Experimental-simulation analysis on mechanical degradation and energy evolution characteristics of sandstone under water-rock coupling effects

Abstract

With increasing coal mining depths, water-rock interactions exacerbate the mechanical degradation of coal-rock masses and geological disaster risks. Investigating the mechanical properties and energy evolution mechanisms of water-bearing sandstone is crucial for ensuring safe mining operations. To address the existing research gap in analyzing energy evolution mechanisms of water-saturated rock masses from a macroscopic perspective and the lack of exploration into energy mechanisms at critical failure points at the mesoscale, this study employs the particle discrete element software PFC3D to establish numerical models of sandstone with varying water contents. Combined with uniaxial compression tests and energy calculation principles, the mechanical degradation laws and energy evolution characteristics of sandstone under water-rock interactions are systematically investigated. The results indicate that the mechanical properties of sandstone exhibit significant degradation with prolonged immersion time, where compressive strength and elastic modulus gradually decrease with increasing water content. Energy evolution during sandstone deformation and failure can be divided into three stages: elastic energy storage, crack propagation energy dissipation, and sudden energy release at failure. Water immersion significantly reduces energy absorption efficiency during the elastic storage stage and increases energy dissipation rates during crack propagation. Mesoscale crack development analysis reveals that water accelerates the extension of initial fractures and the initiation of new cracks, while higher water content promotes a transition from localized to diffuse crack distribution. Additionally, the energy thresholds at critical failure points and failure modes of samples with different water contents show significant correlations, revealing the dynamic regulatory mechanism of water-induced weakening effects on energy accumulation and release in sandstone. These findings provide theoretical support for safe mining and dynamic disaster prevention in deep water-rich coal seams.

Introduction

With the continuous increase in underground coal mining depths, the physical and chemical interactions between groundwater and coal-rock masses have become increasingly complex, leading to structural damage and mechanical degradation of coal-rock masses^1,2,3,4. Water is one of the most active factors inducing geological disasters, as processes such as deformation, instability, and failure of engineering rock masses often involve water participation. Water-rock interactions degrade the mechanical properties of rock masses, determining the rates of energy release and absorption. Sudden energy release can trigger dynamic disasters such as rock bursts^5,6,7,8. Therefore, exploring the mechanical properties and energy evolution mechanism of sandstone under water-rock interaction provides theoretical support and scientific basis for scientifically guiding the safe mining of coal mines.

Over the years, numerous scholars have conducted extensive research on the mechanical properties and energy evolution of sandstone during deformation and failure under water-rock interactions. Deng et al.⁹ investigated the mechanical degradation mechanisms of sandstone under cyclic immersion-drying and hydraulic pressure variations using Three Gorges reservoir sandstone. Zhang et al.¹⁰ conducted uniaxial compression tests on sandstone with varying height ratios under dry and saturated conditions, analyzing stress distribution at interfaces of composite structures. Wang et al.¹¹ performed cyclic water-rock tests on metamorphic sandstone to study its mechanical degradation. Liu et al.¹² compared the mechanical properties and acoustic emission characteristics of sandstone-coal composite structures before and after saturation. Feng et al.¹³ explored the mechanical degradation of altered rocks under triaxial compression after multiple saturation-desaturation cycles. Zhang et al.¹⁴ investigated the creep and acoustic emission characteristics of sandstone surrounding boreholes under varying water contents. Yao et al.¹⁵ analyzed differences in mechanical properties, failure mechanisms, and acoustic emission features of coal-bearing strata under uniaxial compression and shear tests with varying water contents.

With advancements in computational technology, numerical methods have gained prominence in rock engineering. Researchers have utilized the particle discrete element software PFC to study the influence of microstructures on rock mechanical properties and failure characteristics. Liu et al.¹⁶ proposed an index for rock heterogeneity and analyzed its relationship with characteristic stresses. Ding et al.^17,18,19 simulated the effects of specimen-to-particle size ratios, particle size distributions, and aspect ratios on rock strength and deformation. Yang and Zhang et al.^{20,21,22,23,24,25,26} investigated crack propagation in rocks with prefabricated fractures under uniaxial and triaxial compression. Mu et al.²⁷ established a hydro-mechanical coupling model for sandstone using PFC to study acoustic emission and energy evolution during failure. Chen et al.^28,29 simulated hydraulic fracturing processes.

While existing studies have explored the mechanical degradation and energy evolution mechanisms of sandstone under water-rock interactions from multiple perspectives, most research on energy evolution in water-saturated rock masses remains macroscopic, with limited analysis of energy mechanisms at critical failure points under varying water contents. This study combines mesoscale analysis in PFC3D with uniaxial compression tests to investigate crack development characteristics and energy evolution laws in sandstone under different water contents.

Mechanical properties of sandstone under different water contents

Sample preparation and testing methods

In this study, the sandstone of the top plate of 6 coal in Shuangma I Mine of National Energy Group was selected, and then the sandstone specimens were prepared so that the total size was 50 mm×100 mm, and the basic requirements of sampling were strictly in accordance with the national standard “Methods for Determination of the Physical and Mechanical Properties of Coal and Rocks” in the first part of the sampling, to ensure that each group of sandstone was taken from the same level and the same direction, and some of the standard sandstone specimens were as shown in Fig. 1. Before the start of the test, all the specimens were dried, a total of 4 groups, each group of specimens prepared 3, a total of 12, and then made into a sample of water content by immersion. With displacement control during loading and a loading rate of 2 × 10^–3 mm/s. The test was conducted using the MTS815 fully digital hydraulic servo test system, as shown in Fig. 2.

Fig. 1

Part of the rock specimen.

Fig. 2

MTS815 full digital servo compression test system.

Mechanical properties of sandstone under different water contents

Since the pre-peak stress-strain curves of rock masses under the same water content exhibit high similarity^30,31, a single curve was randomly selected for analysis in this study. Figure 3 illustrates the variation in water content of sandstone under different immersion durations. As shown, the water absorption capacity of sandstone gradually stabilizes after 120 h of immersion. Therefore, 120 h was considered the threshold for achieving a saturated state. Figure 4 presents the stress-strain curves of sandstone under varying water contents. At lower water contents, the compaction stage was relatively short due to insufficient water filling in the internal voids, resulting in a higher proportion of the linear elastic stage in the pre-peak phase. As the water content increased, the proportion of the compaction stage expanded significantly, accompanied by a gradual decline in compressive strength and a pronounced post-peak stress drop. This phenomenon is attributed to the enhanced filling of voids by water, where the lubricating effect of moisture facilitates the expansion and interconnection of microcracks and pores. Consequently, the plasticity of sandstone progressively intensified with rising water content.

Fig. 3

The water content change diagram of sandstone under different soaking time.

Fig. 4

Stress-strain curves of sandstone under different water content.

Based on the full stress-strain curves at failure for sandstone under different water contents, three mechanical parameters elastic modulus ${E_0}$, compressive strength ${\sigma _{\text{c}}}$, and peak strain ${\varepsilon _{\text{p}}}$ were derived. To intuitively investigate the variation trends of these parameters with water content and characterize their relationships, fitting analyses were performed. Figures 5, 6 and 7 present the fitted relationship curves between the three mechanical parameters and water content.

Fig. 5

Sandstone elastic modulus fitting curve.

Fig. 6

Sandstone compressive strength fitting curve.

Fig. 7

Sandstone peak strain fitting curve.

It can be seen from Figs. 5, 6 and 7 that the elastic modulus and compressive strength of sandstone are negatively correlated with the water content, while the peak strain is positively correlated with the water content. The elastic modulus of sandstone in the dry state is 7626.58 MPa. When the water contents are 1.33%, 2.43%, and 3.54% respectively, the elastic modulus of sandstone decreases by 34.70%, 46.59%, and 60.33% successively compared with that in the dry state. The compressive strength of sandstone in the dry state is 71.89 MPa. When the water contents are 1.33%, 2.43%, and 3.54% respectively, the compressive strength of sandstone decreases by 26.87%, 40.40%, and 50.23% successively compared with that in the dry state. The peak strain of sandstone in the dry state is 0.0116. When the water contents are 1.33%, 2.43%, and 3.54% respectively, the peak strain of sandstone increases by 18.97%, 23.28%, and 38.79% successively compared with that in the dry state.

Obviously, with the increase of the water content, the degree of deterioration of the elastic modulus ${E_0}$ and compressive strength ${\sigma _{\text{c}}}$ of sandstone gradually increases; the degree of optimization of the peak strain of sandstone gradually increases. This indicates that the water-rock interaction will accelerate the softening of sandstone and the instability of sandstone, resulting in a drop platform of sandstone as the water content increases. It can be concluded that different water contents have a significant deteriorating effect on the mechanical parameters of sandstone. The specific fitting function expressions of the peak strain ${\varepsilon _{\text{p}}}$, compressive strength ${\sigma _{\text{c}}}$, elastic modulus ${E_0}$ of sandstone and the water content are as follows:

$$\left\{ \begin{gathered} {E_0}= - 1268.45w+7241.31 \hfill \\ {\sigma _{\text{c}}}= - 10.1606w+69.3156 \hfill \\ {\varepsilon _{\text{p}}}=0.12w+1.176 \hfill \\ \end{gathered} \right.$$

(1)

Brittleness index (B) is the comprehensive attribute of rock. Under the action of its own heterogeneity and external force, it produces internal non-uniform hook stress and local stress concentration, resulting in local damage and the ability to produce cracks and cracks³². The calculation formula is:

$$B=\alpha \frac{{{\sigma _{\text{c}}}}}{{{\varepsilon _{\text{p}}}}}$$

(2)

where ${\sigma _{\text{c}}}$ is compressive strength, ${\varepsilon _{\text{p}}}$ is peak strain, $\alpha$ is correction coefficient, and there is no actual physical meaning. In this paper, 0.1 is taken.

The brittleness index of sandstone under different water content can be obtained from Eq. (2), that is, the brittleness index B of rock samples with water content of 0%, 1.33%, 2.43% and 3.54% is 61.97, 38.09, 29.97 and 22.22, respectively, as shown in Fig. 8.

When the water content rises from the dry state to 1.33%, the brittleness index of the rock sample decreases by 38.53%. When the water content increased to 2.43%, the brittleness index decreased by 51.64% compared with the dry state. When the water content increased to 3.54%, the brittleness index decreased by 64.14% compared with the dry state. With the increase of water content, the brittleness of the rock sample gradually decreases, which indicates that the internal pores of the rock sample are filled with water molecules, resulting in the softening of the internal structure and some cementing materials, and the stiffness is reduced. Therefore, the displacement control of rock should be paid attention to in the construction project under long-term water-rich environment³³.

Fig. 8

Sandstone brittleness index fitting curve under different water content.

Energy evolution law of sandstone deformation and failure process under different water content

Energy calculation principle

From an energy perspective, the deformation and failure of sandstone under external loading constitute a dynamic evolutionary process involving energy input, accumulation, and dissipation. Energy dissipation accompanies every stage of crack initiation, propagation, and even macroscopic fracture development³⁴. The complete energy evolution process is illustrated in Fig. 9. Therefore, investigating the energy evolution laws of sandstone during deformation and failure under varying water contents holds significant importance for revealing the mechanism of water content’s impact on sandstone damage and failure.

According to thermodynamic principles, the energy U₀ generated by external work is expressed as^35,36,37:

$$U_{0} = U_{d} + U_{e}$$

(3)

where U₀ is the total energy, U_e is the elastic potential energy, and U_d is the dissipation energy.

Fig. 9

The whole process evolution diagram of energy.

It is assumed that there is no heat exchange between the system and the outside world during the test, and the energy U₀ generated by the external force is the energy actually absorbed by the rock sample. Under uniaxial compression conditions:

$$\sigma _{2} = \sigma _{3} = 0$$

(4)

$${U_0}=\int_{0}^{{{\varepsilon _1}}} {{\sigma _1}d{\varepsilon _1}} +\int_{0}^{{{\varepsilon _2}}} {{\sigma _2}d{\varepsilon _2}} +\int_{0}^{{{\varepsilon _3}}} {{\sigma _3}d{\varepsilon _3}} =\int_{0}^{{{\varepsilon _1}}} {{\sigma _1}d{\varepsilon _1}}$$

(5)

$${U_{\text{e}}}=\frac{1}{2}{\sigma _1}{\varepsilon _1}=\frac{{{\sigma _1}^{2}}}{{2{E_{\text{u}}}}} \approx \frac{{{\sigma _1}^{2}}}{{2{E_{\text{0}}}}}$$

(6)

$${U_d}={U_0} - {U_e}=\int_{0}^{{{\varepsilon _1}}} {{\sigma _1}} d{\varepsilon _1} - \frac{{{\sigma _1}^{2}}}{{2{E_0}}}$$

(7)

where σ₁, σ₂ and σ₃ are the maximum principal stress, intermediate principal stress and minimum principal stress of sandstone. ε₁, ε₂, ε₃ are the principal strain along the principal stress; E₀ is the actual elastic modulus of sandstone, and E_u is the unloading modulus.

Energy evolution law of coal rock under different water content

Rock failure is a state instability phenomenon driven by external work. During this process, external forces continuously cause the rock to absorb energy, which dynamically evolves through release and dissipation. Energy release refers to the rapid conversion of elastic strain energy stored in the pre-peak phase into surface energy for fracture propagation and coalescence at the peak point, providing the driving force for rock failure³⁸. Based on the aforementioned energy calculation principles, the energy evolution laws of sandstone during deformation and failure under varying water contents were determined. Furthermore, the loading-induced deformation and failure process of sandstone were divided into four stages according to its stress-strain relationship.

Fig. 10

The energy evolution diagram of sandstone samples during deformation and failure under different water contents: (a) w = 0%; (b) w = 1.33%; (c) w = 2.43%; (d) w = 3.54%.

In the compaction stage (OA), the elastic strain energy and dissipation energy hardly change, and the total strain energy increases slowly. The rock sample has micro-crack closure and expansion at this stage, and the energy development characteristics are very complex, but the three energy values are small. It can be seen from Fig. 10 that at point A, with the increase of water content, the elastic strain energy U_e of sandstone accounts for 59.46%, 69.49%, 71.96%, and 86.28% of the total strain energy U₀, respectively, indicating that the rock sample is dissipated at this stage. Micro-cracks and pore closure account for a relatively low proportion.

In the linear elastic deformation stage (AB), the increase of dissipated energy of rock sample continues to be low, and the increase of elastic energy increases, indicating that the energy absorbed by rock sample from the outside world is mainly stored in the interior of elastic strain energy. According to the calculation, the elastic strain energy growth rates of rock samples with water content of 0%, 1.33%, 2.43% and 3.54% at this stage are 9.44 × 10⁻² MJ m⁻³s⁻¹, 6.86 × 10⁻² MJ m⁻³s⁻¹, 5.07 × 10⁻² MJ m⁻³s⁻¹ and 3.82 × 10⁻² MJ m⁻³s⁻¹, respectively. Therefore, it can be concluded that with the increase of water content, the ability of rock samples to store elastic strain energy is gradually weakened.

In the plastic deformation stage (BC), the stress-strain of the rock sample develops nonlinearly, and a certain number of cracks begin to appear on the surface, and the internal damage begins to intensify. It can be seen from the figure that the increase of elastic strain energy decreases significantly, the increase of dissipation energy begins to increase significantly, and the elastic strain energy reaches the maximum at point C at the peak stress. According to Table 1, it can be seen that at the peak C point of sandstone, the proportion of elastic strain energy to total strain energy decreases gradually with the increase of water content, and the proportion of dissipated energy to total strain energy increases gradually, indicating that at the critical point of plastic deformation stage and failure stage, the degree of water content will affect the proportion of strain energy of rock.

In the post-peak failure stage (after C point), the stress of the rock sample drops rapidly at this stage, the elastic strain energy stored in the interior is quickly converted into dissipated energy, and the dissipated energy density increases greatly, indicating that most of the energy is dissipated in the development of the fracture surface, and the total energy growth rate slows down. It can be seen from Fig. 10 that as the water content of the rock sample increases, the total energy absorbed from the outside is 0.469 MJ m⁻³, 0.411 MJ m⁻³, 0.410 MJ m⁻³, and 0.409 MJ m⁻³, respectively. This shows that as the water content increases, the total strain energy absorbed by the rock sample gradually decreases, that is, the water molecules enter the rock sample to saturation. This stage will weaken its ability to absorb energy.

Table 1 The energy characteristic value at the peak.

Fig. 11

The energy evolution law of sandstone: (a) Total strain energy (U₀); (b) Elastic strain energy (U_e); (c) Dissipative energy (U_d).

FIgure 11 illustrates the variation patterns of total energy, elastic strain energy and dissipated energy in sandstone under different water contents. As shown in Fig. 11a, water content significantly influences energy evolution throughout the entire loading and failure process. At the same strain level, sandstone with higher water content exhibits weaker energy absorption capacity. For dry sandstone, the total absorbed strain energy is 0.469 MJ m^–3, while for saturated sandstone with a water content of 3.54%, this value decreases to 0.409 MJ m^–3. The increasing trend of total energy becomes more gradual with rising water content.

From Fig. 11b, the elastic strain energy at the stress peak decreases to 0.341 MJ m^–3, 0.266 MJ m^–3, 0.209 MJ m^–3, and 0.172 MJ m^–3 as water content increases. This indicates that before reaching w = 2.43%, the variation in elastic strain energy at the peak is relatively significant, whereas beyond w = 2.43%, the changes become more gradual.

As depicted in Fig. 11c, energy dissipation becomes more pronounced before the stress peak under higher water content conditions. This suggests that internal damage within sandstone develops over a longer period prior to failure when water content is elevated. Consequently, in practical excavation scenarios, drier surrounding rock tends to experience abrupt energy release, leading to hazards such as rock ejection, collapse, or even rockburst. To mitigate these risks, high-pressure water jetting can be applied to reduce the probability of rockburst in surrounding rock.

Analysis of crack development of sandstone with different water content based on PFC3D meso angle

In the above chapter, through the uniaxial compression tests on sandstone specimens with different water contents, the macroscopic mechanical deterioration response of sandstone with different water contents has been studied. However, in order to better analyze the distribution of micro-cracks inside the sandstone specimens from the mesoscopic perspective, in the field of rock mass engineering, the numerical calculation method has increasingly become an important technical means to solve some complex engineering problems. The PFC3D software based on the discrete element method is mainly used to simulate the mechanical behavior of granular materials, and is suitable for the research process of the rock mass fracture mechanism and damage evolution, and can accurately analyze the quantitative characteristics of cracks. Therefore, in this paper, PFC3D is used to conduct numerical simulation research on the indoor uniaxial compression tests of sandstone specimens with different water contents, and the evolution characteristics of micro-cracks in sandstone are analyzed from the mesoscopic structural effect.

Establishment of the initial model

The steps to establish the initial model in PFC3D mainly consist of three parts: Firstly, set the parameters of the linear contact model and the random factor; Secondly, it is necessary to create a cylindrical area and generate particles; Finally, achieve an equilibrium state through calculation.

On this basis, since the parallel bond model is a fundamental bond model in the PFC particle flow software and also a bond model suitable for simulating rock materials³⁹, the contact model between particles in this paper adopts the parallel bond contact model, as shown in Fig. 12.

At the same time, in order to restore the uniaxial compression tests of sandstone under different water content conditions described above as much as possible, with the help of the particle flow program PFC3D, a numerical specimen with the same size as that of the sandstone in the conventional uniaxial compression test is constructed. As shown in Fig. 13, a cylindrical area of 50 mm×100 mm is created. The total number of particles in this geometric model is 18,178, and the total number of contacts is 72,261.

Fig. 12

Schematic diagram of the parallel bonding model.

Fig. 13

Initial numerical sample model.

Calibration of microscopic parameters

In order to obtain the mesoscopic parameters of the model that can reflect the macroscopic mechanical deterioration response of the real sandstone specimens, it is necessary to calibrate the mesoscopic parameters of the above initial numerical specimen model. That is, by adjusting the mesoscopic parameters, the macroscopic mechanical behavior exhibited by the numerical specimen can be basically consistent with the results of the uniaxial compression test. At present, since there is no relevant theory that can establish a quantitative relationship between the macroscopic and mesoscopic parameters of the particle flow model, most researchers use the “trial calculation” method to find the mesoscopic parameters that have a greater impact on the macroscopic mechanical parameters, and then focus on calibrating these parameters to achieve the goal of matching the results of the indoor test as soon as possible⁴⁰.

Zhao Guoyan⁴¹ and others used the uniaxial compression test calculation model to study the influence of the mesoscopic parameters of the PFC parallel bond model on the macroscopic characteristics. In order to reasonably obtain the mesoscopic parameters of the model that can reflect the macroscopic mechanical deterioration response of the real coal specimens, a sensitivity analysis of the mesoscopic parameter λ will be carried out below. The calibration of other mesoscopic parameters in PFC3D is shown in Table 2.

Table 2 PFC3D mesoscopic parameter table.

Sensitivity analysis of parallel bond radius multiplier λ 

Set the mesoscopic parameter, the parallel bond radius multiplier λ, to 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, and 1.5 respectively. The uniaxial compression stress-strain curves and sensitivities of sandstone under different radius multipliers λ are shown in Fig. 14.

Fig. 14

Effect of the bonding radius multiplier λ on the mechanical properties of the model: (a) Stress-strain curve; (b) Peak stress; (c) Peak strain; (d) Modulus of elasticity.

As can be seen from the analysis of Fig. 14, with the increase of the bond radius multiplier, the peak strength, peak stress, and elastic modulus of the coal model increase accordingly. The relationship between them can be expressed by Eq. (8). Combining with the indoor test curves, in this paper, λ = 0.9, λ = 1.1, λ = 1.3, and λ = 1.5 are selected as the mesoscopic bond radius multipliers for sandstone specimens with different water contents respectively.

$$\left\{ \begin{gathered} y=-24.62+59.85x \hfill \\ {R^2}=0.978 \hfill \\ y=0.00635+0.00618x \hfill \\ {R^2}=0.941 \hfill \\ y=-875.22473+3675.8889x \hfill \\ {R^2}=0.991 \hfill \\ \end{gathered} \right.$$

(8)

Sensitivity analysis of particle friction coefficient f _c

During the simulation process, to avoid the influence of the particle friction coefficient on this experimental study, the parallel bond radius multiplier λ is kept at 0.7, and the values of other mesoscopic parameters are the same as those in Table 2. Only the value of the particle friction coefficient fc is changed, which are set to 0.05, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, and 0.85 respectively. The number of cyclic iterations is the same as that mentioned above. The stress– strain curves are obtained, and based on this, the trend graphs of the mechanical parameters are plotted respectively, as shown in Fig. 15.

Fig. 15

Effect of particle friction coefficient f_c on model mechanical properties: (a) Stress-strain curve; (b) Peak stress; (c) Peak strain; (d) Modulus of elasticity.

As can be seen from the analysis of Fig. 15, when the value of fc is in the range of 0.45–0.85, the overall stability of its stress - strain curve and the three mechanical characteristic parameters is more stable compared to the range of 0.05–0.35. Therefore, the value of the particle friction coefficient fc is set to 0.45.

Error analysis of PFC3D model and test curve

The numerical simulation results of the uniaxial compression of sandstone with different water contents are simulated according to different parallel bond radius multipliers and compared with the experimental results to verify the rationality of the mesoscopic parameters in Table 2. The comparison between the numerical simulation curve and the indoor test stress - strain curve is shown in Fig. 16. The comparative analysis of the stress - strain curves between the numerical simulation and the indoor test in the figure shows that the two have a high degree of consistency in the pre - peak stage. However, limited by the numerical model’s ability to characterize the discreteness of the post - peak mechanical behavior of the coal body, the simulation accuracy in the residual stress stage is significantly reduced.

Fig. 16

Simulated and experimental stress-strain curves of sandstone specimens with different water contents: (a) λ = 0.9; (b) λ = 1.1; (c) λ = 1.3; (d) λ = 1.5.

The error values of the three mechanical parameters between the numerical simulation curve of the sandstone specimen and the experimental stress - strain curve are shown in Table 3. Among them, the average error of the peak stress is 1.06; the average error of the peak strain is 1.75 × 10^–3; and the average error of the elastic modulus is 1209.39. The above data show that the numerical simulation results are in good agreement with the experimental curve results, and it is reasonable and feasible to adopt the mesoscopic parameters in Table 2.

Table 3 Comparison of mechanical parameters between uniaxial compression test and numerical simulation of sandstone specimen.

Analysis of micro-fracture development characteristics of sandstone with different water content

Figure 17, through integrated analysis of 3D crack distributions (shear cracks: purple; tensile cracks: green) and stress-strain curves, reveals distinct stage-dependent characteristics in sandstone crack evolution. During the pre-peak stage, shear cracks (initiation point a) develop earlier than tensile cracks (initiation point b), with the latter emerging at the elastoplastic transition. Pre-peak damage is primarily dominated by shear crack accumulation. Post-peak, both crack types surge, but shear cracks account for over 70% of the total increment, indicating shear instability as the dominant failure mechanism. Elevated water content accelerates crack propagation: moisture lubrication reduces interparticle friction, promoting shear crack initiation, while pore water pressure weakens effective stress, accelerating tensile crack coalescence. In conclusion, sandstone damage evolution is shear-dominated, and water-rock coupling effects exacerbate disaster progression through enhanced crack development.

Fig. 17

Stress-strain curves and crack development trend of sandstone samples with different water contents: (a) w = 0%; (b) w = 1.33%; (c) w = 2.43%; (d) w = 3.54%.

The destabilization process of rock damage is fundamentally a macroscopic manifestation of the initiation, propagation, and coalescence of internal microcracks. Figure 18 illustrates the microcrack development in sandstone under varying water contents, highlighting distinctions in crack evolution during deformation and failure. Table 4 quantifies crack counts, revealing that as water content increases (0–3.54%), shear cracks rise from 10,405 to 10,453, tensile cracks from 1,863 to 2,530, and total cracks increase by approximately 6%. The underlying mechanisms include: (1) Water lubrication reduces interparticle friction and weakens cementation strength, promoting shear crack initiation and existing crack propagation; (2) Pore water pressure diminishes effective stress, accelerating the coalescence of pore-fracture networks and leading to tensile crack proliferation. These findings demonstrate that water-rock coupling exacerbates sandstone damage through shear-dominated and tensile-assisted pathways.

From the above analysis, it is evident that total cracks, shear cracks, and tensile cracks in sandstone exhibit an upward trend with increasing water content.

Fig. 18

Micro-fracture development of sandstone with different water content: (a) Total crack; (b)Shear fissure; (c) Tension crack; (d) Fitting curve.

Table 4 Number of cracks in sandstone with different water content.

Conclusions

• 1. As the water content increases, the peak stress, elastic modulus, and brittleness index of sandstone gradually decrease, while the peak strain increases instead. The deterioration trends all show a rapid decline first and then a gentle slowdown.

• 2. With the increase of the water content, the proportion of elastic strain energy of sandstone in the compaction stage gradually increases, indicating that the energy dissipation is more significant, but the value is relatively low. At the elastic-plastic boundary, the proportion of dissipated energy of sandstone significantly increases, indicating that irreversible plastic deformation begins to occur inside, and the growth rate of elastic strain energy gradually slows down and reaches its peak at the failure point. In the post-peak stage, the higher the water content of sandstone is, the more gradually its ability to absorb the total strain energy decreases.

• 3. The increase in water content intensifies the propagation of mesoscopic cracks in sandstone through the effects of lubrication, softening, and pore water pressure. Among them, shear cracks dominate the damage process. The numerical model effectively reveals the mechanical response before the peak, but the simulation accuracy after the peak needs to be further optimized.