Experimental investigation of failure characteristics of deep surrounding rock containing an inclined joint under true triaxial compression

1 Introduction

Deep tunnels and underground caverns are often built in rock masses under high three-dimensional stress. Excavation changes the original stress field. High tangential stress can then develop around the tunnel boundary. This stress concentration may cause crack initiation, crack growth, and local sidewall failure. Classical laboratory studies have shown that brittle rock failure is closely related to crack opening, dilation, and the three-dimensional stress state (Brace et al., 1966; Mogi, 1967; 1971). Therefore, true triaxial loading is useful for reproducing the stress conditions of deep surrounding rock.

The intermediate principal stress has a clear effect on rock strength and failure mode. This effect cannot be fully represented by conventional triaxial tests. Mogi (1967) showed that the intermediate principal stress changes the strength of rocks. Later studies developed true triaxial criteria and numerical descriptions for hard rocks under general stress states (Pan et al., 2012; Chang and Haimson, 2012). These studies provide a basis for testing tunnel specimens under controlled three-dimensional loading.

Natural rock masses usually contain joints, fractures, bedding planes, and other structural planes. These weak planes guide the path of crack growth. They also change the stress distribution around an excavation. For tunnel models, sidewall spalling and block detachment are often controlled by the combined action of boundary stress and structural defects. Laboratory observations have shown that tangential stress concentration can drive progressive sidewall damage in hard rock tunnels (Pan et al., 2020). Recent true triaxial tests have also shown that the geometry of an opening and the position of defects can strongly affect tunnel damage and spalling behavior (Wibisono et al., 2024; Zhang et al., 2025).

Acoustic emission is an effective method for tracking the internal cracking process of rock. AE events are generated when microcracks form or grow. Their hit count, ringing count, energy, and amplitude can reflect the degree of internal damage. Lockner (1993) summarized the value of AE monitoring in rock fracture studies. Moment tensor and parameter-based AE methods have also been used to interpret crack mechanisms in rock (Ohtsu, 1991; Chang and Lee, 2004). Under true triaxial loading, AE precursor information can show the transition from quiet cracking to unstable fracture (Liu et al., 2023).

The AE b-value is commonly used to describe the relative scale of AE events. A high b-value usually means that small-scale crack events are dominant. A low b-value often indicates that large cracks are increasing. Dong et al. (2022) showed that b-value analysis can provide useful information on granite failure under true triaxial stress. In addition, RA-AF analysis is often used to classify tensile and shear cracks. Du et al. (2020) and Li et al. (2022) showed that the RA-AF distribution can help distinguish crack types during rock fracture. However, the division line should be calibrated for a given rock type and test system.

Although many studies have examined tunnel sidewall failure and AE behavior, experimental evidence concerning the position of a single inclined structural plane relative to a circular opening remains limited. This study therefore presents a specimen-scale comparison of three sandstone specimens with d = 5, 10, and 15 mm under one common true triaxial stress path. Stress-time response, sidewall failure, AE hit count, ringing count, b-value, and RA-AF classification were examined together. The objective is to identify associations between structural-plane position and the observed failure and AE responses for a fixed 45° plane.

2 Experimental setup

2.1 Testing material

Sandstone was selected as the testing material. Three cubic specimens were prepared, with one specimen assigned to each structural-plane distance. Each specimen measured 100 mm × 100 mm × 100 mm and contained a circular opening with a diameter of 30 mm and one structural plane. The structural plane had a nominal inclination of 45° and a nominal length of 30 mm. Its vertical distance from the tunnel center was defined as d, with d = 5, 10, and 15 mm for specimens S5, S10, and S15, respectively. These nominal dimensions are the geometric variables preserved in the experimental record. Quantitative pre-test measurements of aperture, surface roughness, tip radius, machining tolerance, and machining-induced damage were not part of the original test design and cannot be reconstructed reliably after destructive failure. The plane inclination was held constant, i.e., all comparisons in this study are conditional on the nominal 45° configuration. The specimen geometries are shown in Figure 1.

2.2 Testing devices

The true triaxial loading system can apply independent loads in three directions. It can therefore reproduce the three-dimensional stress state of deep surrounding rock. In the Z-direction, the maximum axial load is 3000 kN. In the X- and Y-directions, the maximum lateral load is 2000 kN for each direction. The confining pressure in each direction can be controlled independently. The loading rate can be adjusted from 0.01 to 10 kN/s.

During the tests, an AE monitoring system recorded real-time cracking signals. AE sensors were attached to each specimen surface to form a three-dimensional monitoring network. The measured background noise was below 40 dB, and a 40 dB acquisition threshold was used for all three specimens. The archived experimental record preserves these settings but not the complete instrument metadata requested for retrospective reporting, including the full sensor response, timing parameters, calibration record, and coordinates. These values are therefore not reconstructed from typical settings, and the AE results are interpreted as within-program comparisons obtained with the same recorded sensor arrangement and threshold.

2.3 Loading procedure

Figure 2 shows the true triaxial loading. The test included three main steps. First, the specimen was pre-compacted. This step reduced the gaps between the specimen and the loading plates. Then all measured data were reset to zero. Second, normal stresses were applied in the three loading directions until σx = 24 MPa, σy = 14 MPa, and σz = 12 MPa. Thereafter, σx and σy were held constant while σz was increased until clear sidewall failure occurred. The symbols σx, σy, and σz denote the applied normal stresses in the fixed specimen coordinates, i.e., (σ1, σ2, σ3) = (σz, σx, σy). Compressive stress is taken as positive.

3 Results

3.1 Mechanical and failure properties

Figure 3 shows the applied stress components as functions of time for S5, S10, and S15. After the initial triaxial loading phase, σx and σy were held at 23 and 13 MPa, respectively, while σz was increased. Loading stopped at maximum σz values of 50.17, 48.99, and 47.94 MPa for S5, S10, and S15, respectively. The total spread was 2.1 MPa, or 4.2% of the S5 value. Because only one specimen was tested at each distance, this small difference cannot be separated from sandstone heterogeneity and is therefore reported descriptively rather than as a statistically established distance effect.

Figure 4 shows the macroscopic failure of S5 (d = 5 mm). Several cracks formed near the end of the structural plane, consistent with local stress concentration and stress deflection around the weak plane. One dominant inclined crack extended toward the lower part of the opening and was associated with local cracking on the right sidewall. Rock fragments detached from the left sidewall, where a V-shaped damage pit was observed.

Figure 5 shows the failure pattern of S10 (d = 10 mm). The visible failure zone was concentrated near the structural plane and the left sidewall. Compared with S5, the photographs suggest more extensive slab detachment and a more distinct V-shaped groove. Inclined cracks were visible at the groove tip, and local slab cracking occurred on the right sidewall without complete separation. Sliding was also visible along the structural plane.

Figure 6 shows the failure pattern of S15 (d = 15 mm). The photographs show damage over a broader visible region than in S5 and S10, together with sliding and block detachment along the weak plane. Increasing d changes the positions of the plane and its tips relative to both the opening and the specimen boundaries.

AE monitoring was used to study the internal cracking process of the three specimens. The AE hit count, ringing count, b-value, RA-AF distribution, and crack type evolution were analyzed. These AE parameters help link microcrack activity with the observed macroscopic failure.

3.2 Time evolution of AE count

Figure 7 shows AE hit count versus loading time. S5 exhibited low activity during the initial stage, whereas S10 and S15 showed earlier increases. The original explanation based only on proximity to a loading boundary was removed because the specimen coordinate system and boundary distances do not justify that attribution. A larger d simultaneously changes the plane-tip position relative to the opening and the external boundaries, which may alter local stress concentration, crack-tip activation, and potential sliding. Near final failure, the hit counts of all specimens increased sharply, consistent with rapid crack interaction and coalescence. Because only one specimen was tested at each distance, the between-specimen differences are interpreted as comparative observations.

Figure 8 shows the change in AE ringing count with loading time. The ringing count of S5 changed with the loading stage. Before 400 s, the ringing count remained very low. After 400 s, a small number of AE ringing events appeared. Around 1200 s, the ringing count increased sharply. This sharp increase corresponded to rapid crack growth and sidewall failure. The ringing count of S10 showed a similar trend. Few AE ringing events were recorded before 700 s. After this time, low-level ringing events appeared. When the loading time exceeded about 1050 s, a large number of ringing events occurred. This indicated that crack interaction became strong and the specimen entered the final failure stage. S15 showed a longer quiet period than S5 and S10. Very few ringing signals were recorded before 1100 s. After 1100 s, the AE ringing count increased suddenly. Its peak level was about 5–12 times higher than those of S5 and S10. This large increase corresponded to severe brittle failure and complete damage of the specimen. These results show that a larger structural plane distance leads to a longer quiet period, followed by a more abrupt AE response.

3.3 Crack scale

The AE b-value describes the relative frequency of small- and large-amplitude events. For events above the completeness amplitude Amin, the amplitude-frequency relation is written as log₁₀ N = a− b × A_dB/20, where N is the cumulative number of events with amplitude A not less than a, and b is the fitted slope magnitude. An increase in b indicates a larger relative contribution from small-amplitude events, whereas a decrease indicates a larger relative contribution from high-amplitude events. Figure 9 shows the b-value evolution during loading.

The archived post-processing record does not preserve the full amplitude interval, moving-window size, step length, completeness threshold, goodness-of-fit rule, or outlier treatment. The original raw waveform and event-selection workflow needed for a defensible sensitivity reconstruction is also unavailable. A new sensitivity result is therefore not reported retrospectively. Instead, the broad fluctuations are retained as descriptive observations, and no robust monotonic distance law is inferred from the b-value curves. In the initial stage, the calculated b-values fluctuated strongly. This behavior may reflect compaction-related microcracking, but it may also be sensitive to event count, completeness amplitude, and moving-window selection. The reported ranges for S5, S10, and S15 were 0.28–2.32, 0.21–2.21, and 0.16–4.32, respectively. The high local values in S15 indicate that small-amplitude events dominated within those specific windows; they should not be interpreted independently of window stability. During the σz holding and subsequent loading stages, the b-value decreased in several intervals and fluctuated strongly near final failure, indicating changing proportions of low- and high-amplitude events. The reported final-stage ranges were 0.12–3.80 for S5, 0.13–3.60 for S10, and 0.08–3.30 for S15.

3.4 Crack classification

In AE analysis, RA is defined as RA = T_r/A_max, where T_r is rise time and Amax is maximum amplitude. Average frequency is defined as AF = N_c/D, where N_c is threshold-crossing count and D is signal duration. Low-RA/high-AF events are commonly associated with tensile cracking, whereas high-RA/low-AF events are commonly associated with shear cracking. The classification boundary used here is AF = k₀ × RA: events above the line are classified as tensile-type and events below it as shear-type. The archived export does not retain a sufficiently complete unit definition for every native AE parameter; therefore, k₀ is treated only as a system-specific boundary applied consistently within the present dataset rather than as a dimensionally transferable criterion.

Figure 10 shows the tensile- and shear-classified AE fractions versus the normalized loading stress σ_z/σ_zmax. At σ_z/σ_zmax = 0.20, the shear-classified fractions of S5, S10, and S15 were 14.9%, 18.9%, and 31.3%, respectively. The higher fraction in S15 does not contradict its longer low-activity period: the fraction describes the composition of the events recorded within a stress interval, whereas the quiet period describes their absolute activity. Thus, a small number of early events can be predominantly shear-classified while total AE activity remains low. This pattern may reflect localized plane-tip adjustment or sliding before rapid crack coalescence, but the mechanism requires stress-field or deformation validation. Between normalized stresses of 0.20 and 0.80, the shear-classified fraction increased in all specimens. Above 0.80, the tensile-classified fraction increased. The turning points were 0.84 for S5 and 0.76 for both S10 and S15; they are treated as candidate specimen-level precursors rather than universally validated instability thresholds.

3.5 Limitations of this study

The original experimental program was designed to compare nominal structural-plane positions under one loading path. It did not include a comprehensive material-characterization campaign, calibrated three-dimensional failure-surface metrology, or complete archival of all machining and AE acquisition metadata.Because a limited number of specimens were tested at each distance, the range in maximum σz and the differences in AE indicators may therefore include natural sandstone heterogeneity.The results are consequently presented as specimen-level comparisons and are not used for statistical inference or a general engineering law.

The structural-plane inclination was fixed at 45°. Distance and orientation were not varied independently, and a multi-inclination factorial assessment would require a separate experimental design. The present observations therefore cannot establish an orientation-independent distance effect. The classified fractions and b-value trends are therefore used as comparative, specimen-level indicators under a common loading path rather than as direct proof of fracture mechanism or universal precursor thresholds. Confined shear-dominated validation and a prospective window-sensitivity study would be needed for stronger inference. In addition, the quasi-static loading and observed sidewall peeling, slab cracking, sliding, and block detachment is promising in our future study.

4 Conclusion

The distance between a structural plane and a tunnel opening affects the failure of deep surrounding rock. Within the tested 45° configuration, respectively the maximum σ_z values for S5, S10, and S15 were 50.0, 49.0, and 47.9 MPa, respectively. The observed failure patterns were local sidewall cracking for S5, more extensive peeling and a V-shaped groove for S10, and broader visible damage with sliding for S15. AE hit count and ringing count exhibited staged evolution. S15 had the longest low-activity period and the most abrupt final increase in ringing count. This combination indicates delayed but concentrated event activity in that specimen; it does not by itself establish a general distance-controlled precursor law. The b-value and RA-AF results provide complementary specimen-level descriptions of event amplitude and apparent crack mode. The shear-classified fraction at σz/σz,max = 0.20 was 14.9%, 18.9%, and 31.3% for S5, S10, and S15, and the corresponding turning-point ratios were 0.84, 0.76, and 0.76.

The combined macroscopic and AE observations provide an exploratory comparison of three structural-plane positions for one fixed inclination and loading path. Replicated tests, additional inclinations, quantitative failure mapping, and confined RA-AF calibration are required before broader engineering generalization.

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Footnotes

Edited by: Wenling Tian, China University of Mining and Technology, China

Reviewed by: Jinyu Dong, North China University of Water Conservancy and Electric Power, China

Nengzeng Long, Chongqing University, China