Energy Evolution and Water Immersion-Induced Weakening Mechanism in the Sandstone Roof of Coal Mines

The instability of underground spaces in abandoned coal mines with water-immersed rocks is one of the main hazards hindering the geothermal energy utilization and ecological restoration of post-mining areas. This study conducted graded cyclic loading-unloading tests of five groups of sandstone samples with different water contents. The evolution laws of input, elastic, dissipated, damping, and plastic energies were explored in detail, taking into account the damping effect. The normalized plastic energy was used to characterize the damage evolution of sandstone samples, which failure modes were analyzed from both macroscopic and microscopic perspectives. The X-ray diffraction technique and scanning electron microscopy were used to reveal the softening mechanism of sandstone's strength and elastic energy storage limit. The results showed that the graded cyclic loading's input, elastic, and dissipated energies increased gradually. The elastic energy share first increased and then stabilized, while dissipated energy share variation had the opposite trend. In each cycle, the input energy was primarily stored in the form of elastic energy, while the dissipated energy was mainly used to overcome the damping of sandstone. When the normalized number of cycles approached unity, the plastic energy share sharply increased, while that of the dampening energy featured an abrupt drop. Such change indicated an inevitable instability failure of the water-bearing sandstone. As the water content increased, the pore water exhibited more substantial lubrication, water-wedging, and dissolution effects on mineral particles. As a result, the latter obtained a round form, and the elastic energy storage limit of the sandstone decreased. When the water content was increased, the damage factor of sandstone after the same number of cycles increased at a relatively higher rate, and there was a transition of failure mode from brittle to ductile.

2 and spaces in abandoned coal mines. For example, some scholars have suggested constructing underground reservoirs of abandoned coal mines Gu et al. 2015), developing geothermal resources Jardon et al. 2013), and building pumped storage power stations (Fan et al. 2020;Xie et al. 2020).
Complex water-rock interactions, physical effects, and chemical reactions commonly occur in abandoned coal mines due to tidal action and water erosion, significantly deteriorating rock stability and residual strength. This issue was addressed by numerous scholars, who investigated the mechanical characteristics and failure mechanism of water-bearing rocks (Wong et al. 2016;Hashiba et al. 2015) and conducted post-peak cyclic loading-unloading tests for coarse sandstone in natural and water-saturated conditions ). The latter found that the water-saturated coarse sandstone exhibited a more significant increase in lateral and volumetric strains compared with the natural condition. In uniaxial loading-unloading tests, water saturation had an apparent softening effect on post-peak fractured coarse sandstone strength and elastic modulus. Zhou et al. (2016) conducted static and dynamic mechanical tests of sandstone samples with different water contents under the dry-wet cycles.
They found that water-bearing sandstone could gradually restore its mechanical characteristics in dry conditions. The tensile strengths of sandstone with the same water contents were different under drying and water-immersion conditions. Hua et al. (2019) compared the mechanical fracture characteristics of sandstone under dry-wet cycling and long-term water immersion. They reported that dry-wet cycling caused a more significant sandstone fracture performance deterioration than long-term water immersion. Rock damage and failure were closely related to energy accumulation, dissipation, and release. Therefore, some scholars have analyzed the impact of water on rocks from an energy perspective (Li et al. 2015; Wang et al. 2017). Chen et al. (2019) pointed out that the amount of energy released at the sandstone's compaction and elastic deformation stages increased significantly. The water content increased, and the amount of energy released after failure decreased. A higher water content led to a reduction of sandstone's brittleness and enhanced its plastic deformation. Geng et al. (2020) conducted uniaxial compression tests on dry, water-bearing, and saturated sandstone samples.
Their results showed that the water-softened sandstone was more prone to ductile damage and released less elastic energy. Ma et al. (2018) carried out uniaxial compressing testing of gypsum rocks under different durations of water immersion. The results showed that gypsum rocks' input, elastic, and dissipated energies decreased as the water immersion was prolonged.
They further described the damage characteristics of gypsum rock subjected to the water-weakening effect and uniaxial loading via a constitutive damage model based on energy dissipation.
As shown above, the mechanical characteristics, energy evolution, and failure modes of water-bearing sandstone during its deformation and failure processes

Test system
As shown in Fig.2

Experimental scheme and results
Each group of the sandstone samples was further split into subgroups D and X, which were used for the uniaxial compression and uniaxial graded loading-unloading tests, respectively. To improve the experimental accuracy and reduce the randomness of the experimental results, no less than three parallel tests were conducted for each loading scheme and each water content. The uniaxial compression tests were first conducted to obtain the strain-stress curves for different water contents, as shown in Fig. 3  Changes in mineral content and composition did not significantly correlate with the water content.

Characteristics of Sandstone Samples under Cyclic Loading
The softening coefficient was used to characterize the softening properties of sandstone samples with different water contents more intuitively.
The softening coefficient λ was defined as the ratio of the compressive strength Rw of the water-bearing sandstone samples with different water contents to the compressive strength Rd of the dry sandstone, according to the following formula: The smaller the softening coefficient, the stronger the softening and the greater the impact of water on the rocks. As shown in Table 1  For the sake of convenience, the number of cycles to failure was normalized. Figure

Energy conversion theory considering viscoelastic deformation
Under cyclic loading, the entire process of sandstone deformation and failure was accompanied by energy accumulation, release, and dissipation.
According to the first law of thermodynamics, it was assumed that the sandstone was not engaged in thermal exchange with the environment during deformation and failure, and the radiant energy and the energy of the acoustic emission were neglected.
Then, the work done by the press machine to the sandstone samples was the total input energy. As shown in Fig. 6, the energy value for each cycle can be calculated by Eqs.
(3)-(6), according to Xie et al. (2005): where Ui, Uei, and Udisi are the input, elastic, and dissipated energies of the i -th cycle, respectively; i + and i+1 + are the stresses imposed upon the i -th and the i+1 -th loading, respectively; iis the stress imposed upon the i -th unloading.
Rocks are aggregates of mineral particles with complex mineral composition and structure, which implies their significant heterogeneity and anisotropy.
In most studies on the energy evolution law of rocks under graded cyclic loading-unloading, rocks were Rock as an elastoplastic material undergoes no plastic deformation, and its unloading path differs.
Nevertheless, a closed hysteresis loop can still be formed for the rock. Stevens et al. (1980) and Kuwahara et al. (1990) found that under the loading-unloading action, many new microcracks would appear in rocks only when the stress during the second loading exceeded the peak stress upon the first loading. It was believed that during the uniaxial graded loading-unloading, no new cracks were generated in the rocks if the loading stress was lower than the stress imposed during the previous loading.
Hence, there would be no growth in plastic energy.

Energy evolution law
According to theoretical background and formulas (3)-(6) described in section 4.1, the evolution laws of the elastic and dissipated energies were derived, and their shares in sandstone samples with different water contents were calculated and plotted in Fig. 9.It can be seen from Fig.9 that: (1) The input, elastic, and dissipated energies of sandstone samples with different water contents increased with the normalized number of cycles. This was because a larger normalized number of cycles implied a larger work on the sandstone sample exerted by the external force. As a result, the input energy increased. Part of the input energy was stored in the sandstone in the form of elastic energy. The remaining part was dissipated by causing rock damage.
(2) The elastic energy and dissipated energy shares were compared under different water contents. Under the initial cyclic loading, the input energy was mainly in the form of dissipated energy. The dissipated energy share significantly exceeded that of the elastic energy. Under initial loading, the sandstone underwent damage and failure caused by the compression of primary defects, leading to more significant energy dissipation. Besides, the larger the water content, the higher the dissipated energy share and the more severe the sandstone damage under initial loading.
(3) As the normalized number of cycles increased, the elastic energy share gradually increased, and that of the dissipated energy decreased and finally stabilized. These results indicated that the input energy was stored in the sandstone mainly in the form of elastic energy at this stage. The elastic energy share ranged from 0.7 to 0.9.
Besides, the greater the water content, the smaller the elastic energy share, and the more severe the sample damage under the same stress.
(4) When the normalized number of cycles approached unity, the input, elastic, and dissipated energies still kept increasing. The elastic energy share decreased, and that of the dissipated energy increased. This indicated that the microcracks within the sandstone gradually propagated and penetrated the sandstone sample, resulting in its failure. Given the above, it was feasible to predict the sandstone failure based on the energy evolution law.
Using formulas (7)-(9), we calculated the evolution law of the damping energy, plastic energy, and their shares in sandstone samples with different water contents. The results are shown in Fig. 10.
It can be found from Fig.10 that as the normalized number of cycles increased, the damping energy and the plastic energy of the sandstone with different water contents increased gradually. The plastic energy share first decreased rapidly, then stabilized, and later increased abruptly. The damping energy share showed the opposite trend. Such variation was considered relevant to rock compression and peak damage. The analysis of dissipated energy shares in the sandstone samples with different water contents revealed that they decreased with water content. The majority of the dissipated energy in each cycle was spent on overcoming the work done by viscosity.
As the water content increased, the plastic energy share became gradually larger than that of the damping energy.
This indicated that water immersion significantly reduced the work done by the frictional damping between the mineral particles. As a result, the bonding strength between the mineral particles was attenuated, promoting sandstone damage and failure. The variation of the elastic energy share was similar to that of dissipated energy.
When the normalized number of cycles approached unity, the plastic energy share increased abruptly. In contrast, the damping energy share sharply dropped, portending the impending failure of the sandstone sample.

Damage mechanism based on plastic energy
According to the above findings, the input energy under cyclic loading-unloading conditions was stored or released mainly in the form of elastic energy or dissipated in the form of damping energy. Only a small share of the input energy was spent on sandstone damage and failure. Besides, the higher the water content, the larger the plastic energy share under the same stress gradient. To characterize the degree of rock damage and failure, Liu et al. (2018) performed normalization of the dissipated energy. They analyzed the cumulative damage law of rocks under cyclic loading. Plastic energy was a primary factor causing rock damage, while the damping energy did not lead to residual deformation and damage. Therefore, it was considered more accurate and reasonable to use normalized plastic energy to characterize rock damage. The damage factor (D) was defined as the ratio of cumulative damage to total damage in the following equation: where Upi is the plastic energy generated during the i -th cycle, while Up is the total plastic energy.
The damage variable estimated by this formula varied between zero and unity, satisfying the principle of damage irreversibility. Taking a dry sandstone sample (X-0) as an example, the damage factor evolution curve was plotted in Fig.11 and subdivided into three stages, which differed by the variation trend of damage factor, defined as the derivative of the damage factor concerning the number of cycles: decelerating growth, stable growth, and accelerating growth.
At the stage of decelerating growth, the damage factor grew at a saturating rate under the initial cyclic loading due to rock anisotropy and heterogeneity. The damage factor reached 35% at the stage of decelerating growth. At the stable growth stage, the damage generated per cycle gradually approached a constant value as the graded cyclic loading increased. This stage accounted for the largest majority of the loading-unloading cycles. The above results indicated that the damage accumulated stably, while microcracks initiated and propagated without coalescing and penetrated the samples' bulk. When the damage reached about 80%, its accumulation accelerated.
The damage generated in the last 2-3 cycles accounted for nearly 24%, resulting in instability failure. These results indicated that as the test proceeded, the pores and cracks propagated and became interconnected. After the cracks propagated to a certain degree, crack development and damage accumulation were accelerated. As the water content increased, the curve of the damage factor versus the number of cycles shifted towards the Y-axis on the whole. The region corresponding to the decelerating growth stage gradually disappeared. This implied that under the graded cyclic loading conditions, a higher water content corresponded to faster growth of the damage factor. The presence of water accelerated sandstone damage. In the water-saturated sandstone sample (X-100), the damage generated in the first cycle accounted for about 34%.

Fracture Morphology and Failure Modes
Rock damage accumulation is the process whereby microcracks initiate, propagate, and become interconnected within the rocks. Fracture morphology characteristics vary at different stages of crack development.
The fracture surface is where the microcracks and pores are found in large numbers. Microcracks and pores propagate along the weakest plane until the penetrating fracture surface is formed, leading to varying failure modes in the sandstone. We studied the microscopic fracture characteristics of cracks along with the macroscopic failure morphology of sandstone. Therefore, the impact of water on the sandstone failure process was investigated on both microscopic and macroscopic scales. This approach was conducive to disclosing the macroscopic mechanical strength-weakening mechanism and the energy dissipation mechanism in water-bearing sandstone.

Fracture morphology
Flex SEM1000 was applied to observe the typical fracture in dry, semi-saturated, and saturated sandstone samples under grade cyclic loading-unloading. The microstructural changes of the sandstone samples under different magnification factors are shown in Fig. 12. According to the figure, the fractures were serrated in the dry sandstone samples, and the mineral particles had dense structures. The cementing materials between the particles were compacted. Some micro-pores and cracks were only found along the mineral particle boundaries and in the cementing materials. In the semi-saturated sandstone samples, the microstructure patterns varied significantly.
Corrosion pits appeared on the particle surfaces. A large number of secondary minerals and residues adhered to the mineral particle surfaces. In saturated sandstone samples, the dissolution and corrosion of the calcareous cement were significant in loose structures. The cracks developed and propagated, and the mineral particles were more rounded. As analyzed above, the cementation degree decreased in sandstone due to water immersion. The frictional damping between the particles was weakened. Consequently, the sandstone samples gradually evolved from dense structures to loose ones. The water-rock interaction and the loading-unloading cycles promoted damage accumulation and microstructural changes in sandstone samples.

Failure mode
Along with the development of monitoring technologies, digital imaging methods became very instrumental in studying macroscopic crack propagation in rocks. The preparation of artificial speckles on the surface of the water-bearing sandstone samples would inevitably increase the test duration. To mitigate this problem, we used the PhotoInfor and PostViewer image analysis software packages to determine sandstone deformation and failure during the tests (Li et al. 2006). The displacement evolution law on the surface of sandstone samples with different water contents was obtained. Figure 13 shows the cloud maps of displacement field at different time points for the corresponding number of cycles in dry, semi-saturated (water content 1.01%), and water-saturated sandstone samples under grade cyclic loading-unloading. According to Fig. 13 (a), cracks initiated from the upper and lower edges of the dry sandstone sample successively after twenty cycles. Later, the cracks propagated along the principal stress direction and developed into three tensile cracks growing parallel with the loading direction. The sandstone sample underwent splitting failure. According to Fig. 13 (b), cracks initiated from the upper right and the lower middle parts of the semi-saturated sandstone sample successively. The cracks first propagated along the loading direction and then merged into one crack. The sandstone samples had a failure of tensile-shear mixed mode. According to Fig. 13 (c), cracks initiated from the middle of the saturated sandstone sample and gradually propagated. One inclined crack was generated in the upper and lower parts of the sample, respectively. The sandstone sample had a single inclined plane shear failure mode.
As the water content increased, the failure mode changed from tensile-brittle cleavage fracture in the dry state to tensile-shear mixed-mode failure. In the water-saturated state, sandstone samples had a single shear failure with some ductile features. Meanwhile, more and more secondary fissures were generated near the main fracture, resulting in increasingly complicated patterns in the displacement field cloud maps. The most probable reason was that the sandstone bulk was damaged due to the water's lubrication, wedging, and corrosion effects. As a result, a shear zone appeared. Besides, as the water content increased, the shear zone within the sample became increasingly prominent. The presence of the shear zone contributed to the shear slip failure of the sandstone samples under stress.

Discussion
According to the above analyses, the mechanical properties of sandstone samples permanently deteriorated as the water content increased, while their damage accumulated gradually. Both the compressive strength and the energy storage characteristics deteriorated significantly. The above phenomena were primarily attributed to physical interactions and chemical reactions between water and sandstone, which are briefly summarized below.
The coal measures is a lithostratigraphic term for the coal-bearing part of the Upper Carboniferous System, consisting of such rocks as claystone, shale, siltstone, sandstone, etc., interstratified with the beds of coal. Coal measures sandstone is a sedimentary rock composed of mineral particles of varying sizes and shapes. Such sandstone has many defects within, including microcracks, fissures, and pores. In water immersion tests, the water first fills the pores and fissures between the mineral particles rapidly. If the water immersion lasts for a long period, the pore water will gradually permeate to the mineral particle surfaces to form bound water there. Under the external force action, the sandstone samples undergo frictional slip between the mineral particles. As the bound water amount formed on the mineral particle surfaces increases, water's lubricating and softening effects are enhanced. The bonding strength between the particles is weakened. As a consequence, the frictional coefficient and the cohesive force within the sandstone decrease to varying extents.
According to SEM and XRD of typical fractures, the sandstone was mainly composed of quartz, feldspar, and clay minerals; on the microscopic scale, the fracture surface became rounded gradually. The cracks and fissures within the sandstone samples were the primary sites where the physical, chemical, and mechanical interactions occurred between water and rocks. As the water content increased, the calcareous cement was more likely to be dissolved and corroded upon contact with water. The soluble substances went into the immersion solution along with water molecules' movement. Therefore, the pores and fissures became larger and more rounded. In addition, the clay minerals expanded due to water absorption under water-rock interaction. As a result of the expansion stress, stress concentration at the crack tip became more significant, promoting crack initiation and propagation. The mineral particles on the surfaces of new cracks would undergo another round of physical and chemical reactions, including corrosion, dissolution, and water absorption expansion. Such interactions promoted the continuous damage and failure of sandstone. Under the joint action of the above factors, the macromechanical parameters and the energy storage characteristics of sandstone deteriorated as the water content increased.
The performed analysis of the test results revealed that the mechanical parameter deterioration and failure modes of sandstone samples varied with the water content. This implied that the water had varying physical and chemical impacts on sandstone at different stages of water immersion tests. At the initial stage of water immersion, the water-rock interaction was primarily featured by water molecules' absorption onto the mineral particles, which was a physical interaction. The absorption rate was relatively high, and the sandstone strength decreased gradually.
As the water immersion was prolonged, the water content of the sandstone samples became saturated. The water-rock interaction was predominantly the corrosion of mineral particles at this stage, with a progressive enhancement of the chemical reaction. The secondary porosity increased within the sandstone samples under physical actions and chemical reactions. The area of rock-water interaction increased, while the area and degree of bonding between mineral particles decreased. The skeleton of mineral particles was weakened gradually. The sandstone samples became looser and weaker in structure. The brittleness decreased, and the failure mode changed from brittle to ductile.

Conclusions
The results obtained made it possible to draw the following conclusions: (1) As the water content increased, the uniaxial compressive strength, elastic modulus, and elastic energy storage limit decreased gradually in the sandstone samples. Under graded cyclic loading-unloading, the elastic strain during a single cycle increased approximately linearly. As the primary damage, including pores and fissures, accumulated gradually, cyclic loading-unloading curves shifted toward higher strain values. The residual plastic strain first decreased rapidly, then stabilized, and finally showed a minor rise.
(2) Under graded cyclic loading-unloading, the input energy was stored mainly in the form of elastic energy in each cycle; the dissipated energy was primarily spent on overcoming the damping. As the number of cycles increased, the damping energy share first increased gradually and then stabilized. When the normalized number of cycles approached unity, the plastic energy share increased sharply, indicating the ongoing instability failure of the sandstone.
(3) The plastic energy was normalized to plot the damage evolution curve of the sandstone. This curve was subdivided into three stages: decelerated growth, stable accumulation, and accelerated growth. As the water content increased, the slope of the curve of damage factor versus the number of cycles increased gradually at the stage of stable accumulation.
(4) As the water content increased, the pore water exhibited stronger lubrication, wedging, and dissolution effects on mineral particles. As a result, the mineral particles became more rounded. The bonding force between the mineral particles decreased, and the failure mode of sandstone changed from brittle to ductile. material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.