Dynamic Tensile Strength Of Rocks Research Articles

Dynamic Brazilian tests of yellow sandstone under coupled static and dynamic loads

Through a series of static mechanical tests and (SHPB) dynamic impact tests, the static and dynamic mechanical parameters of rock as represented by yellow sandstone are determined, and the Holmquist-Johnson-Cook model parameters of the rock are calibrated using the test data and theoretical calculations. The feasibility of a numerical model is verified, and numerical analysis of the SHPB impact process under different radial pressure pre-loading is carried out on the basis of good verification. The results show that with increasing impact load, the degree of rock breakage increases, as does the dynamic tensile strength. With the application of increasing pre-static pressure, the dynamic tensile strength of the rock decreases gradually, and the maximum radial cumulative strain increases continuously under a given impact pressure, indicating that micro-cracks in the rock develop initially and then expand under the influence of pre-static pressure; the rock is more easily broken, and its weakening degree increases. Under coupled dynamic and static loading, the energy utilization rate of rock in the Brazilian splitting process is jointly affected by axial compression ratio and impact load. Too large a pressure ratio will reduce the strain-rate sensitivity of rock, resulting in low energy utilization rate, while too low an axial compression ratio will make the dynamic tensile strength of rock relatively high, which is not conducive to tensile failure. Therefore, on the premise of clear fracture form requirements, a suitable combination of axial compression ratio and impact velocity can improve the rock crushing effect and energy utilization rate.

Verification of Spalling Tensile Strength of Rocks using 3D GPGPU-accelerated Hybrid FEM/DEM

The spalling test is widely applied for evaluating dynamic tensile strength of rock under high strain-rate condition. The dynamic tensile strength is indirectly measured in the spalling test by theoretically assuming the tensile stress level at the failure position of a cylindrical specimen based on the 1D stress wave propagation theory. However, the theoretical estimation method for dynamic tensile strength have not been fully validated since dynamic tensile strength was determined with insufficient understanding of the fracture process, such as crack propagation and stress distribution in the rock specimen during the spalling test, owing to observational limitations in the experiment. Thus, a proper validation method is required for the proposed method, and numerical simulation can be used to validate the proposed method by reproducing the tensile fracture process of the rock specimen during the spalling test. Thus, the dynamic spalling tensile test for rock specimens was reproduced in this study using the GPGPU-based 3D hybrid FDEM that we recently developed. The dynamic tensile fracturing process was analyzed in the simulation of spalling under various strain-rate conditions. Finally, we discussed the application of various theoretical estimation methods to the 3D spalling test.

Physical and numerical evaluation of effect of specimen size on dynamic tensile strength of rock

It is well known that both the specimen size and the loading rate can affect the tensile strength of rock specimens. In this study, the combined effect of loading rate and specimen size on tensile strength was investigated by performing some physical and numerical Brazilian tests on specimens with notch and without notch. The dynamic tests were performed using the Split Hopkinson Pressure Bar apparatus. A type of dental gypsum commercially known as Snow Rock was used to prepare the molded gypsum specimens for the physical tests. The CA3 computer program was utilized for the numerical simulation. The bonded particle model for simulation of the rock together with the implemented micromechanical model was able to capture many features of the physical test results. It was shown that the notched specimens were much more sensitive to the loading rate. Furthermore, the results suggested that there is a critical stress rate at which the specimen size has no effect on the specimen strength. For loading rates greater than the critical one, with the increase in the specimen size, greater tensile strength was obtained. Fracture mechanics size effect was partially observed for the applied loading rates smaller than the critical rate.

Dynamic tensile failure of Laurentian granite subjected to triaxial confinement

In this paper, a traditional split Hopkinson pressure bar system is modified to be able to conduct dynamic tests on rock specimens under triaxial stress conditions. Granite specimens are manufactured as Brazilian discs to examine the dynamic tensile failure of rocks, and to investigate the influence of the triaxial stress state and loading rate on the dynamic tensile strength of rocks. The experimental results reveal the rate-dependence phenomenon of the tensile strength. The effect of the triaxial stress state is divided into the influence of the hydrostatic stress and that of the pre-tension, and it is found that the dynamic tensile strength of rocks is almost independent on the pre-tension. An empirical equation is proposed to explain the dynamic tensile behaviour of rocks under triaxial stress state and it agrees well with the experimental results. This finding has a certain value for underground excavation that only the hydrostatic pressure needs to be considered to evaluate the dynamic tensile failure of rocks in the intermediate zone.

Impact of wetting-drying cycles on dynamic tensile strength of rock

To study the effect of wetting-drying cycles on dynamic tensile strength of rock, dynamic indirect tension test of sandstone samples after 0, 1, 3, and 5 wetting-drying cycles was conducted. Tensile failure was observed by digital image correlation. The result shows that failure appears in the center of the samples initially, consistent with tensile strain field results obtained by digital image correlation. An empirical formula was derived to link loading rate and dynamic tensile strength of rock after wetting-drying cycles. As the loading rate increases, tensile strength increases significantly. Tensile strength reduces as the number of wetting-drying cycles increases. These results provide reference data for complex engineering problems such as those that occur in coal mining, tunneling and water conservancy.

Fracture of saturated concrete and rocks under dynamic loading

A dynamic tensile strength of rocks and concrete is studied in a wide range of strain rates using a structural-temporal approach. An idea of a material’s fracture incubation time, taken as a scale dependent material constant and as a primary measure of the reaction of materials subjected to dynamic loading, was applied to explain the instability of the ultimate critical stress values in rock materials and concrete. Temporal dependencies (strength – strain rate; pulse amplitude – pulse duration; maximum stress – pulse duration) of the spall strength for short pulse and high rate loading of dry and saturated concrete are compared and discussed. A phenomenon of the greater ultimate stress of concrete and rocks with the highest relative humidity under dynamic loading is explained. It is shown that conventional fracture criteria based only on the strain rate dependence taken from a usual linear loading law may give ambiguous results being applied for other shapes of the pulse. Application of these criteria to the case of short pulse load indicate that they are not adapted to the estimation of threshold loading parameters in the case of non-linear loading history. On the contrary, it is proved that the incubation time fracture model based on a set of material parameters, invariant to the loading history, is applicable for a broad range of load pulse types and shapes.

Dynamic rock tensile strengths of Laurentian granite: Experimental observation and micromechanical model

Tensile strength is an important material property for rocks. In applications where rocks are subjected to dynamic loads, the dynamic tensile strength is the controlling parameter. Similar to the study of static tensile strength, there are various methods proposed to measure the dynamic tensile strength of rocks. Here we examine dynamic tensile strength values of Laurentian granite (LG) measured from three methods: dynamic direct tension, dynamic Brazilian disc (BD) test, and dynamic semi-circular bending (SCB). We found that the dynamic tensile strength from direct tension has the lowest value, and the dynamic SCB gives the highest strength at a given loading rate. Because the dynamic direct tension measures the intrinsic rock tensile strength, it is thus necessary to reconcile the differences in strength values between the direct tension and the other two methods. We attribute the difference between the dynamic BD results and the direct tension results to the overload and internal friction in BD tests. The difference between the dynamic SCB results and the direct tension results can be understood by invoking the non-local failure theory. It is shown that, after appropriate corrections, the dynamic tensile strengths from the two other tests can be reduced to those from direct tension.

Dynamic tensile failure of rocks under static pre-tension

A modified split Hopkinson pressure bar (SHPB) system is utilized to load Brazilian disc (BD) samples statically, and then exert dynamic load to the sample generated by impact. The pulse shaper technique is used to generate a slowly rising stress wave to facilitate the dynamic force balance in dynamic tests. Five groups of Laurentian granite BD samples (with static tensile strength of 12.8MPa) under the pre-tension of 0MPa, 2MPa, 4MPa, 8MPa, and 10MPa were tested under different loading rates. The results show that the rock dynamic tensile strength decreases with the increase of the pre-tension. It is also observed that under the same pre-tension stress, the dynamic tensile strength increases with the loading rate. However, the total tensile strength of the rock is roughly independent of the pre-tension. The failure patterns of the samples also reveal the rate dependence of the dynamic tensile strength of rocks.

Mechanism on simulation and experiment of pre-crack seam formation in stope roof

The pre-crack blast technology has been used to control the induction caving area in the roof. The key is to form the pre-crack seam and predict the effect of the seam. The H-J-C blast model was built in the roof. Based on the theories of dynamic strength and failure criterion of dynamic rock, the rock dynamic damage and the evolution of pre-crack seam were simulated by the tensile damage and shear failure of the model. According to the actual situation of No. 92 ore body test stope at Tongkeng Mine, the formation process of the pre-crack blast seam was simulated by Ansys/Ls-dyna software, the pre-crack seam was inspected by a system of digital panoramic borehole camera. The pre-crack seam was inspected by the system of digital panoramic borehole in the roof. The results of the numerical simulation and inspection show that in the line of centers of pre-hole, the minimum of the tensile stress reaches 20 MPa, which is much larger than 13.7 MPa of the dynamic tensile strength of rock. The minimum particle vibration velocity reaches 50 cm/s, which is greater than 30–40 cm/s of the allowable vibration velocity. It is demonstrated that the rock is destroyed near the center line and the pre-crack is successfully formed by the large diameters and large distances pre-crack holes in the roof.

Some Fundamental Issues in Dynamic Compression and Tension Tests of Rocks Using Split Hopkinson Pressure Bar

Accurate characterizations of rock strengths under higher loading rates are crucial in many rock engineering applications. The split Hopkinson pressure bar (SHPB) system has been used to quantify the dynamic compressive strength of rocks using the short cylindrical specimen and the dynamic tensile strength of rocks using the Brazilian disc (BD) specimen. However, SHPB is a standard tool that is suitable for metal testing; there are some fundamental issues that need to be carefully visited in applying SHPB to rock dynamic tests. This paper addresses several such critical issues, including the choice of slenderness ratio of the compressive specimen, the effect of friction between the sample and bars on the measured results of compressive strength, the necessity of dynamic force balance on the dynamic BD test, and the validity of using the standard BD equation in the data reduction. We show that with proper experimental designs that address these issues, the dynamic compressive strength and dynamic tensile strength of rocks measured using SHPB are valid and reliable.

Semicircular bend testing with split Hopkinson pressure bar for measuring dynamic tensile strength of brittle solids

We propose and validate an indirect tensile testing method to measure the dynamic tensile strength of rocks and other brittle solids: semicircular bend (SCB) testing with a modified split Hopkinson pressure bar (SHPB) system. A strain gauge is mounted near the failure spot on the specimen to determine the rupture time. The momentum trap technique is utilized to ensure single pulse loading for postmortem examination. Tests without and with pulse shaping are conducted on rock specimens. The evolution of tensile stress at the failure spot is determined via dynamic and quasistatic finite element analyses with the dynamic loads measured from SHPB as inputs. Given properly shaped incident pulse, far-field dynamic force balance is achieved and the peak of the loading matches in time with the rupture onset of the specimen. In addition, the dynamic tensile stress history at the failure spot obtained from the full dynamic finite element analysis agrees with the quasistatic analysis. The opposite occurs for the test without pulse shaping. These results demonstrate that when the far-field dynamic force balance is satisfied, the inertial effects associated with stress wave loading are minimized and thus one can apply the simple quasistatic analysis to obtain the tensile strength in the SCB-SHPB testing. This method provides a useful and cost effective way to measure indirectly the dynamic tensile strength of rocks and other brittle materials.

Effect of the Strain Rate and Water Saturation for the Dynamic Tensile Strength of Rocks

Effect of the Strain Rate and Water Saturation for the Dynamic Tensile Strength of Rocks

Strain-rate dependency of the dynamic tensile strength of rock

Dynamic tension tests based on Hopkinson’s effect combined with the spalling phenomena were performed on Inada granite and Tage tuff to investigate the strain-rate dependency of the dynamic tensile strength of rock. The static tensile strengths were determined and compared with the dynamic tensile strengths. The fracture processes under various loading conditions were analyzed using a proposed finite element method to verify the differences between the dynamic and static tensile strengths and the strain-rate dependency. These analyses revealed that the differences were due to the stress concentrations and redistribution mechanisms in the rock. The rock inhomogeneity also contributed to the difference between the dynamic and static tensile strengths. An increase in the uniformity coefficient stimulated a reduction in the strain-rate dependency; i.e., the strain-rate dependency of the dynamic tensile strength was caused by the inhomogeneity of the rock. The fracture processes and principal stress fields in the specimens at high and low strain rates were analyzed to investigate fracture formations at various strain rates. Higher strain rates generated a large number of microcracks; the interaction of the microcracks interfered with the formation of the fracture plane. The observed dynamic tensile strength increase at a high strain rate was caused by crack arrests due to the generation of a large number of microcracks.

Wave propagation from an explosive source

The model proposed describes the radiation of the primary seismic pulse from an explosive source. The model incorporates a viscous Voigt liquid in description of the nonelastic rock deformation that the explosion causes. The problem is solved in the frequency domain, followed by Fourier synthesis to obtain waveforms. Comparisons of the theoretical results with field data in three sedimentary environments of shale, sandstone, and marl indicate good quantitative agreements in shape and duration of transient pulses. Values of angular normal stress obtained at the deformed boundary suggest a dynamic tensile strength of rocks that decreased with duration of the tensile stress transient. The radius of the deformed zone (B) scales with the charge size Q approximately as [Formula: see text] where n is [Formula: see text] or larger.