Effects of prior cyclic loading damage on failure characteristics of sandstone under true-triaxial unloading conditions

Abstract

To investigate the effects of prior cyclic loading damage in rocks on subsequent unloading failure characteristics under true-triaxial conditions, a series of complicated unloading tests incorporating the damage-controlled cyclic loading path and stress σ₃ unloading path was conducted using a true-triaxial test system. The experimental results reveal that the prior cyclic loading damage has an impact on the strength and deformation characteristics, energy conversion and failure mode. As the number of prior cyclic loads increases, the unloading strength and Young's modulus increase firstly and then decrease, while the peak unloading strain, as well as the ratio (η) of crack damage stress to peak unloading stress, exhibits a descending trend. The energy storage capacity of rock samples is dramatically reduced as cycle number increases to 10 and enlarged slightly with a further increase in cycle number. Both shear fracture and tensile fracture appear in each rock sample under this unloading condition, as the prior cyclic loading number increases, the dominant failure mode of rock samples changes from tensile failure to mixed tensile-shear failure, then to shear failure, while the failure angle ranging from 65° to 80° deceases firstly and then turns to rise.

Introduction

For many rock engineering projects, such as underground cavern, tunnel, hydropower station, it is inevitable that the rock mass will be subjected to cyclic loads from drilling, blasting, earthquake, etc.1, 2, 3, 4 Difference between rock properties makes the responses of rocks to cyclic loads distinct. Under a certain cyclic loading condition, some rock properties may exhibit hardening characteristics while others can be gradually weakened as the cycle number increases.⁵ To ensure the long-term reliability of rock engineering structures, considerable efforts have been put into investigating the mechanical behavior of rocks under cyclic loadings. The cyclic loading test is distinguished from monotonic loading test by an imposed repeated load or displacement. Cyclic stress amplitude can be constant or increasing step by step.⁶ Previous research on constant-amplitude cyclic loading tests showed that the maximum stress, amplitude, frequency, waveform, as well as confining pressure were among the important factors affecting the mechanical behavior of rocks.7, 8, 9 Momeni et al. found that the fatigue life of Alvand monzogranitic rocks increasing in a power function with the decrease of maximum stress and decreasing in an exponential function with the increase of loading frequency. Moreover, increasing-amplitude caused a gradual reduction in residual axial and lateral strain of specimens.¹⁰ Tao et al. used two loading waveforms in cyclic loading tests and found that rock deformation caused by sine waveform loading was larger than that by triangle waveform loading.¹¹ In terms of the energy, Meng et al. explored the energy evolution and dissipation characteristics of red sandstones under uniaxial loading and unloading conditions and proposed that energy evolution is closely related to the axial loading stress.¹² Bagde and Petros studied the behavior of rocks under dynamic cyclic loading conditions and found that with the increase of loading frequency and amplitude, the dynamic energy generally showed an increasing trend.¹³

Furthermore, much attention has been paid to the law of rock damage accumulation which is helpful for evaluation of fatigue life and establishment of damage model under cyclic loading conditions.^14,15 The technique of digital image correlation (DIC) was applied by Song to obtain the displacement and strain fields of sandstone under cyclic uniaxial compression, and two factors (the damage localization factor and damage severity factor) were proposed to characterize the fatigue damage evolution.¹⁶ Guo et al. defined a fatigue damage variable for rock salt in accordance with the strains, and observed that the process of damage evolution could be divided into three obvious stages.¹⁷ Li et al. paid attention to the damage evolution of chemical corroded limestone subjected to cyclic loading. In their tests, both mechanical cyclic damage and chemical erosion damage were taken into consideration, and the rock porosities measured by Nuclear Magnetic Resonance (NMR) were selected as the key parameter for damage variable.¹⁸ Chen et al. proposed that the damage evolution of rocks was driven by energy conversion and a damage coefficient defined by dissipated energy could reasonably evaluate the damage status of rocks under cyclic loading.¹⁹ Munoz and Taheri pointed out that both the degradation of stiffness and accumulated irreversible axial strain should be considered for description of damage process.²⁰ Jiang et al. selected the ratio of current cumulative AE numbers to the cumulative AE numbers when the rock failed as a fatigue damage variable.²¹ Xiao et al. adopted six damage variables to reflect the fatigue damage evolution of granite. Among them, the fatigue damage variable defined in terms of residual strain was deemed to be an ideal variable for its clearly physical meaning.²²

In most constant-amplitude cyclic loading tests, the progressive pre-peak damage of a sample was readily characterized with ever-changing mechanical parameters in each cycle. However, if the applied maximum stress was less than the threshold for fatigue failure, the pre-peak damage correlated to the progressive failure of rock might not be fully exhibited. Therefore, damage-controlled cyclic loading tests, involving increasing maximum stress or displacement, were adopted by some scholars. Martin and Chandler performed a series of damage-controlled tests on Lac du Bonnet granite to explore the impact of damage on the stress levels corresponding to crack initiation and crack damage.²³ Eberhardt et al. investigated the accumulating rock damage and its effect on fracture characteristics in damage-controlled cyclic loading tests.²⁴ Yang et al. analyzed the damage characteristics of sandstone under increasing-amplitude cyclic loading conditions, and found that the damage value characterized by axial residual strain was larger than that defined by radial residual strain before the occurrence of peak strength, whereas after the peak strength, the radial damage value was higher than axial damage value.²⁵ In addition, attention was paid to the elastic moduli evolution with increasing damage during increasing-amplitude cyclic stressing experiments.²⁶

Cyclic loading tests on rocks have enhanced our understanding in mechanical behavior of rock mass undergone cyclic loads from nature and human activities. Nevertheless, almost all the laboratory cyclic loading tests carried out centered on uncovering the rock behaviors only during the process of cyclic loading. Actually, in underground engineering projects, the cyclic loading may not directly lead to the final failure of rock mass when the cyclic peak load is not high enough, but it may be considered as a primary factor influencing the mechanical behavior of rock mass subjected to subsequent stress conditions. It is likely that the rock mass which has been subjected to various cyclic loads from human activities will be excavated following the construction plan. An example of this is two adjacent tunnels with different excavating sequence. The disturbance from the firstly constructing tunnel has a great impact on the excavation behavior of rock mass involved in the subsequent tunnel. In such case, the relationship between the pre-peak rock damage induced by cyclic loads from blasting or mechanical vibration and subsequent excavation behavior should be explored in depth for the engineering safety.

Extensive studies have been conducted to investigate the rock failure characteristics during the process of excavating underground space or in laboratory unloading tests. Li et al. demonstrated the influence of unloading rate and stress release path on the deformation and fracture characteristics of rock mass through mathematical physics and numerical simulations methods.²⁷ Feng et al. studied the mechanical responses of a deep circular tunnel to the nearby structure plane under unloading conditions.²⁸ Fan et al. analyzed the strainburst characteristics of tunnels with different tunneling methods during the excavation process.²⁹ Zhou et al. used the NMR technique to investigate the damage evolution of marble samples under an unloading confining pressure state.³⁰ In particular, with the help of novel true-triaxial apparatuses, the mechanical response of surrounding rock during excavation could be obtained by manipulating three principal stresses acting on a specimen in the laboratory.³¹ Su et al. mentioned that the excavation of underground space changes the stress state of rock mass near the excavated boundary: the radial stress σ_r decreases rapidly, the tangential stress σ_θ increases gradually, and the axis stress σ_a varies little.³² Li et al. carried out a series of true-triaxial unloading tests on different rock materials through unloading σ₃ and loading σ₁. The failure characteristics effected by sample height-to-width ratio and intermediate principal stress were fully analyzed.³³ He et al. paid attention to the AE characteristics of the limestone bursts under true-triaxial unloading conditions.³⁴ The results of true-triaxial tests conducted proved that the stress path of unloading σ₃ and loading σ₁ could much better reflect the conversion of three-dimensional stress in practical excavation engineering. However, the pre-peak rock damage caused by cyclic loads was often neglected by researchers when they studied the unloading behavior of rock materials.

This paper reports on an experimental study that investigates the effects of pre-damage of rock mass ever undergone cyclic loading on subsequent excavation unloading characteristics. To facilitate exhibiting the full range of progressive pre-damage in rock samples, the damage-controlled cyclic loading with increasing-amplitude loads was interpolated into the conventional stress path used in the true-triaxial unloading tests. The newly designed stress path was performed on sandstone samples by means of the GCTS Triaxial Rock Testing System (RTX-3000), and the relationship between prior cyclic loading damage and failure characteristics of samples under true-triaxial unloading conditions was established, which is central to evaluating the excavation unloading behaviors of pre-damaged rock mass ever undergone various disturbances in practical engineering.