The development of the Brazilian disc test for determining indirect tensile strength and its applications in rock mechanics are reviewed herein. Based on the history of research on the Brazilian test ...by analytical, experimental, and numerical approaches, three research stages can be identified. Most of the early studies focused on the tensile stress distribution in Brazilian disc specimens, while ignoring the tensile strain distribution. The observation of different crack initiation positions in the Brazilian disc has drawn a lot of research interest from the rock mechanics community. A simple extension strain criterion was put forward by Stacey (Int J Rock Mech Min Sci Geomech Abstr 18(6):469–474,
1981
) to account for extension crack initiation and propagation in rocks, although this is not widely used. In the present study, a linear elastic numerical model is constructed to study crack initiation in a 50-mm-diameter Brazilian disc using FLAC
3D
. The maximum tensile stress and the maximum tensile strain are both found to occur about 5 mm away from the two loading points along the compressed diameter of the disc, instead of at the center of the disc surface. Therefore, the crack initiation point of the Brazilian test for rocks may be located near the loading point when the tensile strain meets the maximum extension strain criterion, but at the surface center when the tensile stress meets the maximum tensile strength criterion.
Cracking and coalescence behavior in a rectangular rock-like specimen containing two parallel (stepped and coplanar) pre-existing open flaws under uniaxial compression load has been numerically ...studied by a parallel bonded-particle model, which is a type of bonded-particle model. Crack initiation and propagation from two flaws replicate most of the phenomena observed in prior physical experiments, such as the type (tensile/shear) and the initiation stress of the first crack, as well as the coalescence pattern. Eight crack coalescence categories representing different crack types and trajectories are identified. New coalescence categories namely “New 1” and “New 2”, which are first observed in the present simulation, are incorporated into categories 3 and 4, and category 5 previously proposed by the MIT Rock Mechanics Research Group, respectively. The flaw inclination angle (β), the ligament length (
L
) (spacing between two flaws) and the bridging angle (α) (inclination of a line linking up the inner flaw tips, between two flaws) have different effects on the coalescence patterns, coalescence stresses (before, at or post the peak stress) as well as peak strength of specimens. Some insights on the coalescence processes, such as the initiation of cracks in the intact part of specimens at a distance away from the flaw tips, and coalescence due to the development and linkage of a number of steeply inclined to vertical macro-tensile cracks are revealed by the present numerical study.
Cracking processes have been extensively studied in brittle rock and rock-like materials. Due to the experimental limitations and the complexity of rock texture, details of the cracking processes ...could not always be observed and assessed comprehensively. To contribute to this field of research, a numerical approach based on the particle element model was used in present study. It would give us insights into what is happening to crack initiation, propagation and coalescence. Parallel bond model, a type of bonded-particle model, was used to numerically simulate the cracking process in rock-like material containing a single flaw under uniaxial vertical compression. The single flaw’s inclinations varied from 0° to 75° measured from the horizontal. As the uniaxial compression load was increased, multiple new microcracks initiated in the rock, which later propagated and eventually coalesced into longer macrocracks. The inclination of the pre-existing flaw was found to have a strong influence on the crack initiation and propagation patterns. The simulations replicated most of the phenomena observed in the physical experiments, such as the type, the initiation location and the initiate angle of the first cracks, as well as the development of hair-line cracks, which later evolved to macrocracks. Analyses of the parallel bond forces and displacement fields revealed some important mechanisms of the cracking processes. The first cracks typically initiated from the tensile stress concentration regions, in which the tensile stress was partially released after their initiation. The tensile stress concentration regions subsequently shifted outwards close to the propagating tips of the first cracks. The initiation and propagation of the first cracks would not significantly influence the compressive stress singularity at the flaw tips, which was the driving force of the initiation of secondary cracks. The initiation of microcracking zone consisting almost exclusively of micro-tensile cracks, and that of microcracking zone consisting of micro-tensile cracks and mixed micro-tensile and shear cracks, were found to be correlated with two distinct types of displacement fields, namely type I (DF_I) and type II (DF_II), respectively.
The onset of the 2019-20 winter influenza season in Hong Kong coincided with the emergence of the coronavirus disease epidemic in neighboring mainland China. After widespread adoption of large-scale ...social distancing interventions in response to the impending coronavirus disease outbreak, the influenza season ended abruptly with a decrease to a low trough.
In practice, the peak shear strength of rock joints is not dictated only by the surface roughness, but also the degree of matching between the joint surfaces. The latter is due to ...alteration/dislocation caused by external factors, such as the vibration due to nearby blasting, excavation or earthquake. In the present study, the peak shear strengths of rock joints under different contact states are investigated by direct shear test using artificial rock joints. The rock joints under different contact states are modeled by imposing varying magnitude of horizontal dislocation along the shear direction between the upper and lower rock blocks. The peak shear strength was found to decrease with increasing dislocation. A new empirical shear strength criterion is put forward to capture the peak shear strength of un-matching rock joints as an extension of a previously published peak shear strength criterion for matching rock joints by the first author and his co-workers. In the present proposed criterion, a new joint contact state coefficient, which is a function of the normalized dislocation and the quantified three-dimensional roughness metric of joint surface, is proposed. The good agreement between calculated values and test results indicates that the proposed criterion is capable of estimating the peak shear strength of rock joints under different contact states. The proposed criterion is expressed in a quantitative way and the required parameters can be easily determined in the laboratory.
Let (Ω,A,μ) and (Γ,B,ν) be two arbitrary measure spaces, and p∈1,∞. SetS(Lp(μ))+:={f∈Lp(μ):‖f‖p=1;f≥0μ-a.e.}, that is, the positive part of the unit sphere of Lp(μ). We show that every surjective ...isometry Φ:S(Lp(μ))+→S(Lp(ν))+ can be extended (necessarily uniquely) to an isometric order isomorphism from Lp(μ) onto Lp(ν). A Lamperti form, i.e., a weighted composition like form, of Φ is provided, when (Γ,B,ν) is localizable (in particular, when it is σ-finite). On the other hand, we show that for compact Hausdorff spaces X and Y, if Φ is a surjective isometry from the positive part of the unit sphere of C(X) to that of C(Y), then there is a homeomorphism τ:Y→X satisfying Φ(f)(y)=f(τ(y)) for f∈S(C(X))+ and y∈Y.
A reduction of uniaxial compressive strength (UCS) by the presence of water has been ascertained in many sedimentary rocks and even some metamorphic rocks experimentally. This paper reports and ...discusses the influence of water content and anisotropy on the strength and deformability of two meta-sedimentary rocks by triaxial compressive tests. Before conducting the triaxial tests, the physical properties of meta-siltstone and meta-sandstone specimens have been carefully examined. The water contents of both tested rocks are very low, for instance, 0.17% for meta-siltstone and 0.10% for meta-sandstone. The porosities of the tested rocks are analyzed by the technique of mercury intrusion porosimetry (MIP). It shows that the meta-sedimentary rocks have very low porosity, 0.18% for meta-siltstone and 0.53% for meta-sandstone on average. The thin section analysis reveals that the meta-siltstone contains more hydrophilic substances such as clay minerals than the meta-sandstone, and both two meta-sedimentary rocks are characterized by distinct beddings and laminae. Even though the water contents of two tested rocks are very low, they significantly influence the triaxial compressive strength and deformability. The reduction of strength by water content is found to be related to a reduction of friction angle in the Mohr–Coulomb failure criterion, while a reduction of mi value in the Hoek–Brown failure criterion on the other hand. The influence of water on deformability of tested rocks is reflected as a reduction of Young's modulus and increase of Poisson's ratio, which indicates that the wet meta-sedimentary rocks will deform more than that of the dry ones under the same stress condition. The experimental studies show that the anisotropy associated with bedding in rock specimens plays a weakening effect on the triaxial compressive strength for both tested rocks, appearing more severely for meta-siltstone. In general, the triaxial compression strength of rock specimens with transverse bedding planes is higher than the ones with longitudinal bedding planes no matter for meta-siltstone or meta-sandstone (both dry and wet conditions) under the same confining stress. With regard to the stiffness, both the tangent and secant Young's moduli of the two tested rocks with transverse bedding are less than the ones with longitudinal bedding, appearing more conspicuously for the meta-siltstone. The paper also discusses the axial strain calibration by two different measurement techniques, one by the linear variant difference transducer (LVDT) technique and the other one by axial strain gages. It shows that the axial strain ratio coefficient k (εLVDT/εstrain) decays with the deviator stress. In our present study, the secant modulus Estrain is usually about 1.4–1.8 times of ELVDT at the peak strength point. The correlation between mechanical properties and physical properties of the two tested rocks are also discussed in the paper.
► Conducted triaxial compressive tests on two low porosity meta-sedimentary rocks. ► Correlated the mechanical properties of the rocks with their physical properties. ► Presence of water and rock anisotropy reduced rock strength and stiffness. ► Axial strain obtained by LVDT technique was calibrated against that by strain gages.
Let F(X),F(Y) be sufficiently large sets of nonnegative continuous real-valued functions defined on completely regular spaces X,Y, respectively. Let Φ:F(X)→F(Y) be a surjective map satisfying ...thatf∨g>0⟺Φ(f)∨Φ(g)>0,∀f,g∈F(X). In many cases, we show that there is a homeomorphism τ:Y→X such thatΦ(f)(y)≠0⟺f(τ(y))≠0,∀f∈F(X),∀y∈Y.
Assume X,Y are locally compact Hausdorff (resp. separable and metrizable) and Φ:C0(X)+→C0(Y)+ (resp. Φ:Cb(X)+→Cb(Y)+) is a surjective map. We show that Φ preserves the norms of infima, i.e.,‖Φ(f)∧Φ(g)‖=‖f∧g‖,∀f,g∈C0(X)+ (resp.Cb(X)+), if and only if there is a homeomorphism τ:Y→X such thatΦ(f)(y)=f(τ(y)),∀f∈C0(X)+ (resp.Cb(X)+), ∀y∈Y.
Cerebellar ataxia is often the first and irreversible outcome in the disease of ataxia-telangiectasia (A-T), as a consequence of selective cerebellar Purkinje neuronal degeneration. A-T is an ...autosomal recessive disorder resulting from the loss-of-function mutations of the ataxia-telangiectasia-mutated ATM gene. Over years of research, it now becomes clear that functional ATM-a serine/threonine kinase protein product of the ATM gene-plays critical roles in regulating both cellular DNA damage response and central carbon metabolic network in multiple subcellular locations. The key question arises is how cerebellar Purkinje neurons become selectively vulnerable when all other cell types in the brain are suffering from the very same defects in ATM function. This review intended to comprehensively elaborate the unexpected linkages between these two seemingly independent cellular functions and the regulatory roles of ATM involved, their integrated impacts on both physical and functional properties, hence the introduction of selective vulnerability to Purkinje neurons in the disease will be addressed.
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