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This study proposes a fractal damage calculation method that understands the blasting damage laws at the macroscopic, mesoscopic, and microscopic scales of rock. The findings indicated that the binary graph derived from the Moments algorithm can represent minute cracks and exhibit less noise within the image. This makes the algorithm suitable for identifying and extracting macroscopic damage. A three-dimensional (3D) reconstruction technique offers visualization of the macroscopic rock damage following an explosion. The extent of this damage is quantitatively assessed using the box dimension. In addition, a multifractal method is introduced to comprehensively evaluate the macroscopic and mesoscopic damage to rock post-blasting. The multifractal dimension calculations analysis reveals that the mesoscopic damage to rock following blasting is a significant factor in the overall blasting damage. The box dimension presents a straightforward, macroscopic evaluation method for assessing 3D macroscopic fractures. On the other hand, the multifractal dimension can more accurately evaluate the macroscopic cracks and mesoscopic damage resulting from blasting. Both methods emphasize different aspects and are equally effective for assessing blasting damage. Highlights: This study proposes a fractal damage calculation method that understands the blasting damage laws at the macroscopic, mesoscopic, and microscopic scales of rock. The box dimension is a straightforward macroscopic evaluation method for assessing 3D macroscopic fractures. The multifractal dimension more accurately evaluates the macroscopic cracks and mesoscopic damage from blasting. After ordinary charge initiations, blasting damage exhibited a bimodal distribution along the borehole's axis, peaking in the charging section. [ABSTRACT FROM AUTHOR]

Creep tests under constant stress are among the most important tests for investigating the time-dependent behavior of rock. In previous studies, creep tests were conducted under various loading and environmental conditions; however, it was very difficult to demonstrate accelerating creep at failure at stresses less than 50% of strength in conventional creep tests. In this study, a new test method is proposed that combines an alternating loading-rate test and a creep test in the post-failure region. The accelerating creep as well as the loading-rate dependence of strength were successfully obtained simultaneously from a single specimen. This test method was applied to three rock types under dry and wet conditions. The results of Sanjome andesite under both dry and wet conditions, Kimachi sandstone under dry conditions, and Tage tuff under dry conditions showed a similar relationship between creep strain, creep strain rate, and residual time (i.e., creep lifetime minus elapsed time), from high to low creep stress levels, and a close relationship between accelerating creep and the loading-rate dependence of strength. Further, the mechanism responsible for the time dependence was found not to change significantly from high to low stress levels. In contrast, different results were obtained when high and low creep stress levels were compared in Kimachi sandstone and Tage tuff under wet conditions. The larger increase in creep strain with increasing creep strain rate at lower creep stress levels was related to the shape of the stress–strain curve in the post-failure region. Highlights: A new test method was proposed that combined an alternating loading-rate test and a creep test in the post-failure region. Accelerating creep at failure was discussed in detail based on the test results from high to low creep stress levels. Test results showed a close relationship between accelerating creep and the loading-rate dependence of strength. [ABSTRACT FROM AUTHOR]

Rock naturally contains numerous defects, and both loading rate and defect geometry affect the loading capacity of rock structures when subjected to dynamic impact loads. Understanding the rate-dependent mechanical response and characterizing geometry-related fracture parameter of defected rocks are crucial to safety assessment of rock engineering. In this paper, the effects of loading rate and notch parameter on dynamic brittle fracture behavior of Fangshan granite weakened by a blunt V-notch are experimentally studied. First, the dynamic fracture experiments on blunt V-notched semi-circular bend (BVNSCB) specimen of Fangshan granite with different notch geometries are performed using the split Hopkinson pressure bar (SHPB) system. Second, the dynamic fracture processes of blunt V-notched rocks are recorded using an ultrahigh-speed camera, and the mechanical responses to different impact loading conditions are obtained via digital image correlation (DIC) method. Third, the effects of loading rate and notch parameter on the dynamic fracture parameters including notch fracture toughness, crack propagation toughness, and crack velocity are discussed to reveal the fracture mechanism of blunt V-notched rocks subjected to impact loads. It is found that dynamic notch fracture toughness obtained from DIC method is usually larger than that measured directly from conventional maximum impact load method. The maximum tangential stress (MTS) criterion eliminating the effect of the fracture process zone (FPZ) at blunt V-notch tip is used to correct the apparent notch fracture toughness value measured from the maximum load method. The results show that corrected notch fracture toughness values are in good agreements with those obtained from the DIC method. This study is significant for dynamic fracture analyses and strength assessments of rock masses containing notches or other defects with complex geometry. Highlights: Effects of loading rate and notch geometry on dynamic fracture behavior of blunt V-notched rocks are studied. Dynamic notch fracture toughness and crack propagation toughness are simultaneously determined. DIC method is used to track the development of FPZ at blunt V-notch tip and quantify the FPZ length. [ABSTRACT FROM AUTHOR]

Understanding the response mechanism of multiparameter rock fractures can improve the accuracy of crack diagnosis. In this study, three types of rock samples with notches were subjected to three-point bending tests. The fracture morphology was observed using scanning electron microscopy, and real-time resistivity and acoustic emission (AE) data were used to describe the crack propagation. The spatial distribution of the electric potential was simulated based on practical crack morphologies and can explain the correlation between rock fracture and rock resistivity or AE. The results reveal that the initiation and propagation of cracks reconstructs the electrical potential distribution characteristics of the rock samples and changed their overall resistivity. The crack growth rate was proportional to the rate of increase in the resistivity rate, and the resistivity increased with nonuniform crack growth. Crack geometry complexity affected circuit connectivity, and a higher resistivity change rate was typically caused by cracks with more uniform propagation. The resistivity variation had the same trend as the fracture toughness, whereas the AE energy exhibited a similar trend to the fracture energy evolution. The cumulative AE count of the granite fracture was the largest, and the peak AE count of coal was larger than that of sandstone. In the main frequency band of 100 ± 25 kHz, a relatively large AE event occurred during crack initiation, and the AE amplitude of granite was the largest. The primary fracture propagation increased the peak AE count, amplitude, energy, and fracture energy release efficiency. During rock fracture, the opening of a microscopic bedding plane and a matrix fracture results in time-varying resistivity and AE characteristics. The complementary electrical and acoustic parameters help describe the details of crack propagation behaviour. Highlights: Cracks restructure the electrical potential distributions in rock samples and change the resistivity. The acoustic emission (AE) energy exhibits a similar trend to the fracture energy evolution. The relationship between the resistivity and AE is mutually verified and complementary. [ABSTRACT FROM AUTHOR]

Highlights: The experimental survival probability of one irregular shaped rock was established via 105 drop tests using mortar replicas. The derivation and validation of an analytical model to predict the survival probability of brittle rocks of irregular shape upon collinear impact is presented. The survival probability predicted by the model was found to fall withing 5% of the experimental data with an excellent goodness of fit coefficient (R2 ~ 93%). [ABSTRACT FROM AUTHOR]

In this paper, the Pull-Off Test (POT) was analyzed as a method for determining the mode I fracture toughness (KIc) of rock and concrete. POT is submitted to tensile load (which causes a simpler stress state than tests submitted to bending and compression load) and its execution is easy, replicable and can be performed in laboratory and in situ (being its great advantage). A ratio between the dimensions of the POT was proposed to meet the Linear Elastic Fracture Mechanics requirements and the POT literature recommendations. Parametric studies were performed using numerical analysis and it was concluded that the POT is suitable for KIc testing, since mode I prevails in the test, and an equation was proposed for determining KIc in homogeneous rock and concrete (micro-concrete and mortar). A practical example of the method application was provided and KIc was determined for some homogeneous rocks. A similar result was achieved between POT and Semi-Circular Bending test. Highlights: The Pull-Off Test was analyzed as a method for determining the mode I fracture toughness of rock and concrete. The execution of the Pull-Off Test is easy, replicable and can be performed in laboratory and in situ. A ratio between the dimensions of the Pull-Off Test was proposed. The Pull-Off Test is suitable for mode I fracture toughness testing, since mode I prevails in the test. An equation was proposed for determining the mode I fracture toughness via Pull-Off Test of homogeneous rocks and concretes (micro-concrete and mortar). [ABSTRACT FROM AUTHOR]

Highlights: Anapparatus with precise controllability and large stiffness was designed to investigate the mechanical behavior of rock grain interface. The fracture toughness and tensile strength of the rock GI are scattered and follow an exponential probability distribution function. The validity of the obtained grain interface strength parameter was verified by a numerical model. [ABSTRACT FROM AUTHOR]

Depending on the type of failure mechanism, the strength of intact rock may be susceptible to the effects of scale. The influence of scale is apparent in the spalling of rock around underground openings. To reconcile field-scale observations, an understanding of the unconfined rock strength has to be appreciated from the standpoint of energy instability, particularly for instances in which the mechanism of failure involves propagation of fractures. Fracture energy principles were used to create a link between laboratory-measured uniaxial compressive strength (UCS) and rock failure as observed in spalling around circular openings. An Instability Line (IL) is proposed to predict the stresses above which spalling could occur with different opening diameters. Good comparisons were obtained for a range of dimensions from small boreholes to large tunnels. Based on field observations and analytical study, the results suggest that two conditions are required for spalling to occur. The first is that the crack initiation stress has to be exceeded, and the second is that the stress needs to be above the IL. The findings suggest that the effects of scale are limited by the crack initiation stress. For large-diameter openings, instability occurs immediately at crack initiation stress, whereas for smaller-diameter openings instability occurs at higher stresses post-crack initiation stress. Highlights: This paper aims to explain the discrepancies in the rock mechanics literature to predict spalling for small-diameter boreholes as against large-diameter tunnels. The failure mechanism of spalling is studied based on the framework of energy stability. An Instability Line is proposed based on the analytical study. The results of the analytical study compared well with published laboratory and field observations. The results suggest that two conditions are required for spalling to occur. The first is that the crack initiation stress has to be exceeded, and the second is that the stress needs to be above the Instability Line. The findings suggest that the effects of scale are limited by the crack initiation stress. [ABSTRACT FROM AUTHOR]

With the development of 3D printing and computer numerical control machining techniques, extremely complicated models physically simulating the underground structures in rock engineering were conducted. Whether these artificial materials can accurately simulate the cracking and failure modes of natural rocks should be studied. The present study uses an artificial material-moulded gypsum to compare with the mechanical behaviours of natural marble from the perspective of brittleness. The comparison can provide an insight into the feasibility of the physical simulation. In addition, to investigate the strain rate influence on brittleness with the background of dynamic loading related to rock engineering, the rate dependence of the brittleness is investigated considering the size effect. Six types of brittleness indexes proposed in the quasi-static loadings are studied under various loading rates with strain rates ranging from 10–6 to 103 s−1. The result indicates that not all the brittleness indexes are applicable in the dynamic regime. Two brittleness indexes are suggested to evaluate the dynamic gypsum brittleness due to its reasonable depiction of real dynamic brittleness. Gypsum is more brittle than marble under both quasi-static and dynamic loadings based on the analysis of brittleness indexes and cracking behaviour. Meanwhile, the experimental and numerical results confirm the influence of the brittleness of material on the cracking behaviours and imply that the artificial material should be assessed to ensure the validity and feasibility before the physical simulation of rock structures in engineering. Highlights: The brittleness of 3D printing material in physical simulation should be considered. The dynamic brittleness of gypsum and marble is compared. The brittleness indexes are extended into the dynamic condition. Brittleness index can affect the cracking behaviour. The feasibility of 3D printing in rock mechanics should be evaluated before experiments. [ABSTRACT FROM AUTHOR]

The fatigue damage evolution of rocks subjected to cyclic loading and unloading has always been a hot spot that receives worldwide attention in the field of rock mechanics. Recent studies that rely on advanced nondestructive testing (NDT) techniques enable accurate monitoring and assessment of the dynamic damage in cyclically loaded rocks, and well contribute to revealing the complicated failure mechanism. These works are critical to ensure safe underground tunnelling and mining activities. As a promising NDT technique, the electromechanical impedance method (EMI) has been successfully applied to many aspects in structure health monitoring. In this paper, the EMI method was extended to measuring the rock fatigue damage. Firstly, uniaxial cyclic compression tests with increasing amplitude were performed on three types of cylindrical rock specimens, including sandstone, granite and carbonaceous shale. The varying mechanical properties and energy conversion characteristics were analyzed. In particular, the damage evolution characterized by elastic energy dissipation was determined. Concurrently with cyclic tests, conductance signatures in response to two excitation modes of the surface-bonded piezoelectric transducers were collected, and the spectral localized and overall variations were analyzed. It is discovered that the resonant frequency shift and the statistic metric MAPD within the transverse mode-dominated frequency range could accurately indicate the rock fatigue damage. This research sufficiently confirms the effectiveness and reliability of the EMI method in quantifying the accumulative damage of different rocks under uniaxial cyclic loading and unloading. [ABSTRACT FROM AUTHOR]

The fracture toughness reflects the rock resistance to crack propagation, and therefore represents an important parameter for rock fracture assessments. From a strict point of view, the real fracture toughness ( K IC ) corresponds to a cracked situation in which the notch radius is theoretically equal to zero. However, most of the defects in rocks have a finite radius and, therefore, should be studied as notch-type defects. Here, the notch effect is numerically studied together with the influence of the grain size and the sorting coefficient (grain size uniformity) on the apparent fracture toughness ( K IN ). To this end, several four-point bending tests with different U-shaped notch radii, mean grain sizes and degrees of uniformity in grain size and shape have been simulated using the Discrete Element Method. In order to represent the grains of the rocks, the Voronoi tessellation is used to create randomly sized and distributed polygonal blocks. These Voronoi polygons have been defined, on the one hand, by an average edge length of 1, 2 and 3 mm, and, on the other hand, by a different number of iterations (n ) in the relaxation process during the generation of the polygons, which defines the grain size uniformity. The numerical analyses performed and the interpretation of the results show a clear notch effect in all the studied cases, as the apparent fracture toughness ( K IN ) increases with notch radius. Finally, the obtained stress fields at the notch tip have been compared to those obtained from the traditional finite element method. Highlights: Four-point bending tests with U-shaped notches simulated using the Discrete Element Method. Different notch radii, mean grain sizes and degrees of uniformity are studied. Results show a clear notch effect, increase of apparent fracture toughness with notch radius. Interpretation of the results using the Theory of Critical Distances. A linear relation between the critical distance of the rock and the grain size is observed. The critical distance slightly increases when less uniform grains are studied. [ABSTRACT FROM AUTHOR]

Tensile strength is a vital mechanical property of rock and the deformation and failure process of rock under tension is of much significance in rock mechanics and engineering. In this study, a micro analysis on rock direct tensile failure was made based on the newly introduced quantitative analysis of acoustic emission (AE) waveforms. Direct tensile tests of common rocks were carried out, accompanied by real-time AE monitoring. The spatial and temporal distributions of AE signals were studied over the whole loading process. Distribution and evolution laws of dominant frequencies of AE waveforms with normalized applied stress were statistically analyzed. The statistical relationship between the energy ratios of AE waveforms distributed in low and high dominant frequency bands (L-type and H-type waveforms) and peak strengths of rock specimens was built. Microstructural observations with SEM were further conducted. Results show that the dispersion degree of rock tensile strength corresponds to the complexity of mineral composition. Initial release moments of L-type waveforms appeared earlier than H-type waveforms. L-type waveforms of the same proportion carry more energy compared to H-type waveforms in rock subjected to tension. There is an overall downward trend for peak strength of rock specimens with the increasing energy ratios of L-type waveforms. The tensile strength of rock obtained by fitting in this study is smaller than that obtained by averaging. There exist micro shear fractures during the macro tensile failure process of rock according to the microstructural observations with SEM. The peak strength corresponding to the case that L-type waveforms (or micro tensile failures) account for 100% can be considered as the "ideal" tensile strength from the microscopic perspective. The determined tensile strength by fitting can be used as a conservative design parameter for rock engineering. Highlights: Statistical relationship between energy ratios of AE waveforms distributed in low and high dominant frequency bands and peak strengths of rocks under tension is built. There exist micro shear fractures during the macro tensile failure process of rock. Peak strength in the case that L-type waveforms (or micro tensile failures) reach 100% can be considered as the "ideal" tensile strength. The determined tensile strength by fitting can be used as a conservative design parameter for rock engineering. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic fracture resistance of blunt V-notched rock samples using the experimental and theoretical methods. The semi-circular bend sample, made of Fangshan granite, weakened by an edge blunt V-notch is selected as the testing rock sample. An empirical formula for calculating the dynamic notch fracture toughness of blunt V-notched samples is established by the stress extrapolation method in the finite-element method (FEM). According to the established empirical formula, the dynamic notch fracture toughness of the testing rock samples under split Hopkinson pressure bar (SHPB) impact loading condition are obtained from the dynamic strain signals in pressure bars. The experimental results reveal that the dynamic notch fracture resistance depends heavily on the opening angle, notch radius, and loading rate. A modified mean stress (MS) criterion is proposed to assess the dynamic fracture onset of blunt V-notched rock samples, which agree well with that obtained from the experimental data. These conclusions show that the proposed experimental and theoretical methods are capable of accurately assessing the dynamic strength of blunt V-notched specimen being tested, which may have significant implications to assess the dynamic fracture in notched rock samples and other brittle components. Highlights: The dynamic notch fracture toughness of blunt V-notched rock specimen under SHPB impact loading is investigated. An empirical formula for calculating mode-I notch fracture toughness of blunt V-notched rock specimen is derived. Dynamic notch fracture toughness is assessed using a modified mean stress criterion considering the effect of loading rate. [ABSTRACT FROM AUTHOR]

With our device, triaxial tensile tests can be performed on rock specimens with a confining pressure of at least 100 MPa. All the component materials of the device are made from high-strength steel, and the elastic modulus, tensile strength, and stiffness values are significantly greater than those of the rock specimens, thus meeting the triaxial tensile test requirements. Keywords: Triaxial extension; Tensile device; Extensile fracture; Tensile-shear failure; Shear failure; SEM; Rock EN Triaxial extension Tensile device Extensile fracture Tensile-shear failure Shear failure SEM Rock 1069 1077 9 02/23/22 20220201 NES 220201 Introduction Laboratory testing is one of the most important means to determine the basic parameters of rock materials and analyze/simulate the failure process or mechanism of rock masses. [Extracted from the article]

Based on the review of a wide range of literature, this paper finds that: (1) the average specific surface energy of various single crystals is only 0.8 J/m2. (2) The average specific fracture energy of the rocks with a pre-crack under static cleavage tests is 4.6 J/m2. (3) The average specific fracture energy of the rocks with a pre-cut notch but with no pre-crack under static tensile fracture (mode I) tests is 4.6 J/m2. (4) The average specific fracture energies of regular rock specimens with neither pre-made crack nor pre-cut notch are 26.6, 13.9 and 25.7 J/m2 under uniaxial compression, tension and shear tests, respectively. (5) The average specific fracture energy of irregular single quartz particles under uniaxial compression is 13.8 J/m2. (6) The average specific fracture energy of particle beds under drop weight tests is 74.0 J/m2. (7) The average specific fracture energy of multi-particles in milling tests is 72.5 J/m2. (8) The average specific energy of rocks in percussive drilling is 399 J/m3, that in full-scale cutting is 131 J/m3, and that in rotary drilling is 157 J/m3. (9) The average energy efficiency of milling is only 1.10%. (10) The accurate measurements of specific fracture energy in blasting are too few to draw reliable conclusions. In the last part of the paper, the effects of inter-granular displacement, loading rate, confining pressure, surface area measurement, premade crack, attrition and thermal energy on the specific fracture energy of rock are discussed. [ABSTRACT FROM AUTHOR]

Fractures provide preferential flow paths and establish the internal "plumbing" of the rock mass. Fracture surface roughness and the matedness between surfaces combine to delineate the fracture geometric aperture. New and published measurements show the inherent relation between roughness wavelength and amplitude. In fact, data cluster along a power trend consistent with fractal topography. Synthetic fractal surfaces created using this power law, kinematic constraints and contact mechanics are used to explore the evolution of aperture size distribution during normal loading and shear displacement. Results show that increments in normal stress shift the Gaussian aperture size distribution toward smaller apertures. On the other hand, shear displacements do not affect the aperture size distribution of unmated fractures; however, the aperture mean and standard deviation increase with shear displacement in initially mated fractures. We demonstrate that the cubic law is locally valid when fracture roughness follows the observed power law and allows for efficient numerical analyses of transmissivity. Simulations show that flow trajectories redistribute and flow channeling becomes more pronounced with increasing normal stress. Shear displacement induces early aperture anisotropy in initially mated fractures as contact points detach transversely to the shear direction; however, anisotropy decreases as fractures become unmated after large shear displacements. Radial transmissivity measurements obtained using a torsional ring shear device and data gathered from the literature support the development of robust phenomenological models that satisfy asymptotic trends. A power function accurately captures the evolution of transmissivity with normal stress, while a logistic function represents changes with shear displacement. A complementary hydro-chemo-mechanical study shows that positive feedback during reactive fluid flow heightens channeling. [ABSTRACT FROM AUTHOR]

This work aims to assess the fracture of U-notched limestone samples subjected to mixed mode I + II loading conditions with a predominant mode I influence, both at room temperature and at 250 °C. This analysis is based on the use of the Theory of the Critical Distances, and more specifically on the use of the Line Method, considering both an analytical and a numerical approach for the definition of the stress fields. An experimental campaign of almost 400 three-point bending tests has been performed as a basis for the fracture assessment of the limestone, using Single Edge Notched Bend (SENB) specimens with notch radii varying from 0.15 mm up to 15 mm, different temperature conditions and variable loading positions. The Theory of Critical Distances has successfully been applied to study the experimental results. The analytical and numerical stress fields for pure mode I fracture assessments provide similar accurate results both at 23 °C and 250 °C. Similarly, the mixed mode (I + II) fracture assessments allow the critical distance (L ) to be characterised for different mode mixities ( M e ), using the stress field around the notch tip obtained from the numerical models. Comparing the values of the critical distance against the mode mixity in isolation, a slight decrease of L is observed as it approaches pure mode I conditions ( M e = 1). However, if the results are analysed separately for each notch radius, L seems to be relatively constant with M e . In parallel, a certain influence of the notch radius on the critical distance is appreciated, which shows an increment both at 23 °C and 250 °C. [ABSTRACT FROM AUTHOR]

This paper presents a new analytical solution for deep circular tunnels in rock with consideration of disturbed zone, 3D strength and large strain. The rock is assumed to be elastic–brittle–plastic and governed by a 3D Hoek–Brown yield criterion. To take the large displacement around a tunnel into account, the large-strain theory is adopted to determine the displacement of rock in the plastic zone. Based on the equilibrium equation, constitutive law and large-strain theory, the governing equations for the stresses and radial displacement around the tunnel were derived and solved by using MATLAB. The proposed solution was validated by using it to analyze a tunnel and comparing the results with those from numerical analysis using a finite difference code. Finally, extensive parametric studies were performed on tunnels in both poor-quality and good-quality rock masses with respect to stresses and radial displacement. The results indicate that the disturbed zone and the flow rule both have significant effects on the stress and displacement distributions around the tunnel. [ABSTRACT FROM AUTHOR]

This paper proposes a unified constitutive model for rock based on the newly modified generalized Zhang-Zhu (GZZ) criterion. The constitutive model adopts a non-associated plastic flow rule and a continuous potential function that takes the three effective principal stresses into account. To reflect strain-softening, strain-hardening, and elastic-perfectly plastic behavior of rock in a unified way, a general expression is proposed to model the post-failure behavior of rock using the deviatoric plastic shear strain as the fundamental variable. The proposed constitutive model has been successfully implemented in a 3D finite-difference code and validated using it to simulate the true triaxial test of two types of rocks and comparing the simulation results with the experimental data. Finally, a 3D numerical model based on the proposed constitutive model is constructed to simulate a highway rock tunnel during construction. The results show that the predicted displacements of the rock tunnel are in good agreement with the field measurements. [ABSTRACT FROM AUTHOR]

In this paper, an empirical relationship between the Unconfined Compressive Strength (UCS) of intact rock and the unit shaft resistance of piles penetrating rock is investigated. A growing number of civil engineering projects are utilizing steel piles driven into rock where a significant portion of the pile capacity is derived from the shaft resistance. Despite the growing number of projects utilizing the technology, little to no guidance is offered in the literature as to how the shaft resistance is to be calculated for such piles. A database has been created for driven piles that penetrate bedrock. The database consists of 42 pile load tests of which a majority are steel H-piles. The friction fatigue model is applied to seven of the pile load tests for which sufficient UCS data exists in order to develop an empirical relation. The focus of this paper is on case histories that include driven pipe piles with at least 2 m penetration into rock. [ABSTRACT FROM AUTHOR]

Dilatancy controlled gas flow is characterized by a series of gas pressure-induced dilatant pathways in which the pathway aperture is a function of the effective stress within the solid matrix. In this paper, a three-dimensional hydro-mechanical model is presented to simulate the gas migration in initially saturated claystone with considerable anisotropy. The governing equations including mass conservation, momentum balance and energy conservation are presented for the unsaturated rock containing three phases, i.e., gas, water and solid grain. The constitutive model is proposed in which two conceptualized fracture sets with nonlinear mechanical behavior and cubic law controlled permeability are inserted, which have a direct effect on the hydro-mechanical behavior of the equivalent continuum. Finally, the developed model is validated against three gas injection tests on initially saturated Callovo–Oxfordian claystone. In general, the model is capable of capturing the main features of dilatancy controlled flow, i.e., anisotropic radial deformation, major gas breakthrough, and mechanical volume dilation of the sample. The proposed model offers additional insight into the relation between gas flow, solid matrix deformation and fracture opening/closure, which helps us get in-depth understanding of this gas transport mechanism. [ABSTRACT FROM AUTHOR]

In the present manuscript, the importance of support type on accurate determination of rock fracture toughness in semi-circular bending (SCB) test is demonstrated. First, by employing the finite element (FE) method, a detailed study is conducted to assess the effect of support friction on the mode I stress intensity factor (SIF) in the SCB specimen. Then, three different rocks and three various support types are utilized to investigate the support type effect experimentally. Both the FE and experimental results show that utilization of different types of supports results in different friction coefficients between the SCB specimen and the bottom supports. This can generate significant errors in calculations of SIF and fracture toughness of rock samples. It is shown that using the fixed or roller-in-groove support types can generate a large amount of error in rock fracture toughness calculations, although, these types of supports are still commonly being used by researchers. [ABSTRACT FROM AUTHOR]

In comparison with other types of construction, the development of rock engineering design codes has been slow. Codes must, however, be developed with relevant discipline-specific characteristics in mind. This paper, therefore, presents a generic design framework for rock engineering. The framework is based on the presumption that rock engineering design must be viewed as decision-making under uncertainty, which makes the design process subject to general risk management principles, as risk is defined as "effect of uncertainties on objectives" (ISO 31000). Thus, rock engineering design codes ultimately need to facilitate design processes that target the risk, to enable design of structures that not only are sufficiently safe and durable and cost-effectively constructed, but also imply safe and healthy work conditions during construction and an acceptably low environmental impact. The presented framework satisfies this fundamental requirement and the authors find codification of its principles to be rather straightforward, as long as the level of detail in the code is governed by a strict application of ISO's general risk management principles. Further details on methods and practical recommendations can instead be supplemented in separate handbooks and application guidelines. [ABSTRACT FROM AUTHOR]

In the present study, I R i SB s sb is determined for three different blocks of Delhi quartzite, and these blocks are identified as slightly weathered quartzite, moderately weathered quartzite, and highly weathered quartzite. For Kota sandstone, the minimum value of peak stress at which specimen failed under cyclic loading is observed to be reduced to 69.91 MPa (Tests 1 and 2 on Kota sandstone), which is 72% of the UCS of Kota sandstone. The normalized elastic modulus degradation equation for Kota sandstone, slightly weathered Delhi quartzite and moderately weathered Delhi quartzite are given in Eqs. From these equations, it may be observed that normalized elastic modulus degradation is exponential in Kota sandstone and moderately weathered Delhi quartzite, whereas it is linear degradation in slightly weathered Delhi quartzite. [Extracted from the article]

The failure mechanisms of rocks as a result of hydro-mechanical coupling effects have not been fully understood due to the limited abilities of conventional triaxial test equipment in measuring both the internal and external damage of rocks simultaneously in real time. This study presents an innovative triaxial testing system for detecting the internal and external damage of rocks. The system consists of an innovatively designed built-in acoustic emission sensor, an optical measurement system and a fully transparent pressure chamber. This work shows that the developed system can capture the internal and external damage behaviour of rocks using triaxial tests. The results demonstrate that the developed built-in acoustic emission sensors can measure the internal damage of rock specimens in an aqueous environment during a load test, while the proposed configuration of the optical measurement system together with the developed imaging construction technique can capture the surface crack development of samples. In addition, the acoustic ring-down counts and event counts can be used to detect the internal damage of the rock specimens, and the ring-down counts reach a significantly high level when the maximum axial force is reached. Furthermore, damage to rock specimens due to triaxial loading first occurs internally, and damage then extends externally. The critical failure point of a specimen can be determined when large fluctuations in the crack fractal dimension and ring-down counts occur simultaneously. [ABSTRACT FROM AUTHOR]

Tailings are man-made soils generated by mining activities. When mixed with cement and water, they form a cemented soil called cemented paste backfill (CPB). CPB is commonly used to backfill underground cavities created by ore extraction. The shear behaviour and resistance of the CPB–rock interface are important parameters for the geotechnical design of underground CPB structures. However, CPB can contain a relatively high amount of sulphate, and no studies have been performed to investigate the effect of the initial sulphate content of CPB on the behaviour and resistance of the interface between rock and tailings backfill that is undergoing cementation. The main objective of this experimental investigation is to, therefore, examine the effects of the initial sulphate content (0 ppm, 5,000 ppm, 15,000 ppm, and 25,000 ppm) of CPB on the shear behaviour of the CPB–rock interface at the early ages of curing (1 day, and 3 and 7 days). The obtained results show that, for samples at a very early age of 1 day, an increase in the sulphate content reduces the shear strength of the CPB–rock interface, whereas, for those cured for a longer period of 7 days, the sulphate can either positively or negatively affect the shear strength of the interface depending on the sulphate content. [ABSTRACT FROM AUTHOR]

Strain energy is one of the key factors that control the brittle failure process of rock mass, such as the onset of accelerating displacement. The phenomenon of accelerating displacement is a necessary and important precursor to predict the brittle failure of rock, and it is attributed to the unstable propagation of micro-cracks when the load reaches or exceeds the crack damage stress threshold. Thus, for the design of underground rock engineering and to ensure proper safety practices, it is important to propose a suitable strain energy criterion that uses the strain energy at the crack damage stress threshold (Wcd) to predict the strain energy at final failure (Wucs). For this purpose, a quantitative strain energy indicator (Wucs/Wcd) was proposed based on two-dimensional renormalization group theory for the prediction of the brittle failure of laboratory-scale rock samples subjected to uniaxial pressure. The indicator is a function of the homogeneity index, m, of the Weibull distribution. The reliability of the strain energy indicator was verified by a series of uniaxial compression tests on 12 shale samples that had different homogeneity indices, m. The heterogeneity of the sample was dominated by different bedding dip angles. The experimental results showed that the quantitative indicator could be used to predict the brittle failure of samples of any type of rock at the laboratory scale using their m values. In addition, the effect of the bedding dip angle on the homogeneity index, m, and the strain energy indicator were discussed based on the experimental results to provide a better understanding of the relationships among heterogeneity, the strain energy indicator, and the other physical and mechanical properties of the shale samples that were tested. Also, the discussion included the effects of the homogeneity of the sample and the strain energy indicator on the physical and mechanical properties of the samples. As a result, some conclusions were obtained that might be applicable to laboratory-scale shale samples. [ABSTRACT FROM AUTHOR]

The European design code for geotechnical engineering, EN-1997 Eurocode 7, is currently under revision. As design of underground openings in rock fundamentally differs from design of most other types of structures, the revised Eurocode 7 must be carefully formulated to be applicable to underground openings. This paper presents the authors’ view of how a design code for underground openings in rock needs to be organized to ensure that new structures are both sufficiently safe and constructed cost-effectively. The authors find that the revised version of Eurocode 7 carefully must acknowledge the fundamental decision-theoretical connection between design and risk management that should permeate all geotechnical design work. Otherwise, if the revised code is not given a risk-based framework, the authors fear that, as a consequence, the observational method will not be favorable to use in excavations of underground openings in rock. Then, cost-effective construction will be very difficult to achieve. [ABSTRACT FROM AUTHOR]

The seismic efficiency of a blast is the percentage of seismic energy in the total energy delivered by the explosives. It is a key indicator of the blast effects in civil engineering and seismic exploration. A method to determine seismic efficiency has been proposed based on the assumption of spherical wave radiation in an indefinite elastic medium and has been used in a series of blast tests performed at the construction site of a nuclear power plant. Analysis of the influencing factors of seismic efficiency shows that seismic efficiency increases with an increasing explosive charge and stemming length of the blastholes, while it decreases with an increasing decoupling coefficient. Generally, seismic efficiency is markedly lower in bench blasts than in paddock blasts due to free surface effects. Under any circumstances, the seismic energy only accounts for a few percent of the explosive energy. A comparison with theoretical solutions proves that the errors in the present method are low and acceptable in engineering. Therefore, some practical measures have been proposed to improve or lower the seismic efficiency according to the specific requirements of the blast operations. [ABSTRACT FROM AUTHOR]

In laboratory fracture toughness studies, the crack growth resistance of rock materials may be influenced by different factors such as specimen geometry, loading conditions, and also the type of pre-notch cut in the test sample. In this paper, a large number of mode I fracture toughness experiments are conducted on an Iranian white rock “Harsin marble” with six different mode I specimens. The selected test specimens are in the shape of cylindrical rod, rectangular beam, and circular Brazilian disk containing either chevron notch or straight crack. The effect of specimen geometry and pre-notch type was investigated statistically, and it was found that the average fracture toughness values of notched specimens were higher than those of the similar specimens but containing straight crack. Meanwhile, the scatters of fracture toughness data for chevron notched specimens were smaller than those for the straight cracked samples. For each set of experimental fracture toughness results, probability of fracture was investigated using two- and three-parameter Weibull statistical distributions. Comparison of the Weibull fitted curves for chevron notched and straight cracked samples with the same geometries demonstrated that the discrepancy between the corresponding curves can be described with a good accuracy by a simple shift factor. In addition, using the extended maximum tangential strain criterion which takes into account the influence of both KI and T-stress terms, the statistical fracture toughness data of chevron notched specimens were predicted in terms of the Weibull distribution parameters of the straight cracked specimens. [ABSTRACT FROM AUTHOR]

Predicting the rock fragmentation obtained in drawpoints or secondary fragmentation is crucial in Block caving application since many engineering decisions are based on this key variable. These can include drawpoints size and spacing, equipment selection; draw control procedures, production rates, dilution entry and operational blasting requirements. Secondary fragmentation depends on several variables including structures, rock mass strength, the vertical pressure acting on the column, the rate of draw, and the height of the ore column. In order to study these variables, 18 experiments on gravity flow under confinement were run to quantify the fragmentation occurring in a draw column. Based on these experiments, a mathematical model was developed the basis of which considers a modified comminution model fitted using the experimental data. Finally, the fitted model was scaled up to represent what is expected to occur in practice compared to field data with an estimated accuracy of around 1.5% of size distributions. An approximation of the secondary fragmentation expected as a function of draw height and vertical pressure, for example for 400 m of ore column (mean vertical pressure of 4.2 MPa), the mean size, d , could decrease from 0.82 to 0.47 m and the large size, d , from 1.08 to 0.62 m. [ABSTRACT FROM AUTHOR]

This paper presents a new experimental method for the characterization of the surface damage caused by a heat shock on a Brazilian disk test sample. Prior to mechanical testing with a Hopkinson Split Pressure bar device, the samples were subjected to heat shock by placing a flame torch at a fixed distance from the sample's surface for periods of 10, 30, and 60 s. The sample surfaces were studied before and after the heat shock using optical microscopy and profilometry, and the images were analyzed to quantify the damage caused by the heat shock. The complexity of the surface crack patterns was quantified using fractal dimension of the crack patterns, which were used to explain the results of the mechanical testing. Even though the heat shock also causes damage below the surface which cannot be quantified from the optical images, the presented surface crack pattern analysis can give a reasonable estimate on the drop rate of the tension strength of the rock. [ABSTRACT FROM AUTHOR]

The present study deals with three-dimensional nonlinear finite element (FE) analyses of a tunnel in rock with reinforced concrete (RC) lining subjected to internal blast loading. The analyses have been performed using the coupled Eulerian-Lagrangian analysis tool available in FE software Abaqus/Explicit. Rock and RC lining are modeled using three-dimensional Lagrangian elements. Beam elements have been used to model reinforcement in RC lining. Three different rock types with different weathering conditions have been used to understand the response of rock when subjected to blast load. The trinitrotoluene (TNT) explosive and surrounding air have been modeled using the Eulerian elements. The Drucker-Prager plasticity model with strain rate-dependent material properties has been used to simulate the stress-strain response of rock. The concrete damaged plasticity model and Johnson-Cook plasticity model have been used for the simulation of stress-strain response of concrete and steel, respectively. The explosive (TNT) has been modeled using Jones-Wilkins-Lee (JWL) equation of state. The analysis results have been studied for stresses, deformation and damage of RC lining and the surrounding rock. It is observed that damage in RC lining results in higher stress in rock. Rocks with low modulus and high weathering conditions show higher attenuation of shock wave. Higher amount of ground shock wave propagation is observed in case of less weathered rock. Ground heave is observed under blast loading for tunnel close to ground surface. [ABSTRACT FROM AUTHOR]

The article focuses on a study regarding the use of overstress model to simulate dynamic split tensile tests and its experimental validation. It mentions the use of tensile strength of rock and rock-like materials for stability and reliability of rock structures. It also mentions the building of finite element methods (FEMs) in brittle materials for cost-effective to observe crack propagation.

The article presents a study which determines Poisson's ratio of rock material by changing its axial stress and unloading lateral stress test. It notes the use of three mechanical indexes including axial stress, lateral stress and the axial strain. The authors also conducted tests on cryptocrystalline amygdaloidal basalt. Results showed relatively consistent to the uniaxial compression tests.

It is known that rigid circular particle models proposed in the literature do not properly reproduce the rock friction angle and the rock tensile strength to compressive strength ratio. A 2D rigid particle model is here presented which tries to overcome these issues while keeping the simplicity and the reduced computational costs characteristic of circular particle models. A particle generation algorithm is adopted which generates polygonal shape particles based on the Laguerre-Voronoi diagrams of the circular particle gravity centres. Several parametric studies are presented to show the influence of the micromechanical properties on both the macroscopic elastic and strength properties. It is shown that a good agreement with the known rock direct tensile to indirect tensile test ratio requires the incorporation of bilinear softening contact laws under tension and shear. Finally, the proposed model is validated against known triaxial and Brazilian tests of a granite rock. [ABSTRACT FROM AUTHOR]

The diametrical compression of a circular disc (Brazilian test) or cylinder with a small eccentric hole is a simple but important test to determine the tensile strength of rocks. This paper studies the failure mechanism of circular disc with an eccentric hole by a 3D numerical model (RFPA3D). A feature of the code RFPA3D is that it can numerically simulate the evolution of cracks in three-dimensional space, as well as the heterogeneity of the rock mass. First, numerically simulated Brazilian tests are compared with experimental results. Special attention is given to the effect of the thickness to radius ratio on the failure modes and the peak stress of specimens. The effects of the compressive strength to tensile strength ratio ( C/T), the loading arc angle (2 α), and the homogeneity index ( m) are also studied in the numerical simulations. Secondly, the failure process of a rock disc with a central hole is studied. The effects of the ratio of the internal hole radius ( r) to the radius of the rock disc ( R) on the failure mode and the peak stress are investigated. Thirdly, the influence of the vertical and horizontal eccentricity of an internal hole on the initiation and propagation of cracks inside a specimen are simulated. The effect of the radius of the eccentric hole and the homogeneity index ( m) are also investigated. [ABSTRACT FROM AUTHOR]

This paper presents a composite element algorithm of coupled normal stress and fluid flow process for fractured rock mass, developed from the composite element method (CEM). The coupled relation between the fracture flow and normal stress makes use of the 'filled model', which examines the asperities in the fracture as a layer of granular medium having high porosity and being clipped by the two parallel plates. The existence of fractures is not considered in the mesh generation, but it will be considered explicitly in the mapped composite element. The coupled normal stress and fluid flow process has been simulated by applying a cross iterative algorithm between the two fields. The proposed algorithm considers not only the flow through the fractures, but also the flow exchange between fractures and the surrounding rock blocks. In addition, it can be used for both the filled and non-filled fractures. The verification of the proposed algorithm has been conducted through the illustration of three examples by comparison with the conventional finite element method (FEM), from which the advantages and reliability of the proposed algorithm have been shown clearly. [ABSTRACT FROM AUTHOR]

The dynamic compressive strength of rock materials increases with the strain rate. They are usually obtained by conducting laboratory tests such as split Hopkinson pressure bar (SHPB) test or drop-weight test. It is commonly agreed now that the dynamic increase factor (DIF) obtained from impact test is affected by lateral inertia confinement, friction confinement between the specimen and impact materials and the specimen sizes and geometries. Therefore, those derived directly from testing data do not necessarily reflect the true dynamic material properties. The influences of these parameters, however, are not straightforward to be quantified in laboratory tests. Therefore, the empirical DIF relations of rock materials obtained directly from impact tests consist of contributions from lateral inertia and end friction confinements, which need be eliminated to reflect the true dynamic material properties. Moreover, different rocks, such as granite, limestone and tuff have different material parameters, e.g., equation of state (EOS) and strength, which may also affect the DIF of materials but are not explicitly studied in the open literature. In the present study, numerical models of granite, limestone and tuff materials with different EOS and strength under impact loads are developed to simulate SHPB tests and to study the influences of EOS and strength, lateral inertia confinement and end friction confinement effects on their respective DIFs in the strain rate range between 1 and 1,000 s. The commercial software AUTODYN with user-provided subroutines is used to perform the numerical simulations of SHPB tests. Numerical simulation results indicate that the lateral inertia confinement, friction confinement and specimen aspect ( L/ D) ratio significantly influence DIF obtained from impact tests and the inertia confinement effect is different for different rocks. Based on the numerical results, quantifications on the relative contributions from the lateral inertia confinement and the material strain rate effect on DIF of granite, limestone and tuff material compressive strength are made. The effects of friction coefficient, L/ D ratio and rock type on DIF are discussed. Empirical relations of DIF with strain rate for the three rock materials representing the true material strain rate effect are also proposed. [ABSTRACT FROM AUTHOR]

In order to better understand opening-mode fracture initiation and propagation perpendicular to the bedding plane at depth in sedimentary rocks, a series of two-dimensional (2D) numerical simulations is conducted. First, the stress states between two adjacent fractures for a typical three-layer model with pre-assigned fractures are simulated. Second, the same three-layer model without pre-assigned fractures is adopted to study the initiation and propagation of fractures in layered rocks. Numerical results show that infilling fractures grow more easily from flaws located near the interface than from those in the middle of the fractured layer. Flaws can begin to propagate to form a complete infilling fracture when the size of the flaws exceeds half of the thickness of the central layer. Under different overburden stress conditions and internal fluid pressure, the numerically obtained ratio of the critical fracture spacing to layer thickness varies between 0.465 and 0.833. This range encompasses the often-cited ratios of spacing to layer thickness in the literature for well-developed fracture sets. In addition, both the fracture pattern and the critical value of the fracture spacing to layer thickness ratio are strongly dependent on the heterogeneous characteristics of the central layer. In cases with a relatively homogeneous central layer, more interface fractures occur, and the interface delamination evidently influences the fracture saturation. [ABSTRACT FROM AUTHOR]

The effect of specimen size on the measured unconfined compressive strength and other mechanical properties has been studied by numerous researchers in the past, although much of this work has been based on specimens of non-standard dimensions and shapes, and over a limited size range. A review of the published literature was completed concentrating on the presentation of research pertaining to right cylindrical specimens with height:diameter ratios of 2:1. Additionally, new data has been presented considering high strength (70 MPa) cement mortar specimens of various diameters ranging from 63 to 300 mm which were tested to failure. Currently, several models exist in the published literature that seek to predict the strength-size relationship in rock or cementitious materials. Modelling the reviewed datasets, statistical analysis was used to help establish which of these models best represents the empirical evidence. The findings presented here suggest that over the range of specimen sizes explored, the MFSL (Carpinteri et al. in Mater Struct 28:311-317, ) model most closely predicts the strength-size relationship in rock and cementitious materials, and that a majority of the empirical evidence supports an asymptotic value in strength at large specimen diameters. Furthermore, the MFSL relationship is not only able to model monotonically decreasing strength-size relationships but is also equally applicable to monotonically increasing relationships, which although shown to be rare do for example exist in rocks with fractal distributions of hard particles. [ABSTRACT FROM AUTHOR]

The degree to which a rock abrades another rock is called its 'abrasivity'. Laboratory tests of abrasivity can be broadly divided into four kinds: drilling, rubbing, turning-operation and tumbling tests. The present study was initiated 30 years ago with the objective of investigating and developing methods for measuring rock abrasivity, and making some contribution towards understanding the relationships between the above test methods. Within the range of tests conducted, the turning-operation test turned out to be superior to the drilling test, albeit slightly, in terms of practicality. We have also conducted in situ tests using rock drills for the last 20 years. The results of those tests have been investigated and compared with the results of laboratory tests. There is a large degree of scatter in the data on gauge loss in button bits, which has obscured any correlations with laboratory data. Some correlations were found between height loss in button bits and laboratory findings. [ABSTRACT FROM AUTHOR]

The dynamic responses such as acceleration, velocity and displacement of geo-materials during fracturing and slippage have not been studied in the fields of geo-engineering and geo-science, as measurement, monitoring and logging technologies were not so advanced in the past. By virtue of the recent advances in these technologies, the authors have been carrying out experiments on geo-materials ranging from very soft materials such as clay to hard rocks such as siliceous sandstone by using different loading schemes and loading frames, as well as rock discontinuities with different surface roughness characteristics. This study describes the experiments and experimental results of the acceleration, velocity and displacement responses of geo-materials during fracturing and slippage under laboratory conditions. The velocity and displacement responses are obtained through the erratic pattern screening integration technique proposed by the authors. We further discuss their implications in geo-engineering and earthquake engineering in relation to permanent surface deformations. [ABSTRACT FROM AUTHOR]

Laboratory testing of rectangular beams using a synthetic rock was used to investigate the onset of dilation and spalling. The beams are axially compressed and subjected to 4-point bending to provide non-uniform compressive stresses. The maximum tangential stress occurs at the top of the beam and rapidly decreases with distance from the top of the beam. This stress distribution was used to simulate the maximum tangential stress distribution found around circular excavations. The results showed using this beam test configuration that the onset of dilation based on beam displacement and visually observed spalling began at approximately the same stress level. Discrete element numerical analyses (particle flow code) were used to evaluate the stress path at various locations in the beams. The analyses revealed that spalling and dilation in the beams occurred well below the peak strength failure envelope determined from conventional laboratory tests. The findings suggest that the onset of dilation in laboratory tests appears to be a good indicator for assessing the stress magnitudes required to initiate spalling. [ABSTRACT FROM AUTHOR]