ISRM Research Articles

The circular disc under rotational moment and friction: application to the cracked Brazilian disc test

Indications from literature suggest that a centrally cracked circular disc subjected to diametral loading exhibits a rigid body rotation tendency due to the inherently asymmetric nature of the displacement field developed (unless the load line is either along the crack or normal to it). In turn, this rotation tendency imposes a counterbalancing distribution of friction stress along the loaded arcs of the disc’s periphery. As a result, parasitic stresses are developed perturbing the stress field developed by the main stimulus (i.e. the diametral compressive load). In this context, a first attempt is described here for the quantification of this perturbation, by considering an intact finite elastic circular disc acted by a central rotational moment and a statically equivalent distribution of counterbalancing friction stresses. The latter are assumed as parabolically distributed along the loaded arcs of the disc’s periphery. Using the complex potentials technique, the parasitic stress field is determined in closed form all over the disc and its main features along strategic loci are explored. This field is then compared to the main stress field produced by the radial pressure, assuming that the disc is compressed between the jaws of the device suggested by the International Society for Rock Mechanics for the standardised implementation of the Brazilian disc test. It is concluded that the perturbation of the main stress field in the vicinity of the disc–jaw interface cannot be neglected: locally, the parasitic stresses are well comparable to the respective ones of the main field. Along this direction, a mixed fundamental problem is then formulated and solved permitting quantification of the central rotational moment by means of the couple of forces produced by the displacement field along the lips of a central crack in a disc radially loaded by uniform pressure.

Influence of rock cradle block geometry on rebound hardness

The Schmidt hammer (SH) testing of cylindrical rock cores requires the use of a cradle block (core holder) to hold the cores firmly during the test. For this purpose, the related International Society for Rock Mechanics (ISRM)-suggested method and American Society for Testing and Materials (ASTM) standard suggest the use of an ‘arch-shaped’ or a ‘V-shaped’ cradle block. However, there is little or no detailed quantitative information in the literature regarding the potential influence of cradle block type on the measured rebound values (R values). With this in view, an investigation was carried out regarding the influence of cradle block geometry on R values, by employing the two cradle blocks specified in the preceding Standards. Using an L-type Digi-Schmidt hammer, SH tests were performed on NX-size cylindrical cores of 20 different rock varieties, both in ‘oven-dry’ and ‘wet’ state. Although the observed differences were usually small, results showed that the magnitudes of the mean rebound values determined in the arch-shaped block (R A) were higher than those determined in the V-shaped block (R V), except in one case. For the oven-dried samples, lowest and highest differences between the means of R A and R V values were 0.37 and 5.92, respectively. In the case of wet samples, the differences ranged from a low of 0.33 to a high of 4.70 in R-units. Statistically significant positive linear correlations were observed between R A and R V values, although the degree of correspondence was relatively lower for rocks having uniaxial compressive strength <50 MPa. The results of additional SH tests carried out on two different engineering materials also indicated that higher mean rebound values could be attained in the arch-shaped block. The results of the present study did not confirm the findings of a previous study where it was found that the V-shaped cradle block gave consistently higher mean rebound values than the arch-shaped one. The possible reasons for this discrepancy were discussed.

Numerical Observation of Three-Dimensional Wing Cracking of Cracked Chevron Notched Brazilian Disc Rock Specimen Subjected to Mixed Mode Loading

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by International Society for Rock Mechanics for measuring mode I fracture toughness of rocks. Subsequently, this specimen geometry has been widely extended to conduct mixed mode fracture tests on rocks as well. A straight through crack front during the fracturing process upon the root of the chevron notch is assumed in the testing principle, but has never been thoroughly evaluated before. In this study, for the first time, the progressive rock fracture mechanism of the CCNBD rock specimen under mixed mode loading is numerically simulated. Specimens under representative mixed mode loading angles are modelled; and the assumption of the straight through crack front growth is critically assessed. The results show that not only the notch tip but also the saw-cut chevron notch cracks during the experiments, yielding a prominent twisted front, far from being straight. The crack front never grows up to the root of the notch ligament and the straight through crack front assumption is never satisfied in the realistic rock fracture progress of this chevron notched specimen subjected to mixed mode loads. In contrast, the fracture progress features typical three-dimensional wing cracking towards the loading ends. The numerically observed progressive fracture mechanism reveals that the measuring principle of mixed mode fracture tests employing CCNBD specimens is significantly violated and the measures of both modes I and II fracture toughness are uncertain.

Critical Aspects of the Cracked Brazilian-disc test Explored by the Method of Caustics

Some critical aspects of the cracked Brazilian-disc test are explored in the light of recently introduced analytic solutions for the stress- and displacement-fields developed in a centrally cracked cylindrical disc under uniform pressure (acting along two finite arcs of its periphery symmetric with respect to the disc's center). The study is focused to the reliable determination of the respective Stress Intensity Factors (SIFs) and also to the role of the actual boundary conditions along the disc-jaw contact arc (assuming that the disc is compressed between the curved jaws of the device suggested by the International Society for Rock Mechanics (ISRM) for the standardized implementation of the Brazilian-disc test). The crack is assumed relatively short with respect to the disc's radius. The results of the analytic approach concerning the SIFs and the length of the disc-jaw contact arc are compared to the respective ones obtained experimentally using the method of Caustics. The agreement is satisfactory at least for load levels for which the linearity assumption is not violated. Taking advantage of the insight gained additional issues related to the validity of the test as a mean to determine mode-I fracture toughness are critically discussed revealing that quite a few questions are still open although the test is standardized by ISRM almost since 20 years.

Fracture Toughness Determined by the Centrally Cracked Brazilian-Disc Test: Some Critical Issues in the Light of an Alternative Analytic Solution

Abstract The centrally cracked Brazilian-disc test is among the configurations proposed for the experimental determination of fracture toughness of brittle rock-like materials. In spite of its wide use and the fact that the test is already standardized by the International Society for Rock Mechanics (ISRM), quite a few issues are still open related especially to the exact expressions of the respective stress intensity factors (SIFs) and the actual shape of the crack during loading. The latter is crucial since for specific crack inclinations, the crack lips are coming in contact and contact stresses appear which alter the boundary conditions, rendering analytic solutions erroneous. In this context, an alternative analytic approach is here introduced assuming that the cracked disc is under uniform pressure along two finite symmetric arcs of its periphery. The main advantage of the present approach is that it provides physically acceptable results independently of whether the crack is under opening- or closing-mode. The results of the analysis are validated against experimental data obtained using the method of Caustics and the Digital Image Correlation (DIC) technique. Based on the analytic solution, some critical practical aspects of the cracked Brazilian-disc test are explored including the influence of the loading type and the length of the loaded arc, the role of the specimen's thickness, the range of crack inclination angles for which generation of contact stress is unavoidable, and the rotation of the crack axis. Moreover, a redefinition of the SIFs in case of Mixed Fundamental problems is proposed. The limitations of the analysis are critically considered and finally some thoughts about the future steps concerning the fracture toughness determination using the cracked Brazilian-disc test are discussed.

Numerical Analysis of Plate-Load Test Results on Fractured Rocks Using an Equivalent-Continuum Model: Case Study of the Bakhtiary Dam Site

AbstractThe plate-load test (PLT) is widely performed at large dam sites to determine the rock mass deformability. Analytical relations based on the theory of elasticity, as suggested by the International Society for Rock Mechanics and the American Society for Testing and Materials test standards, are commonly used to interpret the test results and calculate the rock mass deformation modulus. However, because of inconsistency of the test gallery geometry with the half-space medium assumption embedded in the analytical relations, a systematic error occurs in the calculation of the deformation modulus. Furthermore, when the tests are conducted on jointed rock masses, the test results show a considerable scatter, mainly due to the anisotropy of the deformability of jointed rock masses. In this paper, numerical modeling is used to interpret the results of a series of PLTs conducted at the Bakhtiary dam site in southwest Iran. An equivalent continuum model, called JointedRock, is used to back-calculate the sti...

Numerical Assessment of the Progressive Rock Fracture Mechanism of Cracked Chevron Notched Brazilian Disc Specimens

The International Society of Rock Mechanics (ISRM) suggested cracked chevron notched Brazilian disc method falls into a major testing category of rock fracture toughness measurement by virtue of chevron notched rock samples. A straight through crack front during the whole fracturing process is assumed in the testing principle but is never assessed. In this study, the progressive rock fracture mechanism of cracked chevron notched Brazilian disc rock specimens is numerically simulated for the first time. Two representative sample types with distinct geometry of notch ligaments are modelled. The assumption of a straight through crack front for chevron notched fracture samples is critically assessed. The results show that not only the notch tip but also the saw-cut chevron notch cracks during the experiments. The straight through crack front assumption is never satisfied in the realistic rock fracture progress of chevron notched disc samples. In addition, the crack features prominent curved front, far from being straight. In contrast to the sample type with narrow notch ligament, the acoustic emission (AE) of the simulation on the sample with wide notch ligament depicts obvious biased fracturing of the prescript fracturing route of the notch. The numerically observed progressive fracture mechanism calls for more attention on how to accurately calibrate the critical dimensionless stress intensity factor for a better measurement of Mode I fracture toughness via chevron notched samples.

Application of Digital Image Correlation (DIC) in Dynamic Notched Semi-Circular Bend (NSCB) Tests

Notched semi-circular bend (NSCB) specimen has been successfully used in fracture tests of brittle materials. As a suggested method for measuring the dynamic fracture toughness of rocks by the International Society for Rock Mechanics (ISRM), this method only measures the fracture initiationtoughnessofthesamplewithgivenexternalloadand geometrical parameters. Using the digital image correlation (DIC) method combined with ultra-high speed photography, the objective of this paper is to measure more fracture param- eters of the NSCB specimen loaded by a split Hopkinson pressure bar (SHPB) system. The displacement and strain fields during the fracture propagation process were deter- mined using DIC method. The location of the crack tip, the fracture initiation toughness and the fracture propagation toughness were subsequently calculated using the deforma- tion fields. Compared with the traditional NSCB tests, the optical method of DIC provides much more information on the fracture propagation process.

Evaluation of Mode I Fracture Toughness Assisted by the Numerical Determination of K-Resistance

The fracture toughness of a rock often varies depending on the specimen shape and the loading type used to measure it. To investigate the mode I fracture toughness using semi-circular bend (SCB) specimens, we experimentally studied the fracture toughness using SCB and chevron bend (CB) specimens, the latter being one of the specimens used extensively as an International Society for Rock Mechanics (ISRM) suggested method, for comparison. The mode I fracture toughness measured using SCB specimens is lower than both the level I and level II fracture toughness values measured using CB specimens. A numerical study based on discontinuum mechanics was conducted using a two-dimensional distinct element method (DEM) for evaluating crack propagation in the SCB specimen during loading. The numerical results indicate subcritical crack growth as well as sudden crack propagation when the load reaches the maximum. A K-resistance curve is drawn using the crack extension and the load at the point of evaluation. The fracture toughness evaluated by the K-resistance curve is in agreement with the level II fracture toughness measured using CB specimens. Therefore, the SCB specimen yields an improved value for fracture toughness when the increase of K-resistance with stable crack propagation is considered.

Effects of temperature and confining pressure on mixed-mode (I–II) and mode II fracture toughness of Kimachi sandstone

1. IntroductionFracture mechanics is becoming increasingly important insolving problems relating to rock strength in mining engineeringand civil engineering. For example, fracture mechanics can be usedfor the design of hydraulic fracturing for geothermal energy, oiland natural gas recovery [1–4], as well as for the analysis of rockmass stability in slopes or those associated with excavations [5,6],and determining rock fragmentation by blasting or in the event ofrock burst [7,8].Therefore, it is desirable to investigate the fracture toughness,which is an important rock property that characterizes its fracturebehavior. In this investigation, fracture toughness was determinedat elevated pressures and temperatures simulating the conditionsprevailing underground. A number of test specimen configurationsand methods have been suggested to determine the fracturetoughness of rock materials. The International Society for RockMechanics (ISRM) has incorporated the chevron-notched bendspecimen [9], the short rod specimen [10] and cracked chevron-notched Brazilian disc (CCNBD) specimen [11] into the standardmethod for measurement of the fracture toughness of rock. Thesemi-circular bend (SCB) specimen proposed in [12,13] is com-plementary to the standard method (Fig. 1).Natural crack propagation occurs as a result of the develop-ment and coalescence of tensile and shear cracks. The geometryand loading are defined as mode I (tensile mode), mode II(in-plane shear), mode III (anti-plane shear) crack propagation,and mixed modes of mode I, II, and III. Previous studies on thefracture toughness of rock were mostly focused on mode I crackpropagation. However, actual crack propagation in rock massoccurs not only in tensile mode but also as part of in-plane shearmode. Mode II fracture toughness and the critical stress intensityfactors in mixed mode (I–II) are crucial to gain understanding intorock fracturing. SCB specimen and Cracked Straight ThroughBrazilian Disc (CSTBD) specimen [14] have been used for evaluat-ing mode II and mixed mode fracture toughness of rock, and thePunch-Through Shear test (PTS) specimen [15] has been developedto evaluate mode II fracture toughness of rock. Furthermore, thePTS specimen is adopted as an ISRM suggested method. Conse-quently, many researchers have investigated the mixed mode (i.e.mode I and mode II) and pure mode II fracture toughness of rock[16–23]. In terms of the ratio of mode II fracture toughness, K

A combined analytic and experimental study of the displacement field in a circular ring

An analytic solution for the displacement field developed in an elastic homogeneous circular ring is described assuming that the ring is subjected to diametral pressure which is not constant but rather it varies according to a parabolic law along the contact arcs. The solution is achieved by using Kolosov’s-Muskhelishvili’s complex potentials method. The length of the contact arcs, which is of crucial importance for the application of the analytic solution, is experimentally determined with the aid of a recently introduced modified version of the reflected caustics technique. The overall validity of the solution is experimentally assessed by comparing its predictions against the respective results obtained experimentally using the Digital Image Correlation (DIC) technique. For the implementation of both experimental protocols the device suggested by the International Society for Rock Mechanics (ISRM) for the standardized realization of the Brazilian-disc test was used. The agreement between theory and experiment is found satisfactory as long as the linearity assumption is not violated. The same is true for the comparison between the experimental data obtained from the Reflected Caustics method with those obtained by the DIC technique concerning the length of the contact arc. Based on the analytic solution some critical aspects of the ring test (proposed as a potential substitute of the Brazilian-disc test almost half a century ago by Hobbs) are explored by studying the variation of the displacements along some strategic paths of the ring.

Numerical Simulation of the Rock SHPB Test with a Special Shape Striker Based on the Discrete Element Method

A split Hopkinson pressure bar (SHPB) system with a special shape striker has been suggested as the test method by the International Society for Rock Mechanics (ISRM) to determine the dynamic characteristics of rock materials. In order to further verify this testing technique and microscopically reveal the dynamic responses of specimens in SHPB tests, a numerical SHPB test system was established based on particle flow code (PFC). Numerical dynamic tests under different impact velocities were conducted. Investigation of the stresses at the ends of a specimen showed that the specimen could reach stress equilibrium after several wave reverberations, and this balance could be maintained well for a certain time period after the peak stress. In addition, analyses of the reflected waves showed that there was a clear relationship between the variation of the reflected wave and the stress equilibrium state in the specimen, and the turning point of the reflected wave corresponded well with the peak stress in the specimen. Furthermore, the reflected waves can be classified into three types according to their patterns. Under certain impact velocities, the specimen deforms at a constant strain rate during the whole loading process. Finally, the influence of the micro-strength ratio ( $${{\tau_{\text{c}} } \mathord{\left/ {\vphantom {{\tau_{\text{c}} } {\sigma_{\text{c}} }}} \right. \kern-0pt} {\sigma_{\text{c}} }}$$ ) and distribution pattern on the dynamic increase factor (DIF) of the strength DIF were studied, and the lateral inertia confinement and heterogeneity were found to be two important factors causing the strain rate effect for rock materials.

Slaking behavior of clay-bearing rocks during a one-year exposure to natural climatic conditions

Slaking of clay-bearing rocks, upon exposure to natural climatic conditions, is a common problem at many engineering projects. Depending upon the regional climate, clay-bearing rocks slake in response to heating and cooling, wetting and drying, and freezing and thawing cycles. However, laboratory methods used for assessing the slaking behavior of clay-bearing rocks, including the standardized methods by the American Society for Testing and Materials (ASTM) and the International Society for Rock Mechanics (ISRM), involve only wetting and drying treatments. In this study, we investigated the slaking behavior of clay-bearing rocks by exposing them to natural climatic conditions for a period of one year.Twenty clay-bearing rocks, consisting of 5 claystones, 5 mudstones, 5 siltstones, and 5 shales, were selected for the study. Twelve replicate samples of each rock type were prepared so that each sample consisted of 10 pieces, each piece weighing 40–60g, with a total weight of 450 to 550g. The samples were placed in separate metallic pans and exposed to natural climatic conditions from September 2009 to September 2010. Each month, one replicate sample of each rock type was removed from natural exposure and its grain size distribution was determined. Disintegration ratio (DR), defined as the ratio of the area under the grain size distribution curve of the slaked material for a given sample to the total area encompassing all grain size distributions, was used to evaluate the extent of disintegration upon slaking. DR can range from 0 to 1, with 0 indicating 100% slaking and 1 indicating no slaking. After 3months of exposure to natural climatic conditions, claystones, mudstones, siltstones, and shales exhibited DR values of 0.223, 0.302, 0.698, and 0.494, respectively. These results suggest that, over a given period of time, claystones slake the most and siltstones the least. Relating DR to clay content of the rocks studied reveals that rocks with higher clay contents slake more rapidly and extensively under natural climatic conditions than those with lower clay contents.

Numerical Homogenization of Jointed Rock Masses Using Wave Propagation Simulation

Homogenization in fractured rock analyses is essentially based on the calculation of equivalent elastic parameters. In this paper, a new numerical homogenization method that was programmed by means of a MATLAB code, called HLA-Dissim, is presented. The developed approach simulates a discontinuity network of real rock masses based on the International Society of Rock Mechanics (ISRM) scanline field mapping methodology. Then, it evaluates a series of classic joint parameters to characterize density (RQD, specific length of discontinuities). A pulse wave, characterized by its amplitude, central frequency, and duration, is propagated from a source point to a receiver point of the simulated jointed rock mass using a complex recursive method for evaluating the transmission and reflection coefficient for each simulated discontinuity. The seismic parameters, such as delay, velocity, and attenuation, are then calculated. Finally, the equivalent medium model parameters of the rock mass are computed numerically while taking into account the natural discontinuity distribution. This methodology was applied to 17 bench fronts from six aggregate quarries located in Tunisia, Spain, Austria, and Sweden. It allowed characterizing the rock mass discontinuity network, the resulting seismic performance, and the equivalent medium stiffness. The relationship between the equivalent Young’s modulus and rock discontinuity parameters was also analyzed. For these different bench fronts, the proposed numerical approach was also compared to several empirical formulas, based on RQD and fracture density values, published in previous research studies, showing its usefulness and efficiency in estimating rapidly the Young’s modulus of equivalent medium for wave propagation analysis.

Smooth elastic contact of cylinders by caustics: the contact length in the Brazilian disc test

The smooth contact of two elastic cylinders compressed against each other along a common generatrix is studied analytically and experimentally. The main objective is the quantification of the length of the contact arc. For the analytic study, the complex potentials method is employed while experimentally the contact arc’s length is determined by extending the reflected caustics technique. A series of experiments are then carried out using the device suggested by the International Society for Rock Mechanics for the standardized implementation of the Brazilian test and the typical set-up of the reflected caustics method. The experimental results are compared to the analytically determined ones. The agreement is satisfactory especially for low load levels, ensuring validity of the linear elasticity assumption.

ISRM-Suggested Method for Determining the Mode I Static Fracture Toughness Using Semi-Circular Bend Specimen

The International Society for Rock Mechanics has so far developed two standard methods for the determination of static fracture toughness of rock. They used three different core-based specimens and tests were to be performed on a typical laboratory compression or tension load frame. Another method to determine the mode I fracture toughness of rock using semi-circular bend specimen is herein presented. The specimen is semi-circular in shape and made from typical cores taken from the rock with any relative material directions noted. The specimens are tested in three-point bending using a laboratory compression test instrument. The failure load along with its dimensions is used to determine the fracture toughness. Most sedimentary rocks which are layered in structure may exhibit fracture properties that depend on the orientation and therefore measurements in more than one material direction may be necessary. The fracture toughness measurements are expected to yield a size-independent material property if certain minimum specimen size requirements are satisfied.

Three dimensional analytical solution for finite circular cylinders subjected to indirect tensile test

This paper derives a new three-dimensional (3-D) analytical solution for the indirect tensile tests standardized by ISRM (International Society for Rock Mechanics) for testing rocks, and by ASTM (American Society for Testing and Materials) for testing concretes. The present solution for solid circular cylinders of finite length can be considered as a 3-D counterpart of the classical two dimensional (2-D) solutions by Hertz in 1883 and by Hondros in 1959. The contacts between the two steel diametral loading platens and the curved surfaces of a cylindrical specimen of length H and diameter D are modeled as circular-to-circular Hertz contact and straight-to-circular Hertz contact for ISRM and ASTM standards respectively. The equilibrium equations of the linear elastic circular cylinder of finite length are first uncoupled by using displacement functions, which are then expressed in infinite series of some combinations of Bessel functions, hyperbolic functions, and trigonometric functions. The applied tractions are expanded in Fourier–Bessel series and boundary conditions are used to yield a system of simultaneous equations. For typical rock cylinders of 54mm diameter subjected to ISRM indirect tensile tests, the contact width is in the order of 2mm (or a contact angle of 4°) whereas for typical asphalt cylinders of 101.6mm diameter subjected to ASTM indirect tensile tests the contact width is about 10mm (or a contact angle of 12°). For such contact conditions, 50 terms in both Fourier and Fourier–Bessel series expansions are found sufficient in yielding converged solutions. The maximum hoop stress is always observed within the central portion on a circular section close to the flat end surfaces. The difference in the maximum hoop stress between the 2-D Hondros solution and the present 3-D solution increases with the aspect ratio H/D as well as Poisson’s ratio ν. When contact friction is neglected, the effect of loading platen stiffness on tensile stress in cylinders is found negligible. For the aspect ratio of H/D=0.5 recommended by ISRM and ASTM, the error in tensile strength may be up to 15% for both typical rocks and asphalts, whereas for longer cylinders with H/D up to 2 the error ranges from 15% for highly compressible materials, and to 60% for nearly incompressible materials. The difference in compressive radial stress between the 2-D Hertz solution or 2-D Hondros solution and the present 3-D solution also increases with Poisson’s ratio and aspect ratio H/D. In summary, the 2-D solution, in general, underestimates the maximum tensile stress and cannot predict the location of the maximum hoop stress which typically locates close to the end surfaces of the cylinder.

GIS-based evaluation of rockfall risk along routes in Greece

This article presents a GIS-based system, designed to assist in the management of rockfall risk along Greek routes. The system was developed in two stages; the field data collection led to the implementation of a rockfall rating system with its fundamental parameters, while the data process concluded to a rockfall data base and a GIS-based interface. The fundamental parameters were derived from the rockfall hazard rating system developed by Pierson et al. at the Oregon State Highway Division and provide a coherent approach to decide the type and the cost of protection measures to be applied in an area affected by rockfalls and presents highest rockfall risk. The system presented in this paper as well as the original system comprises exponential scoring functions that represent the increased hazard and reflected in nine categories forming the classification. The method presented in this paper modified certain categories from the original system which were described qualitatively and may lead to quite subjective estimations. These categories are ditch effectiveness; climate and presence of water on slope as well as rockfall history. Moreover, the original category “Geologic characteristic” was changed to Structural and Discontinuities Index; an index that relates blockiness of rock mass and orientation of joints with their weathering condition and their roughness. This index follows the classification of weathering and joint’s roughness suggested by International Society of Rock Mechanics, while other modifications regarding the categories “decision sight distance” and “roadway width” were applied based on Greek standards. An application of this modified method to a 3 km road which connects Athinios port and Fira, the capital of Santorini island, Greece, a high traffic intensity road where rockfalls periodically cause traffic interruptions is presented. The method was applied in fifteen cross sections of slopes adjacent to the road and the analyses showed increased risk and the need for urgent remedial works.

Point Load Test on Meta-Sedimentary Rocks and Correlation to UCS and BTS

Keywords Point load test Meta-sedimentary rock Uniaxial compressive strength (UCS) Brazilian tensilestrength (BTS) Conversion factor1 IntroductionThepoint loadtest hasbeen consideredasacheap andusefultesting method to estimate the strengths of rocks due to itsease of testing, simplicity of specimen preparation, andpossible field application (Broch and Franklin 1972; Bie-niawski 1975; Kahraman and Gunaydin 2009; Basu andKamran 2010). It has been often reported as an indirectmeasure of the compressive or tensile strength of rocks(Fener et al. 2005;C¸obanog˘lu and C¸elik 2008; Heidari et al.2012; Chau and Wong 1996). Samples can be of variousshapes, including cut cylindrical cores tested axially ordiametrically, cut blocks, or irregular lumps [Brook 1985;International Society for Rock Mechanics (ISRM) 1985;American Society for Testing and Materials (ASTM) 2008].The point load test can be used to test both strong and weakrocks (Hardy 1997; Heidari et al. 2012; Tsiambaos andSabatakakis 2004; Kahraman and Gunaydin 2009). Estab-lishing a proper correlation between the uniaxial compres-sive strength (UCS) and point load strength index (I

Recalibration and Clarification of the Formula Applied to the ISRM-Suggested CCNBD Specimens for Testing Rock Fracture Toughness

The cracked chevron-notched Brazilian disc (CCNBD) was proposed by the International Society for Rock Mechanics (ISRM) to test the mode I (opening mode) fracture toughness of rock. The test method has been vigorously discussed and debated, despite being the subject of intensive research for decades. The minimum (critical) dimensionless stress intensity factors affiliated with the formula for calculating the fracture toughness using CCNBD specimens with different geometric parameters remain elusive and complex. The matter cannot be resolved by simply replacing the diameter in the original formula with the radius, as claimed by several authors. In this paper, the formula is fundamentally improved, as wide-ranging minimum dimensionless stress intensity factors pertaining to diversified CCNBD geometries are recalibrated by three-dimensional finite element analysis, and an expression with tabulated coefficients is obtained through curve-fitting the data obtained from the numerical calibration. The present results are shown to be more accurate than those in the literature. Furthermore, the importance of the reasonability of the results is highlighted; a comprehensive comparison of different values shows that the upper bounds of minimum stress intensity factors are violated by the above claim. The confusion resulting from the claim is, thus, clarified conclusively.