Introduction

The stability of rock mass has become a pivotal concern in both underground space utilization and mineral resource extraction extends to greater depths. It behaves as a discontinuous medium that hosts ubiquitous structural planes in nature, such as joints, fractures, and other defects. These cracks govern the mechanical response and dictate the failure mode and strength characteristics of the rock mass under loading1,2,3,4,5,6. Numerous field cases demonstrate that instability and collapse initiate from the initiation, propagation, and eventual coalescence of internal fractures7,8,9. Hence, a thorough investigation of the failure mechanism of fractured rock under stress is essential for clarifying instability mechanisms in underground engineering, guiding safe construction, and preventing geohazards.

Researchers worldwide routinely introduce pre-existing cracks or cavities into rock specimens to replicate internal defects and to quantify how fracture number, size, geometry, and orientation affect mechanical performance and failure patterns. In single-fracture studies, Shen10, Wong & Einstein11, Yang & Jing12, and Cao et al.13 conducted uniaxial compression tests to elucidate the influence of fracture parameters on rock strength and deformation, and they classified crack types and propagation modes. Liu et al.14, Miao et al.15, and Deng et al.16 further explored crack initiation mechanisms in single-fractured rock under compressive loading. For multi-fracture systems, Sagong & Bobet17, Lee & Jeon18, Chen et al.19, Yang et al.20, Lin et al.21, and Xiong et al.22 combined laboratory testing with numerical simulations to systematically analyze crack evolution and ultimate failure modes in multi-fractured specimens. Yang et al.23 observed that the peak strength of specimens containing non-straight fractures increases almost linearly with fracture dip angle. Yuan et al.24 and Huang et al.25 employed PFC2D simulations and experiments to confirm that dip angle governs the failure mode, whereas fracture length controls the fragmentation intensity.

Recently, acoustic emission (AE) monitoring, has emerged as a key tool for capturing the dynamic evolution of cracks, owing to its high sensitivity to micro-fracturing events26,27,28. It is widely employed in experimental investigation, which can bridge crack detection29 and seismic monitoring30. Niu et al.31, Li et al.32, Ma et al.33, and Cheng et al.34 used AE to unravel the microcrack evolution of brittle rock under compression and demonstrated a strong correlation between AE parameters and crack growth. Zhai et al.35 established a quantitative relationship between bedding angle and shear-type AE sources via moment tensor analysis. Ohno & Ohtsu36 pioneered the use of RA (rise time/amplitude) and AF (average frequency) to distinguish crack modes in concrete; this approach has since been widely adopted in rock mechanics. Zhu et al.37 identified crack types based on the variation relationship of RA-AF and clarified the failure modes of specimens at different stages. Sha et al.38 applied RA-AF relationship to analyze crack-type evolution in NSCB and CCNBD specimens and validated the testing methodology from a fracture-mechanics perspective. Liu et al.39, Bi et al.40, Du et al.41, and Yu et al.42 further developed AE-based separation criteria that quantitatively discriminate tensile and shear cracks.

Although significant advances have been achieved in macroscopic mechanical response and failure patterns, the transient process and micro-mechanism of crack initiation and propagation remain insufficiently documented. In particular, quantitative discrimination of crack types based on AE parameters lacks rock-specific separation criteria. Also, the coupled influence of multi-parameters (e.g., dip angle and length) on the failure mechanism and AE response of fractured rock still needs systematic investigation. To address these gaps, this study performs notched semi-circular bend (NSCB) and straight-notched Brazilian disc (SNBD) tests integrated with AE monitoring. A rock-specific tensile–shear separation criterion for marble is established based on the RA-AF relationship. Subsequently, we conduct uniaxial compression tests on specimens containing fractures of varying dip angles and lengths to disclose the micro-failure mechanisms and crack evolution under multi-factor coupling. The results provide new theoretical support for rock-mass damage assessment and stability prediction.

Materials and experimental methods

Specimen preparation

The specimen used in this study is Jingping marble from Sichuan Province of China, with a medium-fine grained crystalline texture and massive structure. Two types of fracture tests were conducted: mode I fracture tests using Notched Semi-Circular Bend (NSCB) method and mode II fracture tests using Straight-Notched Brazilian Disc (SNBD) method. A total of 20 specimens were prepared according to the suggested methods of International Society for Rock Mechanics and Rock Engineering (ISRM)43,44.

The dimensions of specimens are summarized in Table 1, with tolerances within ± 1 mm for radius and thickness, and ± 0.5 mm for notch length. Typical NSCB and SNBD specimens are shown in Fig. 1a–b, respectively. Since the specimen preparation is similar to that for uniaxial compression specimens, the detailed procedure is described using uniaxial compression test as follows.

Table 1 The average dimension of specimens for NSCB and SNBD tests (unit: mm).
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Fig. 1
Fig. 1
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Test specimens for (a) NSCB test, (b) SNBD test, and (c) uniaxial compression test.

A total of 45 marble specimens were prepared for uniaxial compression test, including one group of intact specimens (5 nos.) and 8 group of pre-cracked specimens (40 nos.). According to the ISRM suggested method, the specimens were prepared as rectangular prisms with the height of 100 mm and the width of 50 mm. Considering the anisotropy of material, all specimens were cut from the same marble block using a high precision cutting machine along the same direction. Surface flatness was ensured through fine grinding with a planer.

Generally, rock crack is typically simulated by embedding metal plates. It is great challenging to create cracks within natural rock. Thus, we employed high-pressure water jet cutting to fabricate single cracks in intact specimens, which can minimize additional damage to crack tips. P-wave velocity of each specimen was measured using a non-metallic acoustic wave instrument (DJUS-050). Specimens with the required velocity were then selected for uniaxial compression test.

The dimensions of the specimens are listed in Table 2. The tolerances for length, width, and height within ± 1 mm, while the tolerance for crack length within ± 0.5 mm. Pre-cracked specimens are divided into two series in Fig. 1c: one with a fixed crack angle (θ = 45°) and varying crack lengths (5 mm, 10 mm, 15 mm); the other with a fixed crack length (10 mm) and varying crack inclination angles (15°, 30°, 45°, 60°, 75°, 90°). All cracks are closed and extend through the thickness of the specimen.

Table 2 The average dimension of specimens for uniaxial compression tests (unit: mm).
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Experimental setup and procedure

The mode I and mode II fracture toughness tests were conducted using MTS815 electro-hydraulic servo-controlled rock mechanics testing system at Shaoxing University. This system has a maximum compression capacity of 4600 kN and a tension capacity of 2300 kN. The loading rate for both NSCB and SNBD tests was set to 0.001 mm/s. Before each test, a pre-load of 0.5 kN was applied to ensure proper seating of the specimen. During testing, acoustic emission (AE) signals were continuously monitored using a PCI-2 AE system (Physical Acoustics Corporation, USA) equipped with nano30 sensors (frequency range: 20–1000 kHz). The experimental setup is illustrated in Fig. 2a.

Fig. 2
Fig. 2
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Experimental equipment for (a) NSCB and SNBD, (b) uniaxial compression test.

Uniaxial compression tests on pre-cracked specimens were performed using a universal testing machine (UTM5605-600) at Shaoxing University. Axial load was measured using a 600 kN loading cell. Displacement control was applied at a rate of 0.002 mm/s until specimen failure. To minimize end friction effects, vaseline was applied to the loading plates. AE monitoring was carried out using PCI-2 system with a threshold of 35 dB, gain of 40 dB, and sampling frequency of 2 MHz. Four AE sensors were attached to each specimen. The test setup also included a digital image correlation (DIC) system for surface deformation measurement, though only AE results are discussed in this paper. The experimental arrangement is shown in Fig. 2b.

Mechanical and fracture behavior under uniaxial compression

Strength and deformation characteristics

To investigate the influence of crack geometric parameters on the mechanical properties of marble, uniaxial compression tests were conducted on specimens containing pre-existing cracks with varying inclination angles and lengths. Figure 3 presents the typical stress–strain curves of marble specimens. The representative specimens analyzed in this study primarily include 10-15°-5 specimen, 10-30°-4 specimen, 10-45°-5 specimen, 10-60°-2 specimen, 10-75°-4 specimen, 5-45°-4 specimen, and 15-45°-1 specimen. Detailed information on these specimens is presented in the supplementary materials. Here we provide specific descriptions for 10–45° specimens. The test can be divided into four characteristic stages: I. Compaction stage: due to the closure of native microcracks and pre-existing cracks, nonlinear deformation is significant, especially in flawed specimens. II. Elastic deformation stage: the stress–strain relationship is approximately linear with the slope reflecting elastic modulus of marble. III. Stable crack growth stage: the internal microcracks exhibit stable propagation, acoustic emission (AE) activity intensifies (see Sect. “AE response of pre-cracked marble under compression”), and the stress—strain curves fluctuate. IV. Unstable crack propagation stage: main cracks coalesce and bearing capacity is rapidly lost.

Fig. 3
Fig. 3
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Stress—strain curves of specimens with different inclinations and different lengths.

Comparing the curves of intact and flawed specimens reveals that the presence of pre-existing cracks significantly alters the mechanical response of the rock specimens. Stress concentration at the crack tips prolongs the initial compaction stage, and pre-peak curve fluctuations become more frequent, particularly at low inclination angles (e.g., θ = 15°), which is related to the intermittent generation of secondary cracks and local stress release. It is noteworthy that when the crack inclination approaches the loading direction (θ = 90°), its mechanical response approaches that of the intact specimens gradually, whereas an increase in crack length continuously deteriorates its mechanical performance.

Table 3 lists the mechanical parameters of marble specimens with different crack inclination angles and lengths under uniaxial compression. Based on the data in Table 3, the variations of peak strength (σₚ), peak strain (εₚ), and elastic modulus (Ec) with crack inclination angle (fixed length 10 mm) and crack length (fixed inclination 45°) are plotted in Figs. 4 and 5, respectively.

Table 3 Mechanical parameters under uniaxial compression of pre-crack specimens.
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Fig. 4
Fig. 4
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Effect of inclination angle on the mechanical parameters of specimens (a = 10 mm).

Fig. 5
Fig. 5
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Effect of crack length on the mechanical parameters of specimens (θ = 45°).

The peak strength, peak strain, and elastic modulus of marble specimens containing pre-existing cracks are related to the inclination angle of the cracks. As shown in Fig. 4, the peak strength first decreases and then increases with increasing crack inclination angle. The strength reaches its minimum value (39.08 MPa) at an inclination of 30°, which is 4.07% lower than at 15°. This is likely because at this angle, the flaw plane couples with the direction of maximum shear stress, leading to the most significant shear stress concentration, which most easily triggers crack propagation. After the inclination angle exceeds 30°, the strength begins to recover, showing the fastest increase (12.77%) from 30° to 45°. Subsequently, the growth rate slows down, and the strength at 90° (47.62 MPa) approaches that of the intact specimen. This phenomenon indicates that as the inclination angle increases, the disturbance of the crack to the principal stress direction weakens, and its controlling effect on strength consequently decreases. The variation trend of peak strain is basically consistent with that of peak strength, indicating that the crack inclination angle affects not only the strength but also synchronously regulates the deformation capacity of the specimen. The elastic modulus also reaches a trough at 30° (7.45 GPa), further confirming that the specimen is most prone to deformation at this inclination angle.

As shown in Fig. 5, the crack length exhibits a significant size effect on the mechanical properties of the specimens. As the crack length increases from 5 to 15 mm, the peak strength linearly decreases from 47.96 MPa to 38.83 MPa, a reduction of 18.99%. This is mainly attributed to the reduction in effective bearing area and the greater stress concentration degree at the tips of longer cracks. The peak strain and elastic modulus also decrease monotonically with increasing crack length, indicating that specimens with longer cracks fail at lower stress and strain levels, and their overall mechanical properties deteriorate more severely.

Crack evolution and macroscopic failure modes

The failure of fractured rock mass is essentially a process of internal crack initiation, propagation, and final coalescence. This study systematically observed and classified the macroscopic crack paths of post-test specimens. The main crack types are summarized in Fig. 6, including: tensile wing cracks (T-A, T-B), anti-wing cracks (T-C, T-D), shear cracks (S-A, S-B), tensile-shear mixed cracks (M-A, M-B), and far-field cracks (I).

Fig. 6
Fig. 6
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Crack type classification. (a) T-A (tensile crack); (b) T-B (tensile crack); (c) T-C (tensile crack); (d) T-D (tensile crack); (e) S-A (shear crack); (f) S-B (shear crack); (g) M-A(Mixed crack, first shear then tensile); (h) M-B (Mixed crack, first tensile then shear); (i) I (Far-field crack).

The final macroscopic failure patterns of specimens with different geometric parameters are shown in Fig. 7, and their corresponding dominant crack types and failure modes are summarized in Table 4. Analysis shows that the crack inclination angle is the key factor controlling the final failure mode:

  1. i.

    Low inclination angles (15°, 30°): Failure is mainly dominated by tensile wing cracks (T-B, T-D) initiating from the crack tips and propagating along the direction of the maximum principal stress, manifesting typical tensile failure or tensile-shear composite failure.

  2. ii.

    Medium inclination angles (45°, 60°): Failure typically manifests as tensile-shear composite failure. Initial tensile wing cracks, after propagating a certain distance, often induce shear cracks (S-B) developing along the diagonal direction, jointly leading to specimen failure.

  3. iii.

    High inclination angle (75°): Shear failure dominates. Cracks initiate directly from the crack tips in the shear direction and rapidly coalesce, forming clear shear bands, accompanied only by a small number of tensile cracks.

  4. iv.

    Vertical crack (90°): The flaw surface has the least influence on the principal stress direction. Failure is characterized by the random generation and coalescence of numerous far-field cracks (I), belonging to tensile-shear composite failure.

Fig. 7
Fig. 7
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Macroscopic failure modes of specimens under uniaxial compression.

Table 4 Classification of crack types and failure modes of different specimens.
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Therefore, the crack length primarily affects the intensity of failure and the number of secondary cracks. As shown in Fig. 7, as the crack length increases (from 5 to 15 mm), the specimen is more prone to crack propagation, secondary cracks become more developed, the degree of damage intensifies, but the dominant failure mode remains tensile-shear composite. The accelerated damage accumulation with increasing crack length is quantitatively reflected by the higher SIF evolution rates (Fig. 9) and earlier AE activity onset (Fig. 13).

SIF evolution at crack tips

According to the method proposed by Wang45, the calculation of the stress intensity factor (SIF) at the crack tip can be obtained using Eqs. (1) and (2):

$$K_{{\text{I}}} = \sigma_{n} \cdot\sqrt {\pi a}$$
(1)
$${K}_{\text{II}}=\tau \cdot \sqrt{\pi a}$$
(2)

where σn and τ represent the normal stress and shear stress, respectively, acting on the fracture. The stresses on the fracture surface can be determined using Eqs. (3) and (4).

$$\sigma_{n} = \sigma \cdot\cos^{2} \alpha$$
(3)
$$\tau =\upsigma \cdot \text{sin}\alpha \text{cos}\alpha$$
(4)

where σ is the uniformly distributed compressive stress on the upper and lower surfaces of the specimen, a is the crack length; α is the inclination angle of the crack .

Figure 8 demonstrates the SIF evolution with the effect of crack inclination angles. In this study, the entire evolution process of the SIF (KI, KII) at the specimen’s crack tip is divided into four stages based on the percentage of the peak load: I (0–30%, OA), II (30–80%, AB), III (80–100%, BC), and IV (100% to failure, CD).

Fig. 8
Fig. 8
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SIF curves of specimens (a = 10 mm) with different crack inclination angles.

For the mode I SIF (KI), its absolute value decreases significantly with increasing inclination angle (see Fig. 8a). The 15° specimen has the highest KI value throughout the process (peak 4.458 MPa m1/2), while the 75° specimen consistently has the lowest KI values. This indicates that low-angle cracks are more prone to tensile crack propagation. Conversely, the mode II SIF (KII) in Fig. 8b first increases and then decreases with increasing inclination angle, reaching a peak at 60° (2.508 MPa m1/2), which coincides with the macroscopic observation that medium-inclination specimens exhibit the highest degree of shear crack development, as listed in Table 4.

Figure 9 indicates that the crack length significantly accelerates the crack propagation process. As the crack length increases from 5 to 15 mm, the total duration from loading to failure shortens, and the slope (rate of change) of the SIF curves increases. In Stage II, the SIF change rates for the 5 mm, 10 mm, and 15 mm specimens are 3.475 × 10–3, 4.447 × 10–3, and 6.146 × 10–3 MPa m1/2/s, respectively. This indicates that specimens with longer cracks experience faster growth in the stress field intensity at the crack tip and enter an unstable state earlier.

Fig. 9
Fig. 9
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SIF curves of specimens (θ = 45°) with different crack lengths.

A crucial common finding is that regardless of the inclination angle or length, the rates of change of KI and KII both reach their maximum values in Stage IV (unstable propagation to failure stage), confirming that this stage is the critical period for unstable crack propagation and final specimen failure. This is highly consistent with the AE monitoring results (Sect. “AE response of pre-cracked marble under compression”), where AE energy and hit count surge dramatically after the peak.

AE-based analysis of crack evolution mechanisms

Determination of tensile–shear crack classification

The failure of rock primarily involves tensile, shear, and tensile-shear composite fractures. Acoustic Emission (AE) waveform analysis has been widely used in geotechnical engineering to study fracture characteristics of materials. Analysis of AE data helps reveal the failure mechanisms of rocks with different occurrences and scales under uniaxial compression from a microscopic perspective. The fracture mode of marble can be characterized by the variation of the AE characteristic parameters rise angle (RA) and average Frequency (AF) during loading. RA is defined as the ratio of the rise time (from the first threshold crossing to the peak amplitude) to the amplitude of the AE signal (units: ms V⁻1). AF represents the frequency of a complete AE hit signal, calculated as the cumulative ring-down count divided by the duration (units: kHz).

Based on data from the notched semi-circular bend (NSCB) and straight-notched Brazilian disc (SNBD) tests on marble, after excluding samples affected by operational and systematic errors, AE exhibits the unstable crack propagation results from six specimens were selected for analysis. As shown in Fig. 10, the RA-AF data density distribution was plotted by combining multiple datasets from Mode I and Mode II tests. The core data regions for different tests are enlarged within the gray boxes to identify the high-density zones. AE data points located above the dividing line in the density plot of mode I test characteristic parameters were defined as originating from tensile cracks, whereas those below the dividing line in the mode II test plot were defined as shear cracks.

Fig. 10
Fig. 10
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The density distribution plot of the RA-AF distribution.

The RA-AF density distribution for the NSCB tests shows that RA values are mainly distributed between 0–1 ms V−1, and AF values between 30 and 100 kHz. In contrast, SNBD tests are characterized by lower AF and higher RA values, with data concentrated in the region of RA (0–10 ms V⁻1) and AF (0–30 kHz). Accordingly, the tensile crack boundary for marble was determined as Eq. (5), and the shear crack boundary as Eq. (6). AE data above boundary (5) are defined as tensile cracks, and those below boundary (6) as shear cracks.

$$\text{AF}=40\cdot \text{RA}+30$$
(5)
$${\text{AF}} = 20\cdot{\text{RA}} + 3 \,0$$
(6)

AE Response of pre-cracked marble under compression

The variation curves of AE energy and hit count over time are shown in Figs. 11, and 13. Based on the four-stage division of stress intensity factor (SIF) evolution during uniaxial compression (as described in Sect. “SIF evolution at crack tips”), the changes in AE energy and hit counts across these stages were analyzed. Using the RA-AF classification criteria established above, AE data during the tests were processed and calculated. The proportions of tensile and shear cracks in each stage are plotted in Figs. 12 and 14, enabling further analysis of the stage-wise evolution of crack failure mechanisms during uniaxial compression.

Fig. 11
Fig. 11
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AE hit count and energy among different stages with different crack inclinations.

Fig. 12
Fig. 12
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Crack ratio at different stages for specimens (a = 10 mm) with different crack inclinations.

Fig. 13
Fig. 13
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AE hit count and energy among different stages with different crack lengths.

Fig. 14
Fig. 14
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Crack rate among different stages for specimens (θ = 45°) with different crack lengths.

Influence of crack inclination

As shown in Figs. 11a and 12a, for the 10–15° specimen, during the initial 187 s (Stage I), stress concentration occurred at the crack tip with only minor AE energy release, and the hit count remained relatively stable. This stage represents compaction, dominated by tensile failure, with tensile and shear cracks accounting for 85.1% and 14.9%, respectively.

Upon entering Stage II (up to 450.3 s), microcracks gradually increased inside the rock, with both KI and KII values rising rapidly. The AE hit count increased gradually but remained relatively low. Although both tensile and shear cracks increased in this stage, tensile cracks remained dominant at 73.9%.

In Stage III, the growth rate of SIF decreased, and the AE hit count fluctuated while increasing. Tensile cracks accounted for 82.5%, as the pre-existing crack expanded under the influence of the principal stress, leading to further internal microcrack expansion or convergence, storing energy for subsequent macroscopic failure.

Finally, in Stage IV, AE activity was most intense, with AE energy peaking at 625 s and the hit count increasing sharply. The SIF curve dropped rapidly within a short time, and its rate of change reached a maximum. During this stage, surface cracks propagated rapidly towards both ends, forming macroscopic cracks and causing a significant increase in internal shear cracks (34.2%). However, due to the low inclination angle, tensile cracks still predominate overall, consistent with the macroscopic tensile failure mode observed in Sect. “Crack evolution and macroscopic failure modes” (Table 4, Fig. 7).

Figures 11b and 12b show the AE energy, hit count, and crack-type proportions for the 10–30° specimen. In Stage I (first 288 s), AE signals were very sparse, with only slight energy release at the beginning. In this stage, the closure of original microcracks under compression led to a predominance of shear cracks (65.6%). However, due to the scarcity of AE signals, the failure mechanism is difficult to determine accurately. As the test progressed into Stage II (up to 608.5 s), a stress drop occurred at 599.5 s (also observable in the stress–strain curve in Fig. 3a), triggering more active AE signals. The proportion of tensile failure increased from 34.4 to 75.6%, becoming the dominant mode. In Stage III (up to 739.4 s), AE signals remained relatively stable following the stress drop. The proportion of tensile cracks decreased slightly compared to the previous stage. Stage IV (from peak load to 782.9 s) exhibited the most active AE energy, reaching its peak, with a rapid increase in hit count. Macroscopic cracks coalesced, generating extensive shear failure. Analysis of Fig. 12b indicates a significant transition to shear failure in this stage, with the proportion of shear cracks reaching the maximum for the entire test.

Figures 11c and 12c present the results for the 10–60° specimen. Stage I (up to 396.4 s) involved the closure of original microcracks. Compared to the low-angle groups, this specimen had a longer total test duration under uniaxial compression, higher initial AE energy release, and an earlier and faster rise in the AE hit count curve. In this stage, the closure of pre-existing microcracks and pores resulted in a concave-downward SIF curve, indicating nonlinear deformation. The cumulative AE hit count curve was approximately horizontal, and the AE energy histogram was sparse. Tensile cracks accounted for 71.2%.

In Stage II, the AE hit count began to increase, the curve bent upward, and AE activity became more active. This elastic stage saw a slow increase in AE events, with a small number of internal microcracks initiating. As loading continued, internal cracks became more active, generating and extending fine cracks. Compared to the previous stage, tensile cracks transitioned towards shear, with the proportion of shear cracks increasing by about 10%.

In Stage III (up to 688 s), internal cracks entered a stage of unstable propagation, meaning microcracks began to stably nucleate and coalesce, storing elastic energy in the rock. As the load increased, the SIF curve gradually reached its peak, internal cracks continued to coalesce, AE energy fluctuated more frequently, and the hit count rose rapidly. Different types of cracks increased rapidly, and the proportion of tensile-shear mixed cracks increased, indicating impending failure.

In Stage IV (33.7 s after the peak), the SIF curve dropped rapidly from its peak, macroscopic cracks formed through the specimen, and the released AE energy far exceeded that of the previous three stages. The AE hit count curve approached a vertical segment, indicating unstable failure. The proportion of shear cracks reached 71.4%, indicating that failure in this stage was primarily controlled by shear cracks, which aligns with the macroscopic shear-composite failure mode observed for the 60° inclination in Sect. “Crack evolution and macroscopic failure modes” (Table 4).

Figures 11d and 12d show the results for the 10–75° specimen. This group had the longest test duration. Stage I lasted until 458.9 s; an AE energy fluctuation occurred at 54 s, but for the rest of the time, the AE hit count was nearly horizontal, and the system detected almost no energy release. The proportion of crack types was balanced in this stage. In Stage II (up to 759.5 s), AE activity began to increase slowly from the middle of this stage, a small number of AE events occurred internally, and the hit count curve began to climb upward. In Stage III, AE events increased steadily, and the hit count growth rate accelerated further, storing energy for subsequent macroscopic failure. In the first three stages, both tensile and shear cracks increased and were relatively evenly distributed. As the load continued to increase, the core area of the RA-AF distribution moved closer to the axes. In Stage IV (from the peak at 909.7 s to macroscopic failure at 975 s), the AE hit count increased rapidly. A large number of AE signals were generated in only 65.3 s, far exceeding the sum of the previous three stages. A sudden energy release occurred at 975 s, accompanied by instantaneous crack coalescence and specimen failure, with a significant amount of rock powder produced. The proportion of shear cracks reached 77.4%, indicating that failure was primarily controlled by shear cracks, which is consistent with the macroscopic shear failure mode observed for the 75° inclination in Sect. “Crack evolution and macroscopic failure modes” (Table 4).

In summary, the analysis of the tensile-shear crack proportions across the four stages for specimens with different inclination angles reveals that at low angles (15° or 30°), tensile cracks dominate throughout all stages, controlling the failure mode. As the crack inclination angle increases, the failure mechanism in Stages III and IV changes, with shear cracks gradually becoming dominant. The proportion of shear cracks increases starting from Stage III, eventually evolving into shear-dominated failure. This transition aligns well with the macroscopic failure modes summarized in Table 4 and shown in Fig. 7.

Influence of crack length

Figures 13 and 14 illustrate AE energy, hit count, and crack-types for marble with different pre-existing crack lengths under uniaxial compression. It can be clearly observed that as the crack length increases, AE events become active earlier, and the AE hit count also increases. This phenomenon may be related to the greater degree of degradation caused by longer cracks at the same inclination angle.

In Stage I, for the 5 mm and 10 mm groups, almost no AE signals were observed, and the hit count was nearly zero; failure was primarily tensile. The AE hit count curve for the 15 mm specimen rose slightly, indicating that damage occurred earlier under uniaxial compression, and the failure mechanism distribution was more balanced. In Stage II, the first two groups began to generate microcracks, and the AE hit count grew steadily compared to Stage I, with tensile cracks still dominating. The 15 mm group maintained a similar growth rate to the previous stage, with small fluctuations. As the test progressed into Stage III, AE signals in all three groups entered a stage of rapid growth. The first two groups maintained stable growth, with relatively stable crack propagation, and the core area of the RA-AF distribution moved closer to the AF axis, with the proportion of tensile cracks further increasing. The AE signals of the 15 mm group exhibited more complex fluctuations, showing more obvious unstable crack propagation. Stage IV, from the peak load to macroscopic failure, lasted 30.8 s, 24 s, and 41.2 s for the three groups, respectively. The 10 mm group had the shortest duration.

The growth rate of the AE hit count curve accelerated significantly after the peak. At the moment of crack coalescence, a large amount of rock powder was produced, accompanied by a loud sound. Cracks instantly coalesced through the specimen, causing shear failure with the proportion of shear cracks reaching a maximum of 55.6%. The 15 mm group had the longest duration, primarily because its overall AE activity was higher, and AE energy began to dissipate earlier in Stages II and III, resulting in a longer failure time in Stage IV, the peak AE hit count exhibits a significant correlation with the maximum SIF value (Fig. 9), with the maximum SIF value increasing from 2.12 MPa m1/2 to 3.11 MPa m1/2 as AE hit count varies. with both variables demonstrating consistent trends in their variation and a more balanced crack proportion. The experimental results for different crack lengths indicate that tensile failure dominated in the first three stages, while shear cracks increased in Stage IV, ultimately presenting a tensile-shear composite failure mode. This is consistent with the macroscopic observation (Sect. “Crack evolution and macroscopic failure modes”, Table 4) that the dominant failure mode remained tensile-shear composite regardless of crack length, although longer cracks led to more severe damage and more secondary cracks (see in Fig. 7).

Discussion

AE-based RA-AF classification criterion

During acoustic emission (AE) monitoring, the parameters obtained often carry inherent uncertainty. The transient increase in parameter values may not objectively reflect the true state of fractures within rock masses. Consequently, in parameter-based AE monitoring, statistical processing of AE parameters is typically required to further extract corresponding statistical characteristics. Table 5 summarized the research results on the RA-AF relationship in recent years (e.g., Ohno & Ohtsu36, Ou et al.46, Lin et al.47, Wang et al.48, Yu et al.49, Zhang et al.50, Yu et al.42). It has defined the discriminant boundary between tensile and shear fractures as the linear equation y = kx. The boundary slope k = AF/RA has been widely employed as an indicator to distinguish fractures from tensile to shear. Despite its widespread application, the applicability of this method across different rocks still requires further validation.

Table 5 Current research of the RA-AF relationship36,40,41,42,46,47,48,49,50.
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This study builds upon prior work by extending the discriminant function to the form y = kx + b and proposes specific classification boundaries for marble: the tensile fracture boundary is AF = 40 RA + 30, while the shear fracture boundary is AF = 20 RA + 30. This discriminant model significantly enhances the accuracy of distinguishing between tensile and shear fractures. The higher RA values for shear cracks in marble are consistent with their longer rupture duration and lower frequency content, as predicted by seismic source theory. It should be noted that the present study is confined to marble. Whether the proposed discrimination criteria are applicable to other rock types warrants further investigation. It is worth noting in Table 5 that Bi et al.40 and Du et al.41 have already established tensile-shear boundary criteria for diverse rock types (marble, granite, limestone, and sandstone) through experimental studies. Future research should systematically analyze the variation patterns of the tensile-shear boundary across more rock types, representing an area of significant scientific value.

In addition, it is noteworthy that scholars such as Jing et al.51, Chen et al.52, and Lin et al.47 employed a combined approach of acoustic emission (AE) and digital image correlation (DIC) techniques to conduct the failure characterization of specimens at both micro- and macro-scales, thereby providing a multi-faceted, multi-dimensional and highly efficient analytical methodology for this class of research. In the present study, however, it is regrettable that DIC data could not be integrated into the investigation due to experimental constraints.

Effects of specimen size and loading rate

Regarding the size effect, multiple scholars including Chen et al.53, Hu et al.54, Gao et al.55, Li et al.56, and Hu et al.57 have investigated the relationship between the size effect and compressive strength, crack propagation patterns, crack failure modes, and acoustic emission activity through laboratory experiments and numerical simulations. Their research elucidates the influence of the size effect on experimental results. Larger specimens typically contain more natural defects and heterogeneous structures, which may alter crack propagation paths and the spatial distribution of sonic emission events. However, smaller specimens are more susceptible to edge effects, intensifying stress concentrations and thereby accelerating crack breakthrough. Regarding loading rates, studies by Chen et al.58, He et al.59, and Zhang et al.60 indicate that loading rates influence the mechanical properties, crack propagation paths, and failure modes of specimens. Research by Zhai et al.61, Zhou et al.62, and Cao et al.63 demonstrates that loading rates affect acoustic emission characteristics. Additionally, Li et al.64's work shows that loading rates impact the stress intensity factor at crack tips.

The above studies indicate that specimen size and loading rate significantly influence rock mechanical behavior, failure mechanisms, and associated acoustic emission (AE) activity. However, The fixed specimen size and loading rate in this study limit the generalizability of the proposed AE criteria. Future work should include multi-scale specimens and variable loading rates to establish more universally applicable thresholds.

Conclusions

This study systematically investigated the influence of pre-existing cracks on the fracture behavior of marble through integrated uniaxial compression test combining acoustic emission (AE) monitoring and stress intensity factor (SIF) analysis. The main findings are summarized as follows:

  1. (1)

    The establishment of AE-based crack classification for marble (Tensile: AF = 40 RA + 30; Shear: AF = 20 RA + 30) provides a validated, quantitative tool for interpreting AE signals. This approach successfully bridges the gap between macroscopic failure modes and micro-scale crack evolution, demonstrating that AE parameter analysis is not merely a monitoring technique but a powerful diagnostic method for identifying real-time crack types and their transitions during the entire loading process.

  2. (2)

    The synchronous evolution of SIF and AE parameters across the four defined loading stages shows a consistent correlation with macroscopic observations. The finding that the transition from tensile-to-shear dominance in AE signals (particularly in Stages III and IV) perfectly aligns with the shift from tensile-to-shear-dominated macroscopic failure modes (as inclination increases) provides a guidance for predicting ultimate failure patterns based on early-stage AE data.

  3. (3)

    The strong correlation between crack geometry, SIF evolution rates, and AE characteristics (e.g., longer cracks triggering earlier and more intense AE activity) highlights the potential of AE technology as an early warning indicator for rock mass instability. The methodology presented allows for a more nuanced interpretation of in-situ monitoring data, where AE signal types and evolution trends could be used to infer the dominant failure mode and damage stage of fractured rock masses.