Fracture Initiation Stress Research Articles

Rock Fracturing Characteristics and Roadway Expansion Application of Static Crushing Agent under Multi-Row Drilling Condition

Static crushing agent (SCA) offers advantages such as good safety, no harmful gases, and minimal vibration, making SCA ideal for rock crushing in mines or underground engineering. To scientifically implement the section expansion of mine roadway, the rock mechanical parameters, SCA expansion properties, and cracking behavior of surrounding rock were investigated using laboratory tests, numerical simulations, and field experiments. Results indicate that the smaller hole spacing of SCA improves the fracturing effect on rock mass, reduces the required fracture initiation stress and penetration stress, and the presence of a free surface aids in fracture development in the rock mass. Optimal borehole design parameters and spacing distributions of the SCA were determined, and corresponding construction techniques of roadway expansion were proposed. Field tests demonstrate that static crushing technology, under multi-row drilling conditions, is highly effective for rock roadway expansion projects. These findings provide valuable guidance for non-explosive expansion and other roof breaking treatment projects.

Cross-Crack Interaction and Initiation Mechanism Under Hydro-Mechanical Coupling

In this paper, the equation for computing the maximum Stress Intensity Factor (SIF) of cross-crack under hydraulic-mechanical coupling was derived by the dislocation method and the integral equation, and the influence of cross-crack geometric parameters (branch-crack length, pinch angle, inclination angle) on the interacting SIF was analyzed, and its influence law was obtained. Using the maximum shear and tensile SIF ratio criterion as a basis, the fracture criterion of hydraulic-mechanical coupling cross-crack was established, and the initiation process of hydraulic-mechanical coupled red sandstone cross-crack was predicted (including the cross-crack initiation angle, initiation load, and initiation mechanism). Results showed that for cross-crack with the inclination angle fixed ([Formula: see text]), [Formula: see text] of crack tip C decreases slowly. For cross-crack with change of [Formula: see text]. [Formula: see text] of crack tip A increases, and crack tip C decreases with [Formula: see text]. For the cross-crack hydraulic-mechanical coupling test, as the cross-crack angle [Formula: see text] grows, the fracture initiation stress first reduces before increasing. Initiation mechanisms are Mode I fracture and initiation angles are usually negative. The hydraulic-mechanical coupling cross-crack initiation criterion is validated by the experimental findings, which align with the expected outcomes.

Rock Breaking Law Under the Condition of Multi-row Drilling of Static Crushing Agent and Its Application in Roadway Expansion

Static crushing agent (SCA) has the advantages of good safety, no harmful gas and no vibration. It is widely used in rock crushing engineering of mine or underground engineering. Aiming at the performance of static crushing agent with different water-cement ratios, based on the engineering and environmental conditions of roadway side protection in a mine of Shanxi coking coal, the stress-time curve of SCA and the fracturing law of SCA on roadway side rock under the condition of multi-row drilling were studied by means of laboratory test and numerical simulation. The results show that: the smaller the hole spacing, the better the fracturing effect of SCA, the smaller the required fracture initiation stress and penetration stress, and the existence of the free surface contributes to the development of the fracture, and the fracture around the hole extends along the direction of the incoming pressure under the peripheral pressure conditions; the porous SCA fracturing can be used for the high efficiency of underground rock fracturing projects such as rocky roadway spreading and other underground rock fracturing projects. The research results of the project provide a new method for non-blasting roadway expansion, roof picking and other rock-breaking projects in underground coal mines.

Failure mechanism of circlular tunnel supported by concrete layers under uniaxial compression: Numerical simulation and experimental test

Under this study, particle flow code modeling and experimental testing were used to examine the failure behavior of a pre-holed rocklike specimen including concrete interlayers in uniaxial compression. Rectangular pre-holed gypsum samples with interlayer concrete have been made specifically for this purpose. The sample's measurements were 150 mm*150 mm*50 mm, and the hole's diameter was 20 mm. Changes were made to the concrete's length, location, and number. There were 0 and 20 mm between the concrete layer and the hole. The lengths of the concrete were 50, 100, and 150 mm. 20 mm thick concrete was used. This complex was quantitatively tested and simulated under uniaxial loading circumstances. 13 experiments in all have been performed. The findings show that concrete length, concrete layer number, and concrete circumstance all have an impact on the crack growth trajectory. Two tensile fractures started in the hole wall while it was in the middle of the concrete layer and spread parallel to the loading axis until coalescing with the sample edges. By increasing the distance between the concrete layer and the hole, more tensile cracks and oblique fractures occurred. By lengthening the concrete, the model's crack count was reduced. The shear bands at the hole were expanded by extending the distance between the concrete layer and the hole when the hole was encircled by two concrete layers. Additionally, by shortening the concrete, more shear bands were formed close to the hole. Longer concrete had higher young modulus, fracture initiation stress, ultimate strength, and absorbed energy. Additionally, the concrete layer's distance from the hole was increased, which diminished these mechanical qualities. By increasing the number of concrete layers, the concrete's young modulus, fracture initiation stress, ultimate strength, and absorbed energy were all raised. The results of the numerical simulation agree well with those of the experiments. Based on the results of this article, an innovative method and a unique technique can be proposed to install the concrete lining layers at different dimensions around the tunnel in such a way that the circular cross-section of the tunnel remains constant.

Concurrent multiscale modeling of in-plane micro-damage evaluation in Z-pinned composite laminates

Most of the unit cell models for Z-pinned composite laminates (ZCL) are mesoscopic in scale, where the fiber reinforced zone is modeled as homogeneous but without detailed characterization and failure analysis of the fibers and matrix. This paper proposes a new concurrent multiscale unit cell model to investigate the in-plane micro-damage evolution of ZCL. The novelty worth mentioning is the proposed element-based method to generate random microbuckling spatial fibers in the fiber reinforced zone, where the microbuckling is caused by fiber waviness and fiber crimp, and then the mesh of fiber, Z-pin, matrix, and the interface between Z-pin and matrix is regenerated. In-plane tensile tests (ASTM D3039) are conducted for verification. There is good agreement between experiment and simulation, only with deviations of −0.97% and 2.69% for tensile modulus and fracture initiation stress, respectively. The research indicates that in-plane micro-damage initiates from the interface between Z-pin and matrix. The stress concentration and higher local fiber volume fraction, caused by the microbuckling spatial fibers clustered near the Z-pin, play a major role in the evolution of interface damage, crack initiation and growth.

Experimental study on effect of effect time of supercritical CO2 fracturing fluid on mechanical properties of sandstone

Supercritical CO2 fracturing is a novel hydro-free fracturing technology, which has the characteristics of minor damage to reservoirs and higher efficiency. During the process of fracturing, the CO2 fracturing fluid will infiltrate into the pore of rock, resulting in the change of rock mechanics properties. The rock samples were drilled from the same layer, then the supercritical CO2 fracturing fluid was used to soak the rock samples to measure the changes of rock mechanical properties under different soaking time. When the pore pressure is 0 MPa, the fracture initiation stress of rock sample is about 40% of its peak strength, and with the increase of pore pressure, the elastic stage decreases and the plastic stage increases, while the pore pressure reaches 31 MPa, the core fracture initiation stress is about 20% of its peak strength. The results show that with the longer CO2 soaking time, the shorter elastic stage with the longer plastic stage and the weaker compressive strength, the smaller elastic modulus, and the higher Poisson's ratio. This indicates that the strength of rock decreases gradually with the increase of injection time in supercritical CO2 fracturing process, which is conducive to the formation of longer fractures.

Reinforcement of polypropylene with alkali-treated sugarcane bagasse fibers: Mechanism and consequences

Polypropylene composites were prepared from neat and alkali-treated sugarcane bagasse fibers. The results showed that alkali treatment leads to an increase in composite stiffness and strength. A maximum is achieved in these properties at around 5 wt% NaOH content of the treating solution. The increase in properties was assigned to the improvement in inherent fiber characteristics. Acoustic emission testing and electron microscopy showed that the two main local deformation processes related to the fibers are their fracture and debonding; the latter is accompanied by the shear yielding of the matrix. Increased inherent strength of the fibers results in an increase in the fracture initiation stress and fracture energy of the composites. Interfacial adhesion has a slight effect on stiffness, but more significant on strength and impact resistance. Changing adhesion modifies the relative importance of local deformation processes, the number of debonding events decreases, while fiber fracture increases with increasing adhesion. Increased interfacial adhesion improves stress transfer and the load bearing capacity of the fibers as well, but suppresses matrix yielding. Alkali treatment increases inherent fiber strength, which can be directly correlated with composite strength.

Mechanical and Volumetric Fracturing Behaviour of Three-Dimensional Printing Rock-like Samples Under Dynamic Loading

Heterogeneous rock contains numerous pre-existing three-dimensional (3D) cracks, which control its mechanical and fracturing properties. Considerable effort has been devoted to studying the volumetric fracturing behaviour of rock under static loading conditions. Although rock masses are often subject to dynamic impacts such as earthquakes and blasting, the mechanical and volumetric fracturing behaviour of rock under dynamic loading is still poorly understood. In this paper, dynamic laboratory tests were performed on 3D-printed artificial rock samples with 3D embedded flaws created during three-dimensional printing (3DP), with the aim of studying the volumetric fracturing and mechanical properties of these samples under impact with high strain rate. The results show that the dynamic compressive strength and the tangent modulus decrease with an increasing number of flaws, but have very limited effects on the ratio of the fracture initiation stress of the first crack to the peak stress of the sample, the maximum axial strain of the sample and the volumetric fracturing behaviour of the sample. The tensile failure of a sample is caused by the continuous extension of wing cracks from the outer flaw tips. The mechanical and volumetric fracturing behaviour of samples with 3D embedded flaws are strain rate dependent. The tangential modulus and the ratio of the fracture initiation stress of the crack to the peak stress increase significantly when the loading type changes from static compression to dynamic compression. Under dynamic compression, wing cracks can continuously extend to the sample ends, whereas under static compression, wing cracks can intermittently extend only a limited distance. Moreover, the fracturing behaviour of 3D flaw differs from that of 2D flaws under dynamic loading. Under high strain rate loading, wing cracks generated at 3D flaw tips lead to splitting failure of the sample, while shear cracks formed at 2D flaw tips result predominant shear failure of the sample. The findings in this paper could facilitate a better understanding of rock failure subjected to dynamic loading conditions.

Influence of phase and interface properties on the stress state dependent fracture initiation behavior in DP steels through computational modeling

In dual phase (DP) steels, fracture can initiate within the ferrite phase, the martensite phase, or at the interfaces between these phases with the dominant fracture initiation mechanism expected to depend on a number of factors, including the phase and interface properties as well as the applied stress state. The present study aims to identify the links among fracture initiation behavior, phase/interface properties, and stress state in DP steels through finite element analysis using representative volume element (RVE) simulations. An idealized RVE model containing a circular martensite particle was loaded under five different stress states. The RVE model incorporated a ductile fracture criterion for ferrite, a brittle fracture criterion for martensite, and a cohesive zone model (CZM) for the ferrite/martensite interface. A parametric study was performed to determine the relative influence of fracture properties of each constituent and stress state on the failure initiation behavior, and to identify the conditions under which the fracture initiation behavior was stress state dependent.

Elastic-plastic solution and experimental study on critical water pressure inducing hydraulic fracturing in soil

It is widely believed that hydraulic fracturing will occur in the clay core of an earth-rockfill dam if the water pressure in the core increases to levels that are high enough to allow a fracture to form. An elastic-plastic solution to critical water pressure inducing hydraulic fracturing (fracture initiation pressure) in soil is derived based on Mohr-Coulomb shear failure criterion and the theory of cavity expansion. In order to verify the applicability of the criteria presented and study the relations among fracture initiation pressure, tensile strength and stress state of soil, laboratory tests are performed on compacted cuboid specimens by true triaxial apparatus. According to the test results, the cracks of hydraulic fracturing existed perpendicular to the minor principal stress plane. The hydraulic fracturing pressure p f increases with the increase of dry density of specimen, p f shows good linear relationship with σ 2 and σ 3. The prediction from presented equation is compared with test results and other three predictions, of which two are tensile failure (TS) criterion, and the other is Mohr-Coulomb (M-C) criterion. The presented solution is verified, and the other three approaches for p f are evaluated. The comparison indicates that the predicted values from the presented equations agree well with the test values for specimens of low dry density, and the error of the prediction is larger for those of high dry density, especially in lower minor stress states. The predicted average relative error of absolute value R a from TS1 criterion is 13.3% for all specimens of different dry densities, and each prediction is lower than the test data. On the contrary, most of the predicted values from M-C criterion are greater than the test data, but the average relative error from the presented equation is the minimum. Considering the safety of soil works, an equation from TS1 criterion is suggested to evaluate the occurrence of hydraulic fracturing in earth-rockfill dam designing.

Influence of operation factors on brittle fracture initiation and critical local normal stress in SE(B) type specimens of VVER reactor pressure vessel steels

A complex of mechanical tests and fractographic studies of VVER-1000 RPV SE(B) type surveillance specimens was carried out: the brittle fracture origins were revealed (non-metallic inclusions and structural boundaries) and the correlation between fracture toughness parameters (CTOD) and fracture surface parameters (CID) was established. A computational and experimental method of the critical local normal stress determination for different origin types was developed. The values of the critical local normal stress for the structural boundary origin type both for base and weld metal after thermal exposure and neutron irradiation are lower than that for initial state due to the lower cohesive strength of grain boundaries as a result of phosphorus segregation.

Simulation of hydraulic fracturing in quasi-brittle shale formations using characterized cohesive layer: Stimulation controlling factors

Economic production from shale gas cannot be achieved by natural mechanisms alone; it requires technologies such as hydraulic fracturing in multiple stages along a horizontal wellbore. Developing numerical models for hydraulic fracturing is essential since a successful fracturing job in a shale formation cannot be generalized to another due to different shale characteristics, and restricted access to the field data acquisition. The cohesive zone model (CZM) identifies the plastic zone and softening effects at the fracture tip in a quasi-brittle rock such as shale, which leads to a more precise fracture geometry and injection pressure compared to those from linear elastic fracture mechanics. The incorporation of CZM in a fully coupled pore pressure–stress, finite element analysis provides a rigorous tool to include also the significant effect of in situ stresses in large matrix deformations on the fracturing fluid flow components, for instance leak-off. In this work, we modeled single and double-stage fracturing in a quasi-brittle shale layer using an improved CZM for porous media besides including the material softening effect and a new boundary condition treatment, using infinite elements connecting the domain of interest to the surrounding rock layers. Due to the lack of experimental data for the cohesive layer properties, we characterized the cohesive layer by sensitivity study on the stiffness, fracture initiation stress, and energy release rate. We demonstrated the significance of rock mechanical properties, pumping rate, viscosity, and leak-off in the pumping pressure, and fracture aperture. Moreover, we concluded that the stress shadowing effects of hydraulic fractures on each other majorly affects not only fractures’ length, height, aperture, and the required injection pressure, but also their connection to the injection spot. Also, we investigated two scenarios in the sequence of fracturing stages, simultaneous and sequential, with various fracture spacing and recommended the best scenario among them.

The effects of water content, temperature and loading rate on strength and failure process of frozen rocks

The effects of water content, temperature and loading rate on the strength and failure process of rock at sub-zero temperatures were investigated and are presented in this paper. Over the range of temperatures studied there was little change observed in the properties of dry rock. The presence of water in the rock, however, resulted in a marked increase in rock strength and the fracture initiation stress. Rock strength increased with amount of water present and the rate of load application, with the effect being exacerbated at the colder temperatures. Interestingly, the changes in strength were not uniform as there was a greater rate of increase in the tensile strength of rock with temperature than compressive strength. It is postulated that these changes in mechanical properties may be explained in part by a reduction in the stress concentration within the interstitial spaces and cracks of the rock samples tested.

Damage Mechanics Model for Fracture Process of Steel-Concrete Composite Slabs

Composite slab construction using permanent cold-formed steel decking has become one of the most economical and industrialized forms of flooring systems in modern building structures. Structural performance of the composite slab is affected directly by the horizontal shear bond phenomenon at steel-concrete interface layer. This study utilizes 3D nonlinear finite element quasi-static analysis technique to analyze the shear bond damage and fracture mechanics of the composite slabs. Fracture by opening and sliding modes of the plain concrete over the corrugated steel decking had been modeled with concrete damaged plasticity model available in ABAQUS/Explicit module. The horizontal shear bond was simulated with cohesive element. Cohesive fracture properties such as fracture energy and initiation stress were derived from horizontal shear bond stress versus end slip curves. These curves were extracted from bending tests of narrow width composite slab specimens. Results of the numerical analyses match the experimental results accurately. This study demonstrated that the proposed finite element model and analysis procedure can predict the behavior of composite slabs accurately. The procedure can be used as a cheaper alternative to experimental work for investigating the ultimate strength and actual fracture and damage behavior of steel-concrete composite slab systems.

High-strain-rate dynamic mechanical behavior of a bulk metallic glass composite

The high-strain-rate mechanical properties, deformation mechanisms, and fracture characteristics of a bulk metallic glass (BMG)-matrix composite, consisting of an amorphous Zr57Nb5Cu15.4Ni12.6Al10 (LM106) matrix with crystalline tungsten reinforcement particles, were investigated using gas gun anvil-on-rod impact experiments instrumented with velocity interferometry (VISAR) and high-speed digital photography. The time-resolved elastic-plastic wave propagation response obtained through VISAR and the transient deformation states captured with the camera provided information about dynamic strength and deformation modes of the composite. Comparison of experimental measurements with AUTODYN-simulated transient deformation profiles and free surface velocity traces allowed for validation of the pressure-hardening Drucker–Prager model, which was used to describe the deformation response of the composite. The impacted specimens recovered for post-impact microstructural analysis provided further information about the mechanisms of dynamic deformation and fracture characteristics. The overall results from experiments and modeling revealed a strain to failure of ∼45% along the length and ∼7% in area, and the fracture initiation stress was found to decrease with increasing impact velocity because of the negative strain-rate sensitivity of the BMG.

凍結状態にある岩石の強度と変形・破壊挙動

Understanding mechanical behavior of frozen rocks is useful for evaluating the stability of rock slopes in cold regions. In this study, uniaxial compression tests and Brazilian tests were carried out on frozen rock specimens of welded tuff and andesite under -20°C temperature. The fracture process was examined by observing deformation behaviors and AE activities. Effects of water saturation degree on strength and deformability were also investigated. The main results are as follows.1) The fracture process of the frozen rock was similar to that of non-frozen rock and was divided into the following regions. (I) Closure of cracks and pores. (II) Elastic deformation. (III) Fracture initiation and stable fracture propagation. (IV) Unstable fracture propagation. Also, stress levels at the beginning of the region (III) increased with the degree of water saturation. 2) Both strength and strain at peak stress increased as the degree of water saturation increased. The relations between them were able to be approximated by a straight line. Brittleness of rocks decreased with the degree of water saturation since indirect tensile strength was more sensitive to the degree of water saturation than uniaxial compressive strength. 3) The mechanical effect of frozen pore water was considered with an inclusion model. The model predicted the observed phenomenon. Namely, increment in fracture initiation stress, due to frozen pore water in uniaxial tension, was always higher than that in uniaxial compression. The increase in strength was thought to result from relaxation of stress concentration around pores.

Part II. Metallurgical factors governing the H-assisted intergranular cracking of peak-aged Ti-3Al-8V-6Cr-4Mo-4Zr (beta-C)

A previous study (Part I) showed that the solution-treated and aged (STA) (i.e., peak-aged) condition of Beta-C Ti, (σ0.2 pct y = 1260 MPa) possesses an enhanced hydrogen (H) embrittlement susceptibility compared to the solution-treated (ST) condition, (σ0.2 pct y = 865 MPa), as measured by reductions in the fracture initiation stress with predissolved H content and the introduction of an intergranular (IG) fracture mode. It was also shown that yield-strength elevation and the subsequent enhancement in the local hydrostatic stresses within the notch root are not the controlling factors in the H-assisted* IG fracture initiation of the STA condition. Previous work (Part I) implicates a microstructural feature or condition associated with the 500 °C aging treatment. In this study, it is shown that localized internal hydride precipitation at the grain boundaries or alpha beta interfaces was not detected by a variety of experimental methods over the range of internal H contents for which IG fracture initiation was observed. It was also shown that grain-boundary alpha colonies or films are not responsible for the IG fracture initiation in the STA condition. A measured increase in hydrogen embrittlement (HE) susceptibility as a function of aging time at 500 °C is consistent with the segregation or depletion of a critical species at the grain boundary. However, grain-boundary segregation/depletion could not be detected with Auger electron spectroscopy (AES) of specimens fracturing in a vacuum. Compression tests used to characterize and compare the alloys’ slip behavior showed that plastic deformation is concentrated at or near the grain boundaries in the STA condition. Therefore, a possible intergranular fracture initiation mechanism that includes the effects of hydrogen and localized deformation is discussed.

Microstructure effects on microcracking and brittle failure of dolomites

In this paper the influence of microstructure on crack initiation stress and ultimate strength is investigated using results and analysis of 32 triaxial compression tests performed on cylindrical cores of dolomite samples which exhibit a wide range of grain sizes and mosaic textures. All tests were performed at a constant strain rate, under confining pressures between 0 to 40 MPa. The predictive capability of conventional criteria for ultimate strength which are based on empirical fitting parameters such as cohesion and internal friction angle, or mechanical properties such as unconfined compressive strength, is shown to be quite poor, due to the influence of microstructure. Microstructure controls ultimate strength to such a degree that an assumed mechanical property such as unconfined compressive strength may vary by more than a factor of two, where two different microstructure patterns are present. The validity of published analytical expressions which predict fracture initiation stress assuming the sliding crack model is tested using both mean and maximum grain size, and inserting the measured fracture initiation stress as the remote stress. It is shown that these approximate models fail to describe true behaviour because they ignore boundary conditions which exist at the tip of the leading crack at different mosaic textures. Early attempts to discuss the influence of microstructure on rock strength have shown that ultimate strength is inversely related to mean grain size. This study demonstrates that grain size alone can not be used in correlation with ultimate strength. Rather, the combination of both grain size and porosity dominate the mechanical response of the rock. Fracture initiation stress is found to be more sensitive to the influence of grain size than ultimate strength, possibly because the length of initial cracks controls the level of stress concentration at the tip of leading cracks. However, fracture initiation stress is shown to be inversely related to both porosity and mean grain size, thus the importance of porosity in the initiation process must be recognized. Ultimate strength is influenced primarily by porosity and mosaic texture, and is less sensitive to mean grain size, possibly because once fracture propagation is initiated, grain arrangement controls fracture interaction processes which lead to macroscopic failure.

The influence of grain size and porosity on crack initiation stress and critical flaw length in dolomites

Abstract The influence of rock texture on crack initiation stress ( σ i ) and critical flaw length ( L i ) is studied by a series of triaxial tests performed on monomineralic dolomites. The critical flaw length, as predicted by analytical models, is shown to be larger than the measured mean grain size ( d m ) by two–three orders of magnitude. This discrepancy is explained by rock texture variations, which influence the fracture propagation mode and consequently fracture initiation stress. The quantification of rock texture is accomplished using porosity. Fracture initiation stress is shown to be inversely related to both porosity and mean grain size. When porosity is low, the sensitivity of σ i to mean grain size is high. This effect is reduced with higher porosity values. A model for initial flaw length is developed by a synthesis of Griffith initiation criteria with our empirical model for fracture initiation stress. Initial flaw length is found to be directly proportional to the elastic modulus, mean grain size and porosity of the rock. When porosity and mean grain size decrease simultaneously, the initial flaw length rapidly decreases and approaches the mean grain size value. Therefore, the classical assumption that grain size scales initial flaw size is shown to be valid only in the very restricted case of low porosity-low grain size rocks. In such textures, where void space is minimal, available crystal faces function as truly initial flaws, and variations in mean grain size influence crack initiation stress significantly. In more porous textures, however, the initial flaw length is shown to be up to two orders of magnitude higher than the mean grain size in the rock, depending upon the porosity and mean grain size values. In such textures crack initiation stress is much less sensitive to variations in mean grain size, indicating that the role of individual grains is less significant.

The Influence of Grain Size and Porosity on Crack Initiation Stress and Critical Flaw Length in Dolomites

The influence of rock texture on crack initiation stress (σi) and critical flaw length (Li) is studied by a series of triaxial tests performed on monomineralic dolomites. The critical flaw length, as predicted by analytical models, is shown to be larger than the measured mean grain size (dm) by two–three orders of magnitude. This discrepancy is explained by rock texture variations, which influence the fracture propagation mode and consequently fracture initiation stress. The quantification of rock texture is accomplished using porosity. Fracture initiation stress is shown to be inversely related to both porosity and mean grain size. When porosity is low, the sensitivity of σi to mean grain size is high. This effect is reduced with higher porosity values. A model for initial flaw length is developed by a synthesis of Griffith initiation criteria with our empirical model for fracture initiation stress. Initial flaw length is found to be directly proportional to the elastic modulus, mean grain size and porosity of the rock. When porosity and mean grain size decrease simultaneously, the initial flaw length rapidly decreases and approaches the mean grain size value. Therefore, the classical assumption that grain size scales initial flaw size is shown to be valid only in the very restricted case of low porosity-low grain size rocks. In such textures, where void space is minimal, available crystal faces function as truly initial flaws, and variations in mean grain size influence crack initiation stress significantly. In more porous textures, however, the initial flaw length is shown to be up to two orders of magnitude higher than the mean grain size in the rock, depending upon the porosity and mean grain size values. In such textures crack initiation stress is much less sensitive to variations in mean grain size, indicating that the role of individual grains is less significant.