Introduction

In the construction of underground engineering projects, the stability of the surrounding rock is a crucial factor determining the safety and long-term operation of the project1,2,3. The instability or failure of the surrounding rock can not only cause damage to the engineering structure but also trigger severe secondary disasters, leading to significant property loss and casualties4,5,6,7. Shear failure is one of the primary forms of surrounding rock instability8,9,10. As the scale of projects continues to expand, effectively monitoring and predicting surrounding rock failure has become a major research focus and challenge in the fields of engineering geology and geotechnical engineering11,12,13,14,15. The failure process of the surrounding rock is typically accompanied by the accumulation and release of internal stresses, as well as progressive damage to the internal structure of the rock medium. Early identification of precursors to surrounding rock failure and advance warning are of paramount importance for preventing potential engineering disasters.

Acoustic emission (AE) technology and microseismic monitoring technology are widely applied due to their high practicality and sensitivity, making them among the most commonly used methods for monitoring rock failure16,17,18. Despite the significant achievements of AE and microseismic monitoring in rock failure detection, both field measurements and research have revealed certain limitations in their practical application. This is particularly true during the time-dependent failure process of surrounding rock, where AE signals often exhibit a “quiet period,” characterized by a significant reduction or cessation of acoustic emission activity. For example, Jia et al.19 found that with increasing moisture content, the AE signals of sandstone under uniaxial compression notably decreased, and the quiet period lengthened. Song et al.20 conducted a study on the AE characteristics during the deformation of red sandstone under uniaxial compression, observing that the quiet period before the AE peak does not imply that the rock deformation is in a stable phase. During this period, the parameters related to localized deformation zones continued to increase. Li et al.21 carried out uniaxial compression and incremental cyclic loading/unloading tests on six different types of rocks and found that under uniaxial loading, the AE phenomenon exhibited a “quiet period,” which they suggested could serve as a reference for determining rock instability and failure. Liu et al.22 conducted staged cyclic loading/unloading tests on metamorphic sandstone and discovered that AE signals were primarily generated during the loading phase, with almost no AE activity during unloading. Furthermore, a quiet period was also observed during the final loading phase before failure. Wang et al.23 found that in the unstable crack propagation stage of limestone under compression, parameters such as AE count rate, AE energy rate, and AE amplitude sharply decreased. Zhao et al.24 established a rock model with anomalous elastic modulus zones using the PFC2D code and found that the duration of the AE quiet period of the rock was extended by 1 to 5 times. The presence of the AE quiet period presents a challenge for the accurate prediction of surrounding rock failure to some extent.

Resistivity is a fundamental physical property of rock that quantifies its opposition to electrical current flow. Under external loading, defects such as internal pores, fractures, and microcracks in the rock undergo changes, and the closure, initiation, propagation, and coalescence of microcracks, as well as variations in moisture content, can all alter the rock’s electrical resistivity, leading to increase or decrease in resistivity19,25. Since the 1960s, scholars from various countries have conducted studies on the changes in rock resistivity under loading conditions26,27,28,29,30. Sun et al.31 found that the resistivity changes in three types of rocks were closely related to the development of cracks under uniaxial compression, with resistivity exhibiting rapid changes at the critical stress point, which occurs at approximately 75–85% of the applied stress. Li et al.32 discovered a good correlation between the resistivity of coal-bearing rock masses and the stress curve, with resistivity exhibiting a downward fluctuating trend as stress increased. Yin et al.33 showed that sandstone samples subjected to cyclic loading with varying degrees of damage could accurately reflect damage through five different measurement parameters: P-wave amplitude attenuation, resistivity, effective bearing area, and elastic modulus. Jia et al.34 conducted multi-channel resistivity monitoring during the fracture process of sandstone under uniaxial compression, revealing that the anisotropy of resistivity changes could predict the location of fracture planes to some extent and reflect the expansion of subcritical cracks in the rock. This, in turn, enabled them to capture the development of damage during the AE quiet period. These studies suggest that resistivity is an effective parameter for reflecting rock damage and failure.

In addition, the resistivity method has numerous applications in earthquake monitoring and early warning. Over the past few decades, the use of electrical and magnetic methods has observed a significant number of seismic precursor anomalies, leading to electromagnetic methods being regarded as one of the most promising geophysical techniques for achieving breakthroughs in short-term earthquake prediction. Among these methods, the use of electrical resistivity is the most widely applied35. Xie et al.36 found that a decrease in the apparent resistivity was observed in the compressive strengthening region before the earthquake. Through statistical analysis, Du et al.37 found that the magnitude and duration of resistivity decreases exhibited a good linear statistical relationship with epicentral distance and earthquake magnitude. They also observed that, prior to the Wenchuan Ms8.0 earthquake, three nearby stations experienced synchronized decreases in resistivity.

In summary, resistivity can effectively reflect the process of rock damage and failure, and has the potential for prediction and early warning of such failures. However, current research primarily focuses on the resistivity change patterns of rocks under uniaxial compression, with insufficient studies on the resistivity changes, precursor characteristics, and influencing factors during shear processes. Additionally, there is a lack of complementary research on the integration of resistivity changes with AE signals for rock damage and failure monitoring and early warning.

In view of this, by conducting direct shear tests on saturated sandstone under different shear rates, and utilizing resistivity monitoring technology, acoustic emission technology, and DIC technology (Digital Image Correlation technology) to monitor the entire shear process in real-time, we aim to explore the resistivity and acoustic emission response characteristics during the damage and failure process of sandstone under different shear rates. We will analyze the influence of different shear rates on the response patterns of acoustic emission and resistivity, and use damage variables defined based on resistivity and acoustic emission signals to quantitatively analyze the shear damage and failure process of sandstone. Furthermore, we will discuss the precursor information before rock shear failure, aiming to provide experimental evidence for the early warning of rock instability and failure through the combined monitoring of resistivity and acoustic emission.

Test schemes

Preparation of rock samples

The rock samples used in this experiment were medium-grained red sandstone collected from Zigong, Sichuan. Large-volume rock specimens were cored, cut, and polished to minimize data dispersion. All experimental specimens were obtained from the same rock block. A total of 12 red sandstone cubic specimens were used in this experiment. Specimens with similar P-wave velocities were selected based on ultrasonic velocity testing. Since the shear tests are conducted under saturated conditions, wave velocity measurements were performed on saturated rock samples to ensure uniformity in their physical and mechanical properties.The measured P-wave velocities ranged from 3079 m/s to 3234 m/s, with an average velocity of 3177 m/s. The velocity variance was 2282.24 (m/s)2, and the sample standard deviation was 47.80 m/s, meeting the experimental requirements.According to the testing standards of the International Society for Rock Mechanics (ISRM), the rock samples were processed into cubic specimens measuring 100 mm × 100 mm × 100 mm. The parallelism of the end faces was controlled within ± 0.05 mm, and the flatness of the surfaces was controlled within ± 0.02 mm. X-ray diffraction (XRD) analysis indicated that the sandstone was primarily composed of sodium feldspar (52.3%), quartz (40.8%), and calcite (6.9%). No visible joints or fractures were observed on the surface of the specimens. Ultrasonic testing was used to select samples with similar initial wave velocities. Some of the rock specimens are shown in Fig. 1.

Fig. 1
figure 1

Red sandstone specimens.

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The experiment used a vacuum saturation apparatus and an oven to prepare saturated rock samples. The preparation process for the saturated samples is as follows: First, the standard rock sample is placed in an oven at 105°C and dried for 24 h before weighing. It is then placed back in the oven, and its mass is measured every hour until no further change in mass is observed, indicating that the sample has reached a fully dried state. This final dry mass is recorded as md. Next, the dried rock sample is completely immersed in a container filled with distilled water and placed in a vacuum chamber for vacuum treatment. The mass is measured every 4 h and recorded as m until no further change in mass is observed, at which point the sample is considered fully saturated. The final saturated mass is recorded as ms.

The water content of the rock at different immersion stages can be calculated using the following equation:

$$\omega = \frac{{m - m_{d} }}{{m_{d} }} \times 100\%$$
(1)

The relationship between the rock moisture content and soaking time is shown in Fig. 2, which shows that the rock reaches near saturation after 48 h. The basic physical and mechanical properties of the rock samples are presented in Table 1.

Fig. 2
figure 2

Curve of moisture content variation in red sandstone specimens.

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Table 1 Physical and mechanical properties of red sandstone specimens.
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Test equipment

This experiment primarily investigates the AE and resistivity response characteristics during the shear process, and analyzes the differences in the AE quiet period and resistivity changes under different shear rates. To gain a deeper understanding of the shear behavior and micro-damage mechanisms of rocks under static conditions, four slow loading rates were set: 0.1 mm/min, 0.2 mm/min, 0.5 mm/min, and 1.0 mm/min, with displacement-controlled loading. In each shear test, a normal stress of 1.0 MPa was applied. For each loading rate, three specimens were tested under the same experimental conditions. To keep the paper concise, only one representative specimen from each group was selected for analysis. The experiment was conducted using a JAL-1000 rock shear testing machine, which has a maximum vertical test pressure of 500 kN, a maximum horizontal shear force of 1000 kN, a relative measurement error within ± 0.5%, and a shear rate range of 0.001–1 mm/s.

In this study, the resistivity during the shear process was measured using a Keithley 2450 Sourcemeter, which has a resistance measurement range of 10 mΩ to 100 GΩ and a measurement accuracy of up to 0.012%, ensuring the precision of the results. The instrument is connected to a computer for real-time data acquisition and analysis. Conductive adhesive was uniformly applied to both end faces of the specimen, with electrode sheets placed on the upper and lower faces. A constant voltage of 24 V was applied, and insulating plates were placed between the pressure head and the electrode sheets.

For acoustic emission monitoring, the PCI-II multi-channel fully digital AE testing system from Physical Acoustics Corporation (PAC) was used, with a threshold set at 45 dB, preamplifier gain at 40 dB, and a sampling frequency of 1 MHz. To ensure adequate coupling between the AE probe and the specimen, a layer of petroleum jelly was applied to the contact surface of the probe and rock sample, and the probe was secured with insulating tape. To ensure accurate identification of AE events and avoid counting multiple events due to ringing or reflections, standard parameters recommended by the manufacturer and previous studies were used. The hit definition time (HDT) was set to 200 µs to group continuous threshold crossings into single events, and the hit lockout time (HLT) was set to 500 µs to prevent repeated counts due to reverberations. These settings ensure that individual AE events are accurately recorded and not misclassified due to system noise or signal reflection. Prior to each test, a Hsu-Nielsen pencil lead break was performed on the specimen surface for calibration.

To monitor the deformation and failure process of the rock during shear, a Digital Image Correlation (DIC) system was used to record the surface displacement of the specimen in real time. The experimental setup is shown in Fig. 3, and the loading method is illustrated in Fig. 4.

Fig. 3
figure 3

Experimental device.

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Fig. 4
figure 4

Schematic diagram of loading method.

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Test results and discussions

Analysis of shear mechanical properties and deformation characteristics of rocks under different shear rates

Figure 5 shows the relationship between shear stress and shear displacement at different shear rates. As the shear rate increases, the peak shear strength of the sandstone increases. At a shear rate of 0.1 mm/min, the peak strength is 2.39 MPa, while at 1 mm/min, the peak strength rises to 3.41 MPa, an increase of 42.6%. According to the strain rate effect theory, as the strain rate increases, the internal microcracks in the rock do not have enough time to propagate and coalesce, resulting in an increase in shear strength. At lower shear rates, multiple stress drops can be observed after the peak shear strength. The lower the shear rate, the more frequent the stress drops, and the shear failure of the rock exhibits a distinct progressive characteristic. In contrast, at a shear rate of 1 mm/min, after reaching the peak shear strength, the strength decreases rapidly, exhibiting a clear brittle shear failure.

Fig. 5
figure 5

Shear stress shear displacement relationship curve at different shear rates.

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To capture the progressive development of fracturing in the rock specimen under continuous shear loading, the cumulative AE ringing count rate as a function of time at different shear rates is shown in Fig. 6. It should be noted that, since the ringing count is influenced by both the amplitude and the duration of AE events, the contributions of event number and individual event intensity are not distinguished in the analysis. It can be observed from Fig. 6 that as the shear rate increases, the cumulative AE curve rises more rapidly, indicating a more abrupt failure behavior of the rock.

Fig. 6
figure 6

Curves of cumulative AE ringing count rate over time at different shear rates.

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Analysis of resistivity and acoustic emission response characteristics during the shear failure process

The resistivity of the sandstone specimens can be calculated using the following equation :

$$\rho = R\frac{S}{L}$$
(2)

where ρ is the resistivity, R is the resistance (in Ω), S is the cross-sectional area of the specimen (in m2), and L is the length of the specimen (in m). The ratio of the real-time resistivity ρ to the initial resistivity ρ₀ during the loading process is defined as the resistivity ratio α.

Figure 7 illustrates the shear stress, resistivity ratio, and AE ringing count as functions of time under different shear rates for red sandstone. Based on the mechanical behavior and AE response characteristics during the rock shear process, the shear stress-time curve can be divided into four distinct stages: compaction stage, elastic deformation stage, unstable crack development stage, and post-peak residual deformation stage. Each stage exhibits different patterns of resistivity and AE variations.

Fig. 7
figure 7

Curves of shear stress, resistivity, and acoustic emission ringing count rate vs. time during sandstone shear failure at different shear rates: (a) 0.1 mm/min; (b) 0.2 mm/min; (c) 0.5 mm/min; (d) 1.0 mm/min.

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Compaction Stage: In this stage, the internal pores of the specimen are compacted, microcracks are closed, and the particle contacts become more tightly bound. The shear stress curve shows a distinct concave shape with a slow increase. A small number of dense AE signals are detected during this stage. Due to adjustments in the internal pore structure, the original conductive pathways are disrupted, causing resistivity to fluctuate, with a slight overall increase.

Elastic Deformation Stage: As the specimen undergoes further compaction, the shear stress increases almost linearly. The AE signals vary significantly with different shear rates. At a shear rate of 0.1 mm/min, relatively stable acoustic emission signals were continuously recorded. While at a shear rate of 0.2 mm/min, the AE ringing count rate during this stage is significantly reduced. This is because a higher shear rate accelerates the crack propagation velocity, leaving the cracks insufficient time to develop and propagate slowly at multiple locations; instead, they propagate rapidly along a certain weak plane. Since the locations and quantity of crack propagation are relatively reduced, the number of acoustic emission events generated will also decrease accordingly, which in turn results in a reduction in the acoustic emission ring count rate.

At shear rates of 0.5 mm/min and 1.0 mm/min, almost no AE signals are detected, and the AE signal enters the quiet period. Notably, during this stage, the resistivity ratio continues to decrease, indicating localized damage inside the rock. Due to the presence of natural voids and fractures, rock is a typically heterogeneous material. Under loading, stress is initially concentrated at these microstructural defects, such as pores and cracks, leading to the initiation of localized damage or failure. At the scale of the entire specimen, the locations of these localized damages appear to be diffusely distributed, owing to the dispersed nature of pre-existing micro-defects within the rock.This facilitates the formation of new water-film-based conductive pathways, enhancing the overall electrical conductivity of the rock and thereby causing a decline in resistivity.

Figure 8 presents the strain maps recorded by DIC at different shear rates. Taking the A characteristic point on the stress-time curve (approximately 60% of the peak stress) as an example, it is observed that as the shear rate increases, strain localization becomes more pronounced. At a shear rate of 0.1 mm/min, the strain localization band is narrow and has not yet formed a through-going band (Fig. 8a), while at 1.0 mm/min, the strain localization band is significantly wider and has formed a continuous localized strain band (Fig. 8d). This indicates that with increasing shear rate, internal strain accumulation in the rock becomes more significant, leading to earlier brittle and sudden failure. It is important to note that during this period, AE signals remain in the quiet phase (Fig. 7c, d), making it difficult to predict the development of internal rock damage. However, the resistivity consistently decreases with the development of the strain localization band, effectively reflecting the gradual internal damage of the rock. This is significant for compensating for the inability of AE signals to capture internal damage during the quiet phase.

Fig. 8
figure 8

The contour map of the global strain field distribution corresponding to point A during the loading process at different shear rates: (a) 0.1 mm/min; (b) 0.2 mm/min; (c) 0.5 mm/min; (d) 1.0 mm/min.

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Unstable Crack Development Stage: In this stage, microcracks inside the rock enter an unstable expansion phase, and shear stress reaches its peak, accompanied by a brittle stress drop. At lower shear rates (Fig. 7a, b), the peak stress drop ranges from 14.8% to 20.1%, while at higher shear rates (Fig. 7c, d), the peak stress drop reaches up to 88.6%, indicating that with increasing shear rate, the abruptness of rock shear failure intensifies. The resistivity decreases significantly at the point of the first stress drop, suggesting that the resistivity drop can be used as a precursor to shear failure in saturated rocks. It is also noteworthy that, as the shear rate increases, the number of AE signals significantly decreases before the peak stress, entering a near-quiet period (Fig. 7c, 7d). This further demonstrates the complementary relationship between resistivity and AE, where resistivity can compensate for the inability of AE to reflect internal damage during the quiet phase.

Residual Deformation Stage: In this stage, particle sliding and fracture occur within the rock, resulting in shear failure, with the residual shear strength being the final strength. Resistivity remains relatively stable, accompanied by a small amount of AE activity.

From Fig. 7, it can be observed that during the unstable crack development stage, the shear stress experiences a slight drop before reaching the peak stress. This is due to the heterogeneity of the rock; under shear stress, localized stresses within the rock exceed its strength, causing a sudden release of stress and resulting in a stress drop. The changes in the internal pore structure of the rock caused by this stress release alter its conductivity, which is manifested as a sudden drop in resistivity. This is because the pores and fractures inside saturated rocks are filled with conductive aqueous solutions. During the shear failure process of rocks, the newly formed fractures interconnect with one another, allowing the originally scattered conductive channels to be connected. This forms a more unobstructed conductive network, which results in enhanced electrical conductivity of the rocks and a decrease in their electrical resistivity.

To compare the timing of the resistivity drop with that of the AE signals in predicting rock failure, the time of the resistivity drop (At the location indicated by the blue arrow in the figure) during the unstable crack development stage was compared with the time when a significant number of AE signals (At the location indicated by the red arrow in the figure) were generated. The results are shown in Table 2. Experimental data at different shear rates indicate that, overall, the resistivity drop occurs before the significant generation of AE signals, with the timing difference being 54 s earlier for the specimen at 0.1 mm/min, 45 s earlier for the specimen at 0.5 mm/min, and 12 s earlier for the specimen at 1.0 mm/min. Meanwhile, the variation curve of electrical resistivity clearly illustrates a downward trend, with a sharp drop ranging from 5.2% to 11.3%. This indicates that changes in resistivity can effectively reflect the evolution of the rock’s internal microstructure and serve as an early warning indicator for impending failure.

Table 2 Comparison of the time lead of resistivity drop before macroscopic failure with acoustic emission data at different shear rates.
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It is noteworthy that the abrupt drop in resistivity observed prior to rock shear failure in this experiment is consistent with the anomalous decrease in geoelectrical resistivity often recorded before earthquakes. For instance, resistivity monitoring data from stations around the Tangshan earthquake38 indicate that geoelectrical resistivity remained relatively stable from 1970 to 1972, but began to exhibit a significant declining anomaly at the end of 1972, which persisted for up to 2.5 years in and near the epicentral area. Prior to the Wenchuan earthquake, two monitoring stations recorded synchronized changes in resistivity37: CDU (Chengdu station), located 35 km from the epicenter, exhibited a 5.5% decrease; and JYO (Jiangyou station), 150 km from the epicenter, showed a 1.1% decrease. These changes followed a pattern of ‘mid- to short-term pre-seismic resistivity decrease → short-term pre-seismic resistivity increase → earthquake occurrence’ . Earthquakes are generally caused by fracturing or slipping of crustal rock layers under stress, which constitutes a form of shear failure. Geoelectrical resistivity has been recognized as an effective pre-seismic indicator, further supporting the notion that a sudden drop in resistivity may serve as a precursor to shear failure in rocks.

It should be noted that the present experiment was conducted using saturated sandstone, in which water plays a dominant role in electrical conduction. Given that geological bodies are typically water-bearing, this explains the similarity in resistivity variation patterns during shear processes in both laboratory and field settings. In contrast, conduction in dry rocks primarily depends on the conductivity of the solid mineral framework; therefore, the resistivity evolution and precursor characteristics of dry rock under shear will be addressed in a separate study.

Shear failure precursors based on resistivity and acoustic emission damage variables

As indicated by the previous analysis, resistivity can reflect the development of internal damage in the rock during the AE quiet period and can provide an earlier indication that the rock is approaching the failure stage. However, in Fig. 7, it is difficult to quantify the damage evolution and obtain failure precursor information solely through resistivity changes and AE parameters. Since both resistivity and AE signals are closely related to the internal structural changes and crack evolution in the rock, a method proposed by other researchers is adopted to further analyze the damage variable defined based on resistivity and AE information39.

The damage variable Dc based on AE can be expressed as40:

$$D_{{\text{c}}} = D_{{\text{u}}} \frac{{C_{{\text{d}}} }}{{C_{0} }} = \left( {1 - \frac{{\sigma_{{\text{c}}} }}{{\sigma_{{\text{p}}} }}} \right)\frac{{C_{{\text{d}}} }}{{C_{0} }}$$
(3)

where Du is the damage threshold value, Cd is the cumulative ringing counts at any given moment during the rock damage process, C0 is the cumulative AE ringing counts when the damage variable reaches the critical value Du, σc is the residual strength of the rock, σp is the peak strength of the rock.The damage state of the rock can be described by Eq. (3). When rocks are subjected to shear stress, microcracks initiate and propagate. Each cracking event generates an acoustic emission (AE) signal, and the cumulative ring-down count Cd can quantify the total energy release from all damage events. When the acoustic emission ringdown count increases abruptly, the cumulative ringdown count Cd rises significantly, leading to a corresponding increase in the damage variable Dc.

The damage variable Dφ based on resistivity can be expressed as:

$$D_{\varphi } = \frac{{{\Phi }_{0} - {\Phi }}}{{{\Phi }_{0} - {\Phi }_{{\text{s}}} }}$$
(4)

where Φ0 is the initial porosity of the material, Φ is the porosity at any given moment during the rock damage process, Φs is the porosity at the material’s failure point. The relationship between porosity and resistivity can be described by the conductivity theory formula for a two-phase medium proposed by Maxwell41:

$$\sigma_{0} = \sigma_{1} \frac{{3\sigma_{2} - 2{\Phi }(\sigma_{2} - \sigma_{1} )}}{{3\sigma_{1} + {\Phi }(\sigma_{2} - \sigma_{1} )}}$$
(5)

In the equation, σ1 and σ2 represent the conductivities of materials 1 and 2, respectively, σ0 is the overall conductivity of the medium, and Φ is the volume fraction of material 1 in the entire medium.Since Maxwell’s equations can describe the effective electrical conductivity (σ0) of two-phase media (e.g., rock matrix + pores/fractures), when rocks are subjected to shear stress, new cracks form and connect with existing pores/fractures. This process alters both the pore volume fraction (Φ) and the connectivity of conductive paths (such as water-filled pores). Therefore, Maxwell’s equations are capable of capturing how the electrical conductivity of the composite medium (rock + cracks) evolves when Φ (pore/fracture volume) changes due to shear-induced cracking.

Define material 1 as the pores or cracks. When pores or cracks are generated in the rock during the shearing process, they are assumed to be filled with water (w). Define material 2 as the water-bearing rock (R). The porosity of the rock expressed in terms of resistivity can be given as:

$$\Phi = \frac{{3\rho_{R} }}{{\rho_{W} + 2\rho_{R} }}$$
(6)

In the equation, ρW is the resistivity of water, and ρR is the resistivity of the water-bearing rock. Therefore, the variation curves of the damage variables expressed by acoustic emission and resistivity with time under different shear rates can be plotted, as shown in Fig. 9.

Fig. 9
figure 9

Curves of electrical resistivity and acoustic emission damage variable at different shear rates: (a) 0.1 mm/min; (b) 0.2 mm/min; (c) 0.5 mm/min; (d) 1.0 mm/min.

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As can be observed from Fig. 9, regardless of the shear rate (high or low), Dφ (the blue curve) exhibits a significant upward trend before the shear stress reaches its peak. This is because the pores and cracks in saturated rocks are filled with conductive aqueous solutions; the initiation and propagation of cracks rapidly alter pore connectivity, which is thus captured in advance via the resistivity-based damage variable Dφ. For higher shear rates (e.g., 0.5 mm/min and 1.0 mm/min), however, Dc (the red curve) only rises abruptly near the point of failure (when shear stress drops). This is due to the rapid coalescence of cracks and concentrated release of energy under high shear rates: the cumulative effect of acoustic emission signals (ring-down counts) is compressed into an extremely short period before failure, resulting in an extremely narrow “warning window” for Dc. Therefore, Dφ offers a greater advantage in early warning of shear failure in saturated rocks.

Discussion on the characterization results of the two damage models for the shear damage process of saturated sandstone

Acoustic emission (AE) originates from the release of elastic energy during material damage processes (e.g., crack initiation, propagation, and coalescence). When rocks are subjected to shear stress, microcracks initiate and propagate. Each cracking event generates an AE signal, and the cumulative ring-down count \({C}_{d}\) can quantify the total energy release from all damage events. Therefore, the AE-based damage model \({(D}_{c})\) correlates AE activity with the damage state. Since shear-induced cracking is a dynamic process involving continuous energy release, and AE can accurately capture this process, this model enables real-time quantification of damage evolution, making it suitable for monitoring the progression of shear failure.

The resistivity-based damage model (\({D}_{\varphi }\)) relies on the relationship between pore structure, electrical conductivity, and damage. The Maxwell formula is used to describe the effective electrical conductivity (\({\sigma }_{0}\)) of a two-phase medium (e.g., rock matrix + pores/fractures). When rocks are subjected to shear stress, new cracks form and connect existing pores/fractures, which alters the pore volume fraction \(\Phi\) and the connectivity of conductive paths (e.g., water-filled pores). Thus, the Maxwell formula can capture how the electrical conductivity of the composite medium (rock + cracks) evolves as \(\Phi\) (pore/fracture volume) changes due to shear-induced cracking. Since shear-induced cracking directly modifies the connectivity and volume of pores, and resistivity is highly sensitive to these changes (e.g., interconnected cracks create more conductive paths, reducing resistivity), the resistivity-based damage model can correlate macroscopic resistivity variations with the evolution of microscopic pores/fractures during shear deformation.

Note that the AE-based damage model is established on the assumption that during the rock damage process, the cumulative ring-down count is linearly proportional to the damage degree, and therefore, the more severe the damage, the higher the cumulative ring-down count of AE events. However, rock damage involves multiple stages, such as microcrack initiation, propagation, and coalescence. The characteristics of AE energy and ring-down counts may vary across different stages, making it difficult for the linear assumption to fully describe the nonlinear damage process. Meanwhile, the resistivity-based damage variable, on the other hand, is founded on the assumption that rock resistivity is solely controlled by porosity, and that the change in porosity has a monotonic functional relationship with the change in resistivity. In fact, the pore distribution (size, shape, connectivity) in rocks is highly heterogeneous and the Maxwell model, which relies on the assumption of a “uniformly mixed two-phase medium,” deviates from the actual rock structure, leading to insufficient accuracy in porosity derived from resistivity. However, since the process of shear-induced crack formation involves both mechanical damage and microstructural changes, the AE-based damage model tracks the dynamic process of crack propagation (energy release), while the resistivity-based damage model captures the structural impact of these cracks on material properties (changes in pore connectivity/volume). Their combination thus provides a more comprehensive description of shear-induced damage in rocks from dual perspectives.

Conclusions

To investigate the resistivity and acoustic emission response characteristics during the shear failure incubation process of rocks, shear tests were conducted on saturated red sandstone cubic samples under different loading rates. Real-time monitoring of resistivity and acoustic emission during the shear process was carried out. The main conclusions are as follows:

  1. (1)

    With the increase in shear rate, the peak shear strength of saturated sandstone increases, the number of stress drops after the peak decreases, and the failure mode transitions from progressive failure to catastrophic failure.

  2. (2)

    The shear failure process of saturated sandstone can be divided into four stages: compaction stage, elastic deformation stage, crack instability development stage, and residual deformation stage. Resistivity shows small fluctuations, steady decline, sudden drop, and stable phases, respectively, in these stages.

  3. (3)

    With the increase in shear rate, acoustic emission signals significantly decrease before the stress peak, and at higher shear rates, a quiet period is reached. Meanwhile, resistivity exhibits a noticeable downward trend during the acoustic emission quiet period, indicating that resistivity effectively reflects the internal damage development of the rock during the shear failure incubation process, thus compensating for the monitoring gap during the acoustic emission quiet period.

  4. (4)

    The damage variables based on resistivity and acoustic emission show good consistency in reflecting the shear damage of saturated sandstone. However, during the unstable crack propagation stage, the damage variable expressed by resistivity shows a sharper increase earlier than that expressed by acoustic emission, which gives resistivity-based damage variables an advantage in early warning of shear failure in saturated sandstone.