Tensile Strength Of Rock Materials Research Articles

A Comparative Study on the Dynamic Tensile Strength Evaluation Method of Rock Materials

The representative calculation methods of dynamic tensile strength applied to the spalling test are comparatively reviewed in the same experimental cases. The results are compared with those of the ISRM suggested dynamic BD method. Through comparative verification results and analysis of methodological characteristics of each determination method in the spalling test, the most reasonable method for calculating dynamic tensile strength in the high strain rate condition is derived. The local strain rate and apparent strain rate are calculated for the same experimental cases, and the difference in the result values according to the strain rate calculation technique is analyzed through comparative verification of the calculated results. Consequently, the characteristics of each dynamic tensile strength determination method and strain rate calculation method in the spalling test are presented, and the results of the review on the most suitable method for calculating the dynamic tensile strength of rock materials are presented.

Numerical and experimental investigation of the anisotropic tensile behavior of layered rocks in 3D space under Brazilian test conditions

Brazilian disc (BD) testing is a typical method for measuring the indirect tensile strength of rock materials. Both experimental and theoretical studies involving BD testing of anisotropic rocks typically focus on the influence of the 2D bedding effect, where a specimen is parallel to the bedding planes, whereas the influence of the 3D bedding effect combining both the orientation and loading angle has rarely been investigated. Therefore, in this study, BD tests considering the 3D bedding effect were conducted on layered Longmaxi shale, and 3D BD models of layered shale were established using 3D globally embedded cohesive elements with zero thickness. The numerical results were compared to testing results. The 3D BD numerical model was then applied to simulate Asan gneiss and Silurian silty slate to verify the applicability. Finally, the influence of the 3D bedding effect on both the apparent tensile strength (ATS) and failure modes was analyzed. We also considered the influence of the spacing of bedding planes and bedding strength. The results indicated that the numerical results for both the ATS and failure modes were in good agreement with the test results with a maximum error of 17.8% for the ATS. The applicability of the developed 3D BD numerical model to different layered rocks was confirmed by the numerical results for both Asan gneiss and Silurian silty slate. Strong dependencies of the ATS and failure modes on both the orientation (α) and loading (β) angles were observed in the layered Longmaxi shale. The normalized ATS for various orientation and loading angles achieved high values of 3.15 and 2.90, respectively, indicating that the influence of the orientation angle is slightly stronger than that of the loading angle. The Longmaxi shale exhibited a distinct tensile failure mode at α = 0° @ β = 0–15°, α = 0° @ β = 75–90°, and α = 90°, but a more complicated mixed mode of both tensile and shear failure was observed under other conditions. The contribution of shear failure increased significantly at 0° <α < 90° compared to α = 0°. The spacing of the bedding planes had a limited influence on the ATS and failure modes, but the bedding strength had a significant influence. There may be a linear relationship between bedding strength and the spatial distribution parameter of the critical plane approach criterion.

Research of Dynamic Tensile Properties of Five Rocks under Three Loading Modes Based on SHPB Device

The validity of calculating the dynamic tensile strength of rock materials based on dynamic Brazilian tests is problematic. In order to gain a deeper understanding of the effects of three typical loading methods on the damage mechanism of rock specimens in the dynamic Brazilian tests, five different rocks were selected for the study. In the constant incident energy dynamic Brazilian test, the loading modes had a significant effect on the loading rate and dynamic tensile strength of the specimen, with the highest loading rate and tensile strength of the specimens under mode-III loading, followed by mode-I loading and mode-II loading. A high-speed camera and the digital image correlation (DIC) technique were used to successfully capture the rupture process of the Brazilian disc during impact loading. The evolution of the displacement and strain fields of the specimen was obtained by DIC technique, and four typical failure patterns and two rupture characteristics in the dynamic Brazilian test were summarized. The loading mode determined the crack initiation position of the specimen in the dynamic Brazilian test. The results showed that the mode-III loading is the most consistent with the Brazilian test theory, while the mode-II loading violates the test principle.

Evaluating a new method for direct testing of rock tensile strength

Tensile stress is a ubiquitous concern in rock engineering, and it is still a challenging task to determine reasonably the tensile strength of rock materials. The main shortcomings of existing direct tensile testing methods include high requirements for test equipment, complex preparation processes, and high proneness of test failure. For the bonding or clamping method, it is not only difficult to ensure the alignment of tensile stress to the specimen axis, but also easy to break the sample in the bonding or clamping segment. To overcome the shortcomings of the existing methods, a novel direct testing method for tensile strength is examined in this study. This method allows determination of rock tensile strength via conventional rock mechanics testing systems and the test results exhibit good consistency, which has incomparable advantages compared with traditional testing methods.

A New Flattened Cylinder Specimen for Direct Tensile Test of Rock.

In recent decades, researchers have paid more attention to the indirect tensile test than to the direct tensile test (DTT) of rocks, mainly due to difficulties in the alignment and the stress concentration at the end of an intact cylindrical specimen. In this paper, a new flattened cylinder specimen and a clamp device were designed to obtain the true tensile strength of the rock in DTT. Stress distributions of the specimen with different lengths (l) and cutting thicknesses (t) were analyzed, and damage processes of the specimen were monitored by the Digital Image Correlation (DIC), the fractured sections were also scanned. Different mechanical parameters were also obtained by the DTT of the flattened cylinder specimens and the intact cylinder specimens, as well as the Brazilian disc. Research results show that the tensile strength obtained by DTT is smaller than the Brazilian disc and is slightly greater than the intact cylindrical specimen. The flattened cylinder specimen with 0.20 ≤ 2t/D < 0.68 and 0.10 ≤ l/D ≤ 0.20 is recommended to measure the true tensile strength of rock material in DTT. This new shape of the specimen is promising to be extended in the uniaxial or triaxial direct tension test.

Analyses and predictions of rock cuttabilities under different confining stresses and rock properties based on rock indentation tests by conical pick

The rock indentation tests by a conical pick were conducted to investigate the rock cuttability correlated to confining stress conditions and rock strength. Based on the test results, the regression analyses, support vector machine (SVM) and generalized regression neural network (GRNN) were used to find the relationship among rock cuttability, uniaxial confining stress applied to rock, uniaxial compressive strength (UCS) and tensile strength of rock material. It was found that the regression and SVM-based models can accurately reflect the variation law of rock cuttability, which presented decreases followed by increases with the increase in uniaxial confining stress and the negative correlation to UCS and tensile strength of rock material. Based on prediction models for revealing the optimal stress condition and determining the cutting parameters, the axial boom roadheader with many conical picks mounted was satisfactorily utilized to perform rock cutting in hard phosphate rock around pillar.

On the overload phenomenon in dynamic Brazilian disk experiments of rocks

The Brazilian disk (BD) test is one of the testing methods suggested by the International Society for Rock Mechanics and Rock Engineering (ISRM) for determining the static tensile strength of rocks. Meanwhile, it is also the only method suggested by ISRM to determine the dynamic tensile strength of rock materials. However, it is worth noting that both static and dynamic tensile strengths of rocks tend to be overestimated using the BD specimen. This can be partially attributed to the overload phenomenon, which is particularly pronounced in dynamic BD tests. In this manuscript, the physical interpretation of the load used in BD test is revised based on the Griffith criterion. To systemically investigate the mechanism and the loading rate dependence of the overload phenomenon for rock materials, the dynamic BD tests under different loading rates were conducted using split Hopkinson pressure bar (SHPB) system. A strain gauge was attached 5 mm off the disk center to detect the failure onset. Then the transmitted wave signal was recorded and processed according to the distance of wave propagation on the transmitted bar and the specimen. The so-called nominal tensile strength and the real tensile strength were obtained through analyzing. The overload phenomenon was then quantitatively evaluated using the pre-defined overload ratio. Additionally, numerical simulations were carried out through the particle flow code (PFC) to observe the failure processes of the disk specimens in microscale. The loading rate dependency was introduced to revise the micro parameters to get a better simulation result. The overload phenomenon and the overload ratio were observed and calculated. The results show that: (1) the overload phenomenon of tensile strength can be obviously observed in the dynamic BD tests, and the overload ratio of the tensile strength logarithmically increases with the loading rate. (2) The overload phenomenon inspected by numerical simulation agrees well with the experimental observation. These results have demonstrated that the overload phenomenon does exist in dynamic BD tests. Its intrinsic mechanism is related to the geometry of specimen and the principle of the testing method based on the experimental and numerical tests. The overload ratio can reach 40% under a high loading rate. It is thus necessary to correct the result from the dynamic BD test to determine the real dynamic tensile strength using the method proposed in this work.

An Experimental Investigation of the Influence of Loading Rate on Rock Tensile Strength and Split Fracture Surface Morphology

To investigate the effect of the loading rate on the tensile strength of rock material and the morphology of the resulting split fracture surfaces, three types of rock specimens, namely, granite, basalt and limestone, were collected and tested with Brazilian testing under different loading rates. The tensile strength was measured, and the effect of the loading rate on the tensile strength of the rock material was studied. Digital terrain map models of the split fracture surface were obtained with an optical 3D scanning technique, and the effects of the loading rate on the geometry and morphology of the fracture surface were studied. The influence of the loading rate and tensile strength on the roughness was studied quantitatively by calculating the roughness indices of a fracture surface for all three kinds of rock. The research results show that the rock tensile strength increases with the loading rate. A linear relationship was established in double-logarithmic coordinates to describe the relationship between the tensile strength and the loading rate. Four different roughness indices were used to describe the morphology of the split fracture surface. The analysis results show that the magnitudes of all the roughness indices increase with the loading rate. Additionally, the roughness indices for all three types of rock linearly increase with the tensile strength. This linear trend indicates that it is possible to utilize fracture surface roughness indices to estimate rock tensile strength. The current study may motivate further research on the relationship between the morphology indices of rock fractures and mechanical parameters of the rock.

Experimental investigation of rock cuttability based on rock indentation tests by a conical pick

Stress conditions and rock properties significantly influence rock breakage. The rock indentation tests by a conical pick were conducted to investigate the rock cuttability corelated to confining stress conditions and rock strengths. Based on the test results, the regression analyses were used to find the relationship among rock cuttability, uniaxial confining stress applied to rock, uniaxial compressive strength (UCS) and tensile strength of rock material. It was found that the regression models can accurately reflect the variation law of rock cuttability, which presents decreases followed by increases with increases in uniaxial confining stress and the negative correlation to UCS and tensile strength of rock material. The established models are suitable for guiding the rock cutting by conical pick and will provide useful information for mechanized mining in deep hard rock.

Novel Intelligent Approach for Peak Shear Strength Assessment of Rock Joints on the Basis of the Relevance Vector Machine

This study mainly establishes a novel intelligent assessment model for peak shear strength of rock joints based on the relevance vector machine (RVM). RVM is a state-of-the-art soft computing technique that has been rarely utilized in joint shear strength assessment. To establish the hybrid intelligent model, three-dimensional scanning tests and direct shear tests on 36 granite joint specimens were conducted. The peak shear strength ratio (τp/σn) is perceived as an explanation of four types of influencing factors, including joint surface roughness, strength of rock material, basic friction angle, and normal stress. In particular, the compressive strength and tensile strength of rock material are first considered together. A total of 36 experimental data were used in this study to train the RVM model to predict the peak shear strength of rock joints. The performance of the RVM model was assessed using the direct shear test data of rock joints collected from previous researches. Four different kinds of kernel functions were adopted to obtain the optimal model. Results show that the proposed model is significantly efficient in predicting the peak shear strength of rock joints. The proposed model is also a promising tool for peak shear strength of rock joints and provides a new research approach to research the mechanical properties of rock joints.

Multibody failure criterion for the four-dimensional lattice spring model

Although lattice spring models (LSMs) have been increasingly applied in the study of rock fracturing and rock failure, it is still difficult to accurately reproduce high ratios of the uniaxial compressive strength to the tensile strength of rock materials. In this work, a feasible solution is developed for the four-dimensional lattice spring model (4D-LSM) that overcomes this shortcoming by incorporating a multibody failure criterion. The stress tensor of a spring bond is determined by the local deformation state between this bond and its neighboring spring bonds, which is further used to judge its failure state using a stress-based strength model. Then, a cohesive zone model is introduced to describe the postfailure stage of the spring bond. The performance of the proposed solution in reproducing the high ratio of the uniaxial compressive strength to the tensile strength of rock materials is demonstrated via numerical tests. Enriched by the multibody failure criterion, 4D-LSM is demonstrated to solve a broader range of practical problems that involve rock failure.

Measurement of tensile strength of brittle rocks using a half ring shaped specimen

A tensile test using a half ring (HR) shaped specimen is attempted for the determination of the tensile strength of rock materials. The HR test is a 3-point bend test similar to the semicircular bend (SCB) test. However, the HR specimen is a curved prismatic bar. The theoretical tensile strength of this special bar can be obtained by an analytical formula derived from a basic theory of strength of materials. Owing to the eccentricity of the HR specimen, the possibility for a single tensile fracture to begin at the intended location can increase. This may give results that are more accurate than the conventional bending tests. In this paper, after the concept and formula of the HR test are introduced, its applicability to brittle rocks is investigated by FEM simulations and laboratory tests. In the processes, the theories of the Brazilian test and a special SCB test, which is an alternative to the Brazilian test, are used to examine the accuracy of the HR test.

Bending Properties of Granite Beams with Various Section-Sizes in Three-Point Bending Tests

To examine the size effects on the bending strength of rock and determine the relation between Brazilian splitting strength and bending strength, Brazilian splitting tests were performed to measure the indirect tensile strength of rock materials. Three-point bending tests were used to evaluate the bending properties of rock beam by changing the sample cross section size including height, width, and diameter. The peak load increases as section size linearly expands. An exponential relation between the peak load and the cross section area ratio is found for rectangular section with different heights and circular section with different diameters samples, whereas a linear one is observed for rectangular section with different widths samples. The measured peak load ratio for all tested samples actually differs from the theoretical one. The maximum shear stress on the cross section of the sample is linearly affected by the section height and diameter but hardly influenced by the section width. Bending strength is barely affected by section size which leads to the conclusion that no size effect is observed in the tested size range. However, the ratio of bending strength to Brazilian tensile strength is found within 3.81–4.26 for rectangular samples and 3.14–3.48 for circular samples. The obtained bending strength is higher than the Brazilian tensile strength, which is in good agreement with the previous results, and the bending strength to Brazilian tensile strength ratio is associated with the sample section size.

Experimental Study on the Validity and Rationality of Four Brazilian Disc Tests

The validity and rationality of the Brazilian disc test have attracted much attention since it was proposed. To verify the validity of four Brazilian disc tests, red sandstone and yellow rust granite were employed. In these experiments, uniaxial tensile tests and four Brazilian disc tests were performed. Meanwhile, the typical location of the Brazilian discs was arranged with gages to detect the crack initiation location. By analyzing the rationality of the four Brazilian disc tests from two aspects, the crack initiation location and the difference between indirect tensile strength and direct tensile strength, it was found that the Brazilian disc tests without cushion and the Brazilian disc tests with two small-diameter steer rods are suitable for determining the indirect tensile strength of rock materials. However, the Brazilian disc tests with arc loading jaws should be carefully adopted to measure the indirect tensile strength due to their overestimation of the indirect tensile strength. Additionally, flattened Brazilian disc tests were found to be not suitable for measuring the indirect tensile strength of rock materials.

Estimation of uniaxial compressive and tensile strength of rock material from gypsum deposits in the area of Knin

Estimation of uniaxial compressive and tensile strength of rock material from gypsum deposits in the area of Knin

Dog bone shaped specimen testing method to evaluate tensile strength of rock materials

To eliminate the holding and gluing problems making the direct tensile strength test hard to be applied, a new method of testing specimens prepared using lathe machine to make the dog bone shape is assessed whether it could be applied to determine accurate direct tensile strength values of rock materials. A series of numerical modelling analyses was performed using finite element method to investigate the effect of different specimen and steel holder geometries. In addition to numerical modelling study, a series of direct tensile strength tests was performed on three different groups of rock materials and a rock-like cemented material to compare the results with those obtained from the finite element analyses. A proper physical property of the lathed specimens was suggested and ideal failure of the dog bone shaped specimens was determined according to the results obtained from this study.

Determination of spalling strength of rock by incident waveform

An experimental technique for determining the spalling strength of rock-like materials under a high strain rate is developed. It is observed that the spalling strength of a specimen can be determined by only knowing the wavelength, loading peak value and length of the first spallation of an incident wave under a specific loading waveform. Using this method in combination with a split-Hopkinson pressure bar (SHPB) and other experimental devices, the spalling strength of granite specimens under a high strain rate is tested. Comparisons with other experimental results show that the new measuring method can accurately calculate the dynamic tensile strength of rock materials under a high strain rate.

Static and dynamic tensile failure characteristics of rock based on splitting test of circular ring

Static and dynamic splitting tests were conducted on ring marble specimens with different internal diameters to study the tensile strength and failure modes with the change of the ratio of internal radius to external radius (ρ) under different loading rates. The results show that the dynamic tensile strength of disc rock specimen is approximately five times its static tensile strength. The failure modes of ring specimens are related to the dimension of the internal hole and loading rate. Under static loading tests, when the ratio of internal radius to external radius of the rock ring is small enough (ρ<0.3), specimens mostly split along the diametral loading line. With the increase of the ratio, the secondary cracks are formed in the direction perpendicular to the loading line. Under dynamic loading tests, specimens usually break up into four pieces. When the ratio ρ reaches 0.5, the secondary cracks are formed near the input bar. The tensile strength calculated by Hobbs' formula is greater than the Brazilian splitting strength. The peak load and the radius ratio show a negative exponential relationship under static test. Using ring specimen to determine tensile strength of rock material is more like a test indicator rather than the material properties.

A Modified Overstress Model to Simulate Dynamic Split Tensile Tests and Its Experimental Validation

The tensile strength of rock and rock-like materials is universally acknowledged to be much lower than their compressive strength and shearing strength (Meyers and Chawla 1999). Furthermore, the stability and reliability of rock structures are correlated remarkably well with the dynamic tensile strength of rock materials. Therefore, dynamic split tensile tests under high strain rate loads have been an active area of investigation in the field of rock mechanics. Carneiro (1943) first used Brazilian disc specimens to determine the tensile strength of brittle materials. Wang et al. (2004) improved these experiments by using flattened Brazilian discs (FBDs) instead to avoid stress concentration at the loading end. Wang’s method ensures that the initial crack only occurs in the central part of a specimen, which is vital for the validation of a split test. Recently, the split Hopkinson pressure bar (SHPB) has come into use as a general apparatus to determine the dynamic tensile strength of rock-like materials (Saksala et al. 2013; Xu et al. 2014). However, among the failure processes, crack propagation is difficult to observe, which makes it very difficult to judge whether or not the initial crack starts from the center. Finite element methods (FEMs) are widely used to simulate failure in brittle materials (e.g., Hang et al. 2015; Saksala et al. 2015). Compared with laboratory experiments, it is much easier and cost-effective to observe crack propagation in a simulation as long as an appropriate material model is built for the specimens. In this article, we build 3D models of FBD specimens in an SHPB apparatus and use these models to conduct numerical simulations of rock dynamic split tests. A modified overstress constitutive model is applied to describe the rock-like material. The failure patterns resulting from dynamic split tensile tests, as well as crack initialization and propagation, are studied with these simulations. The simulation results are verified by laboratory experiments using the SHPB and a high-speed camera.

Numerical Analysis of Flattened Brazilian Disc Test Based on the Cusp Catastrophe Theory

The Brazilian disc test is a simple and useful technique to determine the tensile strength of rock materials. By using FLAC3D, 63 numerical simulations in total were performed when flattened Brazilian disc coefficient and Poisson’s ratio were different. Based on Griffith theory, the corresponding FISH language was compiled to record the Griffith equivalent stress. Through analysis of numerical simulation results, it is indicated that fracture plane was not the plane going through center of the Brazilian disc, which was in good agreement with the references. In addition, the flattened Brazilian disc coefficients had greater influence on tensile strength than Poisson’s ratio. Based on cusp catastrophe theory, the flattened Brazilian disc coefficient should not exceed 0.035 for the flattened Brazilian disc tests. Consequently, a tensile strength empirical formula considering flattened Brazilian disc coefficient by utilizing the flattened Brazilian disc test was established, which wasσt=0.9993 exp (-11.65ε)2p/πDt,ε≤0.035.