Introduction

Mineral resources constitute the critical material foundation supporting modern industrial civilization. The depth and scale of their exploitation directly influence the process of socio-economic development1,2. With the acceleration of global industrialization, the reserves of easily accessible near-surface resources are gradually depleting. The international mining engineering community is undergoing a strategic transition from shallow to deep mining3,4. Statistics indicate that the mining depth for metals in China is extending downward at a rate of 10–15 m annually, making kilometer-deep mining an inevitable trend in industry development5,6. Deep rock masses exhibit distinct “three-high” environmental characteristics: high in-situ stress, high ground temperature, and high seepage pressure. These complex geological conditions induce intense nonlinear deformation behavior in roadway surrounding rock. Particularly in water-rich strata, water–rock coupling significantly weakens rock structures, triggering engineering hazards such as lining leakage, rock mass argillization, and roof instability. These directly threaten underground operations and cause significant economic losses7,8. Therefore, studying the mechanical properties of water-bearing rock masses under triaxial stress fields from the perspective of energy evolution and constructing corresponding damage constitutive models holds significant scientific value for establishing a theoretical framework for stability control in deep water-rich roadways.

Previous scholars have conducted extensive research on the properties of water-bearing rock masses. For instance, regarding the physicochemical deterioration effects of aqueous environments on rock mass structure, Scuderi et al.9, through experiments on quartz-clay fault fabric evolution, confirmed that hydrochemical effects can induce mineral phase transitions, thereby regulating fault slip stability; Ramazan et al.10 systematically quantified the nonlinear influence of water content on rock crushability, finding that the anti-crushing capacity of saturated rock decreased by over 30% compared to the dry state, exhibiting a brittle-to-ductile transition at a critical water content; Wei et al.11,12,13, in a series of studies, further pointed out that high-humidity environments drive strain localization in fractured sandstone, while hydrochemical corrosion causes the long-term strength of coal-rock combinations to decay exponentially. In terms of mechanical behavior characterization, Li et al.14, through experiments, demonstrated that seepage pressure increases the shear band propagation rate in water-bearing sedimentary rocks by 210% and attenuates peak strength by up to 40%; Qian et al.15, via water pressure-triaxial coupling tests on fractured coal, discovered that water pressure gradients expand the stress corrosion zone at fracture tips by 47%, significantly reducing shear strength. Breakthroughs have been made in research on mechanical responses under extreme environments; Naderi et al.16 confirmed that the lubricating effect of water under extreme confining pressure reduces rock fracture toughness by 18–25%, while Cao et al.17 revealed that the dynamic damage threshold of high-stress water-bearing coal under jet impact exhibits critical confining pressure dependence. In the field of constitutive modeling, Zhonghui et al.18 first established an energy-driven damage constitutive model for water-bearing coal, linking elastic energy dissipation rate with damage variables to achieve quantitative characterization of seepage pressure-strain energy-damage. The rock mass hydraulic damage factor proposed by Elshalkany et al.19, based on a fault-controlled water model, provides new insights for the physical characterization of seepage parameters in constitutive equations.

However, existing research still has limitations. Most studies focus on uniaxial stress or conventional triaxial stress with fixed confining pressure, lacking in-depth analysis of the mechanical response and damage evolution of water-bearing sandstone under true triaxial stress paths that simulate actual deep mining environments. Moreover, although some energy-based damage models have been established, few integrate both water-induced damage (from physicochemical interactions) and mechanically induced damage (from energy dissipation) to comprehensively characterize the coupled damage mechanism of water-bearing sandstone. Given that the essence of rock deformation and failure lies in energy-driven mechanisms, systematically revealing the energy absorption–dissipation-release characteristics of water-bearing rock masses holds key theoretical significance11,20,21,22,23. To this end, this paper takes the deep roadway in the Yingping Section of the Wengfu Phosphate Mine in Guizhou Province as the engineering background. Addressing the issue of local instability in surrounding rock, an analysis of groundwater chemical composition is conducted (measured pH = 6.5, main ions Na+/Cl−). Based on this, sandstone specimens with different water contents are prepared by soaking in a laboratory-configured NaCl solution (pH = 6.5). Mechanical behavior and energy evolution data across the entire path are obtained through triaxial compression tests. Subsequently, a hydro-mechanical coupled damage constitutive model is constructed based on the dissipated energy principle. The model integrates water-induced damage and mechanically induced damage, and its rationality is verified by the high concordance between theoretical curves and experimental stress–strain data, particularly in the pre-peak stage where predicted peak stresses and corresponding peak strains align closely with measured values. This model effectively links water-induced elastic modulus attenuation and mechanical energy dissipation to damage variables, providing a more accurate theoretical basis for stability control of deep water-rich roadways.

Experimental design and methodology

Sample preparation

Sandstone specimens were collected from the underground roadway working face of the Yingping Section at the Wengfu Phosphate Mine in Guizhou Province, China. These specimens are processed into standard cylinder specimens with a size of 50 mm × 100 mm (diameter × height), conforming to the suggested dimensions for rock mechanics testing by the International Society for Rock Mechanics (ISRM)24. To minimize surface flatness effects on experimental results, all specimens were inspected and polished to ensure end-face flatness errors ≤ 0.5 mm. A schematic of the prepared specimen is shown in Fig. 1a. A total of fifteen standard cylindrical specimens were prepared. These were divided into five groups (three specimens per group) based on the target moisture content: dry (0%), 0.52%, 2.56%, 5.01%, and saturated (7.33%). This grouping ensured statistical reliability for comparing mechanical behavior under different conditions.

The porosity of the selected samples was measured in their initial state using an AiniMR-60 nuclear magnetic resonance (NMR) analyzer, yielding an average porosity of 8.57%. The T2 spectrum of the initial sample is illustrated in Fig. 1b. Based on established criteria, pore sizes were categorized into three ranges: mesopores (0–10 ms), macropores (10–100 ms), and super-macropores (≥ 100 ms). Analysis of Fig. 1 indicates that the specimens exhibited 7.2% mesopores, 80.3% macropores, and 12.5% super-macropores, confirming a highly porous sandstone structure dominated by macropores.

X-ray diffraction (XRD) analysis (Fig. 1c) identified the primary mineral components of the specimens as Quartz (33.8%), Muscovite (10.9%), Albite (13.2%), Microcline (18.5%), Kaolinite (2.1%), and Osumilite (15.2%), with Miscellaneous for 6.3%.

Fig. 1
figure 1

Schematic of specimen and initial property measurements.

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Experimental procedure

  1. 1.

    To ensure data accuracy, the following pretreatment steps were implemented:

  2. 2.

    Drying: Specimens were placed in a drying oven at 120 °C for 12 h, then wrapped in plastic film and cooled to room temperature in a desiccator.

  3. 3.

    Saturation: Specimens were immersed in a 0.01 mol/L NaCl solution (pH = 6.5), which was formulated to simulate the in-situ groundwater chemistry of the Wengfu Phosphate Mine (field test data showed groundwater NaCl concentration of 0.008–0.012 mol/L and pH ≈ 6.5). Every 12 h, they were removed, surface moisture was wiped, and weights were recorded until consecutive mass differences stabilized at ≤ 0.01 g, indicating saturation (saturation moisture content = 7.33%). Moisture content (w) was calculated using Formula (1):

$${\varvec{w}}=\frac{{{m_{\text{t}}} - {m_0}}}{{{m_0}}} \times 100\%$$
(1)

where m0 is the dry mass and mt is the measured mass at time t.

The relationship between immersion time and moisture content is plotted in Fig. 2. Specimens with moisture contents of 0.00% (dry), 0.52%, 2.56%, 5.01%, and 7.33% (saturated) were selected for triaxial compression testing.

Fig. 2
figure 2

Moisture content of specimens under varying immersion durations.

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Triaxial compression tests were conducted using a MTS-815 rock mechanics experimental system, with the environmental temperature maintained at 25 ± 1 °C throughout the tests to eliminate temperature-induced interference on water–rock interactions. The principal stresses were set to σz = 20 MPa (axial) and σx = σy = 15 MPa (lateral). This stress ratio was selected to simulate the in-situ stress conditions measured at the deep mining level of the Wengfu Phosphate Mine, where the vertical stress is higher than the horizontal stresses. The loading protocol consisted of two stages: (1) Hydrostatic loading: The three principal stresses were simultaneously loaded to their preset values (σz = 20 MPa (axial), σx = σy = 15 MPa); (2) Deviatoric loading: While maintaining the lateral confining pressures constant at σx = σy = 15 MPa, axial loading was applied at a displacement rate of 0.01 kN/s, with data sampled at 10 Hz until specimen failure. For each moisture content (0%, 0.52%, 2.56%, 5.01%, 7.33%), 5 identical specimens were tested in parallel to ensure data reliability, and the average values of mechanical parameters (peak strength, elastic modulus, Poisson’s ratio) were used for subsequent analysis. The measurement uncertainty of the MTS-815 system for stress is ± 0.1 MPa and for strain is ± 0.0001 mm/mm. To ensure loading rate stability, the system was pre-calibrated before each test, and the axial displacement rate was monitored in real-time to maintain it at 0.01 kN/s with a fluctuation range of less than ± 0.001 kN/s. During sample preparation, the diameter and height of each specimen were measured at 3 different positions using a vernier caliper (accuracy ± 0.02 mm), and specimens with dimensional deviations exceeding 0.1 mm were discarded to ensure sample preparation uniformity. The stress loading path and experimental setup are illustrated in Fig. 3a and b, respectively.

Fig. 3
figure 3

Test loading path and test equipment.

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Results and analysis

Stress–strain curves

Figure 4 illustrates representative complete stress–strain curves of sandstone specimens with varying moisture contents under triaxial compression. Systematic analysis reveals that the deformation and failure process of the rock can be divided into four distinct mechanical response stages: (1) initial compaction (OA), (2) linear elastic deformation (AB), (3) plastic strengthening (BC), and (4) post-peak failure (CD).

During the initial compaction stage (OA), the closure and reorganization of inherent pores and micro-defects under axial loading result in a nonlinear upward concave curve, particularly pronounced at the early loading phase25. As the pores are progressively compacted, the mineral skeleton begins to bear the principal stress, leading to a near-linear increase in the curve. When the axial stress exceeds the elastic limit, microcracks initiate and propagate, marking the transition to the plastic strengthening stage (BC), characterized by a gradual reduction in curve slope until peak strength is reached. Subsequently, the specimen loses load-bearing capacity and undergoes failure in the post-peak stage (CD).

With increasing moisture content, the specimens exhibit enhanced ductility, transitioning from abrupt brittle failure (dry state) to gradual plastic failure (saturated state).

Fig. 4
figure 4

Complete stress–strain curves of specimens under triaxial compression (σz = 20 MPa, σx = σy = 15 MPa).

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To quantify the influence of moisture content on peak strength, Fig. 5 plots the relationship between peak strength and moisture content. The results demonstrate a significant nonlinear negative correlation, exhibiting a two-stage attenuation pattern: In the low moisture range (0% < w ≤ 5.01%), the strength degradation rate is 8.32 MPa/%; In the high moisture range (5.01% ≤ w ≤ 7.33%), the rate decreases to 5.18 MPa/%. This nonlinear weakening effect arises from multi-scale water–rock interaction mechanisms: at the mesoscopic scale, the “lubrication effect” of pore water reduces the friction coefficient between mineral particles. At the micro level, water molecules weaken the binding energy of silicon–oxygen bonds by adsorbing water12; In the macroscopic performance, the development of pore pressure leads to the decrease of effective confining pressure, which follows the Terzaghi effective stress principle26.

Fig. 5
figure 5

Relationship between peak strength and moisture content of sandstone specimens under triaxial compression (σz = 20 MPa, σx = σy = 15 MPa).

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It is noteworthy when moisture content exceeds 5.01%, the strength attenuation magnitude (Δσ = 12.03 MPa) accounts for 22.41% of the total reduction, aligning with critical moisture content theory predictions27. This phenomenon suggests the formation of interconnected water film networks within the rock, triggering synergistic stress corrosion and subcritical crack propagation, which accelerate the loss of load-bearing capacity.

Analysis of mechanical parameters

Based on stress–strain data from triaxial compression tests, this study systematically investigates the quantitative influence of moisture content (ω) on the elastic modulus (E) and Poisson’s ratio (µ) of sandstone using theoretical models. According to Hooke’s law and the generalized plane strain assumption, the elastic parameters are calculated using Formulas (2) and (3):

$$E=\frac{{{\sigma _1} - {\sigma _0}}}{{{\varepsilon _1} - {\varepsilon _0}}}$$
(2)
$$\mu = - \frac{{\Delta {\varepsilon _{2}}}}{{\Delta {\varepsilon _{1}}}}$$
(3)

where σ0 and σ1 represent the initial and final stresses in the elastic deformation stage, ε0 and ε1 denote the corresponding strains, Δε1 is the axial strain increment, and Δε2, Δε3 are the lateral strain increments.

The mechanical properties of the specimens are summarized into Table 1. It can be seen that with the increase of water content, the mechanical properties of the specimens show different degrees of decline.

Table 1 The mechanical parameters of the specimen.
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The results, plotted in Fig. 6, reveal that the elastic modulus E follows an exponential decay relationship with moisture content (R2 = 0.98). As ω increases from 0 to 7.33%, E decreases sharply from 37.02 GPa (dry state) to 11.82 GPa (saturated state), representing a total reduction of 68.07%. Notably, the decay rate of E reaches 4.33 GPa/% in the low moisture range (0% < ω ≤ 5.01%) but slows to 1.51 GPa/% at higher moisture levels (ω > 5.01%). This behavior aligns with Griffith’s crack propagation theory: initial water infiltration preferentially fills macrocracks, significantly reducing the stress intensity factor at crack tips and accelerating stiffness degradation28,29. At higher moisture levels, micropore saturation dominates, leading to a weakened but stabilized softening effect.

Poisson’s ratio µ exhibits an S-shaped growth trend (Fig. 6). When ω rises from 0 to 5.01%, µ increases abruptly from 0.18 to 0.32 (43.75% growth). Beyond ω = 5.01%, the growth rate diminishes to 3.13%, stabilizing at 0.33. This nonlinear response reflects multi-scale water–rock interaction mechanisms: At the mesoscopic scale, the presence of pore water reduces the friction constraint between mineral particles and promotes the release of lateral strain energy more freely13; At the micro level, the lattice expansion effect caused by water molecule adsorption leads to the increase of transverse deformation anisotropy30. Remarkably, the deceleration of µ growth beyond the critical moisture content (ω = 5.01%) suggests the formation of a continuous free water film network, where Terzaghi’s effective stress principle governs deformation, and pore pressure contributes linearly to lateral strain.

Fig. 6
figure 6

Relationship between elastic modulus (E)/Poisson’s ratio (µ) and moisture content of sandstone specimens under triaxial compression (σz = 20 MPa, σx = σy = 15 MPa) (Red arrow: Critical moisture content = 5.01%).

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These findings reflect two key water-induced weakening effects: (1) Pore water pressure reduces effective confining pressure, decreasing shear strength per the Mohr–Coulomb criterion; (2) Polar water molecules adsorb onto mineral surfaces, lowering surface energy and promoting crack propagation31.

Energy evolution mechanisms

Energy calculation principles during rock failure

The analysis of energy evolution during rock deformation and failure under loading is fundamentally grounded in the first law of thermodynamics (energy conservation) and principles of damage mechanics32,33,34,35,36,37,38. The total mechanical work input (U) to the rock specimen is partitioned into two primary components: (1) Recoverable elastic strain energy (Ue), stored within the mineral lattice and associated with reversible elastic deformation; and (2) Irreversible dissipated energy (Ud), consumed by internal damage processes (e.g., microcrack initiation, propagation, and coalescence) and inelastic deformation (e.g., plastic yielding, frictional sliding). The fundamental relationship governing this partition is: (Formula 4):

$$U={U_e}+{U_d}$$
(4)

where U is the total strain energy, Ud represents energy dissipated through internal damage (e.g., microcrack propagation) and plastic deformation (e.g., lattice slip, dislocation motion), and Ue is the elastic strain energy governed by the elastic modulus (E) and Poisson’s ratio (ν).

During triaxial loading, the hydrostatic stress (σ30) initially applies positive work to the specimen. After stabilizing the hydrostatic stress, the axial stress (σz) progressively increases, performing additional positive work through axial compression. Conversely, circumferential expansion under confining pressure (σx, σy) results in negative work. The total strain energy (U) is calculated as (Formula 5):

$$U={U_1}+{U_3}+{U_0}$$
(5)

where U1 is the axial stress work, which represents the mechanical energy input from the outside to the rock during the axial compression process. U3 is the confining pressure work, and the energy is released due to the circumferential expansion (negative value); U0 is the elastic strain energy stored in the initial hydrostatic pressure.

Among them, the positive work done by the axial stress σz on the specimen, this part represents the mechanical work applied by the axial stress to the rock during the compression process, and the formula is calculated by the area integral under the stress–strain curve (Formula 6).

$${U_1}=\int_{0}^{{{\varepsilon _1}}} {{\sigma _{\text{z}}}} d{\varepsilon _z}$$
(6)

In the formula: σz is the axial principal stress; εz is the axial strain.

Because the confining pressure acts on the circumferential direction of the specimen, and the circumferential strain εx, y shows expansion (tensile deformation), the direction of the actual work done by the confining pressure on the specimen in this process is opposite to the direction of deformation, so U3 is negative, representing the release of energy from the rock, as shown in Formula (7):

$${U_3}=2\int_{0}^{{{\varepsilon _3}}} {{\sigma _{x,y}}} d{\varepsilon _{x,y}}$$
(7)

In the formula: σx, y is the lateral principal stress; εx, y is the lateral strain.

The elastic strain energy U0 stored in the initial hydrostatic pressure σ30 is the energy stored in the rock due to elastic compression when the hydrostatic pressure is applied at the initial stage of the test (that is, the confining pressure σ30 is equal in all directions), as shown in Formula (8):

$${U_0}=\frac{{3(1 - 2v)}}{{2E}}{\left(\sigma _{3}^{0}\right)^2}$$
(8)

In the formula: E is the elastic modulus; v is Poisson’s ratio; σ30 is the confining pressure equal to each direction.

The elastic strain energy formula is Formula (9):

$${U_e}=\frac{1}{2}\left({\sigma _z}{\varepsilon _z}+{\sigma _x}{\varepsilon _x}+{\sigma _y}{\varepsilon _y}\right)$$
(9)

The elastic strain energy Ue is the energy that the rock can recover after unloading, and its calculation needs to be based on the generalized Hooke’s law. For conventional triaxial conditions (σx = σy), the relationship between principal strain and principal stress is Formula (10):

$$\left\{ \begin{array}{l} {\varepsilon _z}=\frac{1}{E}\left[{\sigma _z} - v\left({\sigma _x}+{\sigma _y}\right)\right] \hfill \\ {\varepsilon _x}=\frac{1}{E}\left[{\sigma _x} - v\left({\sigma _z}+{\sigma _y}\right)\right] \hfill \\ {\varepsilon _y}=\frac{1}{E}\left[{\sigma _y} - v\left({\sigma _z}+{\sigma _x}\right)\right] \hfill \\ \end{array} \right.$$
(10)

The above strain expression is substituted into the elastic strain energy formula, and combined with the symmetry condition of σz = σy, the Formula (11) is obtained after expansion and simplification:

$${U_e}=\frac{1}{{2E}}\left[\sigma _{z}^{2}+2\sigma _{y}^{2} - 2v\left(2{\sigma _z}{\sigma _y}+\sigma _{y}^{2}\right)\right]$$
(11)

Dissipative energy Ud represents the energy consumed by internal damage (such as microcrack propagation) and plastic deformation of rock, and its value is determined by the difference between total strain energy and elastic strain energy (Formula 12):

$${U_d}=U - {U_e}={U_1}+{U_3}+{U_0} - {U_e}$$
(12)

Energy evolution characteristics

From an energy perspective, the deformation and failure of rock under loading involves energy input, elastic energy accumulation, energy dissipation, and energy release. These processes drive internal damage accumulation until macroscopic instability occurs39. Figure 7 illustrates the relationship between stress, energy, and strain for sandstone specimens at moisture contents of 0%, 0.52%, 2.56%, 5.01%, and 7.33%. The energy evolution curves exhibit distinct characteristics corresponding to different stress-strain stages: compaction, elastic deformation, stable crack propagation, and post-peak failure40,41. During the compaction and elastic stages, the absorbed energy is predominantly stored as elastic strain energy, with minimal dissipation. The elastic energy curve closely aligns with the total energy curve, while the dissipated energy curve remains low and stable. As the specimen transitions into the stable crack propagation stage, the growth rate of elastic energy decelerates, whereas dissipated energy increases sharply, reflecting a redistribution of energy toward plastic deformation and crack extension. In the post-peak failure stage, elastic energy drops abruptly due to brittle stress release, and the stored elastic energy is rapidly converted into dissipated energy, primarily consumed by shear deformation along slip surfaces and crack propagation42,43.

The transition point from the linear elastic stage to the stable crack propagation stage can be qualitatively identified as a damage initiation threshold, characterized by a noticeable increase in the slope of the dissipated energy (Ud) curve and a concomitant decrease in the growth rate of elastic energy (Ue), indicating the onset of significant microcracking. Similarly, the peak stress point often signifies a critical damage state where crack coalescence accelerates.

Fig. 7
figure 7

Relationship curves of stress, energy and strain (σz = 20 MPa, σx = σy = 15 MPa).

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Figure 8 presents the total energy versus strain curves under varying moisture contents. As moisture content increases, the rate of total energy absorption per unit strain decreases. However, the absolute cumulative energy rises, attributed to water-induced softening effects (reduced elastic modulus), enhanced ductility (larger failure strains), and delayed failure mechanisms mediated by pore water pressure. These phenomena highlight the dual role of water in suppressing energy storage efficiency while promoting energy accumulation through prolonged deformation.

Fig. 8
figure 8

Relationship curve between total energy (U) and strain (σz = 20 MPa, σx = σy = 15 MPa).

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The evolution of dissipated energy with strain is shown in Fig. 9. In the early stages (compaction/elastic), dissipated energy remains low but is comparatively higher in drier specimens, indicating greater frictional losses. During stable crack propagation, dissipated energy surges, with the fastest growth observed in dry specimens. Higher moisture content suppresses crack-driven dissipation due to pore water lubrication, which reduces intergranular friction. Post-failure, dissipated energy continues to rise as residual elastic energy is released, particularly in dry specimens, where crack propagation dominates energy consumption.

Fig. 9
figure 9

The relationship curve between dissipated energy (Ud) and strain (σz = 20 MPa, σx = σy = 15 MPa).

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Figure 10 depicts the relationship between elastic strain energy and strain. In the early stages, elastic energy accumulates rapidly, with drier specimens exhibiting higher storage rates. As microcracks initiate during stable propagation, elastic energy growth slows. Post-failure, the release rate of elastic energy decreases with higher moisture content, a consequence of pore water buffering effects that delay stress concentration at crack tips. This behavior is further influenced by water-induced ductility transitions, which shift failure modes from brittle to progressive, requiring phased energy dissipation. Additionally, water molecule adsorption reduces intergranular cohesion, enhancing plastic slip and viscous resistance, thereby converting elastic energy into thermal dissipation. The combined effects of reduced elastic modulus and increased ductility under high moisture conditions collectively weaken energy storage density and slow energy release rates, underscoring the complex interplay between water–rock interactions and energy evolution mechanisms.

Fig. 10
figure 10

Elastic strain energy (Ue) versus strain under varying moisture contents (σz = 20 MPa, σx = σy = 15 MPa).

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The values of total energy, dissipated energy, and elastic stored energy at the peak strength are summarized in Table 2. It can be analyzed that with the increase of water content w, all three show different degrees of decrease. When w increases from 0 to 5.01%, a further comparison of energy conversion efficiency reveals that the increase in water content significantly reduces the elastic energy storage efficiency. Defining the energy storage efficiency as Ue /U, it can be seen that when w increases from 0 to 7.33%, the energy storage efficiency decreases from 79.72 to 28.61%. Especially near the critical point of w = 5.01%, the decreasing gradient of energy storage efficiency sharply drops from 9.47 to 1.58%/%, which is consistent with the inflection point of strength attenuation described earlier. This indicates that under the critical water content, a pore water film is formed, which promotes the conversion of energy to dissipation and weakens the energy storage capacity of the rock.

Table 2 The energy statistics corresponding to the peak intensity.
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Hydro-mechanical damage evolution of sandstone based on the dissipated energy principle

Rock damage induced by water

The water content exerts a significantly detrimental influence on the physical and mechanical properties of rock masses. Water molecules penetrate the rock matrix, weakening the cementation bonds between mineral grains. This degradation process consequently reduces the overall mechanical performance of the rock mass, manifested as a decrease in its elastic modulus. To quantitatively characterize the weakening effect of water content on the mechanical properties, the variation in elastic modulus observed under different saturation levels is employed to represent the damage phenomenon induced by water exposure44. Assuming the rock experiences zero damage at 0% water content (oven-dried state), The water-induced damage variable DW is defined based on the reduction in elastic modulus, which holistically captures the combined effects of physical (e.g., pore water lubrication, reduced effective stress) and chemical (e.g., mineral bond weakening) mechanisms induced by water–rock interaction. This integrated approach provides a practical measure for short-term damage characterization under the tested conditions, though it does not explicitly separate the underlying mechanisms, expressed as Formula (13):

$${D_W}=1 - \frac{{{E_W}}}{{{E_0}}}$$
(13)

where DW is the water-induced damage variable at moisture content w; E0 is the elastic modulus of the dry rock (0% moisture content), representing the undamaged elastic modulus; EW is the elastic modulus of the rock at moisture content w, reflecting the degraded elastic modulus due to water–rock interactions. This definition is rational because elastic modulus is a key parameter characterizing the rock’s ability to resist deformation, and its reduction directly indicates the degree of damage caused by water.

Rock damage induced by mechanical loading

The failure mechanism of a rock mass subjected to triaxial stress fundamentally represents a process of energy transformation. During loading, the energy input from external forces is converted into two primary components: elastic strain energy stored within the rock matrix itself, and dissipated energy consumed by irreversible deformation and damage evolution. Consistent with the framework established in references18,45,46,47,48,49,50,51,52,53,54,55,56,57, the mechanical damage variable DM can be defined as the ratio of cumulative dissipated energy to the total dissipated energy required to attain complete failure, as Formula (14):

$${D_M}=\left( {1 - \frac{{{\sigma _{1s}}}}{{{\sigma _{1c}}}}} \right)\frac{{{U_d}\left( t \right)}}{{U}_{d{\max }}}$$
(14)

where DM is the mechanically induced damage variable; Ud(t) is the cumulative dissipated energy from loading start to time t, reflecting the cumulative damage caused by mechanical loading; Udmax is the total dissipated energy when the rock reaches complete failure (residual strength σ1s), representing the maximum damage potential of the rock under mechanical loading.  

Based on this damage variable definition, the constitutive equation describing the stress–strain relationship of the damaged rock mass is derived the Formula (15):

$${\sigma _1}=2\mu {\sigma _3}+\left( {1 - {D_M}} \right)E{\varepsilon _1}=2\mu {\sigma _3}+\left[ {1 - \left( {1 - \frac{{{\sigma _{1s}}}}{{{\sigma _{1c}}}}} \right)\frac{{{U_d}\left( t \right)}}{{{U}_{d{\max }}}}} \right]E{\varepsilon _1}$$
(15)

This equation links mechanical damage to the stress–strain relationship, where (1 − DM) represents the effective elastic modulus ratio after mechanical damage, and E is the elastic modulus of the undamaged rock (or degraded elastic modulus considering water effect).

Hydro-mechanical coupled damage constitutive model

To analyze the combined influence of water content and triaxial stress on rock damage, the relationship between elastic modulus and water content is established. Utilizing the water-induced damage variable DW defined in Formula (13), the elastic modulus EW at any given water content w can be expressed as Formula (16):

$$E={E_W}=\left( {1 - {D_W}} \right){E_0}$$
(16)

Substituting the expression for EW (Formula 16) into the mechanical damage constitutive equation (Formula 15) yields the hydro-mechanical coupled damage constitutive model, formulated on the dissipated energy principle:

$${\sigma _1}=2\mu {\sigma _3}+\left( {1 - {D_M}} \right)\left( {1 - {D_W}} \right){E_0}{\varepsilon _1}$$
(17)

Finally, the total damage variable D, characterizing the synergistic effect of both water and mechanical damage on the rock mass under varying saturation conditions, is defined as Formula (18):

$$D=\left( {1 - {D_M}} \right)\left( {1 - {D_W}} \right)$$
(18)

The total damage variable D, characterizing the synergistic effect of both water-induced and mechanical damage, is defined based on the series model assumption and the principle of strain equivalence in continuum damage mechanics40. This leads to a multiplicative coupling form: D = (1 − DM)(1 − DW). This formulation implies that the effective load-bearing area of the rock is successively reduced by the water damage factor (1 − DW) and the mechanical damage factor (1 − DM). The nonlinear nature of this coupling captures the interaction between the two damage mechanisms: pre-existing water damage facilitates the progression of mechanical damage, and vice versa. This represents a fundamental departure from simple additive models and is central to the model’s novelty.

The proposed model introduces a unique coupling mechanism that moves beyond simple superposition. It captures the synergistic effect of water–rock interaction and mechanical loading through an energy dissipation framework. Water-induced damage (DW) priorly degrades the elastic modulus, which in turn alters the energy dissipation path during mechanical loading, leading to an accelerated evolution of mechanical damage (DM). This “water-induced stiffness attenuation → altered energy dissipation path → affected mechanical damage evolution” chain embodies the model’s novelty. The effectiveness of this coupling is quantified by the high agreement (R2 > 0.96) between theoretical predictions and experimental data across varying moisture contents.

Model validation

As illustrated in Fig. 11, The theoretical curves show excellent agreement with the experimental data across different confining pressures during the pre-peak stage. Furthermore, quantitative analysis confirms the good fitting quality between the experimental and theoretical stresses, with all R2 values exceeding 0.96. With increasing stress, the axial strain exhibits a linear progression under all confining pressure conditions. Notably, the peak stresses and corresponding peak strains predicted by the theoretical model align closely with the values obtained from experimental measurements.

Fig. 11
figure 11

Actual and theoretical stress–strain curves (σz = 20 MPa, σx = σy = 15 MPa).

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This model reveals the water-mechanical synergistic damage mechanism by coupling water-induced damage DW (physicochemical weakening) and mechanical damage DM (energy characterization of crack evolution). As shown in Fig. 11, the theoretical curve of the specimen with w = 5.01% exhibits an inflection feature in the plastic strengthening stage, which is consistent with the phenomenon of decreased strain hardening rate in the experimental data. This phenomenon arises from the sharp increase in DW under the critical water content, leading to the accelerated propagation of microcracks (nonlinear growth of DM), which verifies the physical rationality of the coupled damage variables in Formula (18).

The model demonstrates strong predictive capability up to and including the peak strength. In the post-peak stage, the theoretical curves qualitatively replicate the rapid stress degradation and the overall descending trend observed in the experiments, reflecting the brittle failure characteristics. The quantitative discrepancies in this phase are anticipated, as the current constitutive formulation primarily characterizes the progressive damage accumulation leading to peak strength and the onset of failure, rather than the complex microcrack coalescence and localization processes that dominate the post-peak response.

Examining the complete stress–strain evolution—encompassing the initial compaction, linear elastic deformation, yield phase, and ultimate brittle failure—reveals that the proposed hydro-mechanical damage constitutive model effectively replicates the characteristic behavioral stages observed experimentally. The strong correspondence between the theoretical predictions and the experimental results across these distinct deformation phases underscores the model’s sound theoretical rationale and practical feasibility for characterizing the complex damage evolution in rock masses under coupled hydro-mechanical loading.

Conclusion

This study takes sandstone from the deep roadway in the Yingping Section of the Wengfu Phosphate Mine, Guizhou Province, as the research object. To address the issue of surrounding rock instability in water-rich strata, standard sandstone specimens with different moisture contents (0%, 0.52%, 2.56%, 5.01%, 7.33%) were prepared using NaCl solution (pH = 6.5) simulating groundwater. Triaxial compression tests (σz = 20 MPa, σx = σy = 15 MPa) were conducted to systematically analyze the effects of moisture content on the mechanical parameters, stress–strain curves, and energy evolution characteristics of sandstone. A hydro-mechanical coupling damage constitutive model integrating water-induced damage and mechanical damage was constructed based on the principle of energy dissipation, and the rationality of the model was verified by comparing theoretical curves with experimental data. The main conclusions are as follows:

  1. 1.

    Moisture content exerts a significant and nonlinear weakening effect on the mechanical parameters of sandstone. A critical moisture content of 5.01% was identified, demarcating two distinct attenuation stages. Below this threshold, the degradation rates for peak strength and elastic modulus were more pronounced (8.32 MPa/% and 4.33 GPa/%, respectively). Above it, the rates decreased (5.18 MPa/% and 1.51 GPa/%). Poisson’s ratio exhibited an S-shaped increase, rising from 0.18 (dry) to 0.33 (saturated). These trends are attributed to multi-scale mechanisms, including pore water lubrication, reduction in effective confining pressure, and weakening of intergranular bonding.

  2. 2.

    The characteristics of energy evolution are profoundly regulated by moisture content. Specimens with higher moisture content, due to enhanced ductility, accumulated more total energy through prolonged deformation processes. However, the storage efficiency of elastic strain energy was significantly reduced, and the growth of dissipated energy was inhibited, primarily due to the lubricating effect of pore water which reduces intergranular friction. In contrast, dry specimens exhibited high elastic energy storage efficiency and a sharp surge in dissipated energy upon failure.

  3. 3.

    A hydro-mechanical coupled damage constitutive model was developed based on the dissipated energy principle and the series model assumption in damage mechanics. The model nonlinearly couples the effects of water-induced damage (DW), and mechanical damage (DM) through the effective integrity factor D = (1 − DM )(1 − DW), the model demonstrated strong agreement with experimental stress–strain data in the pre-peak and peak stages (R2 > 0.96), which captures their synergistic interaction. The model demonstrated strong agreement with experimental stress–strain data in the pre-peak and peak stages (R2 > 0.96), effectively characterizing the damage evolution and providing theoretical support for stability control in deep water-rich roadways. The model successfully captures the qualitative post-peak descending trend, while its formulation prioritizes accurate prediction of the pre-failure behavior.

This study acknowledges certain limitations. The model validation was performed under a specific stress state, and its applicability across a broader range of in-situ stress conditions requires further verification. The definition of DW represents a holistic measure of water-induced weakening without distinguishing between physical and chemical mechanisms, which is adequate for short-term response but may be less accurate for long-term chemical corrosion scenarios. Furthermore, the model’s predictive accuracy in the post-peak stage, while capturing the qualitative failure trend, can be improved. Future research should include tests under varied stress paths, aim to decouple physicochemical damage mechanisms, and explore more sophisticated damage evolution laws or coupling forms to enhance the model’s comprehensiveness and accuracy, particularly for post-failure behavior and long-term predictions.