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Failure modes of (a–b) intact specimen, (c–d) flawed specimen of β = 30°, and (e–f) flawed specimen of β = 90°. Subfigures (a–e) showed Y1 surface of the specimen, and (b–f) showed Y2 surface. The main cracks that caused the failure of the specimen were labeled by thick cyan lines, distinct from other secondary cracks represented by thin cyan lines
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True triaxial experiment with a synchronous acoustic emission (AE) monitoring system is a popular measure for the assessment of strength and cracking behaviors of brittle flawed rocks under anisotropic stress circumstances. This measure was employed to investigate the laboratory-scale brittle failure of flawed sandstone containing two different en...
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Locating cracks in a solid object using acoustic emission (AE) is useful both for detecting defects during safety monitoring and for basic laboratory studies of fractures. We developed an acoustic source location (ASL) method without the use of velocity information with AE in anisotropics plates, such as carbon fiber-reinforced polymers. Assuming t...
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... Yang et al. [32] concluded that the mechanical properties, such as Young's modulus and strength of fractured sandstones decrease with the increase of fracture length; while these properties first decrease and then increase as the fracture inclination angle increases. The cracking behaviors and the acoustic emission characteristics of the rock brittle failure were comprehensively investigated by Zhang et al [33,34]. Jin et al. [29] found that the tensile cracks and shear cracks dominate at small and large fracture inclination angles respectively through experimental studies and PFC numerical simulations. ...
A numerical study was conducted on the damage behaviors of sandstone specimens with an embedded rough fracture under triaxial stress conditions. The discrete element method was used to study the deformation and cracking characteristics, and the effects of triaxial stress state, fracture width and inclination angle on the mechanical properties were also investigated. The results are as follows: (1) The strength of fractured rock decreased with the increase of fracture width ratio and the yield stress under conventional triaxial stress is higher than those under true triaxial tests with the same mean confinement; (2) For fractured rock models with small width ratios (0.2, 0.4 and 0.6), the strength increases as the fracture angle turning towards the principal stress direction. The shear damaged bond ratio decreased with the increase of confining pressure when σ x = σ y , while its ratio increased slightly with the fracture angle when σ x ∕ = σ y ; (3) For the large-width fractured rock model with a width ratio 1.0, the strength first decreased and then increased with the increasing inclination angle. At inclination angles of 0 • and 30 • , damage first occurred near fracture surface, then it propagated along the diagonal direction, and the ratios of bond damage caused by tension and shear failure were almost equal. While the shear damaged bond ratio was much higher than that by tension at inclination angles of 60 • and 90 • .
... In true triaxial compression experiments, effects of intermediate principal stress on fracture are an important issue that should be evaluated. Regarding this issue, we draw a straight line with the length of 5 mm (refer to the recent works in Zhang et al. 2023a) successively along the path of every induced crack from its one tip toward another tip, and the ending tip of the first measurement serves as the starting point for the next measurement until the whole path is completely traveled. For each measurement, we discriminate the cracks growing toward σ 2 from those growing toward σ 3 by the crack orientation-based criterion (see Fig. 9): when the crack inclination angle with respect to σ 3 is smaller than 45°, such crack is termed the σ 3 -orientated crack; and the similar definition is built for the σ 2 -orientated crack. ...
The failure characteristics of layered rocks are a vital issue for stability evaluations of underground engineering projects. Layered rocks in a restricted true three-dimensional (3D) stress state behave substantially differently from those under uniaxial or conventional triaxial stress. In this study, true triaxial experiments are carried out to investigate the mechanical and volumetric fracturing behaviors of layered composite sandstones (LCSs) with a change in grain size (Cgrain size) between the layers. Under true triaxial stress, the strengths of LCSs increase considerably as the Cgrain size value increases, which is first reported. The strength enhancements of LCSs with increased σ2 (intermediate principal stress) and Cgrain size values are related to the enhanced grain interlocking effect and the interface effect between the layers. As σ2 increases, the volumetric fracturing behaviors of LCSs change from 3D failure toquasi-3D failure characterized by delamination fracture. The effects of σ2 on fracture are revealed by quantifying the cracking morphologies on the layer interface. Aided by the nuclear magnetic resonance (NMR) technique, the correlations of rock porosity with the σ2 and Cgrain size values are established. This paper promotes the understanding of the failure mechanisms of LCSs with a contrast in grain size under true triaxial stress and helps interpret field observations.
... All the kidney stones showed avalanches and localised events which match with previous descriptions of wild avalanches and mild events [27,31]. Wild avalanches show correlated cracking like teeth and most brittle materials [51][52][53][54][55][56][57]. Such 'hard' materials break by extended avalanches and complex crack patterns. ...
Kidney stones have a prevalence rate of > 10% in some countries. There has been a significant increase in surgery to treat kidney stones over the last 10 years, and it is crucial that such techniques are as effective as possible, while limiting complications. A selection of kidney stones with different chemical and structural properties were subjected to compression. Under compression, they emit acoustic signals called crackling noise. The variability of the crackling noise was surprisingly great comparing weddellite, cystine and uric acid stones. Two types of signals were found in all stones. At high energies of the emitted sound waves, we found avalanche behaviour, while all stones also showed signals of local, uncorrelated collapse. These two types of events are called ‘wild’ for avalanches and ‘mild’ for uncorrelated events. The key observation is that the crossover from mild to wild collapse events differs greatly between different stones. Weddellite showed brittle collapse, extremely low crossover energies (< 5 aJ) and wild avalanches over 6 orders of magnitude. In cystine and uric acid stones, the collapse was more complicated with a dominance of local “mild” breakings, although they all contained some stress-induced collective avalanches. Cystine stones had high crossover energies, typically ∼ 750 aJ, and a narrow window over which they showed wild avalanches. Uric acid stones gave moderate values of crossover energies, ∼ 200 aJ, and wild avalanche behaviour for ∼ 3 orders of magnitude. Further research extended to all stone types, and measurement of stone responses to different lithotripsy strategies, will assist in optimisation of settings of the laser and other lithotripsy devices to insight fragmentation by targeting the ‘wild’ avalanche regime.
... Due to the engineering disturbance, the stress fields in the surrounding rock mass present a typical anisotropic characteristic (σ 1 > σ 2 > σ 3 ), which is beyond the descriptions of uniaxial and conventional triaxial tests (Zhao et al. 2018;Li et al. 2021b;Feng et al. 2019;Zhang et al. 2023b). To date, there are few attempts on the true triaxial mechanical properties and failure characteristics of LCRs. ...
... At the unstable cracking phase, FPZ of granite can be reactivated and intensified by the increasing stress, which constitutes the Fig. 3 Axial stress vs. time curves and respective AE activities of LCR specimens containing a one interface crack, and b two interface cracks mechanisms for the high-level AE event rate. However, the FPZ cannot be obviously observed in sandstone Zhang et al. 2023b). This is why AE event rate of sandstone remains at the relatively low level in the run-up to failure except for the time window of the stress perturbation, as shown in Fig. 3. Figure 4 shows the failure patterns of the LCR specimen containing one interface crack. ...
The interface crack is the typical defect in fracture mechanics, and it often exists inside the layered composite rocks (LCRs). How does it respond to the stress circumstances with a large anisotropy? Is of paramount importance in the stability evaluation of underground engineering. This issue is addressed in this study where the true triaxial tests with the loading rate of 0.05 mm/min are conducted on the two-layered sandstone-granite composite structures containing the interface cracks. Sandstone and granite have a strength of 92.1 and 135.4 MPa, respectively. Results show that the interface crack significantly weakens the LCR strength under true triaxial stress. The interface crack tips, as typical stress concentrator, are revealed as the main sources of fracture initiation and propagation, and the interface crack tips are also found as an essential joint for the fracture containment within the weaker layer. The fracture cluster is formed ahead of the interface crack tip where tensile fracture co-exists with shear fracture. Moreover, the macro-failure initiation mode exhibits the interface crack tip fracture in the quasi-3D failure manner. Main failure planes of LCRs appear sub-orthogonally to σ3 and display the mode of σ3-transverse-symmetric fracturing. Finally, the coupling mechanisms among the interface crack, the stress anisotropy and the mechanical contrast between the layers are revealed.
... In addition, Pan et al. (2020), Chen et al. (2021), and Singh et al. (2022) also obtained the similar results. Zhang et al. (2023b) found that the AE amplitude distribution of flawed sandstone in the crack growth stage follows the power law, which provides a new insight into the failure mechanism of brittle rock. According to the above findings, AE technology can represent the stress-strain condition inside the coal body and anticipate its failure time; therefore, it was extensively employed in the early warning of coal mine dynamic catastrophes, such as gas outburst and rock bursts (Li et al. 2019). ...
The existence of joints reduces the strength of coal and increases the failure probability of coal pillars. To predict and prevent coal pillar failure, it is necessary to clarify the influence of joint dip angle β on coal strength. In this paper, acoustic emission (AE) and unconstrained compression experiments were carried out on coal samples containing a single natural joint with different dip angles. It is found that the mechanical properties and AE characteristics of jointed samples have obvious anisotropy: (1) as β increased, the peak strength, crack initiation stress, peak strain, crack damage stress, Young’s modulus, and crack closure stress of samples decreased first and then increased, while the residual strength displayed a monotonic decrease. (2) As β increased, the failure mode of the samples changed from splitting to shear, and then back to splitting. (3) The closer the β was to 60°, the lower the sample’s strength was, the more active the AE events were, and the sample was more prone to slide along the joint surface. The findings indicate that coal pillars with a joint dip angle close to 60° are most likely to experience shear failure and instability, and that reinforcement measures should be taken in advance to ensure the safety of mining production.
... AE technology has been employed to investigate large scale excavations when damage occurs at the excavation boundary (Cai et al. 2007;Smith et al. 2014). As shown in Fig. 6, AE technology also has been adapted to damage investigation of rock samples at a laboratory scale (Chang and Lee 2004;Zhang et al. 2023;Zhao et al. 2013a). The AE method has two major problems: the first is to choose a proper threshold for the AE signals, which is adequately high to purify the background noise and low to identify the micro-crack initiation (Singh 2016;Xue et al. 2014). ...
... Recent research by Zhang et al. (2023) shows that the dilatancy boundary of the rocks with pre-existing flaws reaches its peak strength. In contrast, the dilatancy boundary of the intact rock is around 80% of its peak strength. ...
The crack initiation stress threshold ( $${\sigma }_{\mathrm{ci}}$$ σ ci ) is an essential parameter in the brittle failure process of rocks. In this paper, a volumetric strain response method (VSRM) is proposed to determine the $${\sigma }_{\mathrm{ci}}$$ σ ci based on two new concepts, i.e., the dilatancy resistance state index ( $${\delta }_{\mathrm{ci}}$$ δ ci ) and the maximum value of the dilatancy resistance state index difference ( $$\left|{\Delta \delta }_{\mathrm{ci}}\right|$$ Δ δ ci ), which represent the state of dilatancy resistance of the rock and the shear sliding resistance capacity of the crack-like pores during the compressive period, respectively. The deviatoric stress corresponding to the maximum $$\left|{\Delta \delta }_{\mathrm{ci}}\right|$$ Δ δ ci is taken as the $${\sigma }_{\mathrm{ci}}$$ σ ci . We then examine the feasibility and validity of the VSRM using the experimental results. The results from the VSRM are also compared with those calculated by other strain-based methods, including the volumetric strain method (VSM), crack volumetric strain method (CVSM), lateral strain method (LSM) and lateral strain response method (LSRM). Compared with the other methods, the VSRM is effective and reduces subjectivity when determining the $${\sigma }_{\mathrm{ci}}$$ σ ci . Finally, with the help of the proposed VSRM, influences from chemical corrosion and confining stress on the $${\sigma }_{\mathrm{ci}}$$ σ ci and $${\Delta \delta }_{\mathrm{ci}}$$ Δ δ ci of the carbonate rock are analyzed. This study provides a subjective and practical method for determining $${\sigma }_{\mathrm{ci}}$$ σ ci . Moreover, it sheds light on the effects of confinement and chemical corrosion on $${\sigma }_{\mathrm{ci}}$$ σ ci .
... Kabwe et al. (2020b) creep model defines an isotropic damage which grows negatively exponentially over time, and tweaks the Perzyna overstress function to address the limitations of conventional overstress functions. Recent studies have also identified the response to stress release in the tunnel (Liu et al., 2023;Xu et al., 2022) and pre-existing flaws in the rock (Zhang et al., 2023;Zhang andZhou, 2022, 2020a,b) as important factors contributing to creep damage. Liu et al. (2023) have established a fractional viscoplastic model for swelling soft rocks by introducing the Abel dashpot and considering additional swelling damage caused by humidity effect, which more suitable for specific tunnelling. ...
... The stress state of underground rocks can be classified into uniaxial, biaxial and triaxial state (Cai et al., 2020). In underground projects, the unexcavated rock is in a triaxial stress state (Zhang et al., 2023). During excavation, the stresses in the rock at the project boundary are redistributed and are in a static biaxial stress state, i.e., the Frontiers in Earth Science frontiersin.org ...
In order to achieve the highly efficient and accurate identification of fracture modes including tension or shear fractures during rock failure, an intelligent identification method based on Wigner-Ville distribution (WVD) spectrogram features of acoustic emission (AE) signals was proposed. This method was mainly constructed by the following steps: Firstly, AE hits corre-sponding to tension and shear fractures were obtained through conducting the Brazilian disc test (tension fracture) and direct shear test (shear fracture) of limestone. Secondly, the WVD spectro-grams of these tensile-type and shear-type AE hits were respectively extracted and then trans-formed into the image features of relatively low-dimension as the sample set based on the gray-level cooccurrence matrix (GLCM) and histogram of oriented gradient (HOG). Finally, on the basis of the processed and classified sample set of the WVD spectrogram features, an identifica-tion model of rock fracture modes was established by a support vector machine (SVM) learning algorithm. To verify this method, the fracture modes of limestone subjected to biaxial compres-sion were identified by the method. The results showed that the method not only can greatly re-veal the fracture modes change from tension-dominated to shear-dominated fractures, but also has advantages over the RA-AF value method, such as applicability, accuracy and practicality.
... Under biaxial loading, three types of crack coalescence modes including tensile coalescence, shear coalescence, and mixed tensile-shear coalescence were observed. Zhang et al. [24] carried out true triaxial experiments on sandstone with two different en echelon flaws, and the results showed that en echelon flaws significantly weakened the strength and deformability of sandstone, and that the failure of flawed sandstone was mainly induced by en echelon flaws. Chen et al. [25] conducted uniaxial and true triaxial loading and unloading tests on granite with different rock bridge lengths, and they found that the peak strength and AE rate increased with increasing bridge length. ...
... This may be not the actual case for carbonaceous shale due to two aspects of considerations. On one hand, the crack volumetric strain method is possibly not competent for describing the cracking levels in rocks subjected to true triaxial stresses [24]. On the other hand, carbonaceous shale is of strong transverse isotropy due to the presence of natural defects, i.e., bedding planes and pre-existing fissures, making the shale failure characteristics unique and complex. ...
... To that end, the AE method acts as a good experimental tool to reveal the physics. By performing the rising angle (RA)-average frequency (AF)-based fracture mechanism analysis, we can get insights into these two questions [24]. The RA value is the ratio between rise time (RT) and amplitude (A) in the AE signal, measured in ms/V. ...
Carbonaceous shale is the common carrier of underground engineering, and its strength assessment and failure behavior prediction are essential for the analysis of engineering stability. Carbonaceous shale naturally contains defects in different forms such as bedding plane and fissures, acting as the potential sources for the crack development and failure. To investigate the shale behaviors in underground engineering, true triaxial compression experiments are performed on transversely isotropic shale samples containing twin fissures, and the mechanical properties and failure characteristics are the main concern. Results show that the strength difference of shales with the same bedding angle under different σ3 directions, respectively, reaches 33.34 MPa and 9.63 MPa, and the strength difference with the same σ3 direction under different bedding angles attains 43.8 MPa and 20.09 MPa. A new mechanism of the "effect of σ1-defect-coupling-induced fracture" is proposed to interpret the σ1-dominated crack damage, the fissure-dominated crack damage, and bedding plane effect. For the shale, the shear mechanism is dominated during the initial loading stage, while the tensile mechanism is progressively enhanced as the loading proceeds toward the failure. Moreover, nine crack types and five crack coalescence modes are found in current true triaxial experiments. This study provides the experimental basis for the evaluation of the shale behaviors in response to a truly three-dimensional stress circumstance.
... Figure 4b, c shows the loading scheme (see the details in Table 2): (1) the specimen is first subjected to a hydrostatic pressure state (σ 1 = σ 2 = σ 3 ) at a loading rate of 1 kN/s in accordance with the force loading control mode until σ 1 = σ 2 = σ 3 = 30 MPa, followed by a 2 min time window of maintaining the mechanical balance (termed the initial loading stage); (2) under constant σ 2 , the confining pressure (σ 3 ) is gradually unloaded at a unloading rate of 0.05 mm/ min with the displacement loading control mode, while the axial stress (σ 1 ) is synchronously loaded to the specimen at the same rate, until specimen failure (termed the loading-unloading induced failure stage). In each test, the loading system and the AE system are triggered simultaneously such that the temporal correlation of acousto-mechanical data can be ensured (Zhang et al. 2023;Zhang and Zhou 2020a, b;Zhou et al. 2020). ...
Layered composite rocks (LCRs) are often encountered in underground excavation in which extensive deformation, buckling and local collapse near the layer interface frequently occur. However, there is limited advance knowledge of the failure mechanisms of LCRs to interpret the field observations due to the relative scarcity of polyaxial compression testing. To that end, this study conducts the true-triaxial experiments with the acoustic emission (AE) monitoring on the LCR specimens, with the emphases being on the effects of mechanical contrast (MC) between the layers on the fracture behaviors under true-triaxial stresses. First, the strength of LCRs is controlled by the weaker layer. Second, at the unstable fracturing phase, high AE event rate is faithfully recorded but intermittently interrupted by macrofracturing in granite but not in sandstone. Third, main failure planes of LCRs appear sub-orthogonally to σ3 (minimum principal stress), taken the form of delamination fracture and exhibited the mode of σ3-transverse-symmetric fracturing. As the distance from the unloaded surface increases, the fracturing transitions from σ3-transverse-symmetric spalling to σ3-transverse-symmetric shearing. Depending on the MC, both the fracture propagation through the interface and the fracture containment within sandstone are registered. Moreover, the interface effect is numerically revealed through a 3D finite-element modeling. This study gets insights into the failure mechanisms of LCRs with a changing mechanical property in individual layers under true-triaxial stresses.
