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The Uniaxial Compressive Strength (UCS) of rock cores is a key parameter for design analysis of rock engineering projects such as rock tunnels and piles in rockets. Diametral and axial point load tests on cylinder cores have been used to obtain Point Load Strength Index (PLSI). This PLSI is correlated to UCS. Recently, point load tests on irregular lumps are also used to obtain PLSI which is then correlated to UCS. However, the data on this correlation are very limited, especially for Hong Kong rocks. This paper presents the methodology for specimen preparation, testing, and data analysis. Results from irregular lump point load tests, diametral and axial point load tests, and uniaxial compressive tests (a total of 754 specimens of granitic rocks were tested) are then presented, analyzed, and discussed. A correlation between PLSI from irregular lump tests and UCS is established with a suitable size correction function. It is found that the I s(50) of the slightly decomposed Granite is between 7.31 MPa and 8.5 MPa. The I s(50) of the altered rock is 2.35 MPa, where the rock containing weakness plane is 5.59 MPa. The moderately decomposed Granite varies from 2.28 MPa to 4.92 MPa. The weathering affected the PLIS a lot. It is found that the values of power index value m in the size correction function is 0.443–0.600 for slightly decomposed granite (fine to coarse grains) and 0.545–5.562 for moderately decomposed granite (fine to medium and medium grains). Based on our study, for slightly decomposed coarse grain and fine to medium grain Granite, the size correction factor F = ( D e /50) 0.44 (lower bound) is recommend; while for all other weathering conditions and grain sizes, the size correction factor F = ( D e /50) 0.55 (lower bound) is recommended. The correlation between the UCS and PLSI Is (50) of irregular lumps is found to be 22.27, which is very close to the values of 21.61 and 21.72 for diametral and axial PL tests using the size correction factor of F = ( De /50) 0.45 . This indicates that the correlation between UCS and PLSI from point load tests on irregular lumps established in this paper is reliable.

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.

Under extra compressive stress, some phenomena of rock spallings and fractures often exist on rock mass located in sidewalls of underground house and tunnels. It is the reason that the crack growth and coalescence initiation from original flaws (or faults) in rock mass. In the previous studies, many researchers took a flaw as a through flaw (2-dimentional model), but the flaws are not always through the whole rock mass in fact, most of them are only near the surface of rock mass, These are so named as surface flaws. They belong to three dimensional (2-D) flaws. Now, the reports on initiation and growth of 3-D surface flaw are few. So, for the investigation on growth patterns of 3-D surface flaw, a series of samples containing a surface flaw were carried out using frozen casting resin material at about -30°C temperatures. The surface flaw was made of a polyester film was used to model a single closed flaw on rock mass. The experimental results show that the wrapping wing crack (Mode I) initiated at the ends (or tips) of surface flaw first, and then formed a kinking zone (mixed crack zone) at a certain place at the middle of surface flaw region. Some petal cracks (Mode III) and shell-shaped cracks (Mode III) would grow at the middle place of flaw. A big fin crack (Mixed Mode) also emerged in middle of flaw and grown along loading direction. Finally, a team of large cracking curved faces deformed inside the resin specimen; the whole specimen would be splitted off by the initiation and growth of the cracks. The reasons lead to the fracture patterns of 3-D closed surface flaw were provided with brittle fracture mechanics theory in the article, preliminarily.

This paper presents the crack growth mechanism from a 3-D surface flaw on gabbro specimens using strain measurement and acoustic emission (AE) technique. Based on the results of strain and AE measurement, microcracks initiated inside the rock and extend to the surface of the specimen. With the observation from the measurements, four types of crack patterns initiate wing crack, anti-wing crack (opposite direction of wing crack), petal crack and compressive crack. The strain values of anti-wing cracks are larger 1 to 2 times than that of wing crack. The AE energy release from anti-wing crack is higher 2.5 times than that of wing crack, while the energy release form wing crack is the least but the compressive crack is the highest. Thus, the appearance of initiation and propagation of the anti-wing crack and compressive crack are very actively than that of the wing crack. The strain and AE measurement is not only to provide a clear concept on the mechanisms of crack growth form a 3-D surface flaw but also to provide useful knowledge on the AE property of the crack patterns.

A number of instability problems in rock engineering projects are caused by crack propagation. However, crack growth mechanisms from 3-dimentional flaw are not fully understood, in particular for 3-D flaw case with varied dipping angle. This study focuses on 3-D surface flaw using real rock specimens containing a flaw with varied inclination angle α from axial loading and dipping angle γ from specimen surface under uniaxial compression. Acoustic emission technique was used for tracing the initiation and growth of micro-cracks inside of specimen. It was found that crack growth process is affected by the dipping angle γ of the 3-D flaw. When dipping angle γ ≠ 90º, the thickness of rock above the flaw plane is thinner than that of below the flaw plane. As a result, compressive crack and wing crack initiated easily from the thinner flaw tips. And, the normalized stress for crack initiation σi /σc, AE events and the AE energy for crack growth decreases with the dipping angle γ. However, for γ = 90º, the thickness of rock above and below of the flaw tips is the same, it was observed that anti-wing crack (crack growth direction opposite to wing crack) initiated first at a certain place away from the flaw tips, then wing crack and compressive crack emerged at the late stage. For this case, the stress σi /σc, AE events and the AE energy for crack initiation and propagation are at a high value. Thus, for rock mass contains flaws geometry with small dipping angle, some problems of crack propagation may be induced easily during excavation.

Direct shear tests on concrete specimens were conducted to investigate the shearing behaviour of the material under varying normal confining stresses. Test results were analyzed to quantify the mobilization of shear strength components derived from hydrated cement paste–aggregate adhesion, contact friction, shear dilation, and cement–aggregate interlock along the sheared surface under direct shearing. It was found that each component has its unique response in terms of mobilized shear stress and shear displacement. In addition, different modes of failure observed in uniaxial compression, splitting tension, and direct shear tests were identified to delineate the Mohr–Coulomb failure envelope for shear strength of concrete material.

Under the action of compressive load, the growth and coalescence containing flaws in brittle materials (rock and rocklike materials e.g.) will result in the local buckling and global fracture of rockmass. But, the mechanisms on propagation and coalescence of 3-dimensional internal flaws are not clear till now. We examine brittle fractures of manmade specimens using frozen casting resin and rocklike material to observe 3D internal flaws growth process at about -30° C. A team of specimens containing three internal flaws is measured; flaws are made of three parallel oblong aluminum films. The propagation and coalescence pattern of three internal flaws is observed under compressive stress. An interesting phenomenon is that the crack initiated from the second flaw quickly turns to the one induced from the third flaw and forms a bigger fracture plane, then splits the specimen. It shows that the flaw distribution pattern will greatly affect the flaws growth and coalescence process. The mechanisms that lead to the wing and anti-wing crack initiation and coalescence are described.

This study presents a framework for numerical simulations based upon micromechanical parameters in modeling progressive failures of heterogeneous rock specimens under compression. In our numerical simulations, a Weibull distribution of the strength and elastic properties of the finite elements is assumed, and the associated Weibull parameters are estimated in terms of microstructural properties, such as crack size distribution and grain size, through microscopic observations of microcracks. The main uncertainty in this procedure lies on the fact that various ways can be used to formulate a “microcrack size distribution” in relating to the Weibull parameters. As one possible choice, the present study uses the number of counted cracks per unit scanned volume per grain size to formulate the crack distributions. Finally, as a tool, the Rock Failure Process Analysis code (RFPA2D) is adopted for simulating the progressive failure and microseismicity of heterogeneous rocks by using an elastic-damage finite-element approach. To verify our framework, compression tests on marble specimens are conducted, and the measured acoustic emissions (AE) are compared with those predicted by the numerical simulations. The mode of failure, compressive strength and AE pattern of our simulations basically agree with experimental observations.

Statistics of the mechanical and failure properties on the grain scale are often assumed to follow the Weibull distribution in numerical simulations of failure and damage development. To investigate the microstructural basis for such a statistical model of compressive failure in a brittle rock, we consider the development of instability in a wing crack model and establish a methodology whereby the Weibull parameters can be inferred from microstructural data on microcrack density and length statistics for input into finite element simulations. Application of this methodology to six Yuen Long marble samples provides important insights into how different attributes of the microstructure may influence the progressive development of rock failure. The finite element simulations underscore the significant influence of microcrack length statistics, which has not been emphasized in continuum damage mechanics models that usually emphasize the roles of average crack size and crack density. The microstructural data indicate that strength heterogeneity increases with increasing grain size, and this plays a key role in lowering the uniaxial compressive strength, which contributes to the overall decrease of strength with increasing grain size.

Under uniaxial compression, brittle solids are frequently observed to fail by splitting parallel to the direction of loading. Although this failure has long been recognized, considerable confusion regarding how such splitting mechanisms develops still remains. Axial propagation of a crack-like flaw inclined to the loading direction of compression is one of the accepted mechanisms. In this paper, the axial propagation of a pore-like flaw as one of the mechanisms of splitting failure is approached. A series of physical and numerical tests of uniaxial compression on samples containing a single hole with varied diameters and sample widths are carried out to investigate the splitting failure, the failure modes and strength characterization due to crack growth from such flaw. Samples made from the Hong Kong granite are used in the physical tests to study the inference of heterogeneity of solid on crack growth. A Material Failure Process Analysis code (MFPA 2D ) is used as a numerical simulation tool to compare and explain the mode of failure from experiment. Sammis and Ashby [Sammis, C.G., Ashby M.F., 1986. The failure of brittle porous solids under compressive stress states. Acta Metall. 34, 511–526] theoretical crack model is employed to study the inference of sample size and diameter of hole on peak strength.

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.

This study is to evaluate the effect of the heterogeneity on the failure processes and strength characterization of brittle rock containing the single pre-existing crack (or flaw) under uniaxial compression loadings. The numerical simulation reproduces the evolution of the stress and strain fields in flaw propagation process, the mode of acoustic emission related to the heterogeneity of rock and the phenomenon related to discontinuous. It is shown that the lower the value of the homogeneous index, the more influence of local variation on the propagation process of the pre-existing flaw, and there occurs more randomly distributed microfractures throughout the specimen. Studying the details of macrofracture formation in relatively homogeneous specimens, it is interesting to find that there exists a 'constant jump' propagation pattern of the wing crack, which is responsible for the formation of the pre-existing flaw. The numerical results also demonstrate that the stress-strain relation and strength characterization depends strongly on the heterogeneity of the specimen. The heterogeneous rock has a gentler post-peak behavior and lower strength, while the more homogeneous specimen has a higher strength, accordingly, the curve becomes more linear and the strength loss is also rapidly.

It has long been recognized that the strength of brittle rocks decreases with the grain size. However, very few systematic investigation of this phenomenon has been made using numerical method. This paper presents the results of a numerical simulation using the Rock Failure Process Analysis code (RFPA2D) to investigate the effects of grain size on the uniaxial compressive strength and the failure behavior of Yuen Long marble. The Weibull distribution with two parameters (m that characterizes the strength heterogeneity, and σ0 that corresponds to the mean strength of an element) selected based on micromechanical basis is used in the RFPA2D code for simulation. The simulated stress-strain curves of Yuen Long marbles with different grain sizes under uniaxial compressive condition agrees well with the experimental study. The progressive failure process was captured in the numerical simulations. Our simulations also reproduced the influence of grain size, with strength scaling approximately with the inverse square root of grain size, which is in agreement with the previous experimental study.

A major challenge in rock mechanics has been the realistic modeling that can reveal the progressive accumulation of damage and shear localization in a brittle rock under compression. The Rock Failure Process Analysis code (RFPA2D) is an efficient tool and realistic model to simulate such complexities. A key assumption of the code is that the heterogeneity of elastic moduli and failure strength are characterized by the Weibull distribution with two parameters (m and σ0 ). However, these two parameters do automatically not relate to the microstructural parameters, such as grain size and microcrack statistics. Therefore, the purpose of this paper is to elucidate the micromechanical basis of these Weibull parameters, specifically how they depend on microstructural attributes such as grain size and crack statistics. Secondly, a methodology was developed to quantitatively determine the relevant micromechanical parameters for input into the RFPA2D code. Finally, the methodology was implemented by quantifying the microcrack geometry and statistics of real rock and simulating its uniaxial compression and progressive failure behavior. The simulated result agrees well with the experimental study.

Advances in Fracture and Failure Prevention: Proceedings of the Fifth International Conference on Fracture and Strength of Solids (FEOFS2003): Second International Conference on Physics and Chemistry of Fracture and Failure Prevention (2nd ICPCF), Sendai, 20-22 October 2003

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.

For static compressions of spheres, a new stress analysis for isotropic elastic spheres compressed between two flat rigid platens is proposed by incorporating the Hertz contact stress. The predictions of the failure load for various sizes and strengths of spheres agree very well with our static experiments on a brittle plaster material. For dynamic compressions of spheres, a simple crushing analysis illustrates that the size of the contact zone can be estimated quite accurately in terms of the size of the sphere, the dynamic hardness, and the impact energy. Although the maximum contact force at failure is larger in the static case than that in the dynamic case, the energy required for fragmentation of the solid spheres is larger under dynamic test than under static test. Comparisons of the static and dynamic tests show that the impact energy required for fragmentation of a sphere can be approximated as 1.5 times of that for the static test. As expected, the impact energy for fragmentation increases monotonically with the size and strength of the spheres. The contact time at failure, however, does not exhibit a clear trend with the changes in size and strength of the spheres.

Proceedings of Fourth International Conference on Fracture & Strength of Solids : Pohang, Korea, August 16-18, 2000

Fourth International Conference on Fracture & Strength of Solids : Pohang, Korea, August 16-18, 2000

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 examines the effect of the initial crack density and grain size on the uniaxial compressive strength of fine- and coarse-grain Yuen Long marbles. We found experimentally that the peak strength decreases with the inverse square root of the mean grain size, and this agrees with the previous experimental observations by Olsson (1974), Brace (1961, 1964) and Fredrich et al. (1990). However, two different regimes of microcracking dependence on the peak strength are observed: (1) in fine-grain marbles the uniaxial strength drops rapidly with the initial crack density ϵ0; (2) in coarse-grain marbles the strength is roughly constant with the crack density if ϵ0 > 0.025. This observation contradicts the common belief that peak strength decreases monotonically with ϵ0. In an attempt to study the underlying reason for this nonlinear dependence of the crack density, the Ashby-Hallam (1986) model is employed and it predicts that for small ϵ0, the peak strength decreases rapidly with the initial crack density, but when ϵ0 increases beyond a critical value, peak strength becomes relatively insensitive to the crack density. For Yuen Long marbles, the model predicts that the critical ϵ0, which separates the rapidly-decreasing and the roughly-constant regimes, is approximately 0.025, which agrees well with our observed value.

According to unofficial estimation, within the 20th century 3.5millions people die in natural disaster, of which over 40% was by earthquakes. Earthquakes remain one of the worst natural disasters posing threats to human civilization. For example on 21 September 1999, an earthquake of magnitude of 7.6 occurred near Chi-Chi Taiwan, causing about 2317 death, 8722 injured, and 51761 buildings collapses [1]. A surface rupture, which is more than 100 km long is associated with the earthquake. The first 90 km surface rupture running roughly followed the known Chelungpu fault in north-south direction, then the surface rupture turned east creating a new fracture zone going through the Shihkang Dam, at where waterfall was formed from a flat riverbed, and the maximum surface displacement of the surface rupture was about 7 m in both vertical and horizontal directions. This newly formed fault arouse much international attention regarding its formation mechanism and many studies are still ongoing. The fault rupture mechanism is still not fully understood. The rupture mechanisms from pre-existing 3-D fault is worth to investigate for it has both academic merit and of societal need.

1st Canada-US Rock Mechanics Symposium - Rock Mechanics Meeting Society's Challenges and Demands, Vancouver, BC, 27-31 May 2007

1st Canada-US Rock Mechanics Symposium - Rock Mechanics Meeting Society's Challenges and Demands, Vancouver, BC, 27-31 May 2007

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.