Shear strength estimation for Åknes sliding area in western Norway

This paper deals with the unstable rock-slope at Åknes sliding area, located in the county of Møre and Romsdal in western part of Norway. The sliding body has a complex geometry with several sliding planes at different levels, involving unfilled joints, gouge material/brecciated material as well as bridges of intact rock. Stability of the rock slope strongly depends on the shear strength of the sliding plane(s) and this paper discusses the shear strength of the materials present, ranging between the strength of intact rock and crushed, clay containing gouge material. Estimation of the in situ shear strength at the Åknes sliding area is discussed on the basis of triaxial test results and the Barton–Bandis empirical method. Triaxial tests have been carried out on samples of gouge material from a potential sliding plane and intact rock specimens, while the empirical method has been applied for rock joints in the area. Comparison and correlation with experimental results found in literature have also been made. The resultant shear strength range for the zone of sliding has been found to be in the range of 0.5–1.3 MPa, depending on the normal stress and the composition of the sliding zone.     

Applicability of Mohr–Coulomb and Hoek–Brown strength criteria to the dynamic strength of brittle rock

A series of dynamic uniaxial and triaxial compression, uniaxial tension and unconfined shear tests were conducted on the Bukit Timah granite of Singapore. The results are analyzed in this paper in order to examine the validity and applicability of the Mohr–Coulomb and the Hoek–Brown criteria to the rock material strength properties subjected to dynamic loads. The study indicates that rock material strength under dynamic loads can be approximately described by the Mohr–Coulomb criterion, at low confining pressure range. The change of strength is primarily due to the variation of cohesion with loading rate. The rock material strength under dynamic loads is better described by the Hoek–Brown criterion. Assessment of the Hoek–Brown criterion shows that the uniaxial compressive strength increases with increasing loading rate, and the parameter m appears unaffected by the loading rate.     

Non-dilatant deformation and failure mechanism in two Long Valley Caldera rocks under true triaxial compression

We conducted laboratory rock strength experiments in two ultra-fine-grained brittle rocks, hornfels and metapelite, which together are the major constituent of the Long Valley Caldera (California, USA) basement in the 2025–2996 m depth range. Both rocks are banded, and have very low porosity. Uniaxial compression tests at different orientations with respect to banding planes reveal that while the hornfels compressive strength is nearly isotropic, the metapelite possesses distinct anisotropy. Conventional triaxial tests in these rocks reveal that their respective strengths in a specific orientation increase approximately linearly with confining pressure. True triaxial compression experiments in specimens oriented at a consistent angle to banding, in which the magnitudes of the least (σ₃) and the intermediate (σ₂) principal stresses are different but kept constant during testing while the maximum principal stress is increased until failure, exhibit a behavior unlike that previously observed in other rocks under similar testing conditions. For a given magnitude of σ₃, compressive strength σ₁ does not vary significantly in both Long Valley rock types, regardless of the applied σ₂, suggesting little or no intermediate principal stress effect. Strains measured in all three principal directions during loading were used to obtain plots of σ₁ versus volumetric strain. These are consistently linear almost to the point of rock failure, suggesting no dilatancy. The phenomenon was corroborated by SEM inspection of failed specimens that showed no microcrack development prior to the emergence of one through-going shear failure plane steeply dipping in the σ₃ direction. The strong dependency of compressive strength on the intermediate principal stress in other crystalline rocks was found to be related to microcrack initiation upon dilatancy onset, which rises with increased σ₂ and retards the failure process. We infer that strength independence of σ₂ in the Long Valley rocks derives directly from their non-dilatant deformation.     

固体三轴高压下红河断裂带周城断层泥力学性质的研究

在固体三轴高压和应变率4.4×10^-5s^-1下研究了红河断裂带周城断层泥的力学性质。研究结果表明,在差应力作用下,断层泥应力-应变曲线表现出与试件压实、屈服和碎裂流动等不同变形机制对应的非线性,线性等阶段性变化特征。干、湿断层泥破坏应力σ_c随围压σ₃的变化关系分别为在较高围压下,σ_c随σ₃呈线性变化。含水量对变形特征和破坏应力水平有重要影响。干、湿断层泥有效弹性模量E_ed和E_em以及（潮）湿断层泥的初始模量E_om均随围压增加而增加,但干断层泥初始弹性模量E_od近似保持常数。同时,E_oded,E_omem,E_em>E_ed。在试件变形过程中有声发射事件显示,但数量少,辐射弹性波能量小。断层泥试件破坏型式表现为渐进式碎裂流动特征,因此,断层泥变形有利于断层活动呈现稳滑。     

Particle flow code simulation of intact and fissured granitic rock samples

This study presents a calibration process of three-dimensional particle flow code (PFC3D) simulation of intact and fissured granite samples. First, laboratory stress–strain response from triaxial testing of intact and fissured granite samples is recalled. Then, PFC3D is introduced, with focus on the bonded particle models (BPM). After that, we present previous studies where intact rock is simulated by means of flat-joint approaches, and how improved accuracy was gained with the help of parametric studies. Then, models of the pre-fissured rock specimens were generated, including modeled fissures in the form of “smooth joint” type contacts. Finally, triaxial testing simulations of 1 + 2 and 2 + 3 jointed rock specimens were performed. Results show that both elastic behavior and the peak strength levels are closely matched, without any additional fine tuning of micro-mechanical parameters. Concerning the post-failure behavior, models reproduce the trends of decreasing dilation with increasing confinement and plasticity. However, the dilation values simulated are larger than those observed in practice. This is attributed to the difficulty in modeling some phenomena of fissured rock behaviors, such as rock piece corner crushing with dust production and interactions between newly formed shear bands or axial splitting cracks with pre-existing joints.     

Quantitative three-dimensional description of a rough surface and parameter evolution with shearing

The choice of a general criterion to determine the shear strength of rough rock joints is a topic that has been investigated for many years. The major problem is how to measure and then to express the roughness with a number (e.g., joint roughness coefficient) or a mathematical expression in order to introduce the morphology of the joint into a shear strength criterion. In the present research a large number of surfaces have been digitised and reconstructed using a triangulation algorithm. This approach results in a discretisation of the joint surface into a finite number of triangles, whose geometric orientations have been calculated. Furthermore, during shear tests it was observed that the common characteristic among all the contact areas is that they are located in the steepest zones facing the shear direction. Based on this observations and using the triangulated surface data, it is possible to describe the variation of the potential contact area versus the apparent dip angle with the expression A_θ^*=A₀[(θ_max^*−θ^*)/θ_max^*]^C, where A₀ is the maximum possible contact area, θ_max^* is the maximum apparent dip angle in the shear direction, and C is a “roughness” parameter, calculated using a best-fit regression function, which characterises the distribution of the apparent dip angles over the surface. The close agreement between analytical curves and measured data therefore suggests the possibility of defining the influence of roughness on shear strength by the simple knowledge of A₀, C and θ_max^*. Based on the samples studied here, the values of these parameters capture the evolution of the surface during shearing. Moreover, they tend to be characteristic for specific rock types, indicating that it might be possible to determine ranges for each rock type based on laboratory measurements on representative samples.     

考虑各向异性特征的三维岩体结构面峰值剪切强度研究

 由于岩体结构面形貌的复杂性,目前,所提出的峰值剪切强度模型不能够很好地体现其各向异性特征。鉴于此,综合考虑岩体结构面起伏角和起伏幅度,提出一个考虑各向异性特征的综合参数?表征岩体结构面粗糙度的新方法;?由某一方向的起伏角参数SRv和起伏幅度参数A表示;其中参数SRv表示结构面粗糙度的各向异性特征,用变异函数分析方法进行计算获得。然后,应用该法分析Barton十条标准轮廓线,拟合出JRC与参数SRv,A的关系表达式;结合Barton强度公式,给出考虑各向异性特征的岩体结构面峰值剪切强度模型。最后,基于ShapeMetriX3D三维形貌测量系统,在实验室开展类岩体结构面形貌的量测;并应用上述方法估算结构面4个方向上的峰值剪切强度。于此同时,开展该类岩体结构面各向异性的剪切力学试验,通过试验值与估测值的对比分析,验证了所提模型的正确性。研究结果为准确预测岩体结构面抗剪强度提供一种新方法。     

Milk trace elements in lactating cows environmentally exposed to higher level of lead and cadmium around different industrial units

The present investigation was carried out to assess the trace mineral profile of milk from lactating cows reared around different industrial units and to examine the effect of blood and milk concentration of lead and cadmium on copper, cobalt, zinc and iron levels in milk. Respective blood and milk samples were collected from a total of 201 apparently healthy lactating cows above 3 years of age including 52 cows reared in areas supposed to be free from pollution. The highest milk lead (0.85 ± 0.11 µg/ml) and cadmium (0.23 ± 0.02 µg/ml) levels were recorded in lactating cows reared around lead–zinc smelter and steel manufacturing plant, respectively. Significantly (P < 0.05) higher concentration of milk copper, cobalt, zinc and iron compared to control animals was recorded in cows around closed lead cum operational zinc smelter. Analysis of correlation between lead and other trace elements in milk from lactating cows with the blood lead level > 0.20 µg/ml (n = 79) revealed a significant negative correlations between milk iron and milk lead (r = − 0.273, P = 0.015). However, such trend was not recorded with blood lead level < 0.20 µg/ml (n = 122). The milk cobalt concentration was significantly correlated (r = 0.365, P < 0.001) with cadmium level in milk and the highest milk cadmium (> 0.10 to 0.39 µg/ml) group had significantly (P < 0.05) increased milk cobalt. It is concluded that increased blood and milk lead or cadmium level as a result of natural exposure of lactating cows to these environmental toxicants significantly influences trace minerals composition of milk and such alterations affect the milk quality and nutritional values.     

对岩石双剪强度准则的探讨

基于岩土体的双剪强度理论和已有的一些岩石真三轴强度试验资料，提出了一个岩石双剪强度准则的推广型式，探讨了该强度准则相关参数的选取问题，并据此强度准则进一步揭示了岩石的一些强度特性。     

A modified Hoek–Brown failure criterion for anisotropic intact rock

The Hoek–Brown criterion parameters (σ_ci, m_i and s) are significantly influenced by the strength anisotropy of intact rock. In the present study, the criterion was modified by incorporating a new parameter (k_β) to account for the effect of strength anisotropy, thus being able to determine the strength of intact anisotropic rock under loading in different orientations of the plane of anisotropy. The range of the parameter (k_β) for the rocks tested has been analytically investigated by carrying out triaxial tests, in different orientations of the foliation plane. The proposed modification was studied for metamorphic rocks (gneiss, schist, marble), but could also be applied to other rock types exhibiting “inherent” anisotropy, e.g. sedimentary as well as igneous rocks. The proposed modified criterion is intended for use for prediction of strength of intact rock, but can also be extended to rock masses.     

Characterizing rock masses by the RMi for use in practical rock engineering: Part 1: The development of the Rock Mass index (RMi)

The Rock Mass index, RMi, has been developed to satisfy a need for a strength characterization of rock masses for use in rock engineering and design. The method gives a measure of the reduction of intact rock strength caused by discontinuities given by RMi = σ · JP. Here, σ is the uniaxial compressive strength of the intact rock measured on 50 mm diameter samples, and JP is the jointing parameter which is a combined measure of block size (or intensity of jointing) and joint characteristics as measured by joint roughness, alteration and size. This paper describes the method of determining the RMi for a rock mass using various common field observations. The determination of a meaningful equivalent block size is a key issue which is discussed in detail. Several areas of application of the RMi are presented, among others for design of rock support. Discussion of these applications will be developed in Part 2 of this paper.     

Over-consolidation effect on shear behavior of rock joints

Although many researchers have studied the normal and shear behavior of fractures under stresses, the over-consolidation effect on the slip/shear behavior of discontinuities has not been considered. The over-consolidation behavior of non-planar rock fractures should be considered when deposition–consolidation–erosion (or excavation) sequences occur. Plaster replicas of representative natural rock joint surfaces were prepared for this study. In this case, the surface roughness and other geometrical properties remain constant during the laboratory direct shear tests. It was observed that the shear strength within a large range of roughness, joint wall strength and normal stress values significantly increases with increasing over-consolidation ratio. According to the test results, a new model is developed as an extended form of Barton's shear failure criterion for rock joints. This model considers the effect of various paths of normal loading/unloading before shearing and over-consolidation ratio in a fracture. A new joint over-closure (JOC) parameter is also introduced as the ratio of closure in over-closed to normally closed conditions.     

Tunnel roof deflection in blocky rock masses as a function of joint spacing and friction – A parametric study using discontinuous deformation analysis (DDA)

The stability of underground openings excavated in a blocky rock mass was studied using the discontinuous deformation analysis (DDA) method. The focus of the research was a kinematical analysis of the rock deformation as a function of joint spacing and friction. Two different opening geometries were studied: (1) span B = h_t; (2) B = 1.5h_t; where the opening height was h_t = 10 m for both configurations. Fifty individual simulations were performed for different values of joint spacing and friction angle. It was found that the extent of loosening above the excavation was predominantly controlled by the spacing of the joints, and only secondarily by the shear strength. The height of the loosening zone h_r was found to be dependent upon the ratio between joint spacing and excavation span S_j/B: (1) h_r < 0.56B for S_j/B  2/10; (2) stable arching within the rock mass for S_j/B  3/10. The results of this study provide explicit correlation between geometrical features of the rock mass, routinely collected during site investigation and excavation, and the expected extent of the loosening zone at the roof, which determines the required support.     

A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks

In this study we examine seven different failure criteria by comparing them to published polyaxial test data (σ₁>σ₂>σ₃) for five different rock types at a variety of stress states. We employed a grid search algorithm to find the best set of parameters that describe failure for each criterion and the associated misfits. Overall, we found that the polyaxial criteria Modified Wiebols and Cook and Modified Lade achieved a good fit to most of the test data. This is especially true for rocks with a highly σ₂-dependent failure behavior (e.g. Dunham dolomite, Solenhofen limestone). However, for some rock types (e.g. Shirahama Sandstone, Yuubari shale), the intermediate stress hardly affects failure and the Mohr–Coulomb and Hoek and Brown criteria fit these test data equally well, or even better, than the more complicated polyaxial criteria. The values of C₀ yielded by the Inscribed and the Circumscribed Drucker–Prager criteria bounded the C₀ value obtained using the Mohr–Coulomb criterion as expected. In general, the Drucker–Prager failure criterion did not accurately indicate the value of σ₁ at failure. The value of the misfits achieved with the empirical 1967 and 1971 Mogi criteria were generally in between those obtained using the triaxial and the polyaxial criteria. The disadvantage of these failure criteria is that they cannot be related to strength parameters such as C₀. We also found that if only data from triaxial tests are available, it is possible to incorporate the influence of σ₂ on failure by using a polyaxial failure criterion. The results for two out of three rocks that could be analyzed in this way were encouraging.     

Anisotropic strength and deformational behavior of Himalayan schists

Anisotropy, which is characteristic of metamorphic rocks such as schists, is due to a process of metamorphic differentiation. Preferred orientation of minerals like mica and chlorite in response to tectonic stresses makes schistose rocks foliated. As a result their engineering properties vary with the direction of loading.The influence of transverse anisotropy on strength and deformational responses of four schistose rocks obtained from the foundation of two underground powerhouse sites in the Himalayas has been critically examined. Specimens at different orientation (β) of the foliations varying from 0° to 90° with respect to the axial stress (σ₁) in the unconfined state and also in the confined states up to 100 MPa of confining pressure were tested to evaluate the applicability of the non-linear strength criterion for the prediction of triaxial compressive strength and modulus. Based on the analysis of large experimental results it has been possible to predict strength and modulus with minimum pre-evaluation experimental data, i.e. only with three uniaxial compressive strength tests at 0°, 30° and 90° and two triaxial compression tests conducted at convenient confining pressures at β=90°orientation. Predicted non-linear stress–strain curves, using predicted values of strength and modulus have been found to match well with the experimental stress–strain curves even at higher confining pressures.     

岩石节理剪切渗流耦合试验及分析

节理岩体内渗流的发生主要是通过断裂节理网络产生,节理面的几何特性和受力特征决定和影响着节理裂隙的渗透性质,从而极大地影响着水下隧道及地下硐室中的渗流。应用自行研制开发的试验设备(岩石节理单一剪切-渗流试验机(SMT-E-4010)),在恒定法向荷载和恒定法向刚度的边界条件下,对不同接触状态下的岩石断裂节理试件分别进行一系列节理的剪切渗流耦合试验,研究剪切过程中力学性质、水力学性质的变化情况;同时,结合立方准则对试验数据进行分析讨论。试验结果表明:节理力学性质,水力开度和透过率在剪切过程中呈现出两阶段的变化性质。     

Shear strength criteria for rock,rock joints,rockfill and rock masses: Problems and some solutions

Although many intact rock types can be very strong, a critical confining pressure can eventually be reached in triaxial testing, such that the Mohr shear strength envelope becomes horizontal. This critical state has recently been better defined, and correct curvature or correct deviation from linear Mohr–Coulomb (M-C) has finally been found. Standard shear testing procedures for rock joints, using multiple testing of the same sample, in case of insufficient samples, can be shown to exaggerate apparent cohesion. Even rough joints do not have any cohesion, but instead have very high friction angles at low stress, due to strong dilation. Rock masses, implying problems of large-scale interaction with engineering structures, may have both cohesive and frictional strength components. However, it is not correct to add these, following linear M-C or nonlinear Hoek–Brown (H-B) standard routines. Cohesion is broken at small strain, while friction is mobilized at larger strain and remains to the end of the shear deformation. The criterion ‘c then σ_n tan φ’ should replace ‘c plus σ_ntan φ’ for improved fit to reality. Transformation of principal stresses to a shear plane seems to ignore mobilized dilation, and caused great experimental difficulties until understood. There seems to be plenty of room for continued research, so that errors of judgement of the last 50 years can be corrected.     

断续节理直剪试验与PFC2D数值模拟分析

 在以往有关断续节理模型试验和数值模拟的研究基础上,设计不同连通情况和法向应力的断续节理模型材料直剪试验,并采用颗粒流离散元软件PFC2D对模型试验进行全真数值模拟。以贯通节理试样、完整试样的剪应力–应变数值模拟曲线和模型试验曲线吻合作为PFC细观力学参数选取准则,并利用获得的细观力学参数对共面断续节理试样直剪试验进行数值重现。对比分析数值模拟曲线和模型试验曲线,对断续节理受剪贯通的力学机制进行研究。根据模型试验和数值试验的成果,分析断续节理预剪面上应力随剪应变的演化过程,发现剪切过程中的剪胀效应使得岩桥承担更多的压应力,从而提高了岩桥的抗剪强度。对断续节理岩体在直剪加载条件下的破坏机制进行讨论,将整个剪切过程分为线弹性阶段、初裂阶段、峰值阶段、峰后阶段及残余阶段5个阶段。     

岩石破损过程强度变化规律实测研究

 岩石材料强度会随着破裂发展而逐渐衰减,详细介绍自行设计的岩石强度衰减测试方法,试验思路、试件制作及关键技术;通过自行设计的直剪试验,测得常规压缩试验破裂得到的不规则损伤岩块在直剪过程中的剪应力–压应力关系曲线,由其拟合得到库仑强度曲线,并与已有(单、三轴)压缩试验数据线性拟合得到的莫尔强度包络线进行比较,分析讨论岩石在破损过程中材料强度(黏聚力和内摩擦角)变化规律,澄清现有黏聚力和内摩擦角变化规律2种完全相对立观点的适用范围。研究结果表明,由完整岩样进行单、三轴试验测得的黏聚力明显大于不规则岩块直剪试验结果,这主要是岩样在单、三轴压缩破坏过程中产生的损伤所致,而不是试验方法所导致的偏差;黏聚力反映的是岩石本质强度特性,受不同应力状态的影响较小。岩样单、三轴压缩试验测得的内摩擦角小于岩块直剪试验结果,这主要是受到不同应力状态和岩石缺陷分布的影响。在岩石破损过程中,内摩擦角随损伤的发展具有先快速增大至最大值后大幅降低直至保持一定趋势不变的规律。内摩擦角反映的是岩石摩擦强度特性,受不同应力状态的影响较大。黏聚力对应力水平的敏感程度远小于内摩擦角。岩石在破裂前后自身材料强度会产生明显衰减。     

Study on strength of artificially frozen soils in deep alluvium

This paper describes a series of stress-controlled uniaxial compressive tests performed on frozen loess and triaxial compressive tests performed on frozen/unfrozen loess, which experienced K₀ consolidated process before freezing, to study the stress–strain–strength behaviour of an artificially frozen soil in deep alluvium. The aim of subjecting the triaxial test samples to K₀ consolidation was to simulate the forming process of deep soils. These tests examined the influence of the initial confining pressure and the temperature of frozen soils on stress–strain–strength behaviour. An analysis of the mechanical behaviour of artificially frozen soil is performed from interpretation of results from the unconfined and triaxial compressive tests of frozen/unfrozen soils, in which the influence of both the degree of cementation arising from the interparticle bonding and the initial confining stress was investigated. For deep artificially frozen soils, it was concluded that the unconfined compressive strength is a direct measurement of the degree of cementation. Consequently, the triaxial compressive strength can be expressed as a function of only two variables: (1) the internal angle of the shearing resistance of the unfrozen soils; and (2) the unconfined compressive strength. Data from additional experiments performed later verified the validity of proposed relationship in evaluating the strength of deep artificially frozen soil.