A review of the tensile strength of rock was conducted to determine the relationship between direct tensile strength (DTS) and Brazilian tensile strength (BTS) and to examine the validity of estimating tensile strength from other measured properties, such as the crack initiation (CI) threshold. A data set was gathered from the existing literature where tensile values could be reliably correlated with unconfined compressive strength or CI values. It was determined that the BTS obtained in standard testing is generally greater than the equivalent DTS and that this relationship is rock type dependent. CI yields a reasonable estimate of tensile strength and this correlation is improved when the BTS values are reduced to DTS values by rock type specific correlations. The factor f, in DTS = f BTS, can be considered to be approximately 0.9 for metamorphic, 0.8 for igneous and 0.7 for sedimentary rocks. The relationships presented demonstrate that there is wide scatter in the available data for estimating tensile strength likely due to both specimen variability and testing configuration, including platen geometry and relative stiffness. Estimates of tensile strength should only be used for preliminary design purposes and measurements should be made to confirm preliminary assumptions for each design.

A Review of the Tensile Strength of Rock: Concepts and Testing

The dominant anisotropy (foliation and bedding) of geological materials, especially of foliated metamorphic rocks such as slates, gneisses, phyllites or schists, and sedimentary rocks with bedding planes, leads to complex fracture mechanical behavior. A series of Brazilian tests on Mosel slate were conducted considering different foliation-loading angles. Fracture patterns and strength of samples were analyzed. In addition, the deformation process and failure behavior of the foliated rock samples during the Brazilian tests were simulated using the discrete element method. The influence of anisotropic strength parameters of weak planes was studied numerically. A diagram of failure mode distribution marked with typical failure fracture patterns for Brazilian tests of transverse isotropic rocks was developed, which results in better understanding of failure modes of Brazilian tests on foliated rocks and allows a more reliable interpretation of strength parameters. It reveals, how the microparameters influence the bearing capacity and failure modes of Brazilian tests for anisotropic rocks.

Brazilian Tests on Transversely Isotropic Rocks: Laboratory Testing and Numerical Simulations

Failure of transversely isotropic rock under Brazilian test conditions

A three-dimensional meso-scale approach to concrete fracture based on combined DEM with X-ray μCT images

Rock engineering is highly susceptible to cyclic loads resulting from earthquakes, quarrying or rockbursts. Acquiring the fatigue properties and failure mechanism of rocks is pivotal for long-term stability assessment of rock engineering structures. So far, significant progress has been gained on the mechanical characteristics of rocks subjected to cyclic loading. For providing a global insight of typical results and main features of rocks under cyclic loading conditions, this study comprehensively reviews the state-of-the-art of deformation and failure mechanism and fatigue constitutive relationship of rocks subjected to cyclic loading in the past 60 years. Firstly, cyclic tests on rocks are classified into different types based on loading paths, loading parameters, loading types and environment conditions. Secondly, representative results are summarized and highlighted in terms of the fatigue response of rocks, including the deformation degradation, energy dissipation, damage evolution and failure characteristics; both laboratory testing and numerical results are presented, and various measurement techniques such as X-ray micro-computed tomography (micro-CT) and digital image correlation (DIC) are considered. Thirdly, the influences of cyclic loads on the mechanical characteristics of rocks are discussed, including the cyclic stress, frequency, amplitude and waveform. Subsequently, constitutive relationships for rocks subjected to cyclic loading are outlined, in which typical fatigue constitutive models are compared and analyzed, regarding the elastoplastic model, the internal variable model, the energy-based damage model and the discrete element-based model. Finally, some ambiguous questions and prospective research are interpreted and discussed.

A review of experimental and theoretical research on the deformation and failure behavior of rocks subjected to cyclic loading

Brazilian tensile strength tests on some anisotropic rocks

A nonlinear parallel-bonded stress corrosion (NPSC) model is proposed to simulate the fatigue characteristics of artificial rock (concrete) during cyclic loading. Numerical simulations of fatigue tests replicate the main mechanical features of concrete specimens subjected to cyclic loading observed in the laboratory. A nonlinear reduction speed of the bond diameter between two bonded particles represents the damage rate induced by the fatigue load. The damage rate is proportional to the maximum cyclic load level when the minimum cyclic load level is fixed. Compared with laboratory data, a logarithmic function of bond diameter in the NPSC model resulted in the best fit to simulate the fatigue behaviour of concrete. The simulation includes acoustic emission (AE) monitoring during fatigue tests. The axial strain of the assembly is governed by the evolution of bond breakages. The sum of released bond strain energy is documented as value proportional to cumulative AE energy. The simulation results show very similar evolution compared with laboratory data, which verifies the effectiveness of AE energy simulation.

Bonded-particle model-based simulation of artificial rock subjected to cyclic loading

Three-dimensional particle model based numerical simulation on multi-level compressive cyclic loading of concrete

An accurate quantification of the frictional behaviour of joints under cyclic normal load conditions during the cyclic shear process is important to characterize the joint and fault interactions during earthquakes and rock bursts. We conducted experimental studies and numerical simulations to investigate the cyclic frictional responses of planar joints subjected to cyclic changes of normal loads. Experiments were conducted on artificial rock-like planar joints using a large shear box device (GS-1000), with different vertical and horizontal impact frequencies, vertical impact load amplitudes, horizontal shear displacement amplitudes, and normal load levels. The average normal displacement of the upper block increased with decreasing normal load and decreased with increasing normal load during each cycle. The normal displacement decreased gradually with increasing number of shear cycles due to damage to the micro-asperities at the contact surface. Shear force and the apparent coefficient of friction (k = FShear/FNormal) changed cyclically with a change in shear direction, where k followed a square wave curve with the same peak value at the stable shear stage. The cyclic normal load amplitudes, horizontal shear displacement amplitudes, cyclic normal load frequencies, cyclic horizontal shear frequencies, and static normal force levels had little influence on the peak values of k. Numerical simulations proved that the spatial movement pattern of the loading plate and upper block of the specimen rotated clockwise or anti-clockwise at different shear displacements. Due to the rotation of the upper block, shear and normal stresses distributed at the contact surface were inhomogeneous, which generated a stress gradient along the interface. Consequently, the samples were damaged at the two edges due to the high local stresses. Finally, a mathematical equation is proposed, which can be used for predicting the shear strength of planar joints under cyclic changes of shear velocity and normal load.

Martin Herbst

Papers

Brazilian tensile strength tests on some anisotropic rocks

Bonded-particle model-based simulation of artificial rock subjected to cyclic loading

Three-dimensional particle model based numerical simulation on multi-level compressive cyclic loading of concrete

Cyclic Frictional Responses of Planar Joints Under Cyclic Normal Load Conditions: Laboratory Tests and Numerical Simulations

Drawing mechanism of fractured top coal in longwall top coal caving