Initiation Stress Research Articles

Mechanical behavior and acoustic emission characteristics of intact granite undergoing direct shear

Shear behaviors of core samples from a deep geothermal exploration well was investigated using direct shear tests. The fracturing process inside the intact rock samples during shear was monitored using acoustic emission (AE) technique. The results show that three shear stages including compaction, quasi-elastic and failure phases can be easily divided based on the shear stress-shear displacement or the cumulative AE parameters-shear displacement curves. Three characteristic stresses in terms of crack initiation stress, crack damage stress and peak strength are defined for intact rock samples undergoing shear. The crack initiation stress is about 0.80 times of the peak strength, and the crack damage stress is about 0.88 times of the peak strength. In addition, the different shear behaviors and AE characteristics between intact rocks and rock fractures are compared. AE events are scattered in the pre-peak stage but are localized around the fracture surface in the post-peak stage, while AE events are located along the shear zone in intact rock samples.

Study on the effect of water on electromagnetic radiation characteristics of fractured sandstone under load

A large number of electromagnetic radiation (EMR) signals are released during loading failure of rock mass, and these signals which contain complex and abundant fracture information can provides precursor of rock mass instability. In order to investigate the effect of water on the EMR characteristics of fractured sandstone, a uniaxial compression experiment was performed on the dried and saturated sandstone samples with prefabricated parallel double cracks. The EMR signals during loading failure of rock samples were acquired and their mechanical properties and EMR signal characteristics were analyzed. Besides, the precursor of rock sample instability was extracted based on the critical slowing down theory. The experimental results show that compared with the dried rock sample, the saturated rock sample has lower compressive strength, starts to crack earlier, and exhibits a more complicated failure mode. During the loading failure of rock samples, their EMR signals respond well to the fracturing and damage. The cumulative number of pulses of saturated rock sample grows uniformly, while that of dried rock sample show a “gentle-violent” rising mode. Moreover, the cumulative number of pulses of dried rock sample is greater than that of saturated rock sample. Water reduces the crack initiation stress level, and the saturated rock sample is the first to experience a sudden jump of EMR pulse. With the increase of the loading stress, the dominant frequency of EMR gradually transitions from low frequency to high frequency. Compared with dried rock samples, saturated rock samples have a lower proportion of high-frequency signals. Since the dominant mechanism of EMR varies with the change of failure stage, water first promotes the EMR signals of rock samples in the early stage of loading; then, it weakens the EMR signals in the middle and late stages of loading. Based on the critical slowing down theory, the EMR pulse signals were analyzed, which conduces to the extraction of potential precursor of rock sample failure and instability. Compared with dried rock samples, the precursory characteristic of saturated rock sample is more obvious. The research results provide some guidance for the stability of water-bearing fractured rock mass and the monitoring and early warning of related geological hazards.

Experimental investigation on fracture behaviors and acoustic emission characteristics of sandstone under different strain rates

To further investigate differences of fracture behaviors and acoustic emission characteristics of rock under different strain rates, unconfined uniaxial compressive tests of thirty cylindrical specimens with 50 mm in the diameter and 100 mm in the height were performed within quasi-static strain rates of 10–5–10–2 s−1 by rock material testing system and multi-channel acoustic emission (AE) monitoring system. The uniaxial compressive strength, peak strain and elasticity modulus, failure mode, fractal dimension and equivalent average size of the rock fragments, and the three-dimensional spatial distribution of acoustic emission events were obtained and analyzed. The experimental results verify that the uniaxial compressive strength, elasticity modulus and peak strain are strain rate-dependent significantly. Particularly, with increasing strain rates, macroscopic failure modes present three types of single shear failure, multiple shear failure, and shear and tensile mixed failure, and the rock fragments show a smaller equivalent size and a larger fractal dimension, which resulted in a higher fragmentation degree. Besides, it is noted that the evolution process of acoustic emission ring-down count and spatial distribution of events under different strain rates are closely related to macroscopic failure modes. Furthermore, characteristic stresses based on the evolution process of acoustic emission ring-down count, such as the elastic stress, initiation stress and yield stress, were analyzed deeply at different strain rates. A simplified rock model consisting of discrete fracture network and equivalent elementary volume was proposed to discuss the effect of strain rate on energy accumulation and dissipation. Finally, to better reveal the micro mechanism of the effect of strain rates on rock mechanical behaviors, the microscopic fracture morphology was observed and characterized by means of scanning electron microscopy. The experimental results should be taken into account in underground mining, tunnel excavation and other rock engineering activities.

Experimental and numerical study on crack propagation and coalescence in rock-like materials under compression

The discontinuous crack surface in a rock affects the stability of the whole rock system. The experiments in this paper were carried out by prefabricating rock-like specimens with different types of flaws, then the specimens were tested under uniaxial compression. Moreover, based on the theory of particle flow, PFC2D software was used for numerical simulation, and the comparative analysis of the experimental and simulative results was carried out to obtain the crack initiation sequence, propagation phenomenon, and failure mode of rock specimens with different flaw types. The results indicated that the wing crack started at the tip of flaw and the form of crack assumed split failure, followed by shear failure caused by the secondary crack. The tensile failure degree decreases and the influence of shear failure increases with the increase of flaw angle. The wing crack and secondary initiation stress value is 35%–55% and 85%–95% of the peak stress value. Crack coalescence appeared in adjacent flaws of rock-like specimens with multiple parallel single flaws, single-cross flaws and double-cross flaws, and the coalescence phenomenon always occurs when the stress peak value is reached. With the number of flaws increasing, the splitting failure of rock-like specimens became more and more serious, the splitting failure of double cross-flaw specimen is the most serious. As for the specimen with single-cross flaw, the wing crack would be produced at the tip of the flaw with larger obliquity. The results of this paper may offer certain reference value for the study on the mechanism of rock crack.

Experimental and Numerical Studies on Crack Initiation and Coalescence in Sandy Mudstone with Prefabricated Cross-Flaws Under Uniaxial Compression

The purpose of this paper is to study the crack initiation, propagation, and coalescence of the sandy mudstone sample with two sets of prefabricated cross-flaws under uniaxial compression. This study is different from previous studies on single or multiple parallel prefabricated flaws. The prefabricated cross-flaws are characterized by the dip of the rock bridge with the direction of the main flaw ( β ) and the angle between the direction of main and minor flaws ( γ ). The effects of these two parameters on crack initiation, propagation, coalescence, crack initiation stress, and coalescence stress are analyzed. Moreover, numerical simulation of the uniaxial compression experiments is performed using PFC2D with a flat-joint model, and the simulation results are in good agreement with those from the experiments. The results demonstrate that the dip angle of the rock bridge with the direction of the main flaw ( β ) has strong effects on the crack initiation and coalescence stresses. The larger the angle between the direction of main and minor flaws γ , the greater the crack initiation and coalescence stresses. The crack initiation stress is reduced for the case with cross-flaws compared with that with non-cross-flaws. Meanwhile, the connection type of main flaws and the width of the crack coalescence zone are difficult to observe through the experiments and are discovered from the numerical simulation.

Experimental Study on Failure Behaviour of Ligaments Between Strike-Inconsistent Fissure Pairs Under Uniaxial Compression

Aiming at the fact that discontinuities in rock mass exhibit different orientations, uniaxial compression tests of resin specimens containing a strike-inconsistent fissure pair were carried out to investigate the failure behaviour of the ligaments. Combined with computerized tomography scanning technology, cracking behaviour and ligament failure pattern were revealed. The failure characteristics and mechanical properties of specimens were studied. The results indicate that the primary cracks generally initiate at a local point of the pre-existing fissure tip, then integrate into a wavy-shaped crack, and develop into a large wrapping crack over time. With the variation of fissure deflection angle, the ligament exhibits three failure patterns: spalling failure, coalescence of cracks at the proximal end and incoherence at the distal end, and torsional failure. The crack initiation stress generally exhibits an increasing trend as fissure deflection angle increases. Peak stress and strain difference are closely related to fissure deflection angle and failure pattern. The mechanical properties of specimens with parallel fissure deflection are the most affected by the fissure deflection angle, followed by those with steep fissure deflection, and those with gentle fissure deflection are minimally affected.

A New Rock Brittleness Index Based on the Characteristics of Complete Stress–Strain Behaviors

Rock brittleness is an essential mechanical property, which plays a significant role in rock classifications and rockburst risk evaluations. To overcome the problems associated with the traditional brittleness indexes not comprehensively charaterizing the rock strength and deformation behaviors, this study systematically summarized the existing rock brittleness indexes. Then, a novel brittleness index (BICSS) based on the complete stress–strain curves of rock under different confining pressures was proposed. Its advantages included innovatively considering the characteristic stresses and strains at the stage of crack initiation, the peak points, and residual points. The index also described the stress growth rates from the pre-peak crack-initiation stress to the peak stress points, as well as the stress drop rates from the peak stress to the residual stress points. This study conducted uniaxial and triaxial compression tests of metamorphic sandstone, granite, and gneiss obtained from a deeply buried long-line tunnel group. The aforementioned tests were combined with wave velocity tests and thin-section identification tests using polarizing microscopy techniques. The reliability and applicability of the index were then successfully verified. The results showed that the BICSS could not only quantify and classify the brittleness characteristics of different rock types and characterize the confining pressure inhibition behaviors of rock brittleness, but could also comprehensively express the influences of homogeneity, mineral compositions, and particle sizes on the rock brittleness. Finally, through the parameter sensitivity analysis of the BICSS, the influences of subjective errors in the results of the cracking initiation stress and strain values caused by the different selections during the linear elastic phase could be successfully excluded, resulting in the further verification of the stability of the BICSS.

Experimental Study on Mechanical Property and Pore Distribution of Limestone Specimens after Heat Treatment under Different Heating Conditions

The thermal effect of rocks not only depends on the temperature level but also may be influenced by the factors including heating environment, heating rate, and cooling method. In this study, approximate vacuum (V) and air circulation (A) heating condition are, respectively, applied on the limestone specimens in the whole heating process. Then, physical, mechanical, and nuclear magnetic resonance (NMR) tests were carried out to investigate the effect of heating conditions on the rock properties. The results show that heating conditions have significant effects on mechanical properties of limestone specimens (including peak strength, elasticity modulus, secant modulus, and crack initiation stress), which are due to the interference effect on the oxidation and thermal decomposition. It is worth noting that the significant temperature range of the heating condition is 450 ∼ 750°C, during which the mechanical performances of heat‐treated specimens under V condition obviously outperform those under A condition. Combining the NMR results and the microstructure images from scanning electron microscope (SEM) technology, the evolution of pore distribution was revealed. As temperature increases from room temperature to 900°C, porosity increases gradually. However, pore distribution changes from small and medium pores dominating to large pore dominating and then to medium pore dominating. For limestone specimens after high‐temperature treatment above 450°C, mineral crystals may melt and reconsolidate, filling in some of the previously large pores generated by thermal decomposition.

Numerical Analyses of Fracturing Behavior and Strength of Specimens with Two Parallel Infilled Flaws under Uniaxial Compression

Grouting is a common method used to fill rock joints to improve the stability and integrity of rock mass in geotechnical engineering, and the filling has been observed to have an effect on crack behavior and mechanical property. To investigate this topic, a numerical study of crack behavior and mechanical property of rock samples with two parallel open flaws or infilled flaws under uniaxial compression was conducted in this research. The smooth joint model was proved to be suitable to simulate the interface between rock material and grout material. The occurrence of shear cracks at the interface between rock material and grout material as well as the occurrence of tensile cracks in the grouting material has been successfully simulated in this research. Numerical results indicate that grouting can reduce the tensile force near the flaws, suppress the generation of tensile cracks, and improve the initiation stress of the sample. The tensile force in the specimens with infilled flaws is smaller than that with open flaws, which lead to the improvement of the peak strength of the sample. Moreover, crack development and mechanical properties of samples are affected by bridge inclination angle and flaw inclination angle.

Mean and residual stress effects on fatigue behavior in a pre-strained corner of stainless steel sheet

There are many thin-walled corners in the components of automobiles, machines, and structures. It is essential to elucidate their fatigue properties and influence factors. Parameters for stress–strain behavior of ferritic stainless plane sheet and pre-strained sheet were obtained under tensile, bending, and cyclic bending loads using the Ramberg–Osgood model. The parameters were integrally used as the fundamental characteristics of bending fatigue behavior for obtaining the mean stress and crack initiation stress amplitude from the measured strains in the curved portion of corner specimens. Bending fatigue tests of pre-strained corner specimens were carried out, and the relationships between the crack initiation strain amplitudes and the mean strains were verified. The strain amplitude ratios of the curved inside to outside portion were analyzed. The residual stress and hardness were measured, and work hardening effect on the inside was higher than that on the outside for improving fatigue strength. The fatigue limit of the corner specimen with the radius ratio of 1.3 was 23% higher than the unworked plane sheet. The effects of mean stress and residual stress on the fatigue strength were analyzed using the fatigue limit–static stress relation equations, indicating that the Gerber parabola can be used for fatigue limit predictions in the stress ratio range of R < –0.5 and that the Goodman line can be used after the point of R = –0.5. The SWT function can be used to accurately predict the fatigue lives in various conditions of stress amplitudes combined with static stresses.

The DEAD-box RNA helicase eIF4A1 interacts with the SWI2/SNF2-related chromatin remodelling ATPase DDM1 in the moss Physcomitrella

eIF4A is a DEAD box containing RNA helicase that plays crucial roles in regulating translation initiation, growth and abiotic stress tolerance in plants. It also functions as an ATP-dependent RNA binding protein to curb granule formation by limiting RNA-RNA interactions that promote RNA condensation and formation of ribonucleoprotein particles in vivo. Helicase activity of eIF4A is known to be dictated by its binding partners. Proteins interacting with eIF4A have been identified across land plants. In monocots a close link between eIF4A regulated processes and DNA methylation in epigenetic regulation of plant development is inferred from interaction between OseIF4A and the de novo methyltransferase OsDRM2 and loss-of-function studies of these genes in Oryza sativa and Brachypodium distachyon. In the moss Physcomitrella patens, eIF4A1 encoded by Pp3c6_1080V3.1 interacts with the heterogeneous nuclear ribonucleoprotein (hnRNP) PpLIF2L1, homolog of which in Arabidopsis regulates transcription of stress-responsive genes. In this study, using different protein-protein interaction methods, targeted gene knockout strategy and quantitative expression analysis we show genetic interaction between PpeIF4A1 and the putative nucleosome remodeler protein PpDDM1 and between PpDDM1 and PpLIF2L1 in vivo. Stress-induced co-expression of PpeIF4A1, PpDDM1 and PpLIF2L1, their roles in salt stress tolerance and differences in subnuclear distribution of PpLIF2L1 in ppeif4a1 cells in comparison to wild type suggest existence of a regulatory network comprising of RNA helicases, chromatin remodelling proteins and hnRNP active in stress-responsive biological processes in P. patens.

Failure characteristics of surrounding rocks along the radial direction of underground excavations: An experimental study

For the in situ surrounding rocks of underground excavations, the radial stress corresponding to the minimum principal stress σ3 varies with increasing distance away from the excavated boundary. To characterize the rock failure along the radial direction of an excavation, true triaxial compression tests with different σ3 values (0.5, 5, 10, 15, 20, 25, and 30 MPa) were performed. The characteristic stresses (including the crack initiation stress σi, crack damage stress σd, and peak stress σs) and failure mode of the tested specimen under different σ3 conditions were systematically investigated. The experimental results indicate that with increasing σ3, the characteristic stresses increase monotonically and continuously. The increasing rate of the characteristic stresses with σ3 ranging from 0 to 10 MPa is higher than that with σ3 ranging from 10 to 30 MPa, indicating that low σ3 impose a greater effect on the characteristic stresses than high σ3. In addition, the failure mode of the tested specimen changes from tensile-shear failure mode I (with vertical tensile cracks and oblique tensile-shear cracks developing along the σ2 direction) to tensile-shear failure mode II (with oblique tensile-shear cracks developing only along the σ2 direction) to tensile-shear failure mode III (with oblique tensile-shear cracks along both σ2 and σ3 directions) as σ3 increases. Then, the failure characteristic of the surrounding rocks of the underground excavation was characterized based on the obtained experimental results. When maximum radial stress σr encountered near the excavated boundary is much smaller than the axis stress σa, the surrounding rocks will exhibit a “Ternary failure characteristic”, i.e., with an increase in the distance from the excavated boundary along the radial direction, the failure mode of the surrounding rocks after excavation changes from tensile/splitting failure mode to tensile-shear failure mode I and then to tensile-shear failure mode II. When the maximum σr encountered near the excavated boundary approximates the original σa, the surrounding rock masses will exhibit a “Quaternary failure characteristic”. Specifically, the corresponding failure mode along the radial stress direction away from the excavated boundary changes from tensile failure mode to tensile-shear failure mode I then to tensile-shear failure mode II and finally to tensile-shear failure mode III.

Strain localization and cracking behavior of sandstone with two gypsum-infilled parallel flaws

The infilled flaws within rocks significantly influence the mechanical behavior of non-through flawed rocks. To investigate the influence of infilling on strain localization in the pre-cracking, cracking and cracking coalesce stages, experimental and numerical investigations were conducted on sandstone containing two gypsum-infilled parallel flaws, but of different flaw geometric configurations. The full-field strain evolution and progressive cracking process are analyzed using the acoustic-optical-mechanical methods, while the stress evolution and stress transfer by infilling were studied by the particle flow code modeling. The results show that the major principal strain of flawed sandstone with infilling changes from the diffused ellipse to highly localized linear strip with the increase of loading level, while the shear strain keeps a diffused ellipse shape invariable. The shear strain localization of infillings with a large flaw inclination initiates at a lower loading level than that of small one. The peak strength and Young’s modulus of flawed sandstone show a first decrease, then increase and finally decrease trend with the ligament angle increasing from 0° to 150°, and both achieve their minimums at 60°. Ten types of cracks were observed, and four patterns of crack coalescence were identified. By comparison with sandstone of open flaws, the flaw infilling simplifies the geometric pattern of produced crack networks, which is quantitatively characterized by fractal dimension analysis. The numerical modeling shows that the infilling enlarges the compressive bond force zone and decreases the tensile bond force zone in the surrounding areas of pre-existing flaw, thus increasing the reinforcement coefficient. Moreover, the flaw geometric configuration has a significant influence on the reinforcement coefficient. It is also found that the increment of reinforcement coefficient defined by crack initiation stress is greater than those defined by either crack coalescence or peak stresses.

Hybrid lattice/discrete element method for bonded block modeling of rocks

The Hybrid Lattice/Discrete Element Method is proposed for Bonded Block Modeling of rocks. The method is a combination of the Rigid Body Spring Network Lattice Model with the Discrete Element Method. The main advantages of the new method are: (i) it operates based on either a homogeneous or heterogeneous material assumption, with heterogeneity being represented by means of the Weibull probability distribution applied to elasticity and strength parameters; and (ii) it provides for a direct material calibration scheme for rock models based on both assumptions, which does not require trial-and-error iterations. Thirteen rock types, including igneous, metamorphic, and sedimentary ones were simulated in the two-dimensional version of the method considering both assumptions, and their numerical macroscale properties were compared to the laboratory ones. Results show that while deformability and peak strength properties were accurately represented by the homogeneous models, linear elastic-brittle behavior manifested. On the other hand, the heterogeneous models presented non-linear stress–strain behavior and provided reasonable matches for the following laboratory properties: Young modulus, Poisson’s ratio, crack initiation stress, crack damage stress, unconfined compression strength, and direct tensile strength.

Cracking behaviours of rock‐like materials containing three preexisting flaws after high‐temperature treatments

AbstractThe mechanical properties and cracking behaviours of rock‐like materials containing three preexisting flaws after high‐temperature treatments are studied. The temperature variations of 25°C, 70°C and 140°C are chosen to explore the influence of temperature, and the ligament angle variations of 75°, 90° and 105° are chosen to explore the effect of preexisting flaws. The crack initiation and coalescence modes and specimen failure after high‐temperature treatments are recorded by a high‐speed dynamic analysis system. Seven modes of crack initiation and ten types of crack coalescence are recorded in the rock‐like specimens. With an increase in temperature and ligament angle, the mechanical properties such as peak strength, peak strain and crack initiation stress change regularly. Furthermore, the experimental results demonstrate that the temperature has a significant impact on the complete stress–strain curves and cracking behaviours of flawed rock‐like materials.

Mechanical failure dependence on the electrical history of lead zirconate titanate thin films

Piezoelectric micromechanical systems (piezoMEMS) are often subjected to harsh mechanical and electrical loads during operation. This study evaluates the effects of the electrical history of a lead zirconate titanate (PZT) layer on the electro-mechanical response and structural limits of multilayer stacks. Electro-mechanical characterization was performed under biaxial bending employing the Ball-on-three Balls (B3B) test on virgin, poled, and DC biased (80 kV/cm) samples. No significant effect on the characteristic strength or Weibull modulus of the stack was observed. However, the crack initiation stress was highest for the virgin samples (σ0 ∼ 485 ± 30 MPa); this decreased for both poled samples (σ0 ∼ 410 ± 30 MPa), and samples measured under 80 kV/cm (σ0 ∼ 433 ± 30 MPa). in situ εr and loss tangent measurements suggested electromechanical loading conditions can destabilize the domain structure. Overall, the electrical history and electromechanical loading conditions can reduce the PZT film’s fracture resistance.

Fracture Propagation of Rock like Material with a Fluid-Infiltrated Pre-existing Flaw Under Uniaxial Compression

Crack propagation can gradually reduce the strength of the rock and eventually result in rock failure. Coupling effect of stress and seepage in fracture could accelerate the rock failure process. In this work, a set of water sealing device is developed to apply different fluid pressures in the pre-existing fracture in specimens made of rock-like material. We have carried out uniaxial compression tests on specimens at different pre-existing flaw dip angles (30°, 45°, and 60°) coupled with fluid pressures in the fracture. Through laboratory experiments and numerical simulations, we find that without fluid pressure in the pre-existing flaw, wing cracks and secondary cracks appear at the pre-existing flaw tips. With the increase of the fluid pressure in the flaw, the propagation of secondary cracks is restrained, no secondary cracks appear at the flaw tips. The increase of fluid pressure accelerates the wing crack propagation, inhibits the secondary cracks, and causes the specimen to undergo tensile failure. Compared with the specimen without the fluid pressure in the flaw, the fluid pressure in the flaw promotes wing crack initiation and propagation, and causes the initiation stress of the wing cracks and the peak strength of the specimens to decrease gradually. With or without fluid pressure in the fracture with the increase of the flaw dip angle, the initiation stress of wing cracks and peak strength of the specimen first decrease and then increase. When the pre-existing flaw dip angle is 45°, the peak strength and the initiation stress are the lowest.

Fracture evolution and failure mechanism of rock-like materials containing cross-flaws under the shearing effect

Shear failure of rock masses along discontinuities is one of the dominant failure modes of underground tunnels and rock slopes. In this paper, the shear fracture evolution and failure mechanism of rock-like materials containing cross-flaws are first reported based on a developed CZM-FEM method. The laboratory uniaxial compression and corresponding numerical tests were initially performed to acquire the mechanical parameters of rock-like materials. Subsequently, the direct shear test of rock-like materials containing two sets of cross-flaws was conducted, the effect of the main flaw and secondary flaw angles were considered. At last, the mechanical properties and fracture behaviors, and the coalescence mechanism were investigated and concluded. The results indicate that four typical stages are observed during the shearing process of rock-like materials with cross-flaws, which are the linear elastic stage, crack strengthening stage, plastic softening stage, and residual strength stage, respectively. Note that the mechanical properties (i.e., peak, residual shear strength, and the crack initiation stress) and cracking behaviors are strongly dependent on the angles of the main and secondary flaws as well as the loading conditions (i.e., shear rates and constant applied normal stresses). In addition, the coalescence mechanism of rock bridge between the two cross-flaws can be classified into three types, which are the mixed shear tensile-tensile damage, shear-tensile damage, and tensile damage, respectively; Similarly, the coalescence paths can also be identified as three types, respectively, the connection between the main flaw and the secondary flaw, linkage by the two main flaws, and the penetration dominated by the coalescence of the main flaw and the secondary flaw.

Effect of Sediment Supply on Cyclic Fluctuations of the Disequilibrium Ratio and Threshold Transport Discharge, Inferred From Bedload Transport Measurements Over 27 Years at the Swiss Erlenbach Stream

AbstractBedload transport in natural channels typically shows large fluctuations even for constant hydraulic forcing. It has been shown that the threshold shear stress for initiation of motion depends, for example, on the bed morphology and on channel slope and that it may be influenced by flood history effects. This study is based on a unique data set of continuous field observations of bedload transport acquired during 27 years with impact plate measurements and involving more than 500 sediment‐transporting flood events. A disequilibrium ratio is defined which represents the observed bedload mass per event divided by the bedload mass calculated via a bedload transport equation integrated over the time of a flood event. The disequilibrium ratio varies in a cyclic behavior around equilibrium conditions defined by its median value. The mean duration of a cycle depends on upstream sediment supply or availability on the bed, and longer cycles are associated with a larger active layer on the bed. A memory effect is evident regarding the temporal evolution of both disequilibrium ratio and bed state as reflected by threshold transport conditions, determined from the observations as the critical discharge at the start and at the end of a bedload‐transporting event. The disequilibrium ratio and the threshold transport discharge are inversely correlated with each other, likely providing a feedback mechanism governing the fluctuations around an equilibrium state. Accounting for the memory effect, that is, for the bed state after the previous event, improves the prediction of bedload transport for the following event.

Transgranular fracturing of crystalline rocks and its influence on rock strengths: Insights from a grain-scale continuum–discontinuum approach

The aim of this study is to understand the effects of micro-heterogeneity, such as grain size, morphology and mineralogy, on the initiation, propagation and coalescence of microcracks in heterogeneous materials. A multiscale grain-breakable continuum–discontinuum model incorporating realistic micro-heterogeneity reproduction method is proposed to investigate the fracturing behaviours and confinement mechanism of rocks. Crack initiation and damage stresses are intrinsic properties of rocks determined by grain-scale heterogeneity. Intergranular tensile cracks are primarily initiated as a result of local stress heterogeneity along grain boundaries. The subsequent generation of transgranular shear cracks implies a rapid proliferation of grain-crossing fractures, leads to large-scale crack interaction and coalescence. The effect of confinement inhibits crack extension and increases the appearance of shear-induced grain pulverizations. Furthermore, the effects of grain size, grain morphology and mineralogy on macro mechanical properties, including crack initiation stress, crack damage stress, uniaxial compression strength and elastic modulus, are discussed. The simulated results indicate that the larger grain size contributes to stronger local stress heterogeneity, which results in a lower failure strength of rocks. The crack initiation stress is determined by local heterogeneity and is less affected by the change in average grain size. Grain morphology plays an important role in grain interlocking while a reduction in grain size variance leads to a more homogeneous stress field. The mineralogy is evaluated with the aid of a quartz-mica-feldspar diagram, and the quantitative relationships between mineralogy and the macro-scale mechanical properties of rocks are discussed.