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The possibility of testing irregular lumps under the point load strength test (PLST) was investigated theoretically and experimentally. In particular, a new analytical solution for stress d...

This study considers the effects of cyclic differential heating on the velocity of the subcritical crack growth (SCG) from a central notch in rock beams under four-point bending test. Beams of both Carrara marble and Fujian granite are subjected to non-uniform heating, with heating from the top surface containing the notch (at about 60° Celsius) and with cooling to the bottom side with no notch (at about 25° Celsius). Beams are heated for 7–188 days before they are subject to constant load creeping test under four-point bending configuration, and the compliance method is used to interpret crack growth from the crack mouth opening displacement (CMOD). The compliance method is verified by using acoustic emissions from cracking events together with simultaneous microscopic observations. It was discovered that a microcrack processing zone (PZ) was observed in the form of white patches ahead of the notch tip during the creeping test, followed by sudden jumps of macrocrack growth. Linear elastic fracture mechanics (LEFM) is used to calculate the local stress intensity factor, which is then further related to crack growth velocity, through the commonly adopted power law. After the application of non-uniform cyclic heating, the P-wave velocity of Fujian granite increases (due to microcrack closure) whilst that of Carrara marble decreases (due to parallel crack formation). The SCG parameters in the power law (power index n and threshold velocity v0) are obtained. There is no clear trend in the variation of the SCG parameters with the number of heating cycles. However, these parameters are used to simulate subcritical crack growth velocity for both heated and unheated specimens. In the light of fracture mechanics analysis, we conclude that Fujian granite is clearly preferable to Carrara marble in making rock panels on cladding of buildings.

This study investigates the changes in the ultrasonic and mechanical properties of a rock, by means of ultrasonic wave velocity measurements on a brittle limestone containing natural fractures and bedding subjected to uniaxial compression tests . The results showed that natural fractures and bedding reduced the velocity of ultrasonic waves and the mechanical strength of the limestone. Combined with the analysis of X-ray CT images of the samples, we found that the orientations of the bedding and of the pre-existing penetrating fractures affected the direction of subsequent crack propagation under uniaxial compressional loading. The initial disturbance factor D and the intactness factor s were calculated through the use of equivalent medium theory and Hoek–Brown strength model. The relationship between s and D was empirically characterized by an exponential fitting. A parameter b was introduced that can be calculated from the s–D relationship. This parameter represents a strength index for the pre-existing natural fractures. Based on the value of b, the limestones studied were classified into four types: fissures and bedding, infilled fractures and bedding, main infilled fractures, and nearly intact.

This study investigated the change of stress with crack development, using the numerical code RFPA3D, so as to understand the crack coalescence mechanisms occurring within a heterogeneous solid containing multiple holes loaded in a state of uniaxial compression. A full discussion is presented on a statistical analysis of observed microcracks data, and on the appropriate parameter selection based on those microcrack statistics. The simulated peak stress results and coalescence patterns using the selected parameters were found to closely resemble previous experimental observations. A full investigation and discussion of the stress distributions around holes during the crack growth and coalescence processes is presented for heterogeneous sample cases. Under applied loading, crack initiation, growth direction and coalescence pattern are strongly influenced by the shape of the interaction tensile zone formed between holes. Acoustic emission (AE) analysis in relation to the numerical simulations indicates that no case of pure tensile crack coalescence occurs between holes. Three modes of coalescence are classified: Ts mode (tensile mode coalescence with shear), MT mode (mixed mode coalescence with tensile mode dominant) and M mode (mixed mode coalescence). The crack coalescence mechanisms and patterns were further investigated by changing the parameters of normalized bridge length (d/r), bridge angle β and number of holes. A precise crack coalescence criterion is proposed.

The instability problem in the presence of multiple openings is complicated, depending not only on the in situ stress field and the rockmass geological condition, but also on the size, distribution and the distances between the multiple openings. The aim of the experimental study presented in this paper is to examine crack initiation and coalescence mechanisms and failure behaviour in a granite material containing multiple holes under uniaxial compression. In this paper, the holes distribution in the samples were varied between array modes to random mode with varied hole separation distances ‘ d ’ (or bridge length), bridge angles ‘ β ’ (angle between the line connecting the centres of two holes and the axial loading direction), hole diameter ‘2 r ’, and the number of holes in the specimen. The hole distribution strongly affects the stress for crack initiation, coalescence and peak value, and the scence patterns. The coalescence mechanisms for multiple hole samples depend on the bridge angle β and the normalized bridge length d / r . A criterion for coalescence mechanism related to holes distribution is proposed. The modified Sammis and Ashby (1986) [36] crack model can predict the peak stress and agree well with the experiment. Results analysis shows that peak stress depends primarily on number of holes coalescence, which is then used to effectively determine the hole defects ensuring integral stability of rockmass around tunnel.

Brittle solids, such as rock or concrete, may contain numerous randomly distributed micro-flaws (e.g. cracks, pores or weak inclusions). When they are loaded in compression, cracks may nucleate from these flaws. These cracks then continue to grow in a stable manner with the increasing axial compression, curving toward an orientation parallel to the direction of axial compression. Their propagation and interaction may lead to the collapse of the solid in a splitting mode. With a newly developed numerical code, MFPA2D (material failure process analysis), heterogeneous solids containing pre-existing single, triple and multi-pore-like flaws are numerically tested to study the mechanisms of compression-induced axial splitting. The interaction of growing cracks with the surfaces of the specimen and with each other in terms of stress field and failure modes is numerically analyzed in detail. Under uniaxial compressions, specimens containing holes in a diagonal array are more conducive to interaction than specimens containing holes arranged either in a horizontal or vertical array. Various parameters, such as hole diameter, specimen width, and the geometrical arrangement of hole locations, that characterize the growth process are quantified. Numerical results mimic the phenomena of experimentally observed splitting failure in brittle solids such as rocks in a realistic way.

The purpose of this study is to investigate experimentally the creeping damage and failure mechanism around an opening in rock-like material containing non-persistent joints. The jointed rock-like specimen is modelled by plaster material, and the underground excavation is simulated by drilling at a certain stress level. In our experimental studies, time evolutions of deformation are recorded at various applied vertical (σ1) and confining (σ3) stress. It is found that with a fixed σ1, tensile mode of creeping failure is dominant when the λ (σ3/σ1) is low (λ=1/3). But when λ is high (⩾1/2), shear mode of creeping failure is dominant. The creeping failure time decreases with the increased λ and stress ratio of σ1/σ1max (σ1max is the maximum stress of a jointed rock-like mass). Furthermore, for the excavation in a low stress level (σ1/σ1max⩽45%), no creeping damage around opening will occur. The stress ratio λ and σ1/σ1max are the important indices indicating the degree of instability of an opening after excavation.

Splitting failure of rock specimen containing pre-existing crack-like flaws under compression is numerically investigated using Rock Failure Process Analysis (RFPA2D). Crack growth from single, triple and multi-crack-like flaws contained in numerical specimens are studied. The analysis of parameters, such as angle and length of the flaws, specimen width and the arrangement of flaw locations, is conducted to examine its influence on the growth and coalescence behaviour. Flaw length, flaw location and stress interaction between the nearby flaws are found to be important factors affecting the behaviour of crack initiation, propagation and coalescence.

This paper presents experimentally obtained results for the coefficient of restitution for spherical boulders impacting on rock slopes. Plaster modeling material is used for casting both the boulders and slopes. It is observed that the normal component of the coefficient of restitution ( R n ) increases with the slope angle α , which agrees with Wu's observations (Trans. Res. Rec. 1–5 (1985) 1031). However, there appears to be no clear correlation between the tangential component of the coefficient of restitution ( R t ) and the slope angle α . When the ratio of the resultant velocities and the ratio of the kinetic energies before and after impacts are used to define the coefficient of restitution (i.e. R V and R E ), a very clear increasing trend in the coefficient of restitution with α is observed. When all data are plotted onto the R t − R n space, our laboratory data fall into the rock slope regime proposed by Fornaro et al. (In: D.G. Price (Ed.), Proceedings of the Sixth International Congress IAEG, Amsterdam, Balkema, Rotterdam, 1990, p. 2173) and also agree with those data gleaned from literature. In addition, the rotational kinetic energy E r , induced at each impact, increases with the slope angle α , achieves a maximum at about α =40°, before decreasing again to a negligible value at α =70°. A simple theoretical model is proposed to explain this observation based on the locking between the boulder and the slope during impact. The α -dependence of E r differs from the recommendation by the Japanese Railway Association that the induced rotational energy is about 10% of that of the translational kinetic energy.

Fractures in the forms of joints and microcracks are commonly found in natural rocks, and their failure mechanism strongly depends on the crack coalescence pattern between pre-existing flaws. However, the crack coalescence pattern of rock specimens containing three or more flaws has not been studied comprehensively. In this paper, we investigate experimentally crack coalescence and peak strength of rock-like materials containing three parallel frictional flaws. Three flaws are arranged such that one pair of flaws lines collinearly and the third flaw forms either a non-overlapping pattern or an overlapping pattern with the first flaw. It is found that the mechanisms of crack coalescence depend on the flaw arrangement and the frictional coefficient μ on the flaw surface. Two “rules of failure” for the specimens containing three flaws are proposed. Rule No. 1: the pair of flaws with a lower value of coalescence stress will dominate the process of coalescence. Rule No. 2: mixed and tensile modes of coalescence are always the dominant modes if the coalescence stress of the two pairs of flaws is very close (say within 5%). In addition, it is found that the peak strength of the specimens does not depend on the initial crack density but on the actual number of pre-existing flaws involved in the coalescence. Comparisons of pattern of crack coalescence with the numerical approach are given in Part II of this study, and the two results agree well. The research reported here provides increased understanding of the fundamental nature of rock failure in uniaxial compression.

This paper presents a new analytic solution for the stresses within an elastic solid finite cylinder subjected to the axial point load strength test (PLST). The displacement potential approach is used to uncouple the equations of equilibrium; then the contact stresses on the end surfaces induced by the point load indentors are expanded in terms of a Fourier-Bessel expansion to yield the unknown constants of the appropriate form of the displacement potential. The solution shows that a zone of higher tensile stress is developed in the vicinity of the applied point loads, compared with the roughly uniform tensile stress in the central portion of the line between the two point loads. This peak tensile stress within the cylinder decreases with increasing Poisson's ratio and the size of the loading area, and it increases with increasing Young's modulus. The tensile stress distributions along the axis of symmetry in a cylinder under the axial PLST are remarkably similar to that observed in a sphere under the diametral PLST. The solution also demonstrates both size and shape effects on the point load strength index (PLSI) that was observed in these experiments. In particular, for a fixed length-to-diameter ratio, the larger the specimen, the smaller the PLSI; whereas for a fixed diameter, the longer the specimen the smaller the PLSI.

This paper investigates the pattern of crack coalescence and strength of a sandstone-like material containing two parallel inclined frictional cracks under uniaxial compression, with changing values of inclination of preexisting cracks α , bridge angle β (inclination between the inner tips of the two preexisting cracks), and the frictional coefficient μ on the surfaces of the preexisting cracks. Three main modes of crack coalescence are observed: the shear (S) mode (shear cracking between the two preexisting cracks); the mixed shear/tensile (M) mode (propagation of both wing and shear cracks within the bridge area); and the wing tensile (W) mode (coalescence of wing cracks from the tips of the preexisting cracks). The M-mode and W-mode of crack coalescence can further be divided into two and six types, respectively. Simple regime classifications of coalescence in the α – β space are proposed for different values of μ (=0.6, 0.7 and 0.9). In general, the S-mode mainly occurs when α=β or when β β *( α , μ )=a−b α , with both a and b depending on μ ; the M-mode dominates when β L > β > β *( α , μ ) (where β L ≈82.5°); and the W-mode is only observed when β > β L . However, more experiments are still required to refine the classification. The observed peak strength, in general, increases with μ . Our results show that the peak strength predicted by the Ashby and Hallam (1986) model basically agrees with experiments. A minimum occurs at about α =65° when the peak strength is plotted against α . For α >45°, the peak strength is essentially independent of the bridge angle β .

Summary We do not think the conclusion by Drs Irfan and Cheung that the strength-index conversion factor is about 24 for Hong Kong rocks is fully justified, at least not at this moment. The claim that “a substantial amount of test data available particularly on granitic and volcanic rocks and marble” is not substantiated by evidence. In particular, as discussed in Section (2)(iii) above, the valid number of available data summarized by Drs Irfan and Cheung for Hong Kong rocks is, actually, in the same order of those tested and presented by us [9]. Further studies are still needed before a conclusive statement can be made. Actually, a comprehensive experimental and theoretical programme has been proposed and funded recently. Therefore, a thorough study will be carried out shortly to verify the preliminary finding by us [1]. In conclusion, we think that we should be more sceptical about all empirical formulae devised based upon a particular set of data and should not adopt indiscriminately such formulae in Hong Kong or elsewhere without sufficient experimental and theoretical verification. Especially, for the present case that the adopted value of 24 may actually overestimate the strength prediction. Nevertheless, we wish to thank Drs Irfan and Cheung for initiating this discussion which, we are sure, will be useful to the rock mechanics community and should provide stimulus for further scientific research and progress in this area of rock mechanics.

This paper compares and contrasts the predicted effective moduli by the self-consistent and noninteracting methods and examines the range of validity for both models; predictions by these two models are compared to experimental observations on natural rocks containing microcracks and artificial rocks containing inserted microcracks. Crack density (e) in real rocks is obtained by counting cracks under microscope and those in replicated rocks is, of course, predetermined; these crack densities are then compared to the crack densities interpreted from the changes in ultrasonic wave speeds, using either self-consistent model or noninteracting crack model. For natural rocks, the noninteracting prediction seems to agree better with experiments than the self-consistent method for E c 0.2, but both theoretical predictions deviate from experimental observation for e > 0.2. For replicated rocks, both theories give prediction comparable to experiments for E c 0.2, but underestimate the actual value for e > 0.2. Therefore, a better damage model is needed for solids with crack density larger than 0.2.

This paper investigates the mechanism of crack coalescence and peak strength of rock-like materials containing parallel frictional cracks under uniaxial compression loading. The specimens used in this study are the sandstone-like material proposed by Wong, Chau 1997 and are containing different number of parallel frictional cracks ranging from two to forty-two parallel cracks. Various values of inclination of preexisting cracks α, bridge angle β (inclination between the inner tips of the two preexisting cracks) and the frictional coefficient μ are used for parametric studies. Two “rules of failure” for the speciments containing three cracks are proposed, and it is being tested with our results. In particular, we found that only crack coalescence between two cracks will occurs (not three) and the pair of cracks with a lower value of peak strength (as predicted by the results of Wong, Chau 1997) will dominate the process of coalescence; and that the mixed and tensile modes of coalescence are the preferential modes and the preferred orientation for crack coalescence is 75°. In contrast to the observation by Horri, Nemat-Nasser 1985 for specimens made of resin, shear zone can also be formed in our specimens containing 18 and 42 cracks under uniaxial compression. In addition, we found that the peak strength of the specimens does not depend on the initial crack density but depends on the actual number of cracks involved in the coalescence. This result provides a plausible explanation for our previous observation (Wong et al. 1996) that the peak strength in Yuen Long marbles does not decrease with the increase of the initial crack density as a threshold value is exceeded.