The purpose of this paper is to provide a comprehensive state of the art of fatigue and cyclic loading of natural rock materials. Papers published in the literature are classified and listed in order to ease bibliographical review, to gather data (sometimes contradictory) on classical experimental results and to analyse the main interpretation concepts. Their advantages and limitations are discussed, and perspectives for further work are highlighted. The first section summarises and defines the different experimental set-ups (type of loading, type of experiment) already applied to cyclic/fatigue investigation of rock materials. The papers are then listed based on these different definitions. Typical results are highlighted in next section. Fatigue/cyclic loading mainly results in accumulation of plastic deformation and/or damage cycle after cycle. A sample cyclically loaded at constant amplitude finally leads to failure even if the peak load is lower than its monotonic strength. This subcritical crack is due to a diffuse microfracturing and decohesion of the rock structure. The third section reviews and comments the concepts used to interpret the results. The fatigue limit and S–N curves are the most common concepts used to describe fatigue experiments. Results published from all papers are gathered into a single figure to highlight the tendency. Predicting the monotonic peak strength of a sample is found to be critical in order to compute accurate S–N curves. Finally, open questions are listed to provide a state of the art of grey areas in the understanding of fatigue mechanisms and challenges for the future.

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Cyclic and Fatigue Behaviour of Rock Materials: Review, Interpretation and Research Perspectives

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.

Experimental Investigation on the Fatigue Mechanical Properties of Intermittently Jointed Rock Models Under Cyclic Uniaxial Compression with Different Loading Parameters

Height of the mining-induced fractured zone above a coal face

Energy evolution characteristics of hard rock during triaxial failure with different loading and unloading paths

Risk assessment of floor water inrush in coal mines based on secondary fuzzy comprehensive evaluation

Characteristics of energy accumulation, evolution, and dissipation in uniaxial cyclic loading and unloading compression of 30 sandstone rock specimens under six different loading rates were explored. Stress–strain relations and acoustic emission characteristics of the deformation and failure of rock specimens were analyzed. The densities and rates of stored energy, elastic energy, and dissipated energy under different loading rates were confirmed, and an effective approach for the equivalent energy surface was presented. The energy evolution of rock deformation and failure were revealed. It turns out that the rock deformation behavior under uniaxial cyclic loading and unloading compression remained almost unchanged compared with that of uniaxial compression. The degree of match between reloading stress–strain curves and previous unloading curves was high, thereby demonstrating the memory function of rock masses. The intensity of acoustic emission fluctuated continually during the entire cyclic process. Emissions significantly increased as the stress exceeded the unloading level. The peak of acoustic emission increased with increasing loading stress level. Relationships between energy density and axial load indicate that the rock mass possesses a certain energy storage limitation. The energy evolution of rock masses is closely related to the axial loading stress, rather than to the axial loading rate. With increasing axial loading stress, stored energy varied most rapidly, followed by that of the elastic energy, then dissipated energy. Energy accumulation dominates prior to the axial load reaching peak strength; thereafter, energy dissipation becomes dominant. The input energy causes the irreversible initiation and extension of microcracks in the rock body. Elastic energy release leads to sudden instability of rock bodies and drives rock damage.

Effects of Acoustic Emission and Energy Evolution of Rock Specimens Under the Uniaxial Cyclic Loading and Unloading Compression

To explore the acoustic emission (AE) characteristics of rock materials during the deformation and failure process under periodic loads, a uniaxial cyclic loading and unloading compression experiment was conducted based on an MTS 815 rock mechanics test system and an AE21C acoustic emissions test system. The relationships among stress, strain, AE activity, accumulated AE activity and duration for 180 rock specimens under 36 loading and unloading rates were established. The cyclic AE evolutionary laws with rock stress–strain variation at loading and unloading stages were analyzed. The Kaiser and Felicity effects of rock AE activity were disclosed, and the impact of the significant increase in the scale of AE events on the Felicity effect was discussed. It was observed that the AE characteristics are closely related to the stress–strain properties of rock materials and that they are affected by the developmental state and degree of internal microcracks. AE events occur in either the loading or unloading stages if the strain is greater than zero. Evolutionary laws of AE activity agree with changes in rock strain. Strain deformation is accompanied by AE activity, and the density and intensity of AE events directly reflect the damage degree of the rock mass. The Kaiser effect exists in the linear elastic stage of rock material, and the Felicity effect is effective in the plastic yield and post-peak failure stages, which are divided by the elastic yield strength. This study suggests that the stress level needed to determine a significant increase in AE activity was 70% of the i + 1 peak stress. The Felicity ratio of rock specimens decreases with the growth of loading–unloading cycles. The cycle magnitude and variation of the Felicity effect, in which loading and unloading rates play a weak role, are almost consistent.

Acoustic Emission Characteristics of Red Sandstone Specimens Under Uniaxial Cyclic Loading and Unloading Compression

This paper presents a case study of water inrush on a mine working face from roof strata. The flow-rock failure process analysis (F-RFPA2D) code with an improved flow-stress-damage (FSD) model was adopted to perform the failure and coupling analysis. The improved FSD model was used to represent the permeability variation at the four stages (elastic, damaged, cracked, and crack closure) of the rock failure process. The fracture initiation, propagation, and coalescence in the stressed strata and the seepage field evolution in the stress field are represented visually during the whole process of water inrush. The failure zone with high permeability induced by mining disturbance becomes the water-conducting zone after full excavation of the coal seam. The height of the water-conducting zone obtained in this study is in reasonable accordance with that predicted by an empirical formula. It is definitely clarified that the water inrush from the roof strata is induced by the failure zone full of vertical coalesced mine fractures. It is unlikely that roof accidents resulting in water inrush would occur if the water-conducting zone does not grow upwards into the aquifer. The main task for mine extraction under a confined aquifer is to locate the aquifer and find the maximum height of the water-conducting zone, which is very important for mine construction and support design.

Application of an Improved Flow-Stress-Damage Model to the Criticality Assessment of Water Inrush in a Mine: a Case Study

To reveal the characteristics of energy accumulation and energy dissipation during rock deformation and failure, cyclic uniaxial compression experiments under 36 different loading and unloading schemes were carried out on 180 red sandstone specimens using an MTS 815 rock mechanics test system (MTS Systems Corporation, Eden Prairie, MN). Based on the theory of thermodynamics and the analysis of the resultant stress-strain curves, a method of calculating the rock energy density from the characteristics of the loading and unloading curves was proposed. The energy densities of rock specimens under different loading and unloading rates were determined. The influence of loading and unloading rates on the rock energy evolution was discussed, and the evolution and distribution laws of energy accumulation and dissipation in the rock during the prepeak stage were revealed. The experimental results showed that rock energy density increases nonlinearly with an increase in the axial loading stress under different loading and unloading rates. The total absorbed energy density increases at the fastest rate, followed by the elastic energy density, and the dissipated energy density increases at the slowest rate. Elastic energy density shows a trend of “increasing first and then decreasing,” while the dissipation energy density shows the opposite trend. In the static and quasi-static loading ranges, the loading and unloading rates have no clear effect on the elastic energy density but have a considerable effect on dissipation energy density. The smaller the loading or unloading rate, the larger the dissipation energy density.

Experimental Research on Rock Energy Evolution under Uniaxial Cyclic Loading and Unloading Compression

Size and strain rate are two key factors that dramatically influence the estimation of rock mechanical behaviors. To better understand the effects of size and strain rate on measured rocks, rock specimens with six different sizes were tested at six different strain rates under uniaxial compression using the MTS 815 Rock Mechanics Test System. Having determined that the size and strain rate significantly affect the peak strain, peak stress, elastic modulus, acoustic emission (AE), and failure pattern of the rock specimens, the relation was established between the strength and the size and strain rate of red sandstone. And the variation was revealed among the size and strain rate, the AE, and the failure pattern. It turned out that the peak stress was negatively correlated with the rock size and was positively correlated with the strain rate. When the length to diameter ratio (L/D) of the rock specimen was less than 2.0, the AE appeared mildly. The AE quantities gradually increased before the peak stress, and then sharply decreased after the peak stress. The failure pattern of the rock specimen was relatively complicated, with a fracture plane appearing along the axial direction. Conical failure type was also presented. When the L/D ratio of the specimen was greater than 2.0, the AE characteristics of red sandstone showed the radical model. There were relatively few AE rings before the peak stress. But the AE rings increased suddenly and dramatically during the peak stress. The rock specimens primarily failed with a single shear plane. Moreover, with an increase in the strain rate, the AE activities were enhanced and the AE quantities increased. When the strain rate of the rock specimen was less than 5.0 × 10−4/s, the rock specimen failed with a shear or tensile-shear pattern. And when the strain rate was greater than 5.0 × 10−4/s, the rock specimen tended to fail in a conical pattern.

Lijun Han

Papers

Effects of Acoustic Emission and Energy Evolution of Rock Specimens Under the Uniaxial Cyclic Loading and Unloading Compression

Acoustic Emission Characteristics of Red Sandstone Specimens Under Uniaxial Cyclic Loading and Unloading Compression

Application of an Improved Flow-Stress-Damage Model to the Criticality Assessment of Water Inrush in a Mine: a Case Study

Experimental Research on Rock Energy Evolution under Uniaxial Cyclic Loading and Unloading Compression

Effects of size and strain rate on the mechanical behaviors of rock specimens under uniaxial compression