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To investigate the energy evolution characteristics of rock materials under uniaxial compression, the single-cyclic loading–unloading uniaxial compression tests of four rock materials (Qingshan granite, Yellow sandstone, Longdong limestone and Black sandstone) were conducted under five unloading stress levels. The stress–strain curves and failure characteristics of rock specimens under the single-cyclic loading–unloading uniaxial compression tests basically corresponded with those of under uniaxial compression, which indicates that single-cyclic loading–unloading has minimal effects on the variations in the loading–deformation response of rocks. The input energy density, elastic energy density and dissipated energy density of four rocks under five unloading stress levels were calculated using the graphical integration method, and variation characteristics of those three energy density parameters with different unloading stress levels were explored. The results show that all three energy density parameters above increased nonlinearly with increasing unloading stress level as quadratic polynomial functions. Meanwhile, both the elastic and dissipated energy density increased linearly when the input energy density increased, and the linear energy storage and dissipation laws for rock materials were observed. Furthermore, a linear relationship between the dissipated and elastic energy density was also proposed. Using the linear energy storage or dissipation law, the elastic and dissipated energy density at any stress levels can be calculated, and the internal elastic (or dissipated) energy density at peak compressive strength (the peak elastic and dissipated energy density for short) can be obtained. The ratio of the elastic energy density to dissipated energy density with increasing input energy density was investigated using a new method, and the results show that this ratio tends to be constant at the peak compressive strength of rock specimens.

HighlightsA dynamic constitutive model for rock materials suited to dynamic cyclic loading was established.The numerical tests on a hard rock under true triaxial dynamic cyclic loading with different loading rates were conducted.The dynamic deformation and mechanical properties of a hard rock were studied.

This work aims at investigating the fracture evolution and energy characteristics of marble subjected to fatigue cyclic loading and confining pressure unloading (FC-CPU) conditions. Although rocks under separated fatigue cyclic loading and triaxial unloading conditions have been well studied, little is known about the dependence of the fatigue damage accumulation on the subsequent confining pressure unloading condition that influences the rock fracture behaviors. In this work, the servo-controlled GCTS 2000 rock mechanical system combined with the post-test X-ray computed tomography (CT) scanning technique were used to reveal the fracture behaviors of the marble samples. The samples were tested at three stages: the static loading stage, the fatigue cyclic loading stage, and the confining pressure unloading stage. Results show that the damage index-cycle number curve shows a different pattern—the damage increasing rate is different for the samples experiencing different fatigue damage. The damage accumulation at the fatigue cyclic stage influences the final failure mode and energy conversion. In addition, post-test CT scanning further reveals the effects of fatigue cycles on the crack pattern, as well as the stimulated crack scale and density after FC-CPU testing depending on the fatigue cycle. Furthermore, the stored elastic energy decreases and the dissipated energy increases with increasing fatigue cycle at the fatigue loading stage, and the energy conversion is consistent with the crack pattern analysis. By investigating the failure mechanism of marble under FC-CPU conditions, a theoretical basis for rock dynamic disaster prediction can be created.

The mechanical behavior of rock under cyclic loading is quite complicated compared to monotonic loading or unloading conditions. The triaxial cyclic loading and unloading testing of rock specimens under 6 confining pressures (σ3) was carried out through the MTS 815 rock mechanics testing system, to explore the strength, deformation, and expansion characteristics of the rock specimens. The stress–strain curves of the rock specimens in the triaxial cyclic loading and unloading testing presented the hysteresis effect. Besides, as σ3 increased, the rock specimen strength increased, while the failure form brittle to ductile. The elasticity modulus (El) increased first and consequently decreased as the cycle index increased, while it increased as σ3 increased. However, the generalized Poisson’s ratio (μl) increased as the cycle index increased, whereas it decreased as the σ3 increased. Based on the Mohr–Coulomb strength criterion and plastic shear strain (γp) as the plastic parameter, the subsequent yield plane model of the loaded rock was characterized by generalized cohesion (c´) and generalized internal friction angle (φ´). Ultimately, the evolution rules of c´, φ´ and Ψ (dilatancy angle), with σ3 and γp were revealed. Moreover, the post-peak dilatancy angle models with regard to the influence of σ3 and γp on the volume dilatancy of the rock specimen were established, which indicated that Ψ increased first and consequently decreased along with the γp increase, whereas it decreased as the σ3 increased.

To investigate the quantification of the extent of damage by considering the energy during rock failure, the pattern of energy dissipation and energy conversion, and the stress–energy mechanism for induced rock failure were analysed under cyclic loading/unloading. Based on damage mechanics, rock mechanics, and energy conservation theory, the test data were analysed. The results showed that the characteristics of hard rock compression are small deformation, high energy, and sudden failure; an elastic–plastic damage constitutive model and a stress–energy–rigidity–damage multi-criteria model for rock failure were established for hard rock. We compared the numerical curves and the experimental curves and found that they coincide. Rock failure is a combination of the results of elastic strain accumulation and dissipation by stress propagation. The key to inducing the energy storage capacity of rock before failure is closely related to the rock damage evolution. The pattern of energy release and dissipation through stress during rock failure was revealed from the perspective of energy using the constitutive model and multi-criteria model established for rock failure; these theoretical studies are very helpful in elucidating the mechanism of rock failure.

Intermittently jointed rocks, widely existing in many mining and civil engineering structures, are quite susceptible to cyclic loading. Understanding the fatigue mechanism of jointed rocks is vital to the rational design and the long-term stability analysis of rock structures. In this study, the fatigue mechanical properties of synthetic jointed rock models under different cyclic conditions are systematically investigated in the laboratory, including four loading frequencies, four maximum stresses, and four amplitudes. Our experimental results reveal the influence of the three cyclic loading parameters on the mechanical properties of jointed rock models, regarding the fatigue deformation characteristics, the fatigue energy and damage evolution, and the fatigue failure and progressive failure behavior. Under lower loading frequency or higher maximum stress and amplitude, the jointed specimen is characterized by higher fatigue deformation moduli and higher dissipated hysteresis energy, resulting in higher cumulative damage and lower fatigue life. However, the fatigue failure modes of jointed specimens are independent of cyclic loading parameters; all tested jointed specimens exhibit a prominent tensile splitting failure mode. Three different crack coalescence patterns are classified between two adjacent joints. Furthermore, different from the progressive failure under static monotonic loading, the jointed rock specimens under cyclic compression fail more abruptly without evident preceding signs. The tensile cracks on the front surface of jointed specimens always initiate from the joint tips and then propagate at a certain angle with the joints toward the direction of maximum compression.

The deformation and failure of rocks result from the dissipation and release of their internal energy. The energy evolution throughout the processes of deformation and failure in rock is a critical research topic. The triaxial cyclic loading and unloading tests under five confining pressures were carried out on high-temperature rock samples to investigate the influences of the confining pressure (σ3) and temperature (T) on their energy evolution and distribution characteristics. The energy densities of rock samples under various confining pressures were calculated by determining the area between the loading and unloading curves, including axial energy densities (u10, u1e, u1d) and circumferential strain energy density (u30). The energy accumulation and dissipation and the effect of σ3 and T on the energy distribution laws of loaded rock samples were analysed. The characteristic energy density (u1t) was used to analyse the accumulation, dissipation and release of energy of the loaded rock sample. u1t increased with the increase in σ3 and decreased with the increase in T. Furthermore, u30 increased with the increase in σ3, which effectively limited the energy dissipation and release due to fracture or failure of the rock sample. With the increase in T, the circumferential strain of the rock sample increased, which led to an increase in u30. At the pre-peak stage, energy accumulation characterised the energy behaviour of the loaded rock sample, and the proportion of the elastic energy density (k1e) was large. At the post-peak stage, energy release and dissipation characterised the energy behaviour of the loaded rock sample, the dissipated energy density proportion (k1d) increased gradually, and the change law for k1e and k1d was considerably affected by the confining pressure and temperature effect. The dissipated energy density of the loaded rock sample was used to establish the energy damage variable and analyse the evolution law of the dissipated energy damage variable of the high-temperature rock sample with σ3 and T. The results of this study can provide guidance for the research on high-temperature rock damage mechanisms and prevention of dynamic disasters of rock underground engineering.

The post-peak behaviour of rocks subjected to cyclic loading is very significant to appraise the long-term stability of underground excavations. However, an appropriate testing methodology is required to control the damage induced by the cyclic loading during the failure process. In this study, the post-failure behaviour of Gosford sandstone subjected to the systematic cyclic loading at different stress levels was investigated using the double-criteria damage-controlled testing methodology, and the complete stress–strain relations were captured successfully. The results showed that there exists a fatigue threshold stress in the range of 86–87.5% of the average monotonic strength in which when the cyclic loading stress is below this threshold, no failure occurred for a large number of cycles and in turn, the peak strength improved up to 8%. Also, the variation of the energy dissipation ratio, rock stiffness and acoustic emission hits for hardening tests showed that cyclic loading in the pre-peak regime creates no critical damage in the specimen, and a quasi-elastic behaviour dominates the damage evolution. The post-failure instability of such tests was similar to those obtained for monotonic tests. On the other hand, by exceeding the fatigue threshold stress, the brittleness of the specimens increased with an increase in the applied stress level, and class II behaviour prevailed over total post-peak behaviour. A loose-dense-loose behaviour with different extents was also observed in the post-peak regime of all fatigue cyclic loading tests. This was manifested then as a secondary inverted S-shaped damage behaviour by the variation of the cumulative irreversible axial and cumulative irreversible lateral strains with the post-peak cycle number. Furthermore, it was confirmed that the damage per cycle in the post-peak regime decreases exponentially with an increase in the applied stress level.

In this study, the influence of cyclic impact loading damage and water saturation on mechanical behavior and Kaiser effect of rock samples was investigated through a series of uniaxial cyclic loading and unloading compression tests. The test results showed that the cyclic loading and unloading strength of rock samples in dry condition gradually decreased with the increase of previous damage, while the cyclic loading and unloading strength of rock samples in saturated condition showed a decrease in cyclic loading strength of 10.95% (3 times), − 5.40% (6 times), and 0.87% (9 times) compared to those not subjected to cyclic impact loading. We have elucidated the mechanism underlying this phenomenon from the perspective of water–rock interaction. Statistical analysis of the Felicity ratio values further revealed that the valid response stress interval of rock acoustic emission (AE) Kaiser effect is negatively affected by previous damage and water saturation. Moreover, the relationship among AE signal energy decay rate and previous damage and water saturation was discussed, negatively impacting the valid response stress interval of rock AE Kaiser effect. The results suggest that drilling of cores from stress-disturbed areas should be avoided as much as possible during the measurement of in situ stress using the rock AE Kaiser effect. The tests should also be conducted with dry rock samples to have a larger response stress interval for the AE Kaiser effect.HighlightsThe wave velocity change rate and porosity were used to characterize the previous damage of rock.The influence of previous damage and water saturation on rock failure mode was evaluated.The strengthening mechanism of water-rock strength was discussed.The influence of previous damage and water saturation on Kaiser effect was studied.

This paper aims to investigate the effects of cyclic shear amplitudes and loading sequences on a soil–structure interface using direct shear tests under a large number of loading cycles. A series of cyclic direct shear tests were performed on a granular soil-rough interface under the constant normal load (CNL) condition. Initially, monotonic interface direct shear tests were carried out as benchmarks to specify test boundaries and proper ranges of assigned cyclic amplitudes. Dry standard Fontainebleau sand in dense and loose conditions and a modified rough surface material were utilized to represent a soil-rough structure interface. A series of CNL cyclic interface direct shear tests was then conducted by varying the applied cyclic shear stress amplitudes and the cyclic loading sequence (small-to-large and large-to-small patterns) with a large number of testing cycles (104). Immediately after the cyclic shear tests were completed, monotonic interface direct shear tests were again performed to examine the post-cyclic behaviour of the soil-rough interface. Test results yielded that the applied cyclic shear stress amplitudes did affect the soil-rough interface by inducing a gradual contraction and an expansion in shear displacement accumulation. The maximum stress ratio could notably influence the volumetric behaviour and shear displacements. The accumulation of mean cyclic displacements was independent of the change in cyclic shear stress amplitudes between two consecutive cyclic loading sequences. The post-cyclic behaviour showed that changing the shear stress cycles between two consecutive packages did not influence the peak stress ratio.