Rate-Dependent Fracturing Mechanisms of Granite Under Different Levels of Initial Damage

Abstract

Excavation of underground spaces often causes significant initial damage to surrounding rock, which can notably alter its mechanical properties. However, most studies on loading rate effects neglect the role of initial damage. This study investigates how initial damage and loading rate together affect granite’s mechanical behavior and fracturing characteristics. Granite specimens with different initial damage levels were subjected to uniaxial compression at varying loading rates to assess their mechanical parameters, stress thresholds, failure modes, energy evolution, and associated acoustic emission (AE) activity. Results indicate that granite’s mechanical behavior exhibits greater sensitivity to loading rate than to initial damage. As the loading rate increases, both strength and elastic modulus initially decrease and then rise, while the dissipated-to-input energy ratio reaches a maximum when the strength is at its lowest. This phenomenon occurs because, when cracks are allowed to fully develop, a relatively higher loading rate increases the likelihood of crack initiation and propagation, thereby reducing strength. The AE responses of initial damage granite samples (IDGSs), including counts, RA/AF value, b-value, and entropy, exhibit stage-dependent variations and contain precursory information before failure. Moreover, AE signals display multifractal characteristics across different loading rates. These findings reveal the mechanisms underlying granite’s mechanical response when both initial damage and loading rate act together: initial damage primarily affects the complexity and number of local microcracks, while loading rate determines the dominant crack initiation and propagation modes. Moreover, how the failure time of IDGSs varies with loading rate can be described by an inverse exponential function. These findings enhance insight into the coupling mechanism of initial damage and loading rate, with significant implications for failure warning and the cost-effectiveness of underground excavation.

1. Introduction

Granite, a highly intact and low-thermal-conductivity crystalline rock [1], is widely encountered in underground engineering projects [2]. The construction of underground spaces induces stress redistribution within the surrounding rock mass, often resulting in varying degrees of initial damage [3,4,5,6,7]. Such initial damage may include microcracks formed by tectonic stress activity [8] as well as disturbance-induced damage caused by excavation [9], drilling [10], and blasting operations [9] (Figure 1). Surrounding rock with initial damage exhibits altered mechanical responses during subsequent excavation, escalating risks of catastrophic failure. In addition, previous studies have shown that the mechanical properties of rock are strongly affected by loading rate [1,11,12,13]. Consequently, it is essential to investigate how loading rate and initial damage level jointly influence granite’s mechanical behavior and failure patterns in order to enhance the safety and cost-efficiency of underground excavation.

Some scholars prepared initial damage materials using different loading methods and investigated their mechanical behavior. Ran et al. [14] performed uniaxial multi-level cyclic tests on coal with different initial damage levels and demonstrated that higher initial damage significantly shortened fatigue life while reducing both strength and deformation modulus. Zhao et al. [15] examined the influence of cyclic impact-induced initial damage on the cyclic loading–unloading strength of sandstones and reported a gradual decrease in strength with increasing damage. Yang et al. [16] conducted uniaxial compression tests on sandstone specimens with initial damage generated under high confining pressure cyclic loading–unloading. Their results indicated that while initial damage did not affect the pore distribution, it modified the fracture mode. Miao et al. [2] examined the influence of initial damage on the uniaxial compressive strength of saturated granite. The findings demonstrated that progressive damage resulted in a degradation of compressive strength and a decrease in axial deformation capacity toward granite failure. Li et al. [17] examined the combined effects of loading rate and initial damage on the energy evolution of sandstone, observing that initial damage slowed the growth of elastic energy and reduced the accumulated elastic energy at failure. Wang et al. [18] applied Split Hopkinson Pressure Bar (SHPB) tests to evaluate the effects of initial damage on dynamic compressive strength and toughness. The results indicated that increasing strain rate intensified the degradation of dynamic strength and toughness as the level of initial damage rose. Huang et al. [19] carried out triaxial multi-level creep tests on coal and observed that both total creep time and failure deviatoric stress decreased with higher levels of initial damage. Hou et al. [5] performed multi-load creep tests on sandstones with varying initial damage levels and proposed a new nonlinear creep–damage model that explicitly accounts for initial damage. Overall, the mechanical response of initial damage samples has been widely examined through a variety of tests, such as creep, fatigue, dynamic, and uniaxial loading. However, the joint effect of initial damage and loading rate has been rarely examined.

Loading rate serves as a key parameter governing the mechanical response of rock materials. Numerous investigations have focused on the rate-dependent behavior of rock materials, considering factors such as lithology [20,21], loading mode (static or dynamic) [22,23], crystal grain size [24], strain energy evolution [25,26], and failure time. Wasantha et al. [13] investigated the coupled effects of strain rate and grain size on the mechanical behavior of sandstone. They observed that sandstones characterized by various grain sizes showed different evolutions in peak stress as the strain rate increased. The authors argued that mineral grain size should be considered an essential parameter when evaluating rock behavior under different loading rates. Yan et al. [27] performed dynamic impact tests on multi-flawed sandstones with different geometries using a Split Hopkinson Pressure Bar (SHPB). It was shown that dynamic strength was notably governed by the combined influence of strain rate and flaw geometry. In addition, a dynamic damage constitutive formulation was established to capture the strength and deformation behavior of rocks containing flaws. Through uniaxial compression tests on granite, Gong et al. [28] revealed the evolution of elastic strain energy under different loading rates and, by employing criteria involving residual elastic energy and related indices, further assessed the rockburst proneness of granite. Liu et al. [29] examined the loading-rate dependence of the dynamic fracture toughness of granite using notched semi-circle bend and short-core-in-compression specimens. It was found that the expansion in the proportion of mesoscopic fracture morphology resulting from shear loading predominantly accounted for the enhancement of dynamic fracture toughness with increasing loading rate. Under quasi-static conditions, Lu et al. [30] reported that both compressive strength and elastic modulus of composite coal–rock specimens increased with loading rate, while mechanical responses became less sensitive to heterogeneity. Shao et al. [12] used time-lapse X-ray computed tomography to study the effects of loading rate on the mechanical properties and fracture activity of shale. The study indicated that variations in loading rate markedly impacted mechanical responses and failure time, whereas the progression of cracking and the associated failure patterns were predominantly determined by pore configuration and pyrite spatial distribution. However, previous research on rate dependence in rock mechanical behavior and mechanisms has primarily focused on intact samples and prefabricated macro-crack samples. Hence, the current findings are insufficient to reflect the rate-dependent mechanical response of damaged surrounding rock.

Stress thresholds, as critical mechanical parameters characterizing crack activity, are essential for understanding the mechanisms of rock failure. Although extensive studies have addressed the rate dependence of rock stress thresholds [31,32,33,34,35], the influence of initial damage has rarely been considered. In parallel, acoustic emission (AE) has proven to be a powerful non-destructive technique for monitoring internal crack evolution and identifying precursors to rock failure [36,37]. Several studies have applied AE monitoring to initialdamage rock subjected to uniaxial compression or cyclic loading–unloading tests [14,17,38,39,40,41]. Nevertheless, existing studies have conducted limited systematic analyses of AE parameters and offer minimal understanding of how loading rate interacts with initial damage, as indicated by AE analysis.

Recent studies in numerical fracture methods, including the use of cohesive-zone models and phase-field fracture models, have made significant advancements in simulating crack propagation in rocks. However, these studies have primarily focused on intact or pre-existing flaw rock specimens [42,43,44,45], with limited attention given to the influence of initial damage. Additionally, the rate-dependent behavior of rock mechanics and failure mechanisms has been extensively studied [46,47,48], but the coupled effects of loading rate and initial damage have not been sufficiently explored. Therefore, investigating the coupled effect of initial damage and loading rate on rock failure mechanisms is essential.

Catastrophic failures in underground rock engineering are often caused by the interaction between initial damage and loading rate. However, the mechanisms underlying crack propagation and failure in IDGS subjected to varying loading rates are not yet fully understood. Therefore, this study aims to systematically investigate how initial damage and loading rate jointly influence the mechanical behavior of granite. In the present work, initial damage in granite was generated by a single loading–unloading cycle, after which uniaxial compression tests were performed on the IDGS under various loading rates. Through examination of the mechanical properties, stress thresholds, strain energy, and AE characteristics of IDGS, the interaction between initial damage and loading rate was elucidated. Furthermore, an empirical model relating loading rate and failure time of IDGS was established, and the precursor identification capability of AE parameters was compared. This study advances the comprehension of how initial damage and loading rate jointly affect the mechanical behavior of granite, providing a theoretical basis to improve excavation efficiency and facilitate early warning of rock hazards in subterranean projects.

2. Materials and Experimental Methodology

The experimental program comprised specimen preparation and characterization, followed by uniaxial compression tests on IDGSs under different loading rates. The overall experimental workflow is illustrated in Figure 2, while detailed procedures are described in the following subsections of this section.

2.1. Specimen Preparation and Test Apparatus

Fine-grained granite specimens were obtained from intact rock blocks from a mine in Zhangzhou, Fujian, China. Their mineralogical composition was analyzed using X-ray diffraction (XRD) (Figure 3b). Quartz, Na-feldspar, plagioclase, biotite, and amphibole are the primary mineral constituents of the granite. According to the International Society for Rock Mechanics and Rock Engineering (ISRM) standards, cylindrical rock specimens were prepared with a diameter of 50 mm and a height of 100 mm [49]. The granite specimens were extracted using in situ core drilling, followed by cutting with a JRDQ-1T program-controlled automatic rock-cutting machine. Both ends of the specimens were polished using a JKSHM-200 double-end grinder to ensure smoothness and to maintain the parallelism of the upper and lower surfaces within 0.05 mm. Rock strength has been found to correlate closely with P-wave velocity in previous studies. To guarantee reliable experimental results, P-wave speeds of the granite specimens were determined, and only those with values ranging from 4300 to 4600 m/s were chosen for subsequent testing (Figure 3a).

IDGSs were prepared and tested using an MTS815 rock mechanics testing apparatus (Figure 4a) at room temperature to assess their mechanical properties under varying loading rates. The apparatus is capable of applying a maximum axial load of 4600 kN and a confining pressure up to 140 MPa. Axial and circumferential extensometers (Figure 4b) were used to record axial and lateral strains at a data acquisition rate of 10 Hz. Real-time monitoring of crack activity during rock failure was performed with a PCI-2 acoustic emission (AE) system (Figure 4a). The AE system allows continuous recording of both waveform data and AE parameters. AE sensors had a resonance frequency of 2 MHz, a preamplifier gain and trigger threshold set at 40 dB, and a sampling rate of 1 MSPS (Mega Samples Per Second). The sensor arrangement is shown in Figure 4b, with probes positioned at the specimen midsection and connected to the AE system via amplifiers. To ensure effective coupling, Vaseline was applied to the ceramic ends of the sensors, and they were fixed onto the specimen surface using rubber caps.

2.2. Preparation of IDGS

Three fresh granite specimens underwent uniaxial compression under axial displacement control at a loading rate of 0.12 mm/min to induce failure. This experiment aimed to obtain the fundamental mechanical properties of granite.

Table 1. Physical and mechanical properties of fresh granites and IDGSs.

No	v1 (m/s)	Initial Damage Variable (IDV) (%)	Unloading Point Stress of IDV (MPa)	UCS (MPa)	Reloading Peak Strength (MPa)
0.12-S1	4550.00	0	0	195.46	/
0.12-S2	4352.17	0	0	197.05	/
0.12-S3	4356.52	0	0	192.87	/
0.06-IDV1	4559.09	10.43	102.05	/	192.64
0.06-IDV2	4581.82	12.43	134.80	/	196.09
0.06-IDV3	4378.26	14.43	156.10	/	194.84
0.12-IDV1	4382.61	10.35	102.05	/	184.56
0.12-IDV2	4559.09	12.75	134.80	/	194.36
0.12-IDV3	4360.87	14.21	156.10	/	181.02
0.3-IDV1	4563.64	10.38	102.05	/	204.24
0.3-IDV2	4550.00	12.56	134.80	/	205.44
0.3-IDV3	4545.45	14.65	156.10	/	198.98
0.6-IDV1	4369.57	10.96	102.05	/	208.03
0.6-IDV2	4356.52	12.13	134.80	/	213.77
0.6-IDV3	4550.00	14.66	156.10	/	206.11
3-IDV1	4550.00	10.20	102.05	/	219.31
3-IDV2	4347.83	12.12	134.80	/	208.07
3-IDV3	4352.17	14.23	156.10	/	213.95

lists the fundamental parameters obtained from these tests, and the associated stress–strain curves are shown in Figure 5a. The stress–strain behavior of granite typically exhibits four distinct stages, determined by three key stress thresholds: the crack closure stress (σ_cc), the crack initiation stress (σ_ci), and the crack damage stress (σ_cd). These regions correspond to the crack closure stage, the linear elastic stage, the stable crack growth stage, and the unstable crack growth stage, respectively [50,51]. In this study, the σ_cc was determined using the Compression Coefficient Response Method [52], the σ_ci was identified by the Lateral Strain Response Method [53], and the σ_cd was defined as the axial stress corresponding to the inflection point of the axial stress–volumetric strain curve [54]. An example for the 0.12-S1 specimen illustrating the identification of these stress thresholds is shown in Figure 6.

To reproduce the damage state induced by excavation and similar activities, IDGSs were prepared using a single loading–unloading cycle on the MTS815 rock mechanics testing system. Three unloading stress levels were selected for this purpose. Two unloading points were located between the σ_ci and the σ_cd, specifically at σ_ci + 20%(σ_cd − σ_ci) and σ_ci + 80%(σ_cd − σ_ci), which correspond to 52.30% and 69.08% of the peak stress, respectively. An additional unloading point was placed beyond the crack damage threshold at 80% σ_f (Figure 7a). To reduce the influence of pre-existing defects on assessing the initial damage condition, each specimen was first loaded to 30% of its uniaxial compressive strength (UCS) and subsequently unloaded to 0.5 kN, thereby eliminating irreversible damage associated with crack compaction. Subsequently, the specimen reached the designated unloading stress level through controlled loading. After maintaining the stress constant for 10 min, the specimen was gradually brought back to the zero-load state at the same displacement rate. The purpose of the holding stage was to ensure sufficient crack development at the selected stress level. The IDGSs were prepared using a load-controlled loading–unloading procedure, with both loading and unloading rates set to 60 kN/min. The loading path is illustrated in Figure 7b.

The damage variable can quantitatively characterize the internal damage of rocks and provide an indicator for failure prediction [19]. Rock damage is generally described at both macroscopic and microscopic scales. At the microscopic scale, the initial damage variable is generally characterized by the quantity and geometric attributes of microdefects. At the macroscopic scale, mechanical parameters such as P-wave velocity, strain energy [19], and elastic modulus [55] are commonly used to characterize the damage variable. In this study, the initial damage variable (IDV) was defined by the strain energy method proposed by Guo et al. [56], and its calculation is expressed as follows:

$$D_{\mathrm{ini}}={\displaystyle \frac{U_d-U_c}{U_d+U_e-U_c}}$$

(1)

where U_d is the dissipated energy (MJ/m³), U_e is the elastic energy (MJ/m³), and U_c is the plastic energy associated with crack compaction (MJ/m³). A schematic representation of the IDV computation process is presented in Figure 8a.

As shown in Table 1 and Figure 5b, three initial damage states were considered in this study, denoted as IDV1, IDV2, and IDV3, with IDV1 < IDV2 < IDV3. The three initial damage variables are small and closely matched. This indicates that the unloading stress points in the stable crack growth stage and at the onset of the unstable crack growth stage cause only minor damage to the rock. Figure 3a presents the appearance of the three IDGSs, where the damage state cannot be easily distinguished by visual inspection. This suggests that the early development and subsequent growth of internal fractures are beyond visual detection, making early warning impossible. Therefore, investigating the mechanical response and microfracture evolution of granite under different initial damage conditions is essential for timely prediction of potential rock engineering failures.

2.3. Testing Procedure

To examine the mechanical characteristics and failure precursors of IDGSs subjected to various loading rates, uniaxial compression experiments were performed on specimens with three initial damage grades by means of the MTS815 testing apparatus. Axial displacement-controlled experiments were conducted at loading rates of 0.06, 0.12, 0.3, 0.6, and 3 mm/min, equivalent to strain rates of 1 × 10⁻⁵, 2 × 10⁻⁵, 5 × 10⁻⁵, 1 × 10⁻⁴, and 5 × 10⁻⁴ s⁻¹, respectively (Figure 7b). AE signals were captured throughout the experiments using a PCI-2 acoustic emission system. The detailed experimental procedure and steps are summarized in

Table 2. Test scheme and procedure.

No	Loading-Unloading Target I (MPa)	Loading-Unloading Target II (MPa)	Loading-Unloading Rate (kN/min)	Loading Target III	Loading Rate (mm/min)
0.12-S1	/	/	/	Peak	0.12
0.12-S2					0.12
0.12-S3					0.12
0.06-IDV1	58.54	102.05	60	Peak	0.06
0.06-IDV2		134.80			0.06
0.06-IDV3		156.10			0.06
0.12-IDV1		102.05			0.12
0.12-IDV2		134.80			0.12
0.12-IDV3		156.10			0.12
0.3-IDV1		102.05			0.3
0.3-IDV2		134.80			0.3
0.3-IDV3		156.10			0.3
0.6-IDV1		102.05			0.6
0.6-IDV2		134.80			0.6
0.6-IDV3		156.10			0.6
3- IDV1		102.05			3
3- IDV2		134.80			3
3- IDV3		156.10			3

.

3. Test Results

3.1. Mechanical Parameters of Granite Under the Combined Impact of Initial Damage and Loading Rate

3.1.1. Evolution of Stress–Strain Behavior and Peak Strength

The stress–strain curve provides essential data for capturing rock deformation and failure. The complete stress–strain curves for IDGS subjected to varying loading rates are presented in Figure 9a–c. The stress–strain response of all IDGS exhibits four distinct phases: crack closure (I), linear elastic deformation (II), stable crack growth (III), and unstable crack growth (IV). Except for a few specimens, IDGS display similar stress–strain behavior across different loading rates and exhibit brittle mechanical behavior. Before reaching peak strength, axial stress increases approximately linearly with strain. The inclination of the stress–strain curve increases with rising loading rates, and no evident plastic yielding occurs.

In Figure 9d, the influence of loading rate and initial damage on peak strength is presented. Increasing the loading rate decreases the UCS by approximately 4.04% at 0.12 mm/min compared to 0.06 mm/min and increases by about 9.94% relative to the UCS at 0.06 mm/min as the rate rises up to 3 mm/min. Specifically, the UCS corresponding to the three initial damage variables at this loading rate are 184.56 MPa, 194.36 MPa, and 181.02 MPa, respectively. This trend is somewhat different from previous studies in a small range, where UCS was reported to increase consistently with loading rate [11]. In addition, at a constant loading rate, UCS values of IDGSs across varying initial damage levels exhibit minimal differences, with an impact on UCS ranging from −5.12% to +5.31%, suggesting that initial damage exerts only a limited influence on the overall strength of granite.

3.1.2. Stress Threshold and Elastic Modulus

Stress thresholds are characteristic stress values that reflect the internal mechanical state of rock samples and are key parameters for studying mechanical behavior [57]. The variation in stress thresholds (σ_cc, σ_ci, σ_cd) under different loading rates and initial damage conditions is presented in Figure 10a–c. For IDGSs exhibiting an identical damage level, variations in σ_cc, σ_ci, and σ_cd with changing loading rate are insignificant. This finding is consistent with the results reported by Xu et al. [31]. By considering the physical meaning of σ_cc, σ_ci, and σ_cd, it can be concluded that crack closure, initiation, and growth in granite exhibit negligible dependence on loading rate during uniaxial compression. Observations indicate that the influence of initial damage on the stress thresholds exhibits no obvious regularity. Nevertheless, the fluctuation amplitude of σ_ci and σ_cd caused by initial damage tends to decline as the loading rate rises, implying that the dependence of stress thresholds on the degree of initial damage gradually weakens at higher rates.

The elastic modulus serves as a key parameter describing rock deformation and reflecting its resistance to applied loads. It was determined for each IDGS that the elastic modulus was calculated using the 30–70% segment of the uniaxial compressive stress–strain curve, in accordance with ISRM guidelines [58]. Elastic modulus calculation parameters for IDGSs are in

Table 3. Key parameter data for determining the elastic modulus of IDGSs.

No	30% σf (MPa)	70% σf (MPa)	ε Corresponding to 30% σf	ε Corresponding to 70% σf	E (GPa)
0.06-IDV1	57.79	134.86	9.50 × 10−4	19.91 × 10−4	74.03
0.06-IDV2	58.81	137.26	10.88 × 10−4	22.58 × 10−4	67.03
0.06-IDV3	58.46	136.37	11.60 × 10−4	22.93 × 10−4	68.76
0.12-IDV1	55.37	129.17	13.53 × 10−4	26.03 × 10−4	59.05
0.12-IDV2	58.30	136.04	12.23 × 10−4	23.55 × 10−4	68.62
0.12-IDV3	54.30	126.71	15.22 × 10−4	28.06 × 10−4	56.37
0.3-IDV1	61.29	142.93	11.15 × 10−4	22.39 × 10−4	72.59
0.3-IDV2	61.62	143.77	11.58 × 10−4	23.01 × 10−4	71.88
0.3-IDV3	59.66	139.28	10.13 × 10−4	21.99 × 10−4	67.14
0.6-IDV1	62.45	145.55	11.87 × 10−4	21.43 × 10−4	86.92
0.6-IDV2	64.21	149.55	12.43 × 10−4	23.66 × 10−4	75.95
0.6-IDV3	61.98	144.23	9.97 × 10−4	21.28 × 10−4	72.68
3- IDV1	65.27	154.01	9.38 × 10−4	20.13 × 10−4	82.59
3- IDV2	62.24	145.23	10.62 × 10−4	21.43 × 10−4	76.77
3- IDV3	64.18	149.52	11.78 × 10−4	24.62 × 10−4	66.46

, with variation by loading rate and initial damage shown in Figure 10d. According to Figure 10d, the elastic modulus exhibits a strong dependence on loading rate. For loading rates lower than 0.6 mm/min, the elastic modulus first declines and subsequently rises as the rate increases, reaching a minimum at 0.12 mm/min, consistent with the trend observed in UCS. For loading rates exceeding 0.6 mm/min, the variation in the elastic modulus exhibits an opposite trend compared with UCS. Considering the physical significance of the elastic modulus, the deformation response of IDGS at 3 mm/min differs markedly from that at lower loading rates.

3.1.3. Failure Modes

Figure 11 illustrates the failure patterns of IDGSs at varying loading rates. As the rate rises, the failure evolves from pure tensile cracking through a combined tensile-shear stage to an ultimate single inclined plane shear mode. The overall damage becomes more pronounced, accompanied by significant surface spalling. Under identical loading conditions, the quantity of fracture zones and the extent of spalling change with initial damage, showing no obvious pattern. These findings suggest that loading rate predominantly controls the failure mode of IDGS, whereas initial damage exerts only a minor effect.

3.2. Strain Energy Characteristics

Rock deformation and failure are closely linked with energy accumulation, dissipation, and release. Evaluating the energy evolution of IDGS under varying loading rates is essential to clarify the coupling mechanism between loading rate and initial damage. Assuming heat exchange is negligible, the deformation of a specimen under external load can be treated as a closed system [59]. Within this system, the total input energy consists of elastic strain energy stored in the rock and dissipated energy, the latter encompassing energy consumed by plastic deformation and crack growth. The strain energy of rock is defined as follows [60]:

$$U_t={\displaystyle {\int }_{{\epsilon }_0}^{{\epsilon }_1}{\sigma }_1{d}_{\epsilon }}$$

(2)

$$U_e={\displaystyle {\int }_{{\epsilon }_2}^{{\epsilon }_1}{\sigma }_2{d}_{\epsilon }}$$

(3)

$$U_d=U_t-U_e$$

(4)

where U_t, U_e, and U_d represent the total input energy, elastic strain energy, and dissipated energy, respectively, with units of MJ/m³. The stresses on the loading and unloading segments of the stress–strain curve are denoted by σ₁ and σ₂, expressed in MPa. ε₀, ε₁, and ε₂ denote the strain at the start, peak, and end of the cycle, respectively, expressed in mm/mm. Figure 8b shows the quantitative correlation of elastic strain energy with dissipated energy.

Since no unloading test was conducted, the method for computing elastic strain energy can be reduced to the following:

$$U_e={\displaystyle \frac{1}{2E_u}}{\sigma }_1^2\approx {\displaystyle \frac{1}{2E}}{\sigma }_1^2$$

(5)

Here, E_u represents the unloading modulus (GPa) and E the elastic modulus (GPa). Based on the results of a series of loading–unloading tests, Liang et al. [61] reported that the difference between E and E_u is negligible. Therefore, in this study, E was used in place of E_u to calculate the elastic strain energy. Figure 8c illustrates the schematic of the simplified calculation procedure.

The proportions of U_e and U_d in the U_t of IDGS were calculated using the above method. Their variations with loading rate and initial damage are depicted in Figure 12. For most IDGSs, the elastic energy fraction (U_e/U_t) is approximately 90%, indicating that input energy is primarily retained as elastic strain energy. Notably, with increasing loading rate, U_e/U_t first decreases and then increases, whereas U_d/U_t exhibits an opposite trend. At 0.12 mm/min, U_e/U_t reaches its minimum while U_d/U_t is at its peak. Under these circumstances, the energy retention of IDGS is lowest, pre-peak damage is greatest, and microcrack initiation and propagation are most pronounced.

3.3. AE Time–Frequency Domain Characteristics of IDGS Under Different Loading Rates

AE technology enables real-time monitoring of damage evolution and failure modes in rock materials under different loading conditions [62]. Changes in AE parameters (ring counts, AE energy, AF and RA value, b-value, and H-value) elucidate the internal crack evolution and damage characteristics of rock materials [37]. They are crucial for revealing the interaction between initial damage and loading rate on IDGS mechanical behavior. Considering space constraints, only a subset of representative IDGSs at different loading rates (0.06-IDV2, 0.12-IDV2, 0.3-IDV2, 0.6-IDV2, 3-IDV2, 0.3-IDV1, 0.3-IDV3) was selected for detailed analysis. The AE response characteristics are subsequently partitioned according to the four distinct stages defined by the evolution of the IDGS stress–strain curves.

3.3.1. AE Count Characteristics

AE counts reveal the frequency of crack evolution in rock under applied load [1]. Figure 13 depicts the temporal evolution of AE count response and axial stress in IDGSs subjected to varying loading rates.

In the microcrack closure stage (I), IDGS gradually compacts, and the stress–time curve is concave, with minor crack friction. The AE response is limited, and cumulative counts increase at a slow pace. Loading rate and initial damage strongly affect AE features. Higher loading rates increase the intensity of crack closure, reflected in the higher probability of collisions and compressions, and enhance AE activity. At 0.3 mm/min, IDGSs with higher initial damage exhibit more developed microcracks, resulting in increased crack closure and correspondingly elevated AE ring counts. During the elastic stage (II), IDGS undergoes elastic deformation, with sparse AE events and slowly increasing cumulative counts. At the stage of stable crack evolution (III), numerous fresh cracks form, AE activity rises steadily, and both cumulative counts and stress–time curves increase linearly. When entering the unstable propagation period (IV), many microcracks in IDGS initiate, propagate, and coalesce. Crack penetration occurs at peak stress, triggering macroscopic failure. AE activity is pronounced, with high counts and a sharply rising cumulative AE counts curve. Notably, as all IDGSs approach instability, the cumulative AE count rises almost vertically. The abrupt increment point, denoted as “F”, serves as a precursor of critical rock failure.

3.3.2. Crack Propagation Pattern Analysis

The damage and failure patterns of IDGS are strongly linked to the mechanisms of crack development. Different types of cracks generate distinct characteristic AE signals. These signals are mainly attributed to the initiation and evolution of tensile and shear fractures. Average frequency (AF) and the rise angle (RA) have been shown to represent the microcrack propagation modes in rock materials [63]. The AF and RA are defined as follows:

$$RA={\displaystyle \frac{T_{AR}}{A_{AR}}}$$

(6)

$$AF={\displaystyle \frac{N_{AC}}{T_{AD}}}$$

(7)

where T_AR, A_AR, N_AC, and T_AD denote the rise time, amplitude, ring count, and duration, respectively. A schematic illustration is provided in Figure 14.

AE signals induced by tensile and shear cracking exhibit clearly differentiated features. Tensile cracks are associated with high AF values and low RA values, whereas shear cracks show low AF values and high RA values [64]. The failure mode of cracks can be determined using the critical slope ratio, k, with k = 10 serving as the threshold for differentiating crack types [62,65]. The evolution of crack modes during the loading process is analyzed to elucidate the interactive influence of initial damage and loading rate on rock failure mechanisms. The ratio m = RA/AF is employed as an AE parameter to quantify crack evolution. Figure 15a–g shows the evolution over time of m, cumulative m, stress, and the cumulative shares associated with tensile and shear crack development. Events with k > 10 (m < 0.1) are classified as tensile cracks, while events with k < 10 (m > 0.1) are classified as shear cracks.

At the crack closure phase (I), all IDGSs exhibit relatively low m values, with tensile cracks predominating. As the loading rate increases, m values rise, accompanied by a greater occurrence of both tensile and shear cracking. At 0.3 mm/min, higher initial damage leads to an increased proportion of both tensile and shear cracks. Throughout the elastic phase (II) and the stable crack propagation phase (III), m values remain low, and the cumulative m curve rises gradually. Tensile cracks remain dominant, and their proportion grows faster at higher loading rates. Rock deformation reflects the macroscopic response of microcrack evolution, while the elastic modulus measures resistance to deformation. At 3 mm/min, IDGS exhibit a distinct crack evolution pattern, explaining the unusual trend of elastic modulus with loading rate. Throughout the unstable crack growth phase (IV), m values escalate markedly in both magnitude and density, and the cumulative m curve rises steeply, indicating the extensive formation of shear cracks and main fracture zones. Just before failure, both tensile and shear cracks grow rapidly, demonstrating that IDGS instability results from their coupled action. Nevertheless, tensile cracks consistently account for a large proportion, confirming their leading role in failure (Figure 15h). The crack propagation mode is primarily dictated by the loading rate, to which it is more responsive than to initial damage. In all IDGSs, a sudden rise point “F” appears in the cumulative m curve before failure, serving as a precursor of rock failure.

3.3.3. Characteristics of the b-Value

The b-value is commonly used to track the evolution of microcrack dimensions in rocks. Elevated b-values indicate microcrack propagation predominantly through small fractures, whereas reduced b-values correspond to growth dominated by larger fractures. Stable b-values suggest a steady damage state, while sudden fluctuations imply abrupt changes in the microcrack regime [66]. Gutenberg and Richter [67] originally proposed an empirical equation to describe the frequency–magnitude distribution of earthquakes. This equation is also applicable to AE waveforms generated during rock fracturing. Regarding AE waveforms, the G-R relationship is described as follows:

$${\log }_{10}(N)=a-b({\displaystyle \frac{A_{dB}}{20}})$$

(8)

where A_dB represents the AE signal amplitude (dB), and N denotes the total AE events whose amplitudes surpass A_dB. The b-value reflects the relative distribution of AE events with low and high amplitudes.

Figure 16 illustrates the variation trend of the b-value for IDGSs. During the crack closure stage (I), b-values fluctuate at high levels due to pre-existing crack closure. Higher loading rates amplify these fluctuations, reflecting more active microcrack generation. At 0.3 mm/min, b-values fluctuate more with increasing initial damage, indicating that higher initial damage leads to more complex microcrack activity. During the linear elastic stage (II), cracks develop slowly and b-values remain stable. In the stable crack propagation stage (III), numerous microcracks emerge within IDGS. The merging of these cracks into larger ones and the development of dominant fracture zones lead to a decrease in b-values. During the unstable crack growth stage (IV), b-values in IDGS fluctuate sharply once stress exceeds the σ_cd. This reflects the unstable growth of small- and large-scale cracks, with rapid generation and propagation of microcracks leading to macroscopic fractures. Near peak stress, b-values concentrate and drop sharply, indicating crack coalescence and rock failure. Thus, a concentrated b-value distribution and b-values ≤ 1.0 can act as precursors of macroscopic failure.

3.3.4. AE Dominant Frequency Distribution and Energy Characteristics

AE waveform contains rich information on the history of rock deformation and damage [68]. For analysis of AE waveform characteristics, AE time series are converted into the frequency domain using fast Fourier transform in this section. The AE dominant frequency is defined as the frequency corresponding to the maximum amplitude in the AE spectrum [69]. Kong et al. [70] demonstrated that crack initiation and propagation are closely linked to AE dominant frequency distribution. The AE signal spectrum is classified in this study into three frequency domains: low (≤150 kHz), medium (150–250 kHz), and high (≥250 kHz). AE events dominated by tensile cracking generally correspond to higher frequency components, whereas those controlled by shear activity are linked to lower ones. Thus, changes in AE dominant frequency composition reflect transitions in crack types [71]. Additionally, Bhuiyan and Giurgiutiu [72] found that microcrack propagation generates high dominant frequency signals, whereas microcrack surface friction produces low dominant frequency signals. Figure 17 presents the variation trends of AE dominant frequency and energy for IDGSs.

During the crack compaction phase (I), low-frequency signals dominate, while medium- and high-frequency ones occur infrequently, and the corresponding AE energy distribution remains scattered. Higher loading rates concentrate AE energy and increase its magnitude, indicating more intense crack activity. At the same loading rate, specimens with greater initial damage exhibit higher AE energy and a denser distribution. This indicates that their pre-existing pores and cracks are more developed, enhancing microcrack activity during closure. In the elastic stage (II), IDGS undergo elastic deformation with few microcracks, leading to weak AE energy release and correspondingly limited low- and high-frequency signals. With the onset of stable crack propagation (III), AE energy exhibits a pronounced increase, while high-frequency emissions become progressively dominant. This indicates microcrack initiation and growth, accompanied by the formation of many minor and several major fractures, along with a limited release of elastic strain energy. In the unstable crack propagation stage (IV), high-frequency signals remain dominant, and AE energy continues to rise. Near peak stress, low- and high-frequency signals become densely distributed, and AE energy peaks as microcracks rapidly extend and merge into macroscopic fractures. Interestingly, as the loading rate rises, mid- and low-frequency signals first decrease and then increase (Figure 17h). This trend is consistent with that of IDGS strength and indicates the strong influence of shear crack activity.

3.3.5. Characteristics of the Entropy Value

Entropy, introduced by Clausius, quantifies how uniformly energy is spread in thermodynamic systems. A higher degree of uniformity results in a larger entropy value. In information theory, entropy measures uncertainty and represents the average information content of a message. Entropy increases with the volume of information transmitted. In seismology, AE entropy has been applied to analyze the nucleation process of earthquake cases through the increase in entropy [73]. AE entropy is calculated using the following formula:

$$I(x)=-{\displaystyle \sum _{n=1}^N{P}_n(x)\log P_n(x)}$$

(9)

where I(x) denotes the entropy value; N denotes the count of amplitude levels in the AE amplitude sequence; and P_n(x) represents the likelihood of a particular amplitude, determined by dividing the number of AE events in that amplitude interval by the total events recorded. By standardizing the entropy, the normalized entropy value can be obtained, and its formulation is expressed as follows:

$$H(x)={\displaystyle \frac{I(x)}{\log N}}$$

(10)

where H(x) is the normalized entropy value, with N indicating the total count of amplitude levels within the AE amplitude sequence.

The time-dependent variations in stress and normalized entropy are shown in Figure 18. During the initial three stages (I, II, and III), entropy remains low and stable, indicating that only a small number of cracks are generated in IDGS, with AE events mainly concentrated in low-energy magnitudes [37]. At 3 mm/min, entropy during the microcrack closure stage (I) rises significantly, occasionally reaching near-failure levels. Higher loading rates promote crack interactions and friction, enhancing AE activity and producing a more dispersed AE magnitude distribution. Consequently, the unpredictability of crack activity increases under higher loading rates. Throughout the unstable crack development stage (IV), entropy exhibits pronounced fluctuations and sudden increases, associated with microcracks forming, extending, and merging into large-scale fractures. A sharp rise in entropy reflects the impact of high-energy AE events, which result in a more uniform energy-level distribution. In general, before failure, the entropy curve of IDGSs shows a fluctuating upward trend, in contrast to the decreasing b value. Near peak strength, all IDGSs exhibit a sudden entropy rise. H-values ≥ 0.7 can be regarded as a dependable signal for impending rock failure.

3.4. AE Multifractal Features of IDGS Corresponding to Various Loading Rates

Progressive degradation in IDGS subjected to varying loading rates represents a nonlinear and heterogeneous process. AE signals effectively record the nucleation and growth of microcracks, reflecting both the discreteness and nonlinearity of failure [74]. While conventional fractal analysis has been widely applied to AE signals, the use of a single fractal dimension is insufficient to capture the multiscale fluctuations inherent in AE time series [74,75]. To address this, multifractal theory is introduced to quantify the instability and heterogeneity of AE signals [75,76]. In this section, multifractal analysis of AE data collected during uniaxial tests was conducted to explore how the interplay of loading rate and initial damage governs granite failure behavior.

The AE count time sequences of IDGSs at varying loading rates were processed using the box-counting method to obtain their multifractal spectra. The multifractal spectrum width Δθ acts as a quantitative parameter of AE signal variability and can be formulated as follows:

$$\Delta \theta ={\theta }_{\max }-{\theta }_{\min }$$

(11)

where θ_max and θ_min are the extreme values of the singularity index, and Δθ quantifies the separation between subsets of low and high probabilities. An increase in Δθ reflects a more uneven distribution of AE signals, accompanied by stronger fluctuations [14].

The fractal dimension difference Δf, as another key parameter in the multifractal spectrum, captures the difference in fractal dimensions between subsets of AE data with high and low occurrence probabilities. Δf can be formulated as follows:

$$\Delta f=f({\theta }_{\max })-f({\theta }_{\min })$$

(12)

where f(θ) represents the fractal dimension corresponding to the subset specified by θ, indicating its probability of occurrence across the entire set. Δf quantifies the ratio of steady to variable portions within the AE signal. An increased Δf implies a higher chance of energetic events, linked to the growth of the low-probability subset.

Figure 19 depicts the multifractal spectra of AE ring counts for IDGSs subjected to varying loading rates. The consistently positive Δθ values indicate the presence of multifractal properties in AE signals throughout the failure process. The spectra exhibit a similar shape, with f(θ) first increasing and then decreasing as θ increases, indicating comparable progressive failure behavior under uniaxial compression. However, the multifractal parameters Δθ and Δf differ across loading rates and damage levels, implying variations in the micro-damage characteristics among IDGSs.

Δθ increases with loading rate, suggesting greater heterogeneity and complexity of crack behavior at higher rates (Figure 20a). The highest Δθ occurs at 3 mm/min, reaching 1.2584, 1.1295, and 1.1066 for the three damage levels, mainly due to the uneven AE ringing distribution before peak stress. During failure of IDGS, relatively small signals contribute more significantly to the AE time series [14]. The effect of initial damage on Δθ is complex, with no consistent pattern observed.

The variation in Δf with loading rate is more intricate than that of Δθ. Δf exhibits an “N-shaped” trend as the loading rate increases, first rising, then falling, and rising again (Figure 20b). This pattern reflects the complexity of crack modes and the distribution of AE events at different energy levels [74]. Under a 0.12 mm/min loading rate, Δf reaches the top of its N-shaped trend. Before failure, low-probability, high-energy fractures dominate, meaning that large-scale, low-probability cracks govern the process. This results in complex fracture patterns [74], consistent with those observed in Figure 11d–f. At 0.6 mm/min, Δf reaches the trough of its N-shaped trend. In this case, high-energy AE events are less frequent, and small-scale, high-probability cracks dominate. Consequently, the specimens retain greater integrity after failure [75]. Variations in initial damage result in differences in Δf, which in turn lead to distinct fracture modes (Figure 11). However, initial damage has a complex effect on Δf, showing no clear regularity.

4. Discussion

4.1. The Interactive Effects of Loading Rate and Initial Damage on the Mechanical Performance and Cracking Characteristics of Granite

The evolution of cracks in granite is controlled by initial damage and loading rate. Based on the mechanical responses, strain energy evolution, and AE characteristics of IDGS, this section examines how initial damage and loading rate jointly affect damage progression. Figure 21 presents a micro-mechanistic model depicting the influence of these factors on the mechanical response and failure modes of rock.

The initiation and propagation of microcracks exert a significant influence on the mechanical behavior of rocks [77]. Microcracks can generally be classified into four types: intragranular, grain boundary, intergranular, and transgranular cracks [78,79] (Figure 21a). In this study, IDGSs were prepared through a single loading–unloading cycle. Among them, IDV1 and IDV2 correspond to the stage of stable crack growth, while IDV3 represents the unstable growth stage. Owing to heterogeneities in the elastic modulus, size, and spatial arrangement of mineral constituents, the microcrack patterns vary across different deformation stages. S. Ghasemi et al. [77] showed that crack density increases with axial stress during the stable propagation stage but decreases in the unstable stage as microcracks coalesce into larger cracks. In the stable growth stage, intergranular cracks dominate, with most cracks being interconnected to form a complex microcrack network. Cracks are mainly distributed within quartz and plagioclase. Biotite and K-feldspar maintain stable crack densities, and no new cracks occur in quartz grains. By contrast, the unstable stage is characterized by a rapid increase in transgranular cracks. Consequently, a higher level of initial damage promotes both the structural complexity of the microcrack network and significant variations in crack density within granite. From a macroscopic viewpoint, this process manifests as enhanced energy dissipation (Figure 5b).

At a constant loading rate, the peak strength remains nearly unaffected by initial damage, and the stress thresholds show no clear trend. The fluctuation amplitudes of σ_ci and σ_cd at different damage levels decrease with increasing loading rate, whereas σ_cc shows no obvious variation (Figure 10a). In contrast, the AE counts (Figure 13), ratios of tensile to shear cracks (Figure 15a–g), the b-value (Figure 16), and the AE dominant frequency (Figure 17a–g) in the compaction stage are significantly influenced by the initial damage. These findings indicate that initial damage alters the number and complexity of internal cracks and affects localized crack activity, but its influence is mainly confined to the compaction stage. Mineral heterogeneity (e.g., grain size and orientation) and loading rate are likely the dominant factors controlling the overall mechanical behavior and fracture characteristics.

All IDGSs exhibit rate dependence in strength. The strength and elastic modulus first decline and subsequently rise as the loading rate increases, attaining their lowest values at 0.12 mm/min. Strength weakens with increasing loading rate, contrary to the commonly observed strengthening at higher strain rates [1,11,28]. Similar behavior was reported by Wasantha et al. [13] in coarse-grained sandstone. Based on previous mechanistic studies of granite under varying strain rates [29,61,80,81], this rate dependence is inferred to result from the types and densities of cracks within and between minerals. At low loading rates (≤0.12 mm/min), stress redistribution plays a dominant role, allowing cracks to propagate along weak regions at crack tips. Microstructurally, intergranular and grain-boundary fractures prevail. Within this range, IDGS tested at relatively higher loading rates show more active crack initiation and propagation, resulting in greater crack density and higher dissipated energy per unit volume. Consequently, U_d/U_t reaches its peak and U_e/U_t its trough at 0.12 mm/min (Figure 12). At higher loading rates (>0.12 mm/min), stress redistribution is less pronounced, and cracks propagate rapidly near crack tips. The dominant fracture mode is transgranular, appearing as either straight or curved cracks. Transgranular cracks are more difficult to initiate than intergranular cracks. The trends in Δθ (Figure 20a), Δf (Figure 20b), and low- and mid-frequency AE components (Figure 17h) demonstrate the complex evolution of microcracks in IDGS as the loading rate changes.

In summary, mineral heterogeneity (grain size and arrangement) and loading rate primarily govern the granite’s overall mechanical response and microcrack evolution, whereas the effect of initial damage is largely localized. Fracture patterns, resulting from microcrack nucleation and coalescence, represent essential characteristics of the fracture mechanism. The interaction between loading rate and initial damage is further reflected in the macroscopic failure patterns (Figure 11), highlighting their joint control over crack development. The results of this study, compared with other research on the effects of loading rate and initial damage on rock behavior and fracture, are summarized in

Table 4. Summary table of experimental studies on the effects of initial damage and loading rate on rock mechanical behavior and fracture characteristics.

Study	Rock Type	Initial Damage Mode	Loading Conditions	Equipment	Key Findings
Current Study	Granite	SCLU	UL	[AE]	Strength and modulus vary with loading rate, while initial damage influences microcrack complexity and AE signals, with multifractal characteristics.
Wasantha et al. [13] (2015)	Sandstone	Intact	UL	[XRD] + [NMR] + [SEM]	Peak strength increases with strain rate for fine- and medium-grained sandstones, while coarse-grained sandstones show inconsistent behavior.
Kong et al. [82] (2019)	Coal	IC	UL	[AE] + [DIC]	Increased initial damage lowers the compressive strength and elastic modulus.
Huang et al. [19] (2021)	Coal	UCLU	TMCL	[CT]	Increased initial damage reduces creep time, failure stress, and accelerated creep threshold.
Gong et al. [28] (2022)	Granite	Intact	SCLU and UL	[DIC]	Rockburst proneness increases with loading rate, as elastic strain and peak energy rise linearly.
Yang et al. [16] (2022)	Granite	HCPCL	UL	[AE] + [NMR]	High confining pressure cyclic loading increases granite porosity and alters fracture characteristics.
Zhao et al. [15] (2024)	Red sandstone	CIL	UGCLU	[AE] + [NMR]	Cyclic impact damage and water saturation reduce the cyclic loading strength of rocks.
Miao et al. [2] (2024)	Granite	UL	UL	[SEM] + [XRD]	Increased initial damage reduces strength, strain, and expansion, but increases lateral strain.
Jing et al. [83] (2024)	Coal-like specimens	PB	UL	[DIC]	Higher loading rates increase strength, strain, and stress, while elastic modulus fluctuates.
Jiang et al. [37] (2024)	Red sandstone	PSF	UL	[AE] + [DIC]	Fractured rock’s strength and elasticity decrease, increasing with fracture angle.
Ran et al. [14] (2025)	Coal	UCLU	UMCL	[AE] + [CT]	Higher initial damage shortens fatigue life, reduces strength, and decreases deformation modulus.
Shao et al. [12] (2025)	shale	Intact	UL	[CT]	Higher loading rates increase peak strength and shorten failure time.

.

4.2. Occurrence Time and Precursory Warning of Catastrophic Failure of IDGS

Accurate prediction of catastrophic failure of IDGS under varying loading rates requires analysis of failure time and precursory responses. Figure 22a presents the time to failure of IDGSs subjected to varying loading rates. The red curve corresponds to the negative exponential fitting equation that describes how failure duration correlates with loading rate for all IDGSs (Equation (13)). Initial damage exerts little effect. With increasing loading rate, failure time decreases and gradually stabilizes.

$$t_f=82.32\times v^{-0.97}$$

(13)

where t_f is the failure time (s), and v is the loading rate (mm/min).

During progressive rock failure, AE signals primarily capture the evolution of internal microcracks. In addition, they are extensively used as precursors for catastrophic failure prediction [1,37,84], such as cumulative AE counts, RA/AF, b-value, and entropy. To evaluate the relative sensitivity of these parameters, a precursory response coefficient η is proposed and defined as follows:

$$\eta ={\displaystyle \frac{t_f-t_p}{t_f}}$$

(14)

where t_f and t_p denote the failure time of the IDGSs (s) and the moment when precursor information appears in the AE parameters (s), respectively. A larger value of η indicates higher sensitivity of the AE parameter to fracture precursors. When no precursor signal is observed in the AE parameters, η = 0.

Figure 22b–d show that the precursor response coefficient η differs among AE parameters. The cumulative RA/AF value responds first, followed by the cumulative AE counts, whereas the b-value and H-value often show delayed or no response. Hence, the cumulative RA/AF value and AE counts are more sensitive to fracture precursors. It should be noted that comparisons are meaningful only when the loading rate is consistent because the loading rate has a significant impact on the denominator t_f.

4.3. Future Directions in Rock Failure Mechanisms and Initial Damage

As the study of rock failure mechanisms continues to advance, future research will place greater emphasis on the influence of initial damage modes on the mechanical behavior and fracture characteristics of rock masses, particularly in complex initial damage states (such as blasting-induced damage, dynamic disturbance damage, three-dimensional stress damage, and thermo-hydro-mechanical damage). The evolution of rock fractures under these conditions will be a key area of focus. By combining experimental methods, numerical simulations, and multiscale modeling approaches, and utilizing technologies such as acoustic emission (AE) and CT scanning, future research will be more closely aligned with the needs of underground engineering construction. The goal is to better understand rock fracture mechanisms and provide a scientific basis for risk early-warning systems.

In terms of engineering applications, future research on the impact of initial damage on rock mechanical behavior and fracture mechanisms will focus on practical applications in blasting excavation and mechanical excavation (e.g., TBM). In blasting excavation, research will investigate the influence of different blast intensities on the initial damage state of rock masses and its effect on failure modes, with the aim of optimizing blasting designs and improving construction safety. In mechanical excavation (e.g., TBM), studies will analyze the impact of disturbance-induced initial damage at different excavation rates and further explore the crack propagation paths of rock masses under initial damage states that closely mimic real-world conditions. This will help improve TBM processes and optimize cutter configurations. Additionally, future research will incorporate multiscale modeling techniques to optimize excavation processes, providing more precise design guidance for mining operations and underground construction.

5. Conclusions

This study carried out uniaxial compression experiments on various IDGSs at multiple loading rates to analyze their mechanical parameters, energy evolution, failure modes, and AE responses. Results analysis demonstrates that the interplay between initial damage and loading rate dictates the mechanical behavior of granite. Moreover, this study clarified how loading rate affects failure timing and explored the precursor features of AE signals in IDGS. The principal findings are summarized below:

• Granite exhibits an initial reduction followed by a subsequent increase in both strength and elastic modulus as the loading rate rises. Specifically, the peak strength reaches its minimum at 0.12 mm/min and its maximum at 3 mm/min, with a decrease of approximately 4.04% and an increase of about 9.94%, respectively, compared to 0.06 mm/min. An increase in loading rate leads to strength weakening, which opposes the conventional behavior of enhanced strength at higher strain rates. At the minimum strength, U_d/U_t peaks while U_e/U_t reaches its lowest value. The underlying reason is that when cracks have adequate time to evolve, elevated loading rates promote both crack initiation and propagation. Strength and elastic modulus are minimally influenced by initial damage, with UCS variations ranging from −5.12% to +5.31% across different damage levels. At higher loading rates, the dependence of stress thresholds on initial damage weakens. The IDGS failure pattern is largely dictated by loading rate, with only minor influence from initial damage levels.
• The AE counts, RA/AF values, b-values, and entropy of all IDGSs exhibit pronounced stage-dependent features and contain precursory information for rock failure. Initial damage mainly affects crack activity during the compaction stage. The proportion of mid and low dominant frequencies varies with loading rate in the same trend as peak strength. AE time-series data display multifractal characteristics. With increasing loading rate, Δθ generally rises, while Δf follows an N-shaped trend.
• The interactive effects of initial damage and loading rate on granite mechanical behavior are elucidated. Higher initial damage increases microcrack complexity and alters crack numbers. This mainly affects local and compaction-stage crack activity, while the loading rate controls the primary modes and numbers of crack initiation and propagation. Loading rate and mineral heterogeneity, specifically grain size and spatial arrangement, primarily govern granite’s mechanical properties and fracture characteristics, while initial damage has a limited influence.
• Granite’s failure time in uniaxial compression tests follows an inverse exponential trend with respect to the applied loading rate (t_f = 82.32 × v^−0.97). A higher loading rate leads to faster failure, and the failure time gradually approaches a stable value. Initial damage exerts minimal effect on the failure time. The sensitivity of precursor responses differs among AE parameters, following the order of cumulative RA/AF value > cumulative AE counts > b-value > entropy.