Post-peak Stage Research Articles

Dynamic multifractal characteristics of acoustic emission about composite coal-rock samples with different strength rock

In order to investigate the instability mechanism of composite coal-rock samples with different strength rock, several uniaxial compression experiments of composite samples were carried out, and dynamic multifractal characteristics of acoustics emission (AE) of composite samples were analyzed, and the influence of rock strength on the failure mechanism and energy evolution of composite samples was revealed. The results show the variation of dynamic multifractal spectrum of AE reflects the changing of crack propagation mode of composite samples during the deformation process. The increasing of rock strength changes the dominant mechanism of crack propagation in the composite sample before yield deformation. The crack propagation mode in the coal of composite sample with low strength rock changes from shear propagation to tensile-shear coexistence, and the crack in the coal of composite sample with high strength rock expands in the form of tensile-shear coexistence. In the elastic stage of composite samples, Δαm of AE energy in coal increases obviously indicating the crack extension mode is becoming complicated, while Δαm of AE energy and count in rock increases slightly and Δαm of AE count in coal and its variation range are small indicating the crack extension mode is simple. The Δαm ascending range of AE energy in coal decreases gradually and the proportion of Δƒm < 0 is more and more with the increasing of rock strength before yield deformation. In the yield deformation and post-peak stage, Δαm of AE energy of composite sample with higher strength rock is less than lower strength rock, which is resulted from the elastic energy releasing of composite sample with higher strength rock is less than lower strength rock. The research results are of great significance for understanding the deformation and failure mechanism of composite samples and the influence of rock on the failure process of composite specimens.

Clockwise P−T−t paths of late Neoarchean high-pressure pelitic granulites from the Qingyuan terrane, eastern North China Craton

Precambrian high-pressure (HP) granulites provide record for the geodynamic process of ancient continental nuclei. Here we report the newly discovered late Neoarchean HP pelitic granulites in the Qingyuan terrane, eastern North China Craton (NCC). The Neoarchean basement of the Qingyuan terrane comprises meta-supracrustal rocks, tonalite–trondhjemite–granodiorite (TTG) gneisses, and a small amount of charnockites. The HP pelitic granulites were recognized from the meta-supracrustal rocks as fragments within the TTG gneisses. Detailed petrographic observations, mineral chemistry and phase equilibrium modelling results show that the prograde stage (M1) of HP pelitic granulites can be presented by the inclusions of garnet porphyroblasts including kyanite, plagioclase, quartz, biotite and ilmenite. The prograde P−T conditions were constructed via melt-reintegration approach and Ti-in-quartz thermometer (710–745 °C at 8–9.3 kbar). The peak stage (M2) can be represented by the core of garnet porphyroblasts and matrix minerals containing kyanite, plagioclase, quartz, biotite, K-feldspar and rutile with the P−T conditions of 12.2–13.6 kbar and 800–825 °C retrieved by Ti-in-quartz thermometer, garnet-Al2SiO5-plagioclase-quartz (GASP) barometer, garnet barometer and phase equilibria modelling. The peak metamorphic P−T conditions suggest that surficial sediments have been brought to a depth over 40 km. The post-peak stage (M3) is presented by the inner rim of garnet porphyroblasts (recorded in QY01) or the core of garnet (recorded in QY02) with some matrix minerals containing sillimanite, plagioclase, quartz, biotite, K-feldspar and ilmenite, indicating the P−T conditions of 7.8–9.0 kbar and 810 °C combined with Ti-in-quartz thermometer, GASP barometer, garnet barometer and phase equilibria modelling. The final retrograde stage (M4) is presented by the minor matrix sillimanite, plagioclase, quartz, K-feldspar, ilmenite and biotite with the absence of melt and the P−T conditions of 668–733 °C at 5–8 kbar using Ti-in-biotite thermometer. Monazite LA-ICP-MS U-Pb dating reveals the peak or near peak metamorphic ages ∼2.49 Ga of the HP pelitic granulites. Therefore, the HP pelitic granulites of the Qingyuan terrane record the clockwise P−T−t paths with sequential isothermal decompression (ITD) and isobaric cooling (IBC) segments, suggesting a subduction−collision environment at the late Neoarchean (∼2.49 Ga) in the eastern NCC.

Experimental study on dynamic mechanical characteristics and fracture behaviors of coal under water–gas-temperature coupling conditions

The stability of underground spaces in abandoned coal mines is affected by water, gas, temperature, and other dynamic disturbances. Thus, it is important to understand the dynamic behavior of coal in a complex environment for reusing abandoned mines. To this end, a multi-field coupled test system was independently developed to investigate the dynamic behaviors of coal under water–gas-temperature coupling conditions. The results revealed that in the presence of water and gas, the upper part of the coal sample was surrounded by gas, while the lower part was soaked in water. The dynamic stress–strain curve of the coal samples in the coupled water–gas-temperature environment includes a linear elastic deformation stage, rapid crack propagation stage, and post-peak fracture stage. The presence of the water–gas mixing pressure changes the failure of coal from ductile to brittle, whereas an increase in temperature changes the failure of coal from brittle to ductile. The dynamic strength of the coal samples increased linearly with an increase in the impact velocity, strain rate, and water–gas mixing pressure but decreased with an increase in temperature. The failure strain of the coal samples increased linearly with an increase of impact velocity, strain rate, and temperature, but decreased with an increase in the water–gas mixing pressure. In addition, the fracture process of the coal was captured using a high-speed camera, and the results indicated that the cracking degree of the gas part was greater than that of the water-soaked part. Moreover, the influence of various factors on the impact fracture behavior and deterioration mechanism of coal under water–gas-temperature coupling conditions were revealed.

Mechanical behavior of steel-fiber-reinforced self-stressing concrete filled steel tube columns subjected to eccentric loading

Initial self-stress contributes to the pre-peak properties of concrete filled steel tube (CFST) columns, but brings salient brittleness at the post-peak stage. Adding steel fibers can alleviate the friability of concrete, helpful in the post-peak behavior of CFST columns. This study aims to investigate the coupling effect of initial self-stress and steel fibers on the mechanical behavior of CFST columns under eccentric loads. 42 eccentrically loaded specimens are conducted with various levels of self-stress, eccentricity ratio, steel fiber volume percentage, concrete strength grade and steel tube thickness. Moreover, a numerical analysis model is developed to capture the eccentrically loaded behavior of steel-fiber-reinforced self-stressing concrete filled steel tube (SSCFST) columns. The results show that the increases in the ultimate load (Nu) and the corresponding bending moment (Mu) are obtained by the self-stress. Adding steel fibers leads to a slight growth of Nu, but the bending moment shows an obvious growth after the ultimate state, indicating adequate safety margin. The axial-flexural interaction curves possess a more obvious convexity as steel fiber dosage is increased. Based on the numerical results, a new axial-flexural interaction model is proposed, which is capable of considering the influence of steel fiber dosage.

FERROHÖGBOMITE-2S2N IN THE DIATEXITES OF WESTERN SANGILEN, SOUTH-EASTERN TUVA, RUSSIA

In the Western Sangilen (Tuva–Mongolia microcontinent, Central Asian Orogenic Belt, Russia) rare mineral ferrohögbomite-2S2N, for the first time, was found in a deep-seated contact aureole of the early Paleozoic Bayan-Kol gabbro-monzodiorite intrusion. The rocks are diatexites of roof pendant, where metamorphics contact gabbronorite. Diatexites formed as a result of strong melting and desilication of quartz-bearing kyanite-staurolite schists (M1) during progressive thermal metamorphism (M2) near the Bayan-Kol intrusion with peak at 950 °C, 7–8 kbars. Ferrohögbomite-2S2N grains up to 50 μm in size found in ilmenite-corundum-magnetite-hercynite pseudomorphs. The later formed during progressive stage of thermal metamorphism M2 after regional staurolite M1 and are in cordierite-gedrite-plagioclase restite blocks of diatexites. Ferrohögbomite also appeared as thin (1–5 μm) rims around individual grains of hercynite, corundum and magnetite in a rock matrix. According to microtextural features ferrohögbomite grains formed during post-peak metamorphic stage after minerals of pseudomorphs. A univariant mineral reaction of ferrohögbomite-2S2N formation calculated quantitatively in Fe-Al-Ti-Zn-H2O system with program Mathematic 9.0 using electron microprobe chemical composition of minerals of pseudomorphs. The reaction is 0.96Spl+0.194Ilm+0.116Mag+0.036Crn+0.163H2O=0.163Hgb. A local equilibrium value during formation of ferrohögbomite was probably correlated with pseudomorphs size and thus do not transcend 1 mm3. Thermobarometry yields metamorphic temperature and pressure of ferrohögbomite formation as T=665 °C, P=5.8 kbar, which correspond to late retrograde stage of thermal metamorphism of diatexites. To present day in Russia, högbomite group mineral was known only on South Urals and Aldan Shield in Eastern Siberia.

Compressive behaviour of UHPC-filled square high-strength steel tube stub columns under eccentric loading

This paper presents experimental and numerical studies on the compressive behaviour of ultra-high performance concrete (UHPC) filled rectangular high-strength steel tube (UFHST) stub columns under eccentric loading. A total of 16 compressive specimens with a maximum concrete strength of 150 MPa and a maximum steel strength of 846 MPa were designed and tested. The test results showed that the use of high-strength steel tube and UHPC without steel fibres largely enhanced the load-carrying capacity of concrete-filled steel tube columns. The use of fibre-free UHPC adversely influenced the ductility of the columns. The incorporation of steel fibres into UHPC when casting the columns, however, improved the ductility of the composite columns and at the same time gained additional load-carrying capacity. A finite element (FE) model was then developed using ABAQUS and verified with test results. The numerical parametric study using the verified FE model showed that the confinement effect from the high-strength steel tube onto the UHPC was obscure before peak stress of the column was achieved, but was gradually activated/increased in the post-peak stress stage. Therefore, subsequent to the peak value, the axial stress of the confined UHPC experienced a short decrease first and then a continued growth. The findings from the present study set an experimental and numerical basis for future investigations to expose optimistic design of the UFHST stub columns.

Test study on failure and energy supply characteristics of rock under different loading stiffness

Based on the stiffness theory, the stiffness difference and energy supply of surrounding rocks are important inducing factors for rock burst. However, due to the lack of multi-level low stiffness testing machine, there are few experimental studies on rock failure mechanism under the influence of loading stiffness. Aiming at the above problems, this paper improved the rock mechanics testing machine, and developed several sets of low stiffness flexible rings, which realized laboratory test under five different loading stiffness in the range of 0.07 ∼ 0.615GN/m. Based on low stiffness loading device, the mechanical behavior of sandstone specimens was studied. With the decrease of the loading stiffness, the post-peak stage of the stress–strain curve of the specimen changes from step shape to oblique linear shape, and the specimen changes from progressive shear failure to brittle splitting failure. There is a power function positive correlation between the specimen’s post-peak failure duration and stiffness ratio of the testing machine and the specimen, and a power function negative correlation between stress drop rate and stiffness ratio. When the specimen is damaged and the stress is dropped, the deformation of low stiffness testing machine rebounds with high-speed, resulting in an obvious dynamic load behavior. The loading stiffness has little effect on the energy storage and energy dissipation characteristics of the specimen, while the release energy of the testing machine increases as the stiffness ratio decreases, which is the key factor affecting the failure mode of the specimen. According to the test results, a rock burst mechanical model considering the stiffness is established, and the energy supply mechanism of rock burst is quantitatively explained.

Experimental investigation of headed studs in steel-ultra-high performance concrete (UHPC) composite sections

Featuring high compressive and tensile strengths, ultra-high performance concrete (UHPC) is an efficient and durable alternative for conventional concrete in steel–concrete composite sections. However, few experimental studies to date have involved large diameter (≥ 25 mm) headed studs, UHPC with compressive strengths larger than 130 MPa, and relatively low strength but cost-effective UHPC. This study investigates the shear performance of steel headed studs embedded in UHPC through pushout tests with 24 specimens. Specimens included headed studs with diameters of 16 mm, 19 mm, 22 mm, and 25 mm, and either UHPC with compressive strength of 152.5 MPa or a cost-effective UHPC with a strength of 85.7 MPa (named as HPC hereafter). The results showed that smaller-diameter specimens (16 or 19 mm) failed with stud shank fracture, while the larger-diameter specimens (22 or 25 mm) failed at welding lines. Compared to HPC, UHPC did not notably increase the performance of headed shear strength. The load response consisted of a linear stage, a softening stage, and a post-peak stage lasting up to a slip of 10 mm or greater, with high variability in post-peak response among specimens with identical parameters. A global database of 120 push-out test specimens from this study and references was established, covering concrete strengths from 23.5 MPa to 152 MPa. The formulae given by AASHTO LRFD Bridge Design Specification, Eurocode-4, and Chinese code GB50017-2003 overestimated the shear capacity of headed studs by 52 %, 5 % and 53 %, respectively. The equation for the slip modulus slightly overestimated the slip modulus of headed studs. In conclusion, this study broadened the ranges of concrete strength and diameter of headed shear studs, and revealed that the existing equations of predicting shear capacity and slip modulus need improvement.

Effect of interface geometric parameters on the mechanical properties and damage evolution of layered cemented gangue backfill: Experiments and models

• Mechanical properties of LCGB as a function of interface geometry parameters. • Effects of interface geometric parameters on damage evolution of LCGB. • Failure mode of LCGB is affected by interface geometric parameters. • Dynamic crack evolution law of LCGB during loading. Subsequent backfilling of widespread goaf generally necessitates multiple fillings to enrich the goaf, resulting in the layered structure of cemented gangue backfill. Therefore, it is of great significance to study the mechanical properties of layered cemented gangue backfill (LCGB) with different interface geometric parameters to ensure the stability of underground engineering. In this paper, the effects of interface roughness and interface angle on the mechanical properties and damage evolution of LCGB were comprehensively explored using uniaxial compression test, acoustic emission (AE) and digital image correlation (DIC). A numerical model of LCGB was built using simulation software (PFC2D) to demonstrate the dynamic crack evolution of LCGB during loading. The results demonstrate that LCGB's compressive strength and elastic modulus have positive linear and quadratic relationships with interface undulating angle and interface angle respectively, and that the rupture angle, which represents the worst mechanical properties of LCGB, is between 45° and 60°. Increasing the interface undulating angle can enhance the strain hardening characteristics of LCGB during the post-peak deformation stage and release more active AE signals. As the interface angle approaches the rupture angle, the peak stress of LCGB continues to deteriorate, and its AE signal appears more concentrated in the post-peak deformation stage. The surface principal strain of LCGB rises as the interface undulating angle increases, while it reduces first and then increases with the interface angle increases. The simulation process reveals that shear cracks mainly extend along the interface, whereas tension cracks propagation and coalescence the adjacent interface along the axial stress loading direction, and they converge to generate macroscopic defects that cause LCGB unstable failure.

Axial behavior of circular seawater sea-sand coral concrete columns reinforced with BFRP bars and spirals

• Axial behavior of BFRP bars reinforced seawater sea-sand coral concrete columns was studied experimentally. • The load bearing capacity of B-SSCC columns declined as the spiral spacing narrowed paradoxically owing to the significant discontinuity of coral concrete internally. • Columns with dense stirrups showed more pronounced ductility in the post-peak stage compared with B-SSCC square columns. • An ultimate bearing capacity prediction model is established. For the sake of solving the problem of steel reinforcement corrosion in concrete structures and reducing the transportation cost of concrete raw materials at sea in the development of South China Sea Islands, a new type of coral reef sand concrete columns reinforced with basalt fiber reinforced polymer (BFRP) bars and spirals was proposed. In this study a total of 18 circular seawater sea-sand coral reef concrete columns reinforced with BFRP bars and spirals (B-SSCC) were tested under concentric axial loads. Parameters of nominal longitudinal bar diameters and spiral spacing were investigated to obtain variations on crack propagation, failure modes, load bearing capacity, strain and ductility properties. The results indicated that no obvious cracks were observed until the curves reached up to 0.95 P max approximately and the columns experienced more brittle and explosive failure modes with the increase of longitudinal bar diameter and spiral spacing. The load bearing capacity of B-SSCC columns increased with longitudinal reinforcement ratio, however, declined as the spiral spacing narrowed paradoxically. It was owing to the significant discontinuity of coral concrete internally. Compared with B-SSCC square columns, the circular columns with dense stirrups showed pronounced ductile behavior in the post-peak stage, remarked by improved average ductile coefficient β of 22.6%. Finally, a numerical prediction of load bearing capacity was suggested.

Experimental Verification of Theoretical Stress-Strain Model for Compressed Concrete Considering Post-Peak Stage.

The theoretical stress-strain model for compressed composite cement materials’ behavior without empirical coefficients was proposed by Iskhakov in 2018. This model includes the following main parameters describing concrete behavior: stresses and strains corresponding to the border between the elastic and non-elastic behavior stages of a concrete specimen, ultimate elastic strains, and stresses and strains at the end of the post-peak region. Particular attention is focused on the descending branch of the stress-strain diagram, as well as on the analysis of concrete elastic and plastic potentials. These potentials are important for assessing the dynamic response of the concrete element section, as well as for concrete creep analysis. The present research is aimed at experimental verification of the above-mentioned theoretical model. The obtained experimental results are in good agreement with the theoretical ones, which confirms the model’s accuracy and enables a significant reduction in the empirical coefficients number in compressed reinforced concrete elements design. This, in turn, represents the scientific novelty of this study.

Microscopic and Acoustic Interpretations of the Physics of Rock Burst and the Difference in Fracturing Patterns in Class I and Class II Rocks

The progressive microcracking processes in a burst-prone Class II rock, Kuru granite, and a non-burst-prone Class I rock, Fauske marble were investigated, aiming to reveal the physics of rock burst and the difference in burst-proneness in Class I and Class II rocks. The cylindrical rock specimens of Kuru granite and Fauske marble were uniaxially loaded to various levels in both pre- and post-peak stages, which was monitored by Acoustic emission technique. After that, the thin sections parallel and perpendicular to the loading direction were prepared from each unloaded specimen. The observed intergranular and intragranular cracks in thin sections were quantitatively analyzed in their length, width and orientation as well as the fracturing modes. It was found that extensional intergranular cracking dominated the damaging process in Kuru granite in the pre-peak stage. In the post-peak stage, both intergranular and intragranular cracks increased abruptly. The granite specimen finally failed in splitting. Intragranular shear cracking in calcite dominated the damaging process in Fauske marble. A number of shear fractures formed in the marble and finally the marble failed along a shear fracture zone. It was deduced that, under low confining stress, the fracturing process in Kuru granite of Class II was dominated by extensional fracturing in the direction of σ1, which dissipated a relatively small portion of the strain energy in the rock and the remaining energy was released for rock ejection. The fracturing in Fauske marble of Class I was dominated by intragranular shear cracking, which dissipated the entire strain energy.

Mechanical degradation mechanism of rock under seismic disturbance stress

During the action of periodic seismic disturbance stress, the rock mass surrounding buried structures will show fatigue damage owing to cyclic loading. To explore the fatigue characteristics and mechanical degradation mechanism of this process, fatigue loading and uniaxial compression tests were carried out on gypsum samples. The conclusions are as follows. With increasing seismic wave amplitude, the stress loading and unloading velocity gradually increases, and the opening of the stress–strain hysteresis loop gradually increases. With increasing seismic wave frequency, the dip angle of hysteresis loops gradually inclines to the σ -axis (where σ is stress), and the variation amplitude of hysteresis loops on the ε -axis (where ε is strain) decreases gradually. This shows that the greater the amplitude of the seismic wave and the lower the frequency, the greater the damage to rock. Under seismic wave disturbance, with increasing number of disturbances, the original cracks in the sample gradually spread and infiltrate the rock, and secondary cracks gradually develop, indicating that the physical and mechanical properties of the rock gradually deteriorate. There is a strong correlation between the acoustic emission of samples and the stages of the stress–time curve for uniaxial compression. According to the acoustic emission characteristics, the stress–time curve can be divided into four stages: the initial loading stage, the stable crack growth stage, the unstable crack growth to failure stage and the post-peak stage. Compared with the sample before fatigue, the peak strain decreases significantly and the impact energy index increases significantly after fatigue loading. This indicates that some original cracks in the sample are compressed under seismic disturbance, the brittleness of the sample is enhanced and the rockburst tendency is greatly enhanced.

Mechanical Behavior and Failure Process of Hard Rock with Rock Bridge under Uniaxial Compression Test

Abstract The mechanical properties of rock mass are mostly controlled by the structural plane. Rock bridge has an important effect on the failure and stability of rock mass with structural plane. In this paper, the uniaxial compression test of hard rock containing rock bridge is carried out, accompanied by acoustic emission (AE) and high-speed video monitoring. Within the scope of this study, the results show that the uniaxial compressive strength (UCS) of sample with rock bridge increases with the rock bridge length. Under the same stress condition before peak, the strain of the sample decreases with the increase of the rock bridge length (RBL). Under the influence of stress concentration, the cracking of the sample starts from the prefabricated crack tip. The peak AE count of the sample decreases with the increase of RBL. The AE cumulative energy of the sample increases with the increase of RBL. The number of cracks in the sample before the peak is small, and the rapid increase of cracks is mainly concentrated in the main fracturing stage after the peak, while after reaching the residual stage, the increase rate of various types of microcracks in the sample is relatively slow. The numerical simulation results show that the number of all kinds of cracks in the sample before the peak is small, and the number of tensile cracks in the sample is very close to the total number of cracks under different RBLs. With the increase of RBL, the tensile/shear crack ratio decreases. The internal cracks of the sample are mainly concentrated at the peak stress and postpeak stage. The research results of this paper are of great significance to the engineering excavation and safe construction of jointed rock mass engineering.

Experimental investigation on dynamic mechanical properties and fracture evolution behavior of the underground openings with excavation damaged zones

The existence of excavation damaged zone (EDZ) generally influences the stability and safety of the underground openings. To investigate the influence of EDZ on the stability of underground excavation under dynamic stress disturbances, underground excavations with EDZs are represented by holed rock specimens with damage zones. The fracture evolution and dynamic mechanical properties of damaged holed rock specimens under dynamic loads are investigated by using the improved Split Hopkinson Pressure Bar (SHPB). The results have shown that the stress-strain curve of the rock specimens with damage zones is divided into pre-peak and post-peak stages, without compaction and elastic deformation stages. The dynamic strength, peak deformation moduli, and crack initiation stress decrease while the strain rate, absorbed energy, and failure time of holed specimens increase with increasing damage around circular holes. The failure of the holed rock specimens always start from circular holes, and specimens without or with minor damage exhibit overall tensile-shear failure. However, the failure of rock specimens with a greater damage condition mainly appears within damage zones around circular holes in the form of spalling or compression-shear failure, and the failure zone increases with increasing damage of surrounding rocks. The failure around and away from circular holes of specimens without or with minor damage is respectively characterized by intergranular and transgranular cracks. The results of the present study provide implications to the disaster prevention and support design of underground openings with EDZ.

Study on Damage Characteristics of Water-Bearing Coal Samples under Cyclic Loading–Unloading

For underground water reservoirs in coal mines, the complex water-rich environment and changing overburden stress can damage coal pillar dams. In this paper, the coal samples from coal seam 22 of Shangwan coal mine were taken as research objects and the damage mechanism and characteristics of coal samples with different moisture content and wetting-drying cycles under cyclic loading were investigated. The results show that as the moisture content and wetting-drying cycles increase, the post-peak stage of the coal samples under cyclic stress becomes obvious, and the hysteresis loop changes from dense to sparse. Compared to the uniaxial compression experiment, when w = 5.28% (the critical water content), mechanical parameters such as peak strength and modulus of elasticity decrease the most. Under cyclic loading, the damage mode of both sets of coal samples was tensile damage, but the increase in wetting-drying cycles promotes the development of shear fractures. For evaluating fracture types, the RA-AF density map is more applicable to wetting-drying cycle coal samples, whereas for the coal samples with different moisture contents this should be carried out with caution. This study can provide some theoretical basis for the stability evaluation of coal pillar dams in underground water reservoirs.

Analysis of Energy Transmission and Deformation Characteristics of Coal-Rock Combined Bodies

A coal-rock system is a common combination form in coal mines. In order to explore the energy interchange law of a coal-rock combined body and the interaction relationship between the two bodies, loading tests of coal-rock combined bodies with different height ratios were carried out. The loading path of rock in coal-rock combined bodies was demonstrated by means of a single loading and unloading test of the same-sized rock sample. Furthermore, a method to calculate rock energy was proposed based on the area of the loading and unloading curve. The experimental results show that the greater the surrounding rock pressure is, the smaller increase rate of lateral and volumetric strain in the postpeak stage will be when the same height ratio is present. An increase in the surrounding rock pressure causes an increase in the total strain energy density of small-sized rock samples. However, the total strain energy density is always greater than the elastic strain energy density. And the elastic and dissipated strain energy densities also increase, along with the energy dissipation with unloading. When the proportion of coal bodies increases, the energy accumulation also shows an increasing trend. When the height of the coal is greater than half the height of the complete specimen, the coal energy proportion is greater than 60%. After reaching the yield load, the energy in the coal body is dissipated in forms such as plastic deformation, internal damage, block friction, radiation energy, and kinetic energy. Therefore, the energy released is, in part, reflected in the rock body.

Public anxiety through various stages of COVID-19 coping: Evidence from China.

As countries underwent the initiation, peak, post-peak, and early vaccination stages of COVID-19, the changing risk perception, coping behaviors and corresponding psychological stress experienced by the public over time was rarely reported. We conducted a national scale panel study using social-psychological data collected from 5,983 questionnaires to investigate the interactions between anxiety level, risk perception and coping behavior during different stages of COVID-19 in China. We found that sustained perceiving worries of being infected, first due to domestic and then global pandemic, contributed to the persistent high proportion of respondents with anxiety disorders which even gradually increased over time (56.1% during initiation to 60.4% during early vaccination). Gender was the strongest predictor of anxiety at all stages, with females having less confidence in COVID-19 control and always suffering from much higher anxiety levels than males even during the post peak stage. Excessive protective behavior and frequency of access to COVID-related news also contributed to public anxiety. Additionally, public risk perception was significantly associated with their willingness to vaccinate. The findings verify the feasibility of taking stage-specific and gender-based risk communication strategies to alleviate the pandemic-related public anxiety and promote vaccination by influencing public risk perception and guiding coping behaviors.

Effects of combination mode on mechanical properties of bi-material samples consisting of rock and coal

We performed uniaxial compression tests on coal–rock, rock–coal, and rock–coal–rock bi-material samples. We studied their mechanical behavior using an acoustic emission monitoring and digital speckle strain measurement systems. The average uniaxial compressive strengths of the rock–coal–rock, coal–rock, and rock–coal bi-material samples were 20.54 MPa, 14.28 MPa, and 14.03 MPa, respectively. The strength of the coal determines the overall strength of the bi-material sample. However, the overall strengths of the coal–rock, rock–coal, and rock–coal–rock bi-material samples were greater than that of coal by 11.76%, 10.19%, and 31.84%, respectively. A crack in the coal part of a bi-material sample can develop and spread to the rock part, thus resulting in its splitting failure. The rock–coal–rock bi-material samples exhibited plastic failure, while the coal–rock and rock–coal bi-material samples exhibited brittle failure. Progressive failure of the coal sample induced rebound deformation of the rock sample. The rebound deformation rates of the rock–coal–rock, coal–rock, and rock–coal samples were 0.57%, 0.09%, and 0.12%, respectively. In the pre-peak stage, the average elastic energy of the rock–coal–rock bi-material sample was 92.57%, indicating a strong ability to store external energy. In the post-peak stage, the average post-peak release energy of the rock–coal–rock bi-material sample was the largest, but the average surplus energy was the smallest. Therefore, the rock–coal–rock bi-material exhibited the highest macro-cracking but the dynamic behavior was the least prominent. The coal–rock and rock–coal bi-material samples exhibited less prominent macro-cracking after failure but a more pronounced dynamic behavior.

A unified strain-hardening and strain-softening elastoplastic constitutive model for intact rocks

A unified strain-hardening and strain-softening (UHS) elastoplastic constitutive model is developed to capture the nonlinearity of intact rocks. Three new developments are incorporated into the model: (i) a unified strain-hardening and strain-softening rule, which is used to describe the nonlinearity of the stress–strain curve; (ii) the cohesion loss model, which can describe the nonlinearity of the residual strength; and (iii) normalized plastic shear strain, which is adopted as the plastic internal variable. There are 15 model parameters. All of them can be easily obtained by uniaxial compression tests and triaxial tests under different confining pressures. The proposed model has been implemented in FLAC3D and validated against five different types of rocks. The results show that the model can capture the nonlinearity of the stress–strain curve, including both the strain-hardening stage before the peak strength and the strain-softening at the post-peak stage. The model is also able to describe the effects of the confining pressure on the peak strength, residual strength and stress–strain curve. Moreover, the transition from brittle failure to ductile failure under high confining pressure can be well described.