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The stability of coal walls (pillars) can be seriously undermined by diverse in-situ dynamic disturbances. Based on a 3D particle model, this work strives to numerically replicate the major mechanical responses and acoustic emission (AE) behaviors of coal samples under multi-stage compressive cyclic loading with different loading and unloading rates, which is termed differential cyclic loading (DCL). A Weibull-distribution-based model with heterogeneous bond strengths is constructed by both considering the stress–strain relations and AE parameters. Six previously loaded samples were respectively grouped to indicate two DCL regimes, the damage mechanisms for the two groups are explicitly characterized via the time-stress-dependent variation of bond size multiplier, and it is found the two regimes correlate with distinct damage patterns, which involves the competition between stiffness hardening and softening. The numerical b-value is calculated based on the magnitudes of AE energy, the results show that both stress level and bond radius multiplier can impact the numerical b-value. The proposed numerical model succeeds in replicating the stress–strain relations of lab data as well as the elastic-after effect in DCL tests. The effect of damping on energy dissipation and phase shift in numerical model is summarized. Highlights: Fatigue behaviors of coal are reproduced by particle model under DCL Micro seismic monitoring is implemented based on heterogeneous particle model The distinction incurred by DCL is reproduced and revealed [ABSTRACT FROM AUTHOR]

This work aims to experimentally investigate the behaviour of sandstone drilled from an underground coal mine exposed to low-frequency cyclic loading with distinct loading/unloading rates, namely differential cyclic loading (DCL). Three loading modes with different loading/unloading rates were applied. The test results are presented and analysed in terms of dissipated energy ratio (DER), evolution of secant elastic moduli, stress–strain hysteresis and acoustic emission (AE) behaviours. The correlation between DER and maximum cyclic load level is revealed, and a novel method to predict the strength of the rock sample is proposed based on statistics of DER at failure. The hardening behaviour is observed during cyclic loading, which is characterized by gradual enhancement of the secant elastic moduli. The stress–strain hysteresis is determined, which shows that phase shift between stress–strain is loading/unloading rate-dependent. The evolution of AE counts and energy is documented and discussed with respect to the dissipated energy. The results indicate that patterns of AE evolution and Kaiser effect are both influenced by cyclic loading paths. [ABSTRACT FROM AUTHOR]

This work aims to reveal the fracture the damage evolution characteristics of fissure‐holes containing rock under multistage constant‐amplitude variable‐frequency cyclic loads. Testing results show that the peak strength and fatigue lifetime both increase as the fissure angle increases from 10° to 70°. However, the volumetric deformation, AE activities, and crack network scale get to a maximum for a sample having a 50° fissure angle. More small‐sized cracks were formed for rock having a high fissure angle, and the proportion of low‐frequency signal is relatively high. A damage evolution model was proposed based on AE rate, and an inverted "S"‐shaped curve reflects the damage propagation of the experimental data. Additionally, the highlighted internal crack network reveals the crack coalescence and hole spalling behaviors; three types of rock bridge coalescence modes of single tensile coalescence, double‐tensile coalescence, and double shear coalescence were identified. Highlights: Failure of pre‐flawed granite under multi‐level variable‐frequency (MLVF) cyclic loads was discussed.Fissure angle influences the rock deformation, lifetime, AE activities, and the final crack pattern.A damage evolution model was proposed by AE rate to describe three‐phase damage propagation.The crack coalescence behaviors were visualized and three coalescence modes were identified. [ABSTRACT FROM AUTHOR]

This article presents the results for cyclic uni/triaxial tests on the deeply seated granite samples drilled from a −915 m deep tunnel in Sanshandao (SSD) gold mine. The monotonic and cyclic tests were carried out to observe the mechanical responses of the granite samples under different loading regimes. The disparities concerning the strain evolution and compressive strength of granite samples considering monotonic and cyclic uniaxial and triaxial loading are presented. Deformation behaviour, dissipated energy, and hysteresis are documented and evaluated. Quantitative correlations between strain evolution and cyclic stress levels are revealed. The amount of energy transformation during uniaxial and triaxial cyclic loading is determined. The impacts of confining pressure level on ultimate strain, energy dissipation, and stress-strain phase shift are presented. The mechanical responses of the granite samples subjected to different stress paths and loading strategies are summarised, and corresponding interpretations are given to clarify the differences of mechanical behaviour encountered in distinct loading methods. [ABSTRACT FROM AUTHOR]

Rock joints have obvious acoustic emission (AE) Kaiser effect and Felicity effect under multilevel cyclic shear conditions. The TFD-20H/50J rock shear apparatus was used to carry out cyclic loading and unloading joint shear tests, and the acoustic emission parameters and frequency spectrum characteristics of the whole shearing process were analyzed. The results show that, under the cyclic loading, the shear stress-displacement curve forms several cyclic hysteresis loops, and the number of loops increases with the increase of normal stress. With the cycles increase, the shear damage gradually increases, and the Felicity ratio gradually decreases. The Felicity ratio at the final shear failure moment is about 0.94~0.99. The ratio of the RA value (rise time/amplitude) and the average frequency value (RA-AF) is used to classify the cracking mode of the joint sample. There are two AE crack signal types (tensile type and shear type) during shear damage. The peak frequency is displayed as high, medium, and low three frequency bands, which are distributed in the range of 0~35 kHz, 35~122 kHz, and 122~300 kHz, respectively. Both low-frequency and high-frequency signals account for less than 10%, and medium-frequency signals account for more than 90%. The research of the AE monitoring signals of multilevel shear behaviors can help understand the shear-friction mechanisms of rock joints. [ABSTRACT FROM AUTHOR]

• MSC model is proposed to replicate multi-level cyclic loading results. • Damage variable is stress-time dependent in numerical model. • Damage variable is characterized by reduction of bond diameter. • AE characteristics during cyclic loading are simulated based on PFC3D. Under the framework of the particle flow code (PFC), a three-dimensional multi-level stress corrosion model (MSC) is proposed to reproduce the mechanical behaviour of brittle geo-materials and concrete exposed to multi-level cyclic compressive loading. The damage induced by the variable cyclic load levels during consecutive loading stages in numerical simulations is quantitatively characterized by time-stress-dependent reducing of the bond diameter. The change of maximum or minimum load levels correspond to different evolution characteristics of the bond diameter. The simulation results with the adoption of the MSC model shows good consistency with laboratory testing. The MSC model is proved to replicate the mechanical characteristics of concrete samples subjected to cyclic loading with both, variable maximum and minimum load levels. A three-dimensional acoustic emission (AE) monitoring system is implemented into PFC3D. The cumulative AE energy collected during the simulation is designated as the released bond strain energy at bond breakage. The cumulative AE energy in the simulation shows good agreement with laboratory test results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Hysteresis energy-based failure indicators for concrete under cyclic loading conditions are proposed: hysteresis occurrence ratio (HOR) and hysteresis energy ratio (HER) considering the hysteresis characteristics and dissipated energy. A two-step approach to predict the failure of concrete is introduced. The first step: HOR has two critical values. These two critical values for the specific concrete used in our laboratory testing are 75% and 95%. In detail, when HOR is under 75%, the concrete has no risk to fail, when HOR is between 75% and 95%, the concrete has the possibility to fail, when HOR is larger than 95%, the concrete will fail very likely within the next few cycles. The second step contains two criteria: if HOR is larger than 75% and HER is larger than 0.3 at the same time, the concrete will fail. Different multi-level cyclic loading strategies have been designed to verify the effectiveness of these failure indicators and the failure prediction approach. First laboratory test results verified that HOR and HER are reliable failure indicators. [ABSTRACT FROM AUTHOR]

Based on dissipated energy approach (DEA), the energy dissipation characteristics of concrete samples subjected to uniaxial cyclic loading have been investigated. The effect of different cyclic load levels on energy dissipation is quantitatively analyzed by different damage indicators during cyclic fatigue tests. It is concluded that the cumulative speed of energy dissipation and increasing growth-rate of damage indicators in Continuum Damage Theory (CDT) follow an exponential function in relation to the maximum cyclic load level and follow a logarithmic function in relation to the minimum cyclic load level. The loading strategy has an effect on total energy dissipated during fatigue tests, in other words: Energy dissipation and damage evolution are stress path dependent. [ABSTRACT FROM AUTHOR]

The mechanical response of rocks subjected to compressive differential cyclic loading (DCL) with various stress rates is rarely investigated via numerical simulation at the microscopic level. In this study, the behaviour of sandstone is numerically investigated via a 3D particle-based numerical model. A damage model is implemented based on the variation in bond diameter and succeeds in accurately reproducing the stress–strain relations obtained from laboratory tests. Three evolution patterns of bond diameter are used to duplicate the strain rates observed during the laboratory tests. A system similar to AE monitoring is run in simulations, and AE events are recorded, classified, and visualized according to the magnitude of released energy at bond failure. The effect of heterogeneous bond strengths on AE characteristics is discussed. A heterogeneous model is recommended for the realistic reproduction of the onset of cracking as well as stress dependency. A stress rate-induced phase shift in terms of the stress–strain relation is observed in both laboratory tests and numerical simulations. The damping effect is thoroughly considered in the numerical model. [ABSTRACT FROM AUTHOR]

• The evolution of natural stone masonry stiffness exposed to multi-level cyclic load is revealed. • A novel secant modulus-based failure prediction method is proposed. • A constitutive model is proposed to characterize stone deformation under multi-level fatigue load. Stiffness loss and catastrophic failure frequently occur in natural stone masonry subject to freeze–thaw action and cyclic stress, which may incur serious engineering disasters and casualties. This work strives to experimentally unveil the mechanical responses of a medium-grained building sandstone exposed to dual effects of freeze–thaw and cyclic stress. Testing results are presented from the insights of volumetric deformation, secant modulus evolution. A drop in secant modulus of the first cycle is observed in the failure cyclic loading stage, whereas all former stages exhibit a modulus increase. This precursor well applies to all samples which is freeze–thaw and stress level independent. The development of Poisson's ratio as well as stress level at onset of volume reversal are also presented. A theoretical modelling is put forward to characterize the axial and circumferential strains exposed to variable cyclic stress. The model shows decent effectiveness calibrated by testing results, the way to determine constants in models is introduced in detail, which can be used by readers in a broader range of construction materials. [ABSTRACT FROM AUTHOR]

This article aims to numerically investigate the mechanical behaviour of concrete Brazilian Disk (BD) samples when exposed to multi-level cyclic Brazilian loading. A numerical 3D particle-based model was successfully established to simulate the dynamic stress-controlled cyclic testing. A generalized model is proposed based on the time-dependent evolution of bond diameter. This model shows great effectiveness in terms of reproducing the stress-strain curves, axial strain evolution and displacement fields as observed during lab testing. An acoustic emission (AE) tracking algorithm was implemented in the model to characterize and visualize the released AE energy connected with micro fracturing. The AE energy is found to be stress-level dependent which is consistent with lab testing. The failure pattern in numerical simulation is also in line with lab results. The distinctions between cyclic compressive and cyclic Brazilian tests are discussed and summarized. [ABSTRACT FROM AUTHOR]

• AE behavior and P-wave speed of concrete are revealed in cyclic Brazilian test. • Deformation behavior of concrete is revealed in cyclic Brazilian test. • DIC measurement is performed in cyclic Brazilian test. This work aims to investigate the fatigue behaviour of concrete subjected to indirect cyclic tensile loading. A series of laboratory tests were performed based on Brazilian disk-shaped (BD) concrete samples. Two schemes of cyclic loading tests were designed by considering complex variations of maximum and minimum stresses. The effect of loading parameters, such as loading method, maximum and minimum stress, on sample deformation, acoustic emission (AE) characteristics, P-wave speed evolution and failure patterns were analysed. The features of AE behaviour and P-wave speed were compared between monotonic loading and indirect cyclic loading. Insight on the specific fatigue behaviour was obtained from AE hit counts, AE energy and P-wave speed degradation. The failure patterns of BD concrete samples are governed by the loading method as well as the stress paths. The stress paths have a direct and pronounced impact on the distribution of main and sub cracks on the surface of BD sample at failure. [ABSTRACT FROM AUTHOR]

Freeze-thaw-fatigue (FTF) testing was carried out on Tibet marble at lab-scale by considering various Freeze-Thaw (FT) cycles and multi-level cyclic loading. The aim is to investigate the evolution of deformation and damage related parameters as well as the hysteresis behavior. The test results show that an increase of FT cycles and fatigue load level both accelerate the damage rate of marble. A rock suffering more FT cycles shows a much larger axial strain rate, radial strain rate and increasing Poisson's ratio. The relation of axial strain rate, radial strain rate and Poisson's ratio rate versus fatigue load level can be fitted by an exponential function. A warning level is defined according to the evolution of radial strain and Poisson's ratio which can inform before dilation starts. Moreover, the hysteresis behavior of stress-strain is investigated. It has been proven, that the proposed two indexes, "advance ratio" and "lag ratio" are effective precursors for rock failure prediction if subjected to FTF actions. The drastic drop of the "advance ratio" and the increase of the "lag ratio" are the indicators for forthcoming failure. The recommended warning limits for "advance ratio" and "lag ratio" for the tested marble are 5% and 70%, respectively. [ABSTRACT FROM AUTHOR]

• The axial strain for cyclically loaded concrete specimens is inhomogeneous. • The energy dissipation for cyclically loaded concrete specimens is inhomogeneous. • A new definition of P-wave ratio is proposed as an effective fatigue failure precursor. • Monotonically loaded concrete show larger cracks than cyclic loading case. The mechanical behaviour of different parts (top, middle and bottom) of concrete exposed to monotonic and cyclic loading is investigated through laboratory testing. Strain evolution and energy dissipation are found inhomogeneous at different parts of the sample during compressive cyclic loading. The middle part of sample shows larger residual strain rate and dissipated energy than the top and bottom parts when larger load levels are applied. The disparity between the middle part and top/bottom parts reaches the peak value at peak strength. Based on two different cyclic loading strategies, it is concluded that the maximum load level has more pronounced effect on energy dissipation than the minimum load level. The evolution of P-wave speed during cyclic loading is also found inhomogeneous, a new definition of P-wave ratio is proposed as an effective fatigue failure precursor. The failure patterns of concretes subjected to monotonic and cyclic loading are presented, and it is shown that size and type of cracks is directly related to the loading methods. [ABSTRACT FROM AUTHOR]

• Loading frequency has almost no influence on dissipated energy for a single cycle. • Total dissipated energy is related to the total cycle number. • Two hysteresis indexes are proposed to predict fatigue failure of coal sample. • The damage evolution of coal sample subjected to cyclic loading is inhomogeneous. This paper documents investigations of the fatigue behaviour of strong burst-prone coal in terms of energy dissipation, hysteresis and micro-seismicity. The energy dissipation characteristics of the coal subjected to multi-level-frequency cyclic loading were studied. Two hysteresis indexes were proposed according to the stress-strain relation during cyclic loading. These two indexes are effective as twin precursors to predict the fatigue failure of coal samples. The effect of frequency on energy dissipation rate was studied. With the aid of an AE monitoring system and a high speed camera, 3D distribution of AE events and failure patterns were obtained. The damage evolution of coal samples subjected to cyclic loading is not homogenous due to the stiffness effect of the loading platen. The failure patterns captured by high speed camera are consistent with the results characterized by the spatial distribution of the AE events. [ABSTRACT FROM AUTHOR]