Limestone samples were collected from the 1700 m bench on the southern slope of an open-pit mine in Yunnan Province for testing. To minimize variability in the test results due to sample heterogeneity, all samples were extracted from the same location. The limestone blocks were processed into cylindrical specimens with dimensions of 50 mm in diameter and 100 mm in height in accordance with the International Society for Rock Mechanics (ISRM) standards for rock sample preparation. The ends of the cylinders were carefully polished to ensure that the non-parallelism and non-perpendicularity errors were controlled within ±0.02 mm. The samples exhibited a grayish-yellow appearance, a hard texture, high uniformity, and a low degree of weathering.

To ensure the homogeneity of rock samples, a two-step screening process was implemented prior to conducting the experiment.

(1) The dimensions and mass of the processed, dry rock samples were measured, and the initial density was calculated to be 2.737 g/cm³.

After wave velocity screening, samples containing visible joints were eliminated through visual inspection. The selected specimens met the accuracy requirements of rock mechanics testing standards. The processes for producing and screening standard rock cores are illustrated in Figures 1, 2. The 25 rock samples that met the selection criteria were divided into five equal groups (n = 5) and prepared with different w according to five gradient levels: 0%, 25%, 50%, 75%, and 100%. For each water gradient, two samples were designated for UC tests, while the remaining three samples were subjected to uniaxial CLU tests.

The preparation process for limestone samples with different w involved the following steps.

(1) The selected 25 rock samples were placed in an oven at a temperature of 105 C and dried for 24 h (Cao et al., 2024). The mass of each sample was measured consecutively twice. If the measured mass remained unchanged, the sample was deemed fully dried, and its dry mass was recorded.

To facilitate identification, the rock samples were labeled using a marker pen. The first letters indicate the test type: D for UC test and X for CLU test. The second number represents the water saturation, and the third number refer to the number of blocks.

To investigate the M.P. and energy evolution laws of limestone with different w, UC and uniaxial CLU tests were conducted using the RMT 150C digital control electro-hydraulic servo testing machine, as illustrated in Figure 3.

The UC tests employed a staged incremental CLU scheme. Initially, the sample was loaded from 0 MPa to 5 MPa and then unloaded to a stable level of 1.5 MPa. Subsequently, the peak load was incrementally increased by 5 MPa for each stage (10 MPa, 15 MPa, 20 MPa, etc.). The stress was decreased to the baseline value of 1.5 MPa during each unloading stage. The stress path followed a cyclic progression: 0 MPa → 5 MPa → 1.5 MPa → 10 MPa → 1.5 MPa → 15 MPa → 1.5 MPa → 20 MPa, and continued until the sample experienced macroscopic failure. The stress path is shown in Figure 4. The loading system operated under a constant rate of 0.002 mm/s throughout this process.

The rock samples were divided into five groups based on varying saturation levels: 0%, 25%, 50%, 75%, and 100%. Each group contains three samples, resulting in a total of 15 samples. To accurately assess the M.P. and energy evolution characteristics of limestone with different w under CLU conditions, it was essential to carefully control the N. Therefore, a series of UC tests were firstly performed. During these tests, the axial stress-strain data of the limestone samples were continuously monitored. The loading amplitude for the CLU tests was determined based on the results of the UC tests. The key parameters of the samples derived from the UC tests are summarized in Table 1.

This study examined five groups of typical water-bearing limestone with water saturation of 0%, 25%, 50%, 75%, and 100% to analyze the axial stress-strain curves under both UC and CLU conditions, as shown in Figure 5.

As depicted in Figure 5a, the axial stress of limestone increased with increasing axial strain during UC process. Upon reaching the peak stress, a decline in stress was observed as axial strain continues to increased. Notably, this stress drop was more pronounced at lower w. As the w increased, the limestone gradually transitioned to exhibit brittle-ductile characteristics. Figure 5b illustrated that limestone, as an anisotropic material, contains numerous inherent structures. The deformation of limestone samples during the CLU processes includes both elastic and plastic deformation, which is evidenced by the incomplete overlap of loading and unloading curves that creates a distinct hysteresis loop. As irreversible plastic deformation accumulated, the hysteresis loop progressively moved toward the direction of increasing strain. A higher w led to a more noticeable rightward movement of the hysteresis loop.

At lower w, the hysteresis loop appeared relatively sparse at the onset of loading. As loading progressed, the original pores within the limestone were gradually compacted, resulting in a denser hysteresis loop. Conversely, when the w reached 50%, the shape of the hysteresis loop began to reverse, and the hysteresis loop gradually became sparse as CLU continued. The irreversible plastic deformation in the sample gradually increased. Consistent with the behavior observed under UC, limestone specimens subjected to CLU exhibited pronounced ductility characteristics when w was higher than 50%, which were more significant than those observed under UC.

Various materials, including rocks and metals possess, can store information about external influences and display this information through specific physical quantities under certain conditions. This property is called the memory effect (Zhong et al., 2024; Huang et al., 2024; Tian et al., 2023). The memory effect of rocks is of great significance for geological engineering, geostress measurement, and rock stability analysis. The DRA method (Miao et al., 2024; Zhao et al., 2024) has been frequently employed to analyze rock deformation data during CLU processes to obtain memory information of rocks.

The principle of the DRA method is illustrated in Figure 10, where the solid lines i and j denote two successive repeated loading cycles. The strain difference function is defined as in Equation 3: Δ ε i , j σ = ε j σ − ε i σ j > i (3) where ε j σ and ε j σ are the axial strains corresponding to the same axial stress for two adjacent loading curves, as shown in Figure 10a. Assuming that the confining pressure and volumetric strain are positive, the difference in axial irreversible strain Δ ε i , j σ can be derived from Equation 1. The strain difference curve, also known as the DRA curve, is constructed with stress σ on the horizontal axis and strain difference Δ ε i , j σ on the vertical axis, as depicted in Figure 10b. The curve exhibits a distinct inflection point, where the corresponding stress σ D R A represents the memory information σ P . This inflection point is referred to as the DRA inflection point.

To clarify whether the w affects the memory characteristics of limestone and to provide a theoretical basis for rock stability analysis, this study analyzed the loading curves from the fourth and fifth cycles of five types of limestone with different w using the DRA method. The strain differences of limestone with identical w were averaged, and the corresponding DRA curves are presented in Figure 11.

The DRA curves illustrated that the evolution trends for limestone samples with different w remain consistent, with DRA inflection points appearing at approximately the same axial stress levels. This observation reflected a pronounced rock deformation memory effect. Therefore, it can be concluded that while hydration changes macroscopic mechanical parameters, it does not significantly interfere with the memory storage effect related to the internal stress history of the rock.

Figure 12 shows the CLU curves during the mth and (m+1)-th cycles. PQP represents the hysteresis loop formed by adjacent loading cycles, which indirectly reflects the damage process of the rock sample. The area enclosed by ORMO represents the energy input into the rock sample during the mth cycle, while the area enclosed by RMNAQ represents the stored elastic energy during the mth cycle.

During the CLU process, various energy-related parameters can be calculated according to Equations 4–7 (Wang et al., 2025; Sun et al., 2025). U m = ∫ ε 0 ε R σ m + d ε m (4) U e m = ∫ ε Q ε R σ m + − σ m − d ε m (5) U d m = U m − U e m (6) γ = U dm U m (7) where U m , U e m , and U d m are the input energy density from external loads on the rock (MJ/m³), the elastic energy density stored in the rock sample (MJ/m³), and the dissipated energy density (MJ/m³) during the mth cycle, respectively; γ represents the proportion of dissipated energy, which reflects the energy conversion relationship in limestone with different w during compression.

The values of U m , U e m , and U d m for limestone samples with different w during each loading-unloading stage were calculated based on the stress-strain data. The relationship curves between energy density, energy proportion, and N are illustrated in Figure 13.

As illustrated in Figure 13, the energy evolution of limestone with different w during CLU processes was analyzed and compared with the axial strain versus N curve presented in Figure 9a. It was found that the U _m gradually increased with the N, while the U _em first increased and then decreased. The U _dm first remained stable and then suddenly increased.

The energy evolution trends for limestone samples with different w remained consistent. During the initial stage of loading, a significant portion of energy was first converted into dissipated energy, with the dissipated energy reaching a maximum proportion of 85%. This is primarily attributed to the presence of initial cracks and pores within the limestone. As a result, the energy input during the initial loading stage was dissipated in the form of micro-cracking and closure of pores. This phenomenon was manifested as a sharp increase in axial deformation, which corroborates the observation of a large axial strain during the first loading in Figure 9a.

As the N increased, both the U _m from the testing machine and the U _em stored in the sample increased in an orderly manner. At this point, the rock sample remained in the elastic stage, and the dissipated energy in this stage remained basically unchanged. However, as the CLU load reached the peak strength, cracks initiated and irregularly propagated due to the applied load exceeding the ultimate compressive strength of the rock sample. This results in a rapid decrease in U _em and a corresponding surge in U _dm , as a substantial amount of input energy was dissipated through the irregular crack propagation. The proportion of dissipated energy revealed a marked increase in the later CLU stage.

The differences in energy evolution of limestone with different w were comparatively studied. The integral value of the loading curve within the strain range was employed to characterize the energy input by the testing machine. It was observed that during the CLU process, lower w correlates with reduced plastic damage in rock samples for the same N, as well as reduced U _m . As the rock progressed toward failure, the cumulative integral area also decreased accordingly. As the w increased, the plastic deformation of the rock increased from the initial loading stage to rock failure. The U _m and U _dm increased significantly for the same N, while the U _em gradually decreased.

The failure processes of limestone samples with varying w derived from an energy perspective align with the conclusions drawn from the axial strain versus N curve in Figure 9a. This highlights that initial cracks and pores fundamentally contributes to the susceptibility of limestone to damage when exposed to water.

Assuming that there is no heat exchange between the sample and the environment during UC, the energy relationship based on Equation 6 remains valid for limestone with different w, according to the first law of thermodynamics. The relationship between U _em and U _dm is illustrated in Figure 14.

The total energy density and U _em resulting from external loads during the compression of limestones with different w can be expressed by Equations 8 and 9 (Luo et al., 2025): W = ∫ 0 ε 1 σ 1 d ε 1 + ∫ 0 ε 2 σ 2 d ε 2 + ∫ 0 ε 3 σ 3 d ε 3 (8) W e = 1 2 σ 1 ε 1 e + 1 2 σ 2 ε 2 e + 1 2 σ 3 ε 3 e (9)

By incorporating Hooke’s Law, Equation 9 can be further formulated as Equation 10: W e = σ 1 2 + 2 σ 3 2 − 2 μ ¯ × 2 σ 1 σ 3 + σ 3 2 2 E i (10) where W represents the input energy density from uniaxial loading on the rock (MJ/m³); W e denotes the elastic energy density stored in the rock (MJ/m³); E i indicates the elastic modulus of the unloading curve (GPa), and μ represents the Poisson’s ratio.

In the case of limestones with different w under UC conditions, where they are subjected solely to axial loads with zone confining pressure ( σ 2 = σ 3 = 0 ), Equation 8 can be simplified to Equation 11. Furthermore, for computational convenience, the initial elastic modulus E 0 is substituted for the elastic modulus E i of the unloading curve; therefore, Equation 10 can be represented as Equation 12. The damage dissipation energy density under UC conditions is determined using Equation 6. W = ∫ 0 ε 1 σ 1 d ε 1 (11) W e = 1 2 σ 1 2 E 0 (12)

The values of W , W e , W d , and their proportions for limestones with varying w under UC conditions were computed using Equations 6, 7, 11 and 12. The relationship curves between these parameters and axial strain ε 1 are presented in Figure 15.

Figure 15 revealed that under UC conditions, W , W e , and W d gradually decrease as the w of the limestone increases.

Furthermore, the evolution trends of various energy densities under UC conditions were consistent with those under CLU conditions. In the early loading stage, the closure of initial cracks and pores in limestone consumed the majority of the energy. During the intermediate loading stage, the rock sample exhibited primarily elastic deformation behavior, and the input energy was predominantly converted into elastic potential energy and stored within the rock. The energy dissipation process was relatively smooth. As the density of stored elastic energy gradually increased, its proportion rose, while the proportion of dissipated energy decreased. In the later loading stage, when the applied load surpassed the rock’s peak strength, a significant amount of stored energy was dissipated due to crack initiation and unstable growth, resulting in rock failure. At this stage, the proportion of dissipated energy reached its maximum.

A comparative analysis of the energy evolution process of limestone under UC and CLU conditions revealed that, for the same w, the total energy density input, stored elastic energy, and dissipated energy of the rock during CLU were higher than those during UC. This finding indirectly reflected that CLU exert additional pressure on the rock, thereby facilitating increased energy absorption and storage prior to rock failure. This observation aligns with conclusions drawn from the analyses of the stress-strain curves.

The damage evolution of limestone with different w is essentially a dynamic process characterized by the continuous expansion of internal micro-defects and energy dissipation. To quantitatively characterize the damage development in water-bearing limestone during the failure process, this study constructed a damage variable calculation formula for the compression process of water-saturated limestone. This is based on the strain evolution characteristics and energy conversion data obtained from CLU processes outlined in Sections 3 and 4. The formula is grounded in the principle of damage equivalence and references the definition of damage by Yang and Xu, (2025), as shown in Equations 13 and 14. The cumulative damage degree was quantitatively characterized through numerical calculation. D z ε = ∑ 1 m ε 1 p m ∑ 1 n ε 1 p m (13) D z w = ∑ 1 m W d m ∑ 1 n W d m (14) where D z ε represents the cumulative damage parameter based on axial strain; D z w denotes the cumulative damage parameter based on dissipated energy density; ε 1 p m indicates the plastic strain during the mth cycle; and W d m represents the damage dissipated energy during the mth cycle.

Figure 16a,b show the relationship curves between the damage variables and the N based on axial plastic strain and dissipated energy density, respectively. A comprehensive analysis indicated that the cumulative damage of limestone with different w increases with increasing N.

Figure 16a revealed that the relationship curve between the damage variable based on axial plastic strain and the N can be divided into four distinct stages. In the initial stage (the first cycle, from 0 to 1), there was a significant surge in cumulative damage. During the mid-cycle stage, as w decreased from high to low (corresponding cycle ranges: 1–12, 1–10, 1–8, 1-5, and 1–4), cumulative damage increased steadily. In the late cycle stage (12–13, 10–12, 8–9, 5-7, and 4–6), the rate of cumulative damage acceleration increased. In the final stage (12–14, 12–13, 9–10, 7-8, and 6–7), the cumulative damage parameter rose sharply.

Figure 16b indicates the relationship curve between the damage variable and the N based on damage dissipation energy density. It was observed that the cumulative damage increases with increasing N. When the w exceeded 0.8%, the growth rate of damage in limestone accelerated. For the same N, limestone with higher w exhibited greater damage compared to that with lower w.

Overall, limestone with higher w consistently failed earlier than that with lower w under both UC and CLU conditions. This finding underscores the significant impact of water on the mechanical behavior of limestone under load.