A Simplified Failure Criterion for Intact Rocks Based on Rock Type and Uniaxial Compressive Strength

The uniaxial compressive strength (UCS) of intact rock, which can be estimated using relatively straightforward and cost-effective techniques, is one of the most practical rock properties used in rock engineering. Thus, constitutive laws to represent the strength and behavior of (intact) rock frequently use it, along with additional intrinsic rock properties. Although triaxial tests can be employed to obtain best-fit failure criterion parameters that provide best strength predictions, they are more expensive and require time-consuming procedures; as a consequence, they are often not readily available at early stages of a project. Based on the analysis of an extensive triaxial test database for intact rocks, we propose a simplified empirical failure criterion in which rock strength at failure is expressed in terms of confining stress and UCS, with a new parameter which can be directly estimated from the UCS for a specified rock type in the absence of triaxial test data. Performance of the proposed failure criterion is then tested for validation against experimental data for eight rock types. The results show that strengths of intact rock estimated by the proposed failure criterion are in good agreement with experimental test data, with small discrepancies between estimated and measurements strengths. Therefore, the proposed criterion can be useful for preliminary (triaxial) strength estimation of intact rocks when triaxial tests data are not available.     

Application of the Christensen Failure Criterion to Intact Rock

The Christensen criterion, originally introduced in materials science, has a simple mathematical form and uniaxial tensile and compressive strength as the only parameters, making it an attractive candidate for rock engineering purposes. In this study, the applicability of the criterion to rock materials is examined. Explicit equations for application of the criterion under biaxial, triaxial compression, triaxial extension, and polyaxial states of stresses are derived. A comprehensive strength data set including the results of tests on synthetic rock, chert dyke, Carrara marble and Westerly granite is utilized to examine the accuracy of the Christensen criterion to the failure of rock material. The two surprising findings about the Christensen criterion are the zero values of tensile strength and the very low slopes of the failure envelope obtained from fitting analyses for chert dyke and Westerly granite. It is shown that the two problems are interrelated and the values of tensile strength tend to zero to produce higher slopes. It is then mathematically proven that the maximum initial slope of the Christensen failure envelope is limited to 4 in triaxial compression and 2.5 in triaxial extension which is considerably lower than the slope of experimental data. The accuracy of the Christensen criterion was found to be significantly lower than the well-established Hoek–Brown criterion. The circular π-plane representations and brittle-to-ductile transition limits from the Christensen criterion are also inconsistent with the observed behavior of rocks.     

A Criterion for Brittle Failure of Rocks Using the Theory of Critical Distances

This paper presents a new analytical criterion for brittle failure of rocks and heavily over-consolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as half of the critical distance. This fracture criterion is known as the point method, and is part of the theory of critical distances, which is utilised in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, σ ₀, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, σ _c and σ _t. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (σ _c/σ _t = 3–50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low-confining stresses.     

Selecting Equivalent Strength for Intact Rocks in Heterogeneous Rock Masses

Many surface and underground structures are constructed in heterogeneous rock formations. These formations have a combination of weak and strong rock layers. Due to the alternation of the weak and strong layers, selecting the equivalent and appropriate geomechanical parameters for these formations is challenging. One of these problems is choosing the equivalent strength (i.e., uniaxial compressive strength) of intact rock for a group of rocks. Based on the volume of weak and strong parts and their strength, the equivalent strength of heterogeneous rocks changes. Marinos and Hoek (Bull Eng Geol Environ 60(2):85–92, 2001) presented the “weighted average method” for defining the uniaxial compressive strength (UCS) of heterogeneous rock masses based on the volume of weak and strong parts. Laubscher (1977) used the volume ratio of the strength of a weak part to a strong part (UCS weak/UCS strong) to determine the equivalent strength. In this study, the two methods are compared and their validity is evaluated by experimental data and numerical analyses. The geomechanical parameters of two heterogeneous formations (Aghajari and Lahbari) in the west of Iran were estimated using these methods. The results of the present study obtained through numerical analyses using particle flow code are compared with those of previous studies and discussed. Laboratory and numerical results show UCS decrease and approach to weak strength with an increasing in volume of weak part. When strength ratio of strong to weak rock increase, equivalent strength decrease more severely. The findings show that Laubscher’s method gives more appropriate results than the weighted average method.     

基于破碎单位体积岩石能耗量设计坚硬研磨性岩石用钻头方法的研究

深孔钻进时常常遇到坚硬岩石和研磨性岩石,在这种岩石中钻进时钻探技术指标不甚理想。建议以破碎单位体积岩石能耗低的标准来设计和研制孕镶金刚石钻头。按此标准设计的胎体扇形块上带有凸出和低洼切削齿的梳状金刚石钻头,在实验台上进行的试验,试验结果表明,与常规平底胎体金刚石钻头比较,破碎单位体积岩石能耗量降低了,机械钻速提高了,胎体单位进尺磨损量降低了。建议对这种新型钻头给以充分注意并进行进一步研究。     

Estimation of Elastic Modulus of Intact Rocks by Artificial Neural Network

The modulus of elasticity of intact rock (E _i) is an important rock property that is used as an input parameter in the design stage of engineering projects such as dams, slopes, foundations, tunnel constructions and mining excavations. However, it is sometimes difficult to determine the modulus of elasticity in laboratory tests because high-quality cores are required. For this reason, various methods for predicting E _i have been popular research topics in recently published literature. In this study, the relationships between the uniaxial compressive strength, unit weight (γ) and E _i for different types of rocks were analyzed, employing an artificial neural network and 195 data obtained from laboratory tests carried out on cores obtained from drilling holes within the area of three metro lines in Istanbul, Turkey. Software was developed in Java language using Weka class libraries for the study. To determine the prediction capacity of the proposed technique, the root-mean-square error and the root relative squared error indices were calculated as 0.191 and 92.587, respectively. Both coefficients indicate that the prediction capacity of the study is high for practical use.     

无粘性土的一种破坏准则

研究表明,在三轴压缩和伸长试验条件下,土的抗剪强度与莫尔-库仑准则是一致的,而对于一般应力状态下,土体破坏时的应力状态与莫尔-库仑准则有一定的出入。结合以往的真三轴试验结果,建议了一个复杂应力状态下的等效内摩擦角,在此基础上提出了一个考虑中主应力影响的无粘性土（c＝0）的破坏准则。通过和真三轴试验结果比较,发现该准则在π平面内比莫尔-库仑准则更接近于试验结果。该准则有望推广应用到粘性土中。     

在不同加载速率条件下花岗岩的破坏准则

本文应用岩石快速加载设备,系统地研究加载速率在10-1～105公斤/厘米2/秒范围内,花岗岩的抗压、抗拉和抗剪破坏特征,得出强度随加载速率变化的规律,并提出了花岗岩的动力破坏准则.     

Failure Criterion of Granite at Different Loading Rates

A study of failure properties of granite specimens under compression, tension, shear conditions at different loading rates has been conducted. The tests, having loading rates from 10-1 to 108 kg/cm2/sec, were carried out on a fast loading equipment for rock mechanics teat. It has been found that the strength of the granite specimens increases with the increasing of loading rates. Based on this study and some results from field tests, a criterion of dynamic failure of granite is presented.     

Evaluation Criterion and Methods of the Hydrocarbon Generation Potential for China's Paleozoic Marine Source Rocks

中国古生界海相高、过成熟烃源岩原始生烃潜力评价问题是一个没有解决的老问题,至今没有可靠的评价方法与统一评价标准.低成熟元古宇—古生界海相泥岩/页岩与碳酸盐岩地球化学分析揭示,由于有机质组成不同,不同时代烃源岩的有机碳含量与热解生烃潜力之间存在着不同的线性关系.按照岩石热解生烃潜力来衡量,泥岩/页岩与碳酸盐岩作为有效烃源岩的有机质丰度下限没有本质区别,其有机碳含量必须大于0.5％;对于元古宇一下古生界海相烃源岩,达到中等生烃潜力的有机碳含量必须大于0.75％,好烃源岩的有机碳含量必须大于1.5％,很好烃源岩的有机碳含量大于2％,有机碳含量大于4％的属于极好的烃源岩;上古生界海相泥岩各级烃源岩相应的有机碳界线值高于下古生界泥岩.按照低成熟元古宇—古生界烃源岩有机碳含量与热解生烃潜力之间的关系方程,由有机碳含量基本上可以定量评价高、过成熟的元古宇—古生界烃源岩的原始生烃潜力.     

Failure Loci of Some Igneous and Metamorphic Rocks

Summary Experimental evidence from true triaxial tests on dense rocks are analysed with emphasis on the failure modes of these materials under multiaxial loading, ambient temperature and external pressure. The strong dependence of the modes of fracture on the secondary components of applied stresses, and especially on the intermediate principal stress, indicated that the failure surface of these brittle materials may be appropriately described by a failure tensor polynomial criterion. As such, the elliptic paraboloid failure criterion was found to conveniently describe their mode of failure, by considering also the severe influence of anisotropy of the material.  For this purpose, a method developed recently (Theocaris and Panagiotopoulos, 1995a, 1995b) was applied, defining anisotropic hardening plasticity through an appropriate sequence of anisotropic elasticity problems. Assuming a particular path of loading or unloading, we measured the instantaneous tension and compression yield stresses along the transient principal-stress directions. These parameters completely define the instantaneous state of anisotropy of the body for the corresponding loading step, by applying the theory of the elliptic paraboloid failure locus (EPFS) (Theocaris, 1989a). A parameter identification problem was formulated on the constitutive expressions for this most general failure criterion. Then, by applying convenient constraints derived from the EPFS theory, which serve as filters throughout the whole procedure, the characteristic values of terms defining the variable components of the failure tensor polynomial were calculated, as the material was continuously loaded from the elastic into the plastic region and up to the ultimate failure load. Accurate simple tests in uniaxial tension and compression provided sufficient data for the definition of the yield loci of the material, at the considered loading step. These tests may be complemented with biaxial and triaxial modes of loading of the specimens. The results improve the accuracy and sensitivity of the method. All such data were used as input values, for establishing the mode of plastic deformation of the body during particular loading paths.  Moreover, the method employed allows the complete definition of the components of the failure, H, and the strength differential effect, h, tensors at each loading step. These quantities define completely the failure tensor polynomial for each material. Therefore, it presents the important advantage over other experimental methods by clearly indicating the parts contributed to the failure mode (either by plasticity, or by the strength differential effect) and their evolution during plastic deformation.  As convenient prototype materials for testing the method, specimens of metamorphic rocks such as Westerly granite (G), or quartzite (Q) were selected. Interesting results concerning the mechanical and especially the failure modes of such materials were obtained. Furthermore, the mechanical tests indicated clearly some basic properties of these materials as concerns the mode of their structure.     

冻结粉土的动强度特性及其破坏准则

在恒应变速率增长的等应变幅动力模式下，冻结粉动哟度最初随静有效正应力增大而增加；在后者为７－８ＭＰａ时，动强度达到峰值；以后随着静有效正应力继续增大，动强度趋于减小。不同应变速率下的动强度包络线呈现相似形式，服从抛物线破坏准则，研究中引进当量动内摩擦角ψｃ的和当量动内摩擦系数为ｔｇψｃ概念，从而使抛物线破坏准则方程与线性破坏方程在形式趋于一致。当量动内摩擦角ψｃ是一个动态变量，除取决于静有效正应力     

Characterization of Strength of Intact Brittle Rock Considering Confinement-Dependent Failure Processes

As technologies for deep underground development such as tunneling underneath mountains or mass mining at great depths (>1,000 m) are implemented, more difficult ground conditions in highly stressed environments are encountered. Moreover, the anticipated stress level at these depths easily exceeds the loading capacity of laboratory testing, so it is difficult to properly characterize what the rock behavior would be under high confinement stress conditions. If rock is expected to fail in a brittle manner, behavior changes associated with the relatively low tensile strength, such as transition from splitting to the shear failure, have to be considered and reflected in the adopted failure criteria. Rock failure in tension takes place at low confinement around excavations due to tensile or extensional failure in heterogeneous rocks. The prospect of tensile-dominant brittle failure diminishes as the confinement increases away from the excavation boundary. Therefore, it must be expected that the transition in the failure mechanism, from tensile to shear, occurs as the confinement level increases and conditions for extensional failure are prevented or strongly diminished. However, conventional failure criteria implicitly consider only the shear failure mechanism (i.e., failure envelopes touching Mohr stress circles), and thus, do not explicitly capture the transition of failure modes from tensile to shear associated with confinement change. This paper examines the methodologies for intact rock strength determination as the basic input data for engineering design of deep excavations. It is demonstrated that published laboratory test data can be reinterpreted and better characterized using an s-shaped failure criterion highlighting the transition of failure modes in brittle failing rock. As a consequence of the bi-modal nature of the failure envelope, intact rock strength data are often misinterpreted. If the intact rock strength is estimated by standard procedures from unconfined compression tests (UCS) alone, the confined strength may be underestimated by as much as 50 % (on average). If triaxial data with a limited confinement range (e.g., σ₃ ? 0.5 UCS due to cell pressure limitations) are used, the confined strength may be overestimated. Therefore, the application of standard data fitting procedures, without consideration of confinement-dependent failure mechanisms, may lead to erroneous intact rock strength parameters when applied to brittle rocks, and consequently, by extrapolation, to correspondingly erroneous rock mass strength parameters. It follows that the strength characteristics of massive rock differ significantly in the direct vicinity of excavation from that which is remote with higher confinement. Therefore, it is recommended to adopt a differentiated approach to obtain intact rock strength parameters for engineering problems at lower confinement (near excavation; e.g., excavation stability assessment or support design), and at elevated confinement (typically, when the confinement exceeds about 10 % of the UCS) as might be encountered in wide pillar cores.     

An Elastoplastic Model for Partially Saturated Collapsible Rocks

A unified elastoplastic model for describing the stress–strain behavior of partially saturated collapsible rocks is proposed. The elastic–plastic response due to loading and unloading is captured using bounding surface plasticity. The coupling effect of hydraulic and mechanical responses is addressed by applying the effective stress concept. Special attention is paid to the rock–fluid characteristic curve (RFCC), effective stress parameter, and suction hardening. A wide range of saturation degree is considered. The characteristics of mechanical behavior in partially saturated collapsible rocks are captured for all cases considered.