破结构的优势,并在梯段爆破中满足以下两个条件：（1）在设计过程中要尽量使稀疏波及从孔底反射的稀疏波传播过程能在整个孔内每一断面都作用到,即稀疏波到达孔底的时间要比从堵头反射的压力波到达孔底要早;（2）反射压力波应该到达空气与爆生气体接触面的时间比从孔底反射的稀疏波到达空气与爆生气体接触面的时间要早。由此通过计算得到了在梯段爆破工程中合理的空气层长度比例值约为30 %～42 %。计算结论与已有实测成果基本一致。     

Correlation of Schmidt hardness with unconfined compressive strength and Young''s modulus in gypsum from Sivas (Turkey)

This study aims to express the relationships between Schmidt rebound number (N) with unconfined compressive strength (UCS) and Young's modulus (E_t) of the gypsum by empirical equations. As known, the Schmidt hammer has been used worldwide as an index test for a quick rock strength and deformability characterisation due to its rapidity and easiness in execution, simplicity, portability, low cost and nondestructiveness. In this study, gypsum samples have been collected from various locations in the Miocene-aged gypsum of Sivas Basin and tested. The tests include the determination of Schmidt hammer rebound number (N), tangent Young's modulus (E_t) and unconfined compressive strength. Finally, obtained parameters were correlated and regression equations were established among Schmidt hammer rebound hardness, tangent Young's modulus and unconfined compressive strength, presenting high coefficients of correlation. It appears that there is a possibility of estimating unconfined compressive strength and Young's modulus of gypsum, from their Schmidt hammer rebound number by using the proposed empirical relationships of UCS=exp(0.818+0.059N) and E_t=exp(1.146+0.054N). However, the equations must be used only for the gypsum with an acceptable accuracy, especially at the preliminary stage of designing a structure. Finally, by using the obtained Schmidt hammer rebound number from this study, unconfined compressive strength was calculated and compared with the calculated value from different empirical equations proposed by different authors. It can be said that it is impossible to obtain only one relation for all types of the rocks.     

万福煤矿不同含水率砂岩蠕变力学特性试验研究

为研究深部巷道围岩在地下水作用下的长期蠕变力学特性,采用自主研制的深部软岩五联流变试验系统,开展不同含水率(0%、0.8%、1.6%、2.4%、3.3%)下砂岩吸水软化单轴压缩试验及单轴蠕变试验。通过试验结果研究表明：砂岩的单轴抗压强度、弹性模量和蠕变破坏应力与含水率呈指数下降关系,蠕变破坏应力与单轴抗压强度的比值在0.76～0.84之间;砂岩衰减蠕变阶段时间随着含水率的增加而减少,随应力水平的增加而增加。径向应变比轴向应变先进入稳态蠕变阶段,破坏应力下径向应变的加速蠕变阶段开始时间要先于轴向应变;基于稳态蠕变速率曲线确定了砂岩的长期强度,径向稳态蠕变速率确定的值略小于轴向,长期强度与含水率之间满足负指数关系;将蠕变试验中径向应变与轴向应变之比定义为μ_c,提出了基于μ_c值的岩石长期强度确定方法且μ_c值与含水率无关,对于本次砂岩样品可以认为μ_c值大于0.3时样品会在一定时间内发生加速蠕变破坏;随着含水率的增加,样品破坏形态由单斜面剪切破坏逐渐演变至X状共轭斜面剪切破坏。研究结果为地下水作用下巷道长期稳...     

Estimating the Strength of Jointed Rock Masses

Determination of the strength of jointed rock masses is an important and challenging task in rock mechanics and rock engineering. In this article, the existing empirical methods for estimating the unconfined compressive strength of jointed rock masses are reviewed and evaluated, including the jointing index methods, the joint factor methods, and the methods based on rock mass classification. The review shows that different empirical methods may produce very different estimates. Since in many cases, rock quality designation (RQD) is the only information available for describing rock discontinuities, a new empirical relation is developed for estimating rock mass strength based on RQD. The newly developed empirical relation is applied to estimate the unconfined compressive strength of rock masses at six sites and the results are compared with those from the empirical methods based on rock mass classification. The estimated unconfined compressive strength values from the new empirical relation are essentially in the middle of the estimated values from the different empirical methods based on rock mass classification. Similar to the existing empirical methods, the newly developed relation is only approximate and should be used, with care, only for a first estimate of the unconfined compressive strength of rock masses. Recommendations are provided on how to apply the newly developed relation in combination with the existing empirical methods for estimating rock mass strength in practice.     

基于岩石物理模型的页岩孔隙结构反演及横波速度预测

准确预测储层的等效孔隙纵横比对页岩储层岩石物理建模及横波速度预测具有重要意义。为分析页岩储层孔隙纵横比及预测横波速度,提出了基于岩石物理模型的页岩孔隙纵横比反演及横波速度预测方法。本文首先通过岩石物理模型建立岩石的纵、横波速度与孔隙纵横比、孔隙度和矿物组分等参数之间的定量关系,寻找最佳孔隙纵横比;然后通过使理论预测与实际测量的纵波速度之间误差达到最小的方式反演孔隙纵横比,并以此为约束预测横波速度。实际测井数据反演结果表明,龙马溪组页岩地层的孔隙纵横比稳定,而围岩的孔隙纵横比变化范围较大;说明与围岩相比,页岩的孔隙结构更为稳定。同时,预测得到的页岩横波速度与实测横波速度的误差较小,另外对于缺少矿物组分资料的页岩层段,用平均矿物组分预测得到的横波速度误差仍较小;说明与矿物组分相比,龙马溪组页岩的纵、横波速度对孔隙纵横比参数更敏感。综上所述,利用该方法可预测到较为准确的等效孔隙纵横比和横波速度。     

砂土充填大理岩节理的剪切强度经验公式

为研究砂土充填对节理抗剪强度的影响,利用GCTS（RDS?200型）岩石剪切测试系统对4种不同摩擦系数砂土充填的粉晶大理岩节理进行了直剪试验。结果表明：相同法向应力下,未充填节理的峰值剪切应力大于充填节理的峰值剪切应力,说明砂土的存在降低了节理的剪切强度;由节理面三维形貌参数最大谷深 表征节理面粗糙程度,得到了未充填节理的峰值剪切强度公式,公式预测值与试验值基本吻合;得到了用充填砂土摩擦系数表达的充填节理峰值剪切强度公式,公式预测值与试验值较为吻合。研究结论对充填节理岩体稳定性评价具有一定指导意义。     

位移不连续模型在黏弹性节理刚度计算的应用

考虑节理质量对应力波传播的影响,运用波的位移位函数推导了谐波在厚黏弹性节理的透、反射系数计算公式,采用波形相关系数描述子波穿过黏弹性节理的波形变化,讨论具有一定厚度的黏弹性节理简化位移不连续模型的适用条件。设厚黏弹性节理模型和位移不连续模型的透射波波形相关系数为0.9时对应的节理厚度为临界厚度,岩体与节理的阻抗比对临界厚度的影响很小;临界厚度随子波中心频率增大呈负指数减小,入射角越大,临界厚度随中心频率减小得越慢。试验数据分析表明：当节理厚度为0.03 m时,采用位移不连续模型和厚黏弹性模型计算得到的节理力学参数非常接近,随节理厚度和子波中心频率增加,运用位移不连续模型的计算结果偏差越大,试验结果与理论分析是一致的。