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The constant mi is a fundamental parameter required in the Hoek–Brown (H–B) failure criterion for estimating rock strength. Triaxial tests for the calculation of this constant are time-consuming and expensive. In this paper, a new perspective is presented for the physical meaning of the parameter mi of the H–B model in consideration of the contact friction coefficient. A correlation between the contact friction coefficient and mi is established using published data. A practical approach is proposed to determine the value of the parameter mi. In addition, previously proposed methods of estimating the residual strength of rock are reviewed. A novel method based on the H–B failure criterion is established to predict the residual strength of rock. The single model parameter used in the new model controls the residual strength nonlinearity. The strengths predicted by the proposed method for limestone, granite, slate, and sandstone are in good agreement with those measured during laboratory tests. The corresponding errors are within a range of 15%. This method is applied to an actual rock mass around a tunnel in the Hanjiang to Weihe River Project of China. [ABSTRACT FROM AUTHOR]

This study deals with the comparative investigation on various classification/characterization systems for sedimentary rocks in two parts, 40 km-long of the Zagros tunnel, west of Iran. The results of extensive geotechnical explorations and field measurements were applied to obtain the rock mass classification/characterization systems such as Rock Mass Rating (RMR), Rock Condition Rating (RCR), Q-system (Q), Rock Mass Number (QN), Rock Mass index (RMi), Rock Structure Rating (RSR), and Geological Strength Index (GSI) for a wide range of sedimentary rocks. A set of systems inter-relationship is proposed. Some of these correlation relations such as RMR-Q, RMR-RMi, RMi-Q, RCR, GSI-GSI(Cai) are similar to the one or more relations proposed in the previous studies, however, some of them such as RSR-RMR, RSR-Q, RCR-QN and GSI-RMR are not similar to the previous works. Joint set orientation and joint set number are more important parameters that cause weak correlation coefficients where both side classifications are not similar in considering them in calculating values. So it is proposed to find relations between any pairs of systems that both of them consider or not consider these parameters. The relations are proposed for a wide range of sedimentary rocks and can be applied for similar geological environments [ABSTRACT FROM AUTHOR]

Brittle rock contains many microcracks under natural conditions. The theoretical models of brittle rock containing microcracks under the effect of water pressure, axial stress, and confining pressure have not yet been fully elucidated. Therefore, a new model based on a wing crack model and an improved Weibull model was established to analyse the effects of water on the progress of crack initiation, growth, and coalescence. In this improved wing crack model, the water pressure was introduced as a variable, and the analytical stress-crack relationship considering the water pressure was revealed. The relationship between the stress and strain was also obtained. The results revealed that the cracks more readily propagated and failure occurred under higher water pressure. The proposed theoretical curves agree with the experimental data obtained under various water pressures. The effects of water pressure with the change of the crack inclination angle, friction coefficient, crack initiation length, and wing crack length on the wedging force, internal stress, and stress-strain relationship were analysed. The analytical results were validated by experiments. The effect of water pressure on the stress-strain relationship was quantified using an analytical equation whereby the most disadvantageous angle cases, that is, cases wherein the wedging force was maximum, with zero friction were determined. [ABSTRACT FROM AUTHOR]

However, for heavily fractured rock masses without a recognizable structural pattern, the estimation of I J i SB I v i sb is extraordinarily difficult, and thus Sonmez and Ulusay ([31]) suggested a new estimation equation for I J i SB I v i sb , as follows: 2 HT ht Graph where I N i SB I x i sb , I N i SB I y i sb , and I N i SB I z i sb represent the number of joints intersecting three perpendicular scanlines ( I L i SB I x i sb , I L i SB I y i sb , and I L i SB I z i sb ). Then, 14 HT ht Graph where I i i equals 1 to I N i . [Extracted from the article]

The ancient Theban tombs at the hillside cemetery of Sheikh 'Abd el-Qurna (SAQ), west of Luxor, Egypt, were excavated mainly in the Thebes Limestone Formation and show varying degrees of damage of rock pillars and ceilings. In order to understand the rock mass behaviour in selected tombs and its impact on past failures and current stability, we carried out geological mapping and rock mass quality assessments. Our work provides a geological map and geotechnical evaluation of the rock mass of these SAQ tombs and their surroundings. We mapped and described rock fractures in situ and with remote sensing data, and estimated the rock mass quality of the different members within the Thebes Limestone Formation using the Rock Mass Rating (RMR) and Geological Strength Index (GSI) systems. In addition, we conducted a rock pillar analysis. Analyses and mapping were supported by new high-resolution terrain models computed from ground-based and aerial photogrammetry and from terrestrial laser scanning. Our analyses show that the tombs at SAQ have been cut into poor to very good quality rock masses. Rock failures of ceilings and pillars were frequently facilitated by local, unfavourably oriented persistent discontinuities, such as tension cracks and faults. Other failures were related to the disintegration of nodular limestone into individual nodules upon weathering. Our data suggest that, in 18th Dynasty monumental tomb construction, low-strength rock masses rarely resulted in modifications of the planned tomb design in order to minimise the risk of rock falls and collapses. [ABSTRACT FROM AUTHOR]

The rock mass quality in underground excavations and or tunnelling is a key issue in the design of the most suitable support to ground stability. This work aims to discuss the applicability of the latest version of the geological strength index (GSI|2013) in an anisotropic media during ongoing deep underground excavation by drilling and blasting. The study encompasses a comprehensive geological, geotechnical and geomechanical characterisation and evaluation of the excavation faces in the Marão tunnel (north Portugal). In addition, 305 m (two underground sections) of tunnel were mapped in 74 consecutive face underground excavation advances. Geological, geotechnical and geomechanical data relating to the site investigation were collected and computed in each new face advance. The scanline sampling technique was applied on exposed rock surfaces, a geotechnical analysis of the discontinuities was performed, and the block size of the rock mass was determined. Geotechnical and geomechanical zoning of the studied sections were continuously carried out considering the knowledge of the site rock mass characteristics and behaviour. In addition, a comparison was performed between the version of GSI|2013 and its earlier version (namely, GSI|98) and correlated with rock mass rating. The study will contribute to a better understanding of GSI|2013 and its applicability in geoengineering projects in design or excavation work stages. [ABSTRACT FROM AUTHOR]

Rocks are a natural material with strong heterogeneity, and the heterogeneity affects the behavior and failure patterns of rocks and rock masses. Therefore, the factor of rock heterogeneity should not be neglected in cases of highly heterogeneous rock masses. In this study, the effect of heterogeneity on the rock mass stability in an underground coal mine roadway is investigated by introducing a stability analysis method that considers rock heterogeneity. The stability analysis method is combined with field investigation, laboratory testing, and numerical simulation. The rock mass heterogeneity is considered in the light of equivalent material properties, which are the heterogeneous rock mass properties weakened by heterogeneously distributed fractures. A Weibull distribution model is implemented into FLAC3D to characterize the rock mass heterogeneity. Sensitivity analyses regarding the rock mass properties and the mesh dependency are conducted to understand their effect on roadway deformation. A parametric study is performed to investigate the effect of the homogeneity index and other parameters that describe the rock mass fracturing intensity. The results show that the degree of rock mass heterogeneity has a significant effect on the roof deformation, failure extent, and other input parameters that describe the rock mass heterogeneity. The simulation results that are in good agreement with heterogeneity parameter data are estimated in the field. Thus, this method can be used as a back-analysis technique to obtain the homogeneity index and other input parameters through comparison to field deformation data, and can be applied to other engineering cases involving highly heterogeneous rock. [ABSTRACT FROM AUTHOR]

The Hoek–Brown (HB) failure criterion is one of the most widely used failure criteria in rock engineering. Based on the Geological Strength Index (GSI) system, a number of empirical models have been proposed in parallel with this criterion to estimate the strength and deformation properties of rock masses such as uniaxial compressive strength (UCS) and deformation modulus. However, the GSI system does not incorporate the effects of joint orientation β on the quality of a rock mass. This means that these empirical models cannot capture anisotropic rock mass strength caused by joint orientations. In this research, UDEC rock mass models, which are calibrated by laboratory data, are used to investigate the effects of joint orientation on rock mass strength in an unconfined state. The values of UCS obtained from the numerical simulation are then compared with those calculated from traditional empirical UCS models based on the GSI system. The comparison study shows that the value of UCS is significantly overestimated by the traditional empirical model when 10° < β < 45°, which will have serious safety implications for engineering designs. To rectify the problem, based on the analysis of numerical simulation results, an anisotropic weighting factor fβ is proposed to be used to refine the empirical UCS model. The modified UCS model is demonstrated to be capable of giving conservative but more accurate prediction of the rock mass strength for various joint orientations, which will result in more optimal and safer engineering designs. [ABSTRACT FROM AUTHOR]

In tunneling, determining quantitatively the rock mass strength parameters of the Hoek-Brown (HB) failure criterion is useful since it can improve the reliability of the design of tunnel support systems. In this study, a quantitative method is proposed to determine the rock mass quality parameters of the HB failure criterion, namely the Geological Strength Index (GSI) and the disturbance factor (D) based on the structure of drilling core and weathering condition of rock mass combined with acoustic wave test to calculate the strength of rock mass. The Rock Mass Structure Index and the Rock Mass Weathering Index are used to quantify the GSI while the longitudinal wave velocity (Vp) is employed to derive the value of D. The DK383+338 tunnel face of Yaojia tunnel of Shanghai-Kunming passenger dedicated line served as illustration of how the methodology is implemented. The values of the GSI and D are obtained using the HB criterion and then using the proposed method. The measured in situ stress is used to evaluate their accuracy. To this end, the major and minor principal stresses are calculated based on the GSI and D given by HB criterion and the proposed method. The results indicated that both methods were close to the field observation which suggests that the proposed method can be used for determining quantitatively the rock quality parameters, as well. However, these results remain valid only for rock mass quality and rock type similar to those of the DK383+338 tunnel face of Yaojia tunnel. [ABSTRACT FROM AUTHOR]

The basic quality (BQ) system is regarded as the national rock mass classification system that can be appropriate for use in most types of rock engineering in China. Two underlying parameters that the uniaxial compressive strength (UCS) and the rock intactness index (K) are taken into account to access the basic BQ value. However, The K was usually measured by an indirect acoustic wave approach which often cannot reflected the actual conditions. In this study, a direct measured parameter K is recommended to obtain by means of the GSI system to replace the original K, and a new method [BQ] expressed by the new parameter K is proposed. In particular, a graphic method is also presented to determine rapidly and rationally the rock mass classification by the X, Y coordinates of the UCS and the K. In order to further compare the evaluation results and application effects between the [BQ] and the international rock mass classification systems, a comprehensive solution is carried out. First, the evaluation factors of rock mass qualities from all these system are classified according to three groups: the rock mass inherent parameters, external parameters, and construction parameters. Second, the correlations among these evaluation factors in the new [BQ] system and the common international systems (i.e. RMR, Q, and RMi) were compared. And the formulas or charts among the three groups are presented. Finally, five hydropower underground excavations are chosen to analysis the comparison results of the [BQ] system and the international common RMR, Q, or RMi systems. The applicability scope of these international RMR, Q, or RMi systems is also discussed in the context of China's rock characteristics and geological stress conditions. [ABSTRACT FROM AUTHOR]

As soft rocks are likely to soften, slime and swell while contacting water, the existence of soft rocks is harmful for stability of surrounding rocks and supporting structures of tunnels. Through uniaxial and triaxial tests under dry condition and triaxial test with different moisture contents, the mechanical properties and failure modes of soft rocks were studied under conditions that the schistosity plane of the rock samples was vertical to, presented an oblique angle with, and paralleled to the loading direction. The results showed that peak strengths in natural and water-bearing states increased with increasing confining pressures, while those in water-bearing state were 40% lower than those in natural state. The samples were mainly subjected to ductile failure in both natural and water-bearing states while the samples in natural state exhibited a certain brittle failure characteristic in post-peak phase. With the increase of confining pressures, the post-peak curve gradually became gentle after certain brittle failure while the post-peak stresses had an insignificant change. In comparison, the samples in water-bearing state showed significant post-peak disparity, that is, exhibited strong ductile failure characteristic. Moreover, the fitting relationship between triaxial compressive strength and moisture of soft rocks can be expresses as σ = Aω + B ( A < 0, B > 0) while that between elasticity modulus and moisture can be expresses as E = Aω + B ( A < 0, B > 0). [ABSTRACT FROM AUTHOR]

The paper suggests an alternative quantification of the Geological Strength Index (GSI) Chart published by Hoek et al. in Paper prepared for presentation at the 47th US Rock mechanics/geomechanics symposium held in San Francisco (2013). The engineering parameters proposed for the horizontal and vertical axes of the Chart are the most commonly used in routine field investigations on rock masses by means of standard exposure surveys and borehole logging. They mainly include parameters traditionally used for block size characterization (i.e., volumetric joint count Jv, joint spacing S and RQD/Jn factor) as well as other parameters purposely defined in the present study and based on combinations of the traditional ratings of the Bieniawski's RMR classification. Adopting these options, new empirical equations for calculating the GSI have been fine tuned and tested on a real rock mass dataset. The comparison between the GSI values calculated using the new equations and those directly mapped during underground excavations has demonstrated the potentiality of the proposed methodology. The new quantification of the GSI Chart can be regarded as a useful and practical tool suitable to integrate the Hoek et al. (2013) approach. The complementary use of different and independent methods represents an effective practice to properly check and validate the final estimation of the GSI. [ABSTRACT FROM AUTHOR]

Triaxial compression tests were performed to determine the strength and deformability of small-scale rock mass models with multiple joint sets and frequencies under confining stresses up to 12 MPa. The cubical sandstone specimens (80 × 80 × 80 mm) with joint sets simulated by saw-cut surfaces were compressed to failure using a true triaxial load frame. The joint frequencies ranged from 26 to 76 joints per meter. The results indicate that the Hoek-Brown criterion with two material parameters ( m and s) can describe rock mass strengths as well as the three parameter criteria of Sheorey, Yudhbir and Ramamurthy-Arora. The parameter s notably decreases with increasing joint frequency, while parameter m is less sensitive to joint frequency. The confining stresses tend to enhance the effects of joint frequencies on rock mass compressive strengths. The deformation moduli in the direction normal to the joints tend to be lower than those parallel to the joints. They decrease with increasing joint frequency. Goodman's equation was modified here to allow calculation of the deformation moduli of the rock mass along the three principal directions. The modified equation can sufficiently describe the deformation moduli normal and parallel to the joints for one-joint set and three-joint set specimens under all confining stresses. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to present the results of a comparative analysis of the GSI values predicted by different empirical equations currently available in literature which apply the input parameters used in the best known rock mass classification systems, namely the RMR, the Q and the RMi. For this aim, probabilistic analyses based on Monte Carlo simulations have been developed using, as inputs, the geomechanical field data collected for a real rock mass. Afterwards, the GSI outputs obtained from the different empirical approaches have been statistically analyzed and compared. The results of simulations indicate that the diverse relationships may predict dissimilar values of the GSI for the same rock mass. In general, the highest values have been obtained from the equations which apply the RMR input ratings, while the methods based on RMi produced the lowest results. Sensitivity analyses performed on the simulation outputs show that, for the examined case study, the input parameters reflecting the degree of jointing of the rock mass, namely the RQD and the rock block volume, have the largest effects on the calculated GSI, while those describing the characteristics of discontinuities show lesser influence and may depend on the equation adopted. In particular, the GSI estimated from the methods based on the Q and RMi inputs is especially sensitive to the infilling and roughness of discontinuities, while in the methods based on the RMR ratings the discontinuity characteristics influencing the GSI value the most demonstrate to be the aperture, the roughness and the length. The analyses have mainly highlighted the possible uncertainties still related to the quantitative estimation of the GSI and allowed for the recognition of the input rock mass parameters that may have the highest impact on the GSI in the different estimation methods. [ABSTRACT FROM AUTHOR]

Estimation of rock load is very important parameter to design the support system because it is a function of many parameters such as stress magnitude, rock mass behavior, excavation method and etc. Several methods are used to estimate this parameter such as experimental, empirical and numerical methods. In this study based on the actual collected data from five tunnels in non squeezing ground condition, a new empirical method is proposed to estimate the rock load with considering the post failure behavior of rock mass and it is estimated using the drop to deformation modulus ratio (was named η). Finally the relation between the rock load and the drop to deformation modulus ratio, η, in non squeezing ground condition is estimated. Based on the statistical analysis, the maximum correlation between both parameters is achieved using of Eqs. 9-11 to estimate the drop modulus. It is cleared that the amplitude of η, is high and to increase the correlation between mentioned parameters, the classification of data is performed in two methods, in the first method, all data is classified in two classes such as $$\eta \le 0.1$$ and $$\eta > 0.1$$ and in the second method, all data is classified in five classes [according to the proposed classification by Hoek and Brown () and Osgoui and Ünal ()] as very weak (GSI < 30, ICR < 25, without filling and η < 0.01) to very good classes (10 ≤ η < 10,000 and 65 ≤ GSI < 90). Also a statistical analysis is performed to estimate the rock load using the mentioned parameter ( η) in any class. The result shows that there is an inverse relation between both parameters and the best correlation is achieved using of logarithmic equations to estimate the rock load. Also the correlation of first equations obtained from the first method (including two classes such as $$\eta \le 0.1$$ and η > 0.1) is higher than other equations (including five classes) so it is proposed that the mentioned equations are used to estimate the rock load. [ABSTRACT FROM AUTHOR]

The paper focuses on the methods commonly used for measuring and quantifying the joint roughness in the current rock mass characterization practice. Among the different parameters traditionally employed to express roughness, major relevance seems to be gained by the 'Joint Roughness factor' (jR) applied in the Palmström's rock mass characterization index system, having this factor also been integrated in some quantitative methods recently proposed for estimating the geological strength index of a rock mass. Therefore, a new quantitative approach for a more objective estimation of this factor has been fine-tuned and is presented in the paper. The new method has been specifically designed to assist engineering geologists in gaining consistent values of jR on the base of conventional routine field measurements. It can suitably integrate and support the traditional semi-qualitative Palmström's classification of joint roughness, mostly related to more subjective descriptions, to estimate the most representative values of jR to be considered for rock mass characterization. In its original definition, the factor jR is evaluated for two-dimensional joint profiles by the product of a small-scale roughness factor (the joint smoothness or unevenness factor, j) with a large-scale roughness factor (the joint waviness factor, j). In order to reduce the subjectivity on the estimate of these partial factors, a simple analytic equation relating them with some parameters traditionally used to quantify 2D joint roughness is here proposed, providing a continuous gradation among the different ratings of the jR scale and also facilitating the implementation of the factor in probabilistic approaches for managing its inherent uncertainty and variability. The presented method applies best for characterizing hard rock masses well-exposed after blasting (e.g., in dam foundation or quarry slopes) or favourably outcropping on natural rocky slopes, where joint surfaces can generally be easily attained and analysed. [ABSTRACT FROM AUTHOR]

The parameter m is an important rock property parameter required for use of the Hoek-Brown failure criterion. The conventional method for determining m is to fit a series of triaxial compression test data. In the absence of laboratory test data, guideline charts have been provided by Hoek to estimate the m value. In the conventional Hoek-Brown failure criterion, the m value is a constant for a given rock. It is observed that using a constant m may not fit the triaxial compression test data well for some rocks. In this paper, a negative exponent empirical model is proposed to express m as a function of confinement, and this exercise leads us to a new empirical failure criterion for intact rocks. Triaxial compression test data of various rocks are used to fit parameters of this model. It is seen that the new empirical failure criterion fits the test data better than the conventional Hoek-Brown failure criterion for intact rocks. The conventional Hoek-Brown criterion fits the test data well in the high-confinement region but fails to match data well in the low-confinement and tension regions. In particular, it overestimates the uniaxial compressive strength (UCS) and the uniaxial tensile strength of rocks. On the other hand, curves fitted by the proposed empirical failure criterion match test data very well, and the estimated UCS and tensile strength agree well with test data. [ABSTRACT FROM AUTHOR]

This paper presents a new technique for estimating the in situ block size distribution in a jointed rock mass. The technique is based on Monte Carlo simulations using more realistic fracture geometry as its input compared to other block size estimation methods described in the literature. This geometry represents fractures as either polygons or triangulated surfaces and therefore models persistence and truncation of fractures accurately. Persistence has been shown to be critically important for the accurate prediction of block size and shape. We show that for rock masses with relatively small discontinuities, the results of our predictions differ markedly from previous methods which over-predict fragmentation. [ABSTRACT FROM AUTHOR]

Geotechnical design input parameters, such as in situ stress field, rock mass strength parameters and deformation modulus, are never known precisely. There are always uncertainties involved in these parameters, some are intrinsic and others are due to lack of knowledge or understanding of these parameters. To quantify the effects of these uncertainties on tunnel and cavern design, it is necessary to utilize probabilistic analysis methods. In the present study, a quantitative, probabilistic approach to use the Geological Strength Index (GSI) system for rock mass characterization is presented. It employs the block volume and a joint condition factor as quantitative characterization factors to determine the GSI values. The approach is built on the linkage between descriptive geological terms and measurable field parameters such as joint spacing and joint roughness, which are random variables. Using GSI values obtained from field mapping data, and in combination with the intact rock strength properties, the probability density distributions of rock mass strength parameters and elastic moduli of the jointed rock mass can be calculated using Monte Carlo method. Furthermore, probabilistic analysis of tunnel and cavern stability based on the variable input parameters is conducted employing the point estimate method. One example is given to illustrate how to consider the variability of in situ stress and the rock mass properties in tunnel and cavern design. The method presents an approach for systematic assessment of uncertainty in rock mass characterization in rock engineering, and it can assist us to better understand how uncertainty arises and how the rock support system design decision may be affected by it. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The results of geotechnical explorations, engineering geological investigation (including laboratory and in situ tests) and field observations have been used, along with borehole logging charts, to obtain the rock mass geotechnical data. Based on the data, the rock mass along the Sabzkuh water conveyance tunnel route was classified by rock mass rating (RMR), Q-system ( Q), rock mass index (RMi) and geological strength index (GSI) (3 methods). A new series of correlations were established between the systems based on the data collected from the study area. These relationships were then compared with those reported in the literature, and two new relations were recommended. The classifications were utilized to calculate mechanical properties (rock mass strength and deformation modulus) of the rock mass along the tunnel according to available empirical relations, and to distinguish the upper-bound and lower-bound relations. [ABSTRACT FROM AUTHOR]

By applying the Griffith stress criterion of brittle failure, one can find that the uniaxial compressive strength (σc) of rocks is eight times the value of the uniaxial tensile strength (σt). The Griffith strength ratio is smaller than what is normally measured for rocks, even with the consideration of crack closure. The reason is that Griffith’s theories address only the initiation of failure. Under tensile conditions, the crack propagation is unstable so that the tensile crack propagation stress (σcd)t and the peak tensile strength σt are almost identical to the tensile crack initiation stress (σci)t. On the other hand, the crack growth after crack initiation is stable under a predominantly compressive condition. Additional loading is required in compression to bring the stress from the crack initiation stress σci to the peak strength σc. It is proposed to estimate the tensile strength of strong brittle rocks from the strength ratio of $$ R = {\frac{{\sigma_{\text{c}} }}{{\left| {\sigma_{\text{t}} } \right|}}} = 8{\frac{{\sigma_{\text{c}} }}{{\sigma_{\text{ci}} }}}. $$ The term $$ {\frac{{\sigma_{\text{c}} }}{{\sigma_{\text{ci}} }}} $$ accounts for the difference of crack growth or propagation in tension and compression in uniaxial compression tests. $$ {\frac{{\sigma_{c} }}{{\sigma_{ci} }}} $$ depends on rock heterogeneity and is larger for coarse grained rocks than for fine grained rocks. σci can be obtained from volumetric strain measurement or acoustic emission (AE) monitoring. With the strength ratio R determined, the tensile strength can be indirectly obtained from $$ \left| {\sigma_{\text{t}} } \right| = {\frac{{\sigma_{\text{c}} }}{R}} = {\frac{{\sigma_{\text{ci}} }}{8}}. $$ It is found that the predicted tensile strengths using this method are in good agreement with test data. Finally, a practical estimate of the Hoek–Brown strength parameter mi is presented and a bi-segmental or multi-segmental representation of the Hoek–Brown strength envelope is suggested for some brittle rocks. In this fashion, the rock strength parameters like σt and mi, which require specialty tests such as direct tensile (or Brazilian) and triaxial compression tests for their determination, can be reasonably estimated from uniaxial compression tests. [ABSTRACT FROM AUTHOR]

Summary  Discontinuities or joints in the rock mass have various shapes and sizes. Along with the joint orientation and spacing, the joint persistence, or the relative size of the joint, is one of the most important factors in determining the block sizes of jointed rock masses. Although the importance of joint persistence on the overall rock mass strength has long been identified, the impact of persistence on rock strength is in most current rock mass classification systems underrepresented. If joints are assumed to be persistent, as is the case in most designs, the sizes of the rock blocks tend to be underestimated. This can lead to more removable blocks than actually exist in-situ. In addition, a poor understanding of the rock bridge strength may lead to lower rock mass strengths, and consequently, to excessive expenditure on rock support. In this study, we suggest and verify a method for the determination of the block sizes considering joint persistence. The idea emerges from a quantitative approach to apply the GSI system for rock mass classification, in which the accurate block size is required. There is a need to statistically analyze how the distribution of rock bridges according to the combination of joint orientation, spacing, and persistence will affect the actual size of each individual block. For this purpose, we generate various combinations of joints with different geometric conditions by the orthogonal arrays using the distinct element analysis tools of UDEC and 3DEC. Equivalent block sizes (areas in 2D and volumes in 3D) and their distributions are obtained from the numerical simulation. Correlation analysis is then performed to relate the block sizes predicted by the empirical equation to those obtained from the numerical model simulation. The results support the concept of equivalent block size proposed by Cai et al. (2004, Int. J. Rock Mech. Min. Sci., 41(1), 3–19). [ABSTRACT FROM AUTHOR]