Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations

The rock mass failure process is characterized by several distinct deformation stages which include crack initiation, crack propagation and coalescence. It is important to know the stress levels associated with these deformation stages for engineering design and practice.Extensive theoretical, experimental and numerical studies on the failure process of intact rocks exist. It is generally understood that crack initiation starts at 0.3 to 0.5 times the peak uniaxial compressive stress. In confined conditions, the constant-deviatoric stress criterion was found to describe the crack initiation stress level.Here, generalized crack initiation and crack damage thresholds of rock masses are proposed. The crack initiation threshold is defined by σ₁−σ₃=A σ_cm and the crack damage threshold is defined by σ₁−σ₃=B σ_cm for jointed rock masses, where A and B are material constants and σ_cm is the uniaxial compressive strength of the rock masses. For a massive rock mass without joints, σ_cm is equal to σ_cd, the long-term uniaxial strength of intact rock. After examining data from intact rocks and jointed rock masses, it was found that for massive to moderately jointed rock masses, the material constants A and B are in the range of 0.4 to 0.5, 0.8 to 0.9, respectively, and for moderately to highly jointed rock masses, A and B are in the range of 0.5 to 0.6, 0.9 to 1.0, respectively. The generalized crack initiation and crack damage thresholds, when combined with simple linear elastic stress analysis, assist in assessing the rock mass integrity in low confinement conditions, greatly reducing the effort needed to obtain the required material constants for engineering design of underground excavations.     

Strength and failure modes of rock mass models with non-persistent joints

Most problems faced by the practicing rock engineer involve the evaluation of rock mass strength and deformability. The theoretical evaluation of the mechanical properties of fractured rock masses has no satisfactory answer because of the great number of variables involved. One of these variables, the influence of which over rock mass behavior is poorly documented, is the degree of fracture persistence. This paper presents the results of biaxial tests performed on physical models of rock with non-persistent joints. The failure modes and maximum strengths developed were found to depend on, among other variables, the geometry of the joint systems, the orientation of the principal stresses, and the ratio between intermediate stress and intact material compressive strength (σ₂/σ_c). Tests showed three basic failure modes: failure through a planar surface, stepped failure, and failure by rotation of new blocks. Planar failure and stepped failure are associated with high strength behavior, and small failure strains, whereas rotational failure is associated with a very low strength, ductile behavior, and large deformation.     

Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries—Insight from numerical modeling

The influence of the intermediate principal stress on rock fracturing and strength near excavation boundaries is studied using a FEM/DEM combined numerical tool. A loading condition of σ₃=0 and σ₁≠0, and σ₂≠0 exists at the tunnel boundary, where σ₁, σ₂, and σ₃, are the maximum, intermediate, and minimum principal stress components, respectively. The numerical study is based on sample loading testing that follows this type of boundary stress condition. It is seen from the simulation results that the generation of tunnel surface parallel fractures and microcracks is attributed to material heterogeneity and the existence of relatively high intermediate principal stress (σ₂), as well as zero to low minimum principal stress (σ₃) confinement. A high intermediate principal stress confines the rock in such a way that microcracks and fractures can only be developed in the direction parallel to σ₁ and σ₂. Stress-induced fracturing and microcracking in this fashion can lead to onion-skin fractures, spalling, and slabbing in shallow ground near the opening and surface parallel microcracks further away from the opening, leading to anisotropic behavior of the rock. Hence, consideration of the effect of the intermediate principal stress on rock behavior should focus on the stress-induced anisotropic strength and deformation behavior of the rocks. It is also found that the intermediate principal stress has limited influence on the peak strength of the rock near the excavation boundary.     

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.     

Effect of intermediate principal stress on strength of anisotropic rock mass

The Mohr-Coulomb criterion needs to be modified for highly anisotropic rock material and jointed rock masses. Taking σ₂ into account, a new strength criterion is suggested because both σ₂ and σ₃ would contribute to the normal stress on the existing plane of weakness. This criterion explains the enhancement of strength (σ₂ – σ3) in the underground openings because σ₂ along the tunnel axis is not relaxed significantly. Another cause of strength enhancement is less reduction in the mass modulus in tunnels due to constrained dilatancy. Empirical correlations obtained from data from block shear tests and uniaxial jacking tests have been suggested to estimate new strength parameters. A correlation for the tensile strength of the rock mass is presented. Finally, Hoek and Brown theory is extended to account for σ₂. A common strength criterion for both supported underground openings and rock slopes is suggested.     

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.     

Shaft resistance of a pile embedded in rock

A rational calculation procedure is proposed for establishing the shaft resistance of a pile embedded in rock, based upon the Hoek and Brown failure model. The state of the art of the calculation of the pile shaft resistance is analysed. Nearly all the recommendations that have appeared in the technical literature, for calculating the ultimate shear strength of a shaft embedded in rock (τ_ult) propose that τ_ult=ασ_c^k(σ_c;τ_ulten MN/m²) where the coefficient α, considered as a constant dimensional value, ranges from 0.1 to 0.8, if the unconfined compressive strength (σ_c) is expressed in MN/m². In most cases, the exponent k is 0.5.A comparison is made between the results yielded and the different empirical theories that have been put forward with respect to this shaft resistance. It can generally be stated that the results obtained with this theory are reasonable for long and deeply socketed piles (high confining pressures) but the results are on the safe side in some cases where short piles (low confining pressures) are involved.This paper is a continuation of the works developed by the same authors with piles working at the tip, socketed in rock.     

Numerical simulation of the excavation damaged zone around an opening in brittle rock

The micromechanics-based damage model proposed by Golshani et al. [A micromechanical model for brittle failure of rock and its relation to crack growth observed in triaxial compression tests of granite. Mech Mater 2006;38:287–303] is extended so that time-dependent behavior of brittle material can be taken into account, with special attention to the numerical analysis of an excavation damaged zone (EDZ) around an opening, which is a major concern in assessing the safety of underground repositories. The present model is capable of reproducing the three characteristic stages of creep behavior (i.e., primary, secondary, and tertiary creep) commonly observed in the laboratory creep tests. The sub-critical microcrack growth parameters (i.e., n and A) can be determined for Inada granite by fitting the numerical results of elapse time to failure versus the creep stress ratio curve with the experimental data under both dry and wet conditions. It is found that moisture has a significant influence on the parameter A rather than the parameter n. Use of the extended model makes it possible to analyze not only the extension of microcrack length, but also the development of EDZ around an opening as a function of time. The damaged zones mainly develop in the sidewalls of the opening in the case that the vertical stress σ₂₂ is larger than the horizontal stress σ₁₁.     

Estimation of rock modulus: For intact rocks with an artificial neural network and for rock masses with a new empirical equation

The elastic modulus of intact rock is used for many rock engineering projects, such as tunnels, slopes, and foundations, but due to the requirements of high-quality core samples and associated sophisticated test equipment, instead the use of empirical models to obtain this parameter has been an attractive research topic. In the rock mechanics literature, some empirical relations exist between the elastic modulus of intact rock and other rock properties, such as the uniaxial compressive strength (σ_ci), unit weight (γ), Schmidt hammer rebound number, point load index and petrographic composition. However, the past use of specific rock types is the main limitation of the existing empirical equations. In other words, they are not open to the general purpose use. To eliminate this deficiency, a total of 529 datasets, including uniaxial compressive strength, unit weight and elastic modulus of intact rock (E_i), were collected via an extensive literature review. In addition to these datasets, a further total of 80 datasets was obtained from laboratory tests performed on greywacke and agglomerate core samples for this study. To prepare a chart for the prediction of the elastic modulus of intact rock, an artificial neural network was constructed using the large database. In addition, after a brief overview of existing empirical equations, a new empirical equation, which considers RMR and the elastic modulus of intact rock (E_i) as input parameters, is also proposed using worldwide data.     

Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression

This paper presents the findings of an extensive laboratory investigation into the identification and quantification of stress-induced brittle fracture damage in rock. By integrating the use of strain gauge measurements and acoustic emission monitoring, a rigorous methodology has been developed to aid in the identification and characterization of brittle fracture processes induced through uniaxial compressive loading. Results derived from monocyclic loading tests demonstrate that damage and the subsequent deformation characteristics of the damaged rock can be easily quantified by normalizing the stresses and strains observed in progression from one stage of crack development to another. Results of this analysis show that the crack initiation, σ_ci, and crack damage, σ_cd, thresholds for pink Lac du Bonnet granite occur at 0.39σ_UCS and 0.75σ_UCS, respectively. Acoustic emissions from these tests were found to provide a direct measure of the rapid release of energy associated with damage-related mechanisms. Simplified models describing the loss of cohesion and the subsequent development of microfractures leading up to unstable crack propagation were derived using normalized acoustic emission rates. Damage-controlled cyclic loading tests were subsequently used to examine the effects of accumulating fracture damage and its influence on altering the deformation characteristics of the rock. These tests revealed that two distinct failure processes involving the progressive development of the microfracture network, may occur depending on whether the applied cyclic loads exceed or are restrained by the crack damage stress threshold.     

Risk of shear failure and extensional failure around over-stressed excavations in brittle rock

The authors investigate the failure modes surrounding over-stressed tunnels in rock.Three lines of investigation are employed:failure in over-stressed three-dimensional(3D) models of tunnels bored under 3D stress,failure modes in two-dimensional(2D) numerical simulations of 1000 m and 2000 m deep tunnels using FRACOD,both in intact rock and in rock masses with one or two joint sets,and finally,observations in TBM(tunnel boring machine) tunnels in hard and medium hard massive rocks.The reason for 'stress-induced' failure to initiate,when the assumed maximum tangential stress is approximately(0.4-0.5)σ_c(UCS,uniaxial compressive strength) in massive rock,is now known to be due to exceedance of a critical extensional strain which is generated by a Poisson's ratio effect.However,because similar 'stress/strength' failure limits are found in mining,nuclear waste research excavations,and deep road tunnels in Norway,one is easily misled into thinking of compressive stress induced failure.Because of this,the empirical SRF(stress reduction factor in the Q-system) is set to accelerate as the estimated ratio σ_(θmax)/σ_c 0.4.In mining,similar 'stress/strength' ratios are used to suggest depth of break-out.The reality behind the fracture initiation stress/strength ratio of '0.4' is actually because of combinations of familiar tensile and compressive strength ratios(such as 10) with Poisson's ratio(say0.25).We exceed the extensional strain limits and start to see acoustic emission(AE) when tangential stress σθ≈ 0.4σc,due to simple arithmetic.The combination of 2D theoretical FRACOD models and actual tunnelling suggests frequent initiation of failure by 'stable' extensional strain fracturing,but propagation in 'unstable' and therefore dynamic shearing.In the case of very deep tunnels(and 3D physical simulations),compressive stresses may be too high for extensional strain fracturing,and shearing will dominate,both ahead of the face and following the face.When shallower,the concept of 'extensional strain initiation but propagation' in shear is suggested.The various failure modes are richly illustrated,and the inability of conventional continuum modelling is emphasized,unless cohesion weakening and friction mobilization at different strain levels are used to reach a pseudo state of yield,but still considering a continuum.     

A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite

A new true triaxial cell has been designed, fabricated, calibrated, and successfully tested. Its main feature is very high loading capability in all three orthogonal directions, enabling the testing to failure of hard crystalline rocks subjected to large least and intermediate principal stresses. All three principal stresses applied to rectangular prismatic specimens, 19×19×38 mm in size, are servo controlled. The cell was used to conduct an extensive series of tests in Westerly granite. A new true triaxial strength criterion for the rock was obtained that takes into account the effect of the intermediate principal stress. This turns out to be so significant that it raises serious questions about the suitability of criteria such as those named after Mohr, Coulomb, Griffith, and others. Measurements of strain in all three principal directions revealed that the onset of dilatancy relative to the major principal stress at failure rises substantially as the intermediate principal stress increases. The true triaxial tests also demonstrate that for the same least horizontal stress the main fracture dip angle in Westerly granite increases as a function of the intermediate principal stress, suggesting a strengthening effect. Limited thin section and SEM study shows that microcrack propagation, crack localization, and main fracture characteristics are basically similar to those observed in common triaxial tests.     

龙门山北段千枚岩强度及变形特性对比试验研究

对成兰铁路龙门山北段隧道群4种典型千枚岩进行不同加载方位角的强度和变形特性对比试验研究,研究结果表明:加载方位角和岩石矿物成分严重影响千枚岩变形特性,并与围压水平有关。千枚岩单轴抗压强度随方位角变化呈"U"型的各向异性特征,所试验的4种千枚岩各向异性率由大至小对比关系为:HPMPQPCP。试样一般在峰值应力前产生扩容现象,扩容起始应力和形式与加载方位角或层理发育程度相关。三轴压缩试验中,千枚岩垂直层理加载时的峰值强度、长期强度和残余强度比平行层理加载明显偏高,并随围压水平增加而增大。千枚岩不同加载方位角下单轴压缩试验破坏模式归纳为4种:层理面滑移剪切破坏、压拉剪切破坏、张拉破坏、复合破坏。     

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.     

A geo-engineering classification for rocks and rock masses

In this article, an attempt is made to assess the reliability of predicting the uniaxial compressive strength and the corresponding modulus of a rock mass by current approaches. These two basic engineering properties, when estimated from rock mass rating (RMR), Q and geological strength index (GSI), indicate hardly any change in the modulus ratio with the change in the quality of the rock mass from very good to very poor. However, the modulus ratio obtained from the relations involving the joint factor, J_f, indicate a definite decrease in the modulus ratio with a decrease in the quality of the rock mass. The strength and modulus in the unconfined and confined states, the modulus ratio and failure strain in the unconfined case were linked to J_f in earlier publications based on a large experimental database. Some of these relations were adopted to verify the response of jointed test specimens, the response of the rock mass during excavations for mining and civil underground chambers, in establishing ground reaction curves including the extent of the broken zone, and the bearing capacity of shallow foundations.The joint factor is now linked to RMR, Q and GSI. The prediction of compressive strength and modulus of the rock mass appears to be more suitable. For classifying the rock, based on these properties, the Deere and Miller engineering classification, applicable to intact rocks, has been suitably modified and adopted. The results of different modes of failure of jointed specimens establish definite trends of changes in the modulus ratio originating from the intact rock value on the modified Deere and Miller plot. A geo-engineering classification is evolved by considering strength, modulus, quantifiable weathering index and lithological aspects of the rock.     

Variation in strength and creep life of six Japanese rocks

In this paper, variations in strength and creep life are investigated for rocks under various conditions: dry and wet, uniaxial and triaxial, and compressional and tensile. A number of parameters are introduced for this purpose; to assess the time-dependent failure under constant and monotonic loading the following parameters are used: the parameter of time dependency δ, coefficient of creep life α and coefficient of strength β. δ explains the rate dependency of strength or stress level dependency of creep life. α and β are related to each other. Variations in β have been evaluated using data from previous experiments. It is confirmed here that δ, β and variations in β determined by creep tests are in most cases identical to those determined using strength tests. Variation in β in the wet condition is almost the same as that in the dry condition; however, variation in tension increases more than in compression. Under confining pressure, variation in β is reduced for Neogene sedimentary rocks, and does not appear to change for igneous rock and welded tuff.     

Observations and classification of roof strata behaviour over longwall coal mining panels in India

A study has been made of a number of mechanized longwall panels in various coal mines in India, concentrating on the geology, physico-mechanical rock properties and the behaviour of the coal measure roof rocks during mining. The research has highlighted the splitting and caving characteristics of the strata rocks and enabled the development of a roof-rock classification system. Roof rocks are classified into six categories based on the: (a) mean weighted uniaxial compressive strength; (b) RQD; (c) (i) type of rocks, (ii) presence of cracks, fissile beds, splitting, etc., (iii) presence of water; and (d) thickness of bed layer. The behaviour of layers and composite layers in the immediate roof rock mass is also enumerated. Relations between the rock strength properties and values for the bulking factor of the failed rock are included. The concepts of a ‘weighting zone’ and ‘caving zone’ are proposed. The paper also clarifies the occurrence of different types of failure, such as periodic falls. All these findings should be helpful during calculation of the powered support capacity.     

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.     

Strength and failure characteristics of jointed marble under true triaxial compression

The rock structure and three-dimensional stress state play a vital role in the mechanical behaviour of rock masses. Here, a series of true triaxial compression tests (σ₁ > σ₂ > σ₃) are conducted on jointed marble (50 × 50 × 100 mm³) containing a natural stiff joint, taken from the China Jinping Underground Laboratory (CJPL-II) project. The purposes of this study are to investigate the joint effect and estimate the stress dependency of jointed marble. The test results show that jointed marble can fail in four distinct forms, namely, splitting or shearing of intact marble, opening of the joint or sliding along the joint, and these failure modes are influenced by the joint configuration and the minimum and intermediate principal stresses. Generally, jointed marble has more brittle post-peak behaviour than intact marble. The linear Mogi-Coulomb failure criterion can be modified to describe the strength of the jointed marble under true triaxial compression. The jointed marble strength is more sensitive to the minimum principal stress than to the intermediate principal stress. A maximum decline of 25% in strength is observed, which corresponds to a joint dip angle of 60° at σ₂ = 60 MPa and σ₃ = 30 MPa. The link between the experimental results and in situ fracturing at CJPL-II is also demonstrated.

     

Experimental investigation of mechanical properties of bedded salt rock

Because of salt cavern utilization for liquid, gas and solid waste storage, salt rock mechanical properties are needed for assessments of facility, stability and safety. Bedded salt deposits are widespread and used as much or more than diapiric salt bodies as storage facility hosts, but experimental data on the mechanical properties of bedded salt rock with impurities are far less common than data available on relatively pure diapiric salt rocks. Through laboratory uniaxial and triaxial compression experiments on rock salt (halite), interlayers (anhydrite) and bedded composite specimens (anhydrite–halite and mudstone–halite), differences in mechanical properties of the various lithologies are explored. In the composite specimens, the weakest or the most deformable component governs the behavior. Also, the properties of bedded composite lithology specimens tend to be in between the property ranges of the “pure” lithologies. The elastic modulus of the bedded salt rock increases from 5.3 to 24.1 GPa with an increase in the confining stress from 0 to 15 MPa, with some evidence of sample damage. The ductile transition for halite at the strain rates used is at about σ₃10 MPa.With increasing σ₃, the anhydrite–halite composite lithology deformation showed strain hardening and a strong trend to ductile behavior as the halite bands tended to dominate the behavior. Strain incompatibility effects exist along interfaces between creeping and non-creeping phases in anhydrite–halite composite lithologies. Mudstone–halite rocks tended to be extremely weak, compared with all other specimens.