Experimental Study on Rockburst and Spalling Failure in Circular Openings for Deep Underground Engineering

Abstract

This study aims to simulate the process of rockburst and spalling failure of roadway surrounding rock under three-dimensional stress in deep rock engineering. Utilizing an independently developed true triaxial rockburst experimental setup, the failure process of a circular tunnel under initial in-situ stress at a depth of 500 m was investigated using red sandstone with prefabricated holes. A miniature camera device and acoustic emission (AE) monitoring system were used to monitor and record the experimental process in real time. Using the collected data, the process of rockburst and spalling failure of the circular tunnel was reproduced. Finally, the difference between rockburst and spalling failure was analyzed and compared based on four aspects of stress characteristics, acoustic emission characteristics, fragment characteristics, and V-shaped notch morphology characteristics. The experimental results show that the failure of surrounding rock was more likely to occur under dynamic disturbance load, resulting in particle ejection. The spalling failure was found to be a slow and gradual static failure process. The mechanism of rockburst was more complex involving tension-shear coupling failure, whereas, the mechanism of spalling failure was simple involving a tensile failure. Compared with spalling failure, rockburst was more intense, producing more debris, and the V-shaped notch was narrow and deep.

Highlights

• Failure process of rockburst and spalling is reproduced in a laboratory.

• The stress characteristics of rockburst and spalling failure are calculated based on elastic theory.

• Frequency-amplitude characteristics and crack types based on acoustic emission are analyzed.

• The failure intensity of rockburst and spalling is investigated based on the rock fragments and morphology of V-shaped notch.

• The failure process of rockburst and spalling is discussed along with strain energy.

1 Introduction

A large number of deep underground rock engineering projects such as mining, traffic tunnels, and diversion tunnels, have been started to fulfill the ever-growing needs of national economic construction and development. Due to the influence of a complex geological environment, engineering excavation disturbance, and other factors, rock masses in deep underground constructions showcase unconventional failure behavior, which is rarely seen in a shallow rock mass (Martin 1997). Depending on the physical properties of the rock mass as well as the loading conditions, failure can occur violently or gradually. Violent failure can be characterized as a brittle failure (i.e. a sudden loss of strength following little or no plastic deformation post-failure) or a rockburst when coupled with a rapid ejection. A gradual or non-violent failure can be characterized by spalling failure (i.e. non-violent brittle failure) (Keneti and Sainsbury 2018). Rockburst, a dynamic instability phenomenon, is characterized by fragments ejecting violently away from the surrounding rock and energy releasing abruptly (He et al. 2018), as shown in Fig. 1a. Spalling failure is characterized by thin plate-shaped rocks spalling from the surrounding rocks at low velocity, belonging to the static instability phenomenon (Hoek and Martin 2014), as shown in Fig. 1b. These incidents cause casualties and economic losses and pose threat to the deep rock engineering construction.

Fig. 1

Two typical failure modes of the surrounding rock

Researchers across the world have conducted several laboratory simulation studies to investigate the mechanism of spalling failure and rockburst in deep rock masses under extreme stresses. Lee and Haimson (1993) conducted true triaxial compression experiments on granite rock samples with prefabricated circular holes and found that cracks were densely distributed on both sidewalls and parallel to the sidewall, suggesting that spalling failure was mainly caused by tensile cracks. Qiu et al. (2014) studied the mechanism and evolution process of spalling failure using true triaxial loading and unloading experiments and discussed the severity of spalling failure based on the principle of energy balance. Hu et al. (2021) stated that spalling and buckling were two important stages of rock failure, and studied the influence of materials with different tensile strengths on the severity of the spalling failure. Su et al. (2020) studied the acoustic emission (AE) precursor characteristics of instability failure of coarse-grained granite under static or dynamic conditions. Ma and Liu (2022) analyzed the mechanism of slab collapse and the complex movement process of slab collapse by using the discontinuous deformation analysis (DDA) method. Li et al. (2017, 2018a, b) performed true triaxial unloading compression experiments to study the effects of different aspect ratios of a specimen and intermediate principal stresses on rock failure characteristics and found that unloading under true triaxial conditions would lead to spalling failure. Hidalgo and Nordlund (2012) compared laboratory test results with numerical simulation results to analyze the spalling failure process in hard rock. They further demonstrated that the crack initiation strain calculated in the laboratory test was related to the in-situ crack initiation strain.

In terms of the rockburst experiment, Liu et al. (2020) studied the temporal and spatial evolution characteristics of AE and thermal radiation characteristics of granite samples with a prefabricated circular hole under different confining pressures. He et al. (2012, 2015) carried out a true triaxial compression experiment by using cubic red sandstone with a hole in the middle and successfully simulated the rockburst phenomenon. Based on the observations, they concluded that the rockburst process occurred in three stages, i.e., vertical spalling, vertical slab buckling deformation, and rockburst damage. Gong et al. (2017, 2018, 2020; Gong and Si 2021) and Si et al. (2018, 2021) carried out a series of three-dimensional true triaxial compression experiments on red sandstone, marble, granite, and other rock samples with circular, rectangular, and D-shaped holes, and found that the laboratory test results were very similar to the in-situ rockburst characteristics. Zhao et al. (2020) performed triaxial compression experiments on sandstone specimens with a trapezoidal opening to study the influence of different lateral stresses on the rockburst process and failure characteristics. Zhang et al. (2019) used cubic granite with a circular hole to conduct a biaxial compression experiment to simulate the rockburst phenomenon, and studied the spectral characteristics and clustering characteristics of AE signals. Su et al. (2017a, b, 2018, 2019) used true triaxial test equipment to study the influence of loading rate, axial stress, radial stress, temperature, dynamic load frequency, and other factors on rockburst. Si et al. (2022a, b) investigated the rockburst process and characteristics of layered rock and sandstone under different stress states. Li et al. (2021) studied the mechanisms of structural-slip rockburst based on sound waves, acoustic emissions, and failure characteristics of the structural planes. He et al. (2021a, b, c) independently developed a novel high-pressure servo true triaxial rockburst equipment capable of multi-face unloading and conducted a double-faces unloading rockburst experiment on red sandstone to investigate the ejection velocity of rock fragments. Liu et al. (2021) carried out a double-face unloading rockburst experiment on bedding red sandstone and studied the anisotropic evolution process during rockburst.

The preceding studies have substantially advanced our understanding of spalling failure and rockburst in deep underground engineering, revealing the mechanism involved in spalling failure and rockburst. However, existing studies focus solely on either the spalling failure or the rockburst. According to Martin et al. (1999) and Du et al. (2016), there is a strong correlation between spalling failure and rockburst in surrounding rock, wherein, spalling failure is closely related to the triggering of rockburst. Diederichs (2007) stated that spalling failure of surrounding rock can occur before the rockburst, leading to unstable deformation of the approximately parallel rock slabs produced by the spalling, which creates conditions for the energy sudden release of rockburst. At present, very limited works concerning the relation between spalling failure and rockburst have been conducted. Thereby, this study presents two types of rock failure experiments using red sandstone with a prefabricated circular hole to investigate the commonalities and differences between spalling failure and rockburst. In addition, miniature cameras and AE monitoring systems were equipped to monitor and record the process of spalling failure and rockburst. The results are analyzed in detail with a focus on exploring the commonalities and differences between spalling failure and rockburst.

2 Experimental Design

2.1 Rock Specimen

The specimens were selected from red sandstone with good integrity and texture. The specimens were processed into cubic blocks of size 110 × 110 × 50 mm³ with circular holes (Φ50 mm), as shown in Fig. 2. The uniaxial compressive strength, elastic modulus, and Poisson's ratio of red sandstone were 87.07 MPa, 17.38 GPa, and 0.21, respectively. To reduce the experimental error, the surface flatness of the specimens was controlled at ± 0.05 mm, and the deviation of the verticality between adjacent surfaces was ± 0.25°. X-ray diffraction results show that the main mineral composition of sandstone was quartz (63.7%), calcite (13.1%), plagioclase (7.0%), potash feldspar (2.6%), hematite (1.9%), and clay minerals (11.7%).

Fig. 2

Experimental sample

2.2 Test Equipment

The experiment was carried out using an independently developed true triaxial rockburst test system, which mainly included a servo controller, main engine, specimen box, and hydraulic power source. The equipment can simulate rockburst caused by dynamic disturbance load. The maximum load capacity of the equipment was 500 kN, the loading accuracy of force was 0.5 kN/s, and the loading accuracy of displacement was 0.004 mm/s. During the loading process, the force and displacement were dynamically recorded in real time. Micro-II AE monitoring system which is developed by PAC Company was used in the experiment to simultaneously monitor AE signals in the rockburst and spalling failure. The sampling frequency and sampling length were 2 Msps and 4 k, respectively, i.e., 2 M data points were collected every second and 4096 data points were registered for every AE elastic wave. Both preamplifier parameters and acquisition threshold was set as 40 dB to eliminate the electrical, instrumental, and environmental noises. Two wide-band sensors with a resonant frequency of 0–1 MHz were used in the experiment and glued to the rigid plate. The experimental equipment is shown in Fig. 3.

Fig. 3

True triaxial rockburst test system

The sample was in a true triaxial state throughout the experiment. To observe the failure process in the circular hole, a special rigid plate was designed to record real-time visual data. The special rigid plate contains a circular hole of the same size as the sample. A miniature camera device was installed inside the rigid plate, and the shooting direction was aligned with the axis of the hole. Since the sample was in a closed environment during the testing, a light source was added to illuminate the inside of the circular hole to facilitate the observation of experimental phenomena. Figures 4 and 5 show the real-time video acquisition and schematic diagram of the miniature camera device installation.

Fig. 4

Real-time video acquisition device

Fig. 5

Schematic diagram of miniature camera device installation

2.3 Experimental Scheme

In the present study, the initial ground stress was calculated using the empirical formula developed by Huang et al. (2013) to predict ground stress in North China. The relation between in-situ stress and depth is as follows:

$$\left\{ {\begin{array}{*{20}l} {\sigma_{\text{H}} = 0.0233H + 4.6} \hfill \\ {\sigma_{\text{h}} = 0.0162H + 2.1} \hfill \\ {\sigma_{\text{v}} = \gamma H} \hfill \\ \end{array} } \right.$$

(1)

where σ_H is the maximum horizontal principal stress (MPa), σ_h is the minimum horizontal principal stress (MPa), σ_v is the vertical stress (MPa), γ is the bulk density (γ = 27 kN/m³) and H is the depth of the tunnel. The three-dimensional stress at 500 m was calculated as σ_H = 16.3 MPa, σ_v = 13.6 MPa, and σ_h = 10.2 MPa.

The maximum horizontal stress in practical tunnel design is generally parallel to the tunnel's axial direction, thus σ_H is set parallel to the axial direction of the circular hole. Two loading schemes were designed in this study to analyze the rockburst induced by dynamic disturbance load and spalling failure caused by the static load. Firstly, the initial stress level was synchronously loaded at 0.5 kN/s in the X, Y, and Z directions. Once the initial stress level was attained, the load was maintained constant for 60 s. Static load or dynamic disturbance load was then continuously applied in the Y direction using displacement control to simulate spalling failure or rockburst, respectively. The triaxial stresses, σ_H, σ_v, and σ_h, of the rock sample, correspond to the X, Y, and Z directions of the true triaxial rockburst test system, respectively.

Dynamic and static experiments were classified according to the strain rate of the load applied. The distinction between quasi-dynamic experiments and the static experiment was approximately marked at 5 × 10^–4 s⁻¹ (Cai et al. 2007a). In this experiment, ramp disturbance was selected as the dynamic disturbance load. Considering the loading capacity of the equipment, the dynamic disturbance rate was set as 0.5 mm/s (i.e., the strain rate was 4.5 × 10^–3 s⁻¹), which falls in the range of the dynamic loading. The static loading rate was set as 0.004 mm/s (i.e., the strain rate was 3.6 × 10^–5 s⁻¹). Based on the above description, the schematic diagram of the loading path is shown in Fig. 6. The same experiment was repeated thrice to reduce random error and representative samples were selected for analysis and description.

Fig. 6

Schematic of loading path

3 Experimental Results

3.1 Test Curves

Figure 7 shows the actual loading stress path curves of rockburst and spalling failure. During the test, the contact area of the rigid plate with the specimen in the X direction was larger than that in the Y and Z directions (the contact area in the X direction was about 1.01 × 10^–2 m², and in the Y, and Z directions was 5.5 × 10^–3 m²). However, since the loading rates of the forces were the same in all three directions (0.5 kN/s), the stress loading rate in the X direction was smaller than that in the Y and Z directions (the stress loading rate in the X direction was about 0.05 MPa/s, and in the Y, Z directions were 0.09 MPa/s). This implies that before the corresponding initial stress state was reached, the slope of the stress-loading curve in the X direction was smaller than that of the stress-loading curve in the Y and Z directions. It can be seen from Fig. 7a that stress rises sharply and reaches the peak value in a short time period due to ramp dynamic disturbance. The duration of dynamic disturbance lasted less than 3 s. However, since the spalling failure was caused by static loading, the whole loading process took around 350 s, as evident in Fig. 7b.

Fig. 7

Actual loading stress paths in true-triaxial tests

3.2 Failure Process of the Hole Sidewalls

A miniature camera was equipped to record the failure process of the circular hole during the experiment. The typical failure process of rockburst and spalling failure is shown in Figs. 8 and 9, respectively. Figure 8a marks the vertical stress at 13.6 MPa. Herein, the rock was in the initial stress state, and intact. No failure phenomenon was observed. The strain energy generated during the loading stage started accumulating within the surrounding rock, marking the rockburst incubation stage. When dynamic disturbance load was applied (i.e., σ_v = 50.5 MPa), the left sidewall began to experience initial damage, indicating that the stress concentration coefficient of the left sidewall was high. Small particle ejection was observed, but the ejection velocity was low. However, the right sidewall remained intact without damage, as shown in Fig. 8b. After 0.02 s, the vertical stress reached 52.3 MPa, and the second visible particle ejection was observed on the left sidewall (see Fig. 8c), with a significantly higher velocity than that observed in Fig. 8b. Formation of multiple rock slabs on the left side wall accompanied by sight bulging of the right sidewall was seen when σ_v reached 56.3 MPa, as shown in Fig. 8d. As the vertical stress continued to increase, gradual initiation of cracks happened on the left and right sidewalls, which further propagated and penetrated the rock. Rock slabs started to peel off from the left and right sidewalls, as shown in Fig. 8e–g. At 321.24 s, the vertical stress reached the maximum value (i.e., σ_v = 68.9 MPa), and a rockburst occurred. A large number of rock particles and rock fragments were propelled violently outwards from the left and right sidewalls, as shown in Fig. 8h. Based on the observation, the whole process of rockburst can be summarized into four stages: quiet period, particle ejection, rock slabbing, and rockburst.

Fig. 8

Failure process of rockburst

Fig. 9

Failure process of spalling failure

Figure 9 shows the process of spalling failure. When the vertical stress reached 13.6 MPa in Fig. 9a, no visible damage was seen. As the vertical stress continued to increase, micro-cracks appeared on the right sidewall and developed continuously, which resulted in lamellar rock slabs breaking outward to the surface, as shown in Fig. 9b, c. When σ_v = 61.0 MPa, cracks began to appear on the left sidewall, while the rock slabs on the right sidewall continued to develop and curl off towards the surface, resulting in small grains ejection at a low speed, as shown in Fig. 9d. The cracks on the left sidewall developed and expanded over time. The degree of damage on the left and right sidewalls gradually increased. Bulging and peeling off of a large number of rock slabs continued, as shown in Fig. 9e–g. In Fig. 9h, evident characteristics of spalling failure were seen on the left and right sidewalls when σ_v = 64.6 MPa. Many layered rock slabs were formed on the left and right sidewalls, which constantly flaked off from the parent rock under the action of gravity. Thus, the spalling failure process can be divided into four stages during the test: quiet period, particle ejection, rock slabbing, and spalling failure.

Conclusively, it was found that spalling failure and rockburst shared three common stages, but their failure characteristics vary distinctly. The spalling failure was a slow static failure process, whereas, the rockburst was a dynamic failure process. The strain energy in the rock mass dissipated due to crack propagation and the remaining energy was converted into kinetic energy as rock fragments ejected during the rockburst. However, there is not enough remaining energy that gets converted into kinetic energy during the spalling failure.

4 Results Analysis

To further study the difference between rockburst and spalling failure, a detailed analysis was conducted considering four aspects of stress characteristics, AE characteristics, fragment characteristics, and morphology characteristics of V-shaped notch based on simulation experimental results.

4.1 Stress Characteristics

The surrounding rock before failure is assumed to be a homogeneous, continuous, and isotropic elastic body that does not deform along the axial direction of the tunnel (i.e., it is regarded as a plane strain problem). According to the elastic mechanic’s theory, the maximum tangential stress can be obtained:

$$\sigma_{\theta \max } = 3p - q$$

(2)

where p and q are vertical stress and average horizontal stress, respectively. Let p = σ_v and q = σ_h. Then the maximum tangential stress can be expressed as,

$$\sigma_{\theta \max } = 3\sigma_{\text{v}} - \sigma_{\text{h}}$$

(3)

The corresponding stress values σ_v and σ_h are obtained for the sidewall initial damage of spalling failure and rockburst by the visual analysis of the video of the sidewall damage recorded during the test. Substituting σ_v and σ_h into Eq. (3), the maximum tangential stress (σ_θmax) required for sidewall initial failure is obtained. Table 1 lists the Y direction stress values of initial sidewall failure (σ_zi) and σ_θmax.

Table 1 Stress characteristics of sidewall initial fracture

It can be seen from Table 1 that the final failure stress of rockburst and spalling failure are 68.1 MPa and 62.9 MPa, respectively. The experimental results are consistent with the findings of Zhao (2000), which confirms that the dynamic strength of rock failure is higher than the static strength. Furthermore, the ratio of the maximum tangential stress to the uniaxial compressive strength of rockburst and spalling failure are 1.61 and 1.82, respectively. These results agree well with those of Gong et al. (2018) and Hu et al. (2019). This implies that compared with static load, the initial failure of surrounding rock under dynamic disturbance load requires less stress, that is, the initial failure of surrounding rock under dynamic disturbance load occurs sooner than that under static load. This is due to the fact that a high quantity of strain energy accumulates on the left and right sidewalls in a short period of time when a dynamic disturbance load is applied. When the accumulated strain energy exceeds the energy required for rock mass to fail, the strain energy is abruptly released from small areas on both sides of the hole. Spalling failure, on the other hand, is a slow and progressive failure process. In the case of spalling, the strain energy slowly accumulates in the rock mass, and its distribution around the holes is relatively uniform. As a result, the strain energy accumulating in the surrounding rock takes longer to achieve the strain energy required for failure.

4.2 AE Characteristics

The process can be classified into three stages based on the stress path: stage I is the initial stress loading stage, stage II is the stress holding stage, and stage III is the dynamic disturbance load stage or static load stage. Stage I can be subdivided into three sub-stages. Stage I₁ represents the three-way synchronous loading stage, stage I₂ represents the two-way synchronous loading stage, and stage I₃ represents the one-way loading stage.

Amplitude and peak frequency are the main parameters of AE characteristics and reflect the rich information on rock fracture. Figures 10 and 11 show the relationship between the amplitude and peak frequency of rockburst and spalling failure, respectively. As can be seen from Figs. 10 and 11, AE amplitude ranges from 40 to 100 dB and peak frequency ranges from 0 to 400 kHz. According to the experimental results, the amplitude can be divided into five groups: low amplitude (40–60 dB), middle amplitude (60–70 dB), middle and high amplitude (70–80 dB), high amplitude (80–90 dB), and ultra-high amplitude (90–100 dB). Similarly, the corresponding peak frequencies can be divided into four groups: low frequency (0–100 kHz), middle frequency (100–200 kHz), high frequency (200–350 kHz), and ultra-high frequency (350–400 kHz).

Fig. 10

The amplitude-frequency characteristic curves of rockburst

Fig. 11

The amplitude-frequency characteristic curves of spalling failure

During stage I₁, the rock is under triaxial compression and the internal primary cracks are closed_, as seen in Figs. 10 and 11. The AE signals are active, and most AE signals are in the range of low amplitude, medium frequency, and high frequency. Stage I₂ and stage I₃ are two-way loading and one-way loading, respectively, compared with stage I₁. The number of AE is less, and their frequency distribution gradually shifts from middle frequency and high frequency to middle frequency. Stage II is the stress-holding stage, in which the AE signals are scattered, the AE activity is low, and no damage occurs inside the sample. During stage III as seen in Fig. 10, the vertical stress increases dramatically due to dynamic disturbance load, resulting in multiple cracks intersecting each other, and AE signal activity increases. During the period of dynamic disturbance load (i.e., stage III), AE signals (> 70 dB) are generated frequently and concentrated in the range of medium frequency. Moreover, the quiet period of AE can be observed clearly. Stage III in Fig. 11 corresponds to the static load stage. Due to the slow loading rate during stage III, there are many AE signals generated with low amplitude having a frequency in the range of 100–350 kHz. According to the enlarged picture in Fig. 11, the AE signals with low and medium amplitude (i.e., 40–70 dB) are generated during the spalling failure ( to facilitate observation, 40–60 dB low amplitude signals are filtered in the local magnification). However, the quiet period of AE could not be observed during the spalling failure.

The characteristic parameters of AE are summarized in Table 2. The AE signal frequency of rockburst is distributed in the range of 100–200 kHz, while that of spalling failure is in the range of 100–350 kHz, indicating that the AE signal frequency of rockburst is lower than spalling failure. According to Cai et al. (2007b), the high frequency of the AE signal represents small-scale cracks and the low frequency represents large-scale cracks. Therefore, it can be inferred from the results that rockburst is mainly caused by large-scale cracks, while spalling failure is mainly caused by small-scale cracks. And the damage from rockburst, due to large-scale cracks, is more severe. In addition to this, the percentage of AE signals larger than 70 dB generated during rockburst is more than 70%, and the cumulative AE energy is as high as 4.64 × 10⁸ aJ, while the percentage of AE signals larger than 70 dB generated by spalling failure is less than 1%, and the cumulative AE energy is only 0.32 × 10⁸ aJ. With respect to the AE energy aspect, it can be said that rockburst is more severe than spalling failure. It is worth noting that the quiet period of AE can be observed during the rockburst, but there is no quiet period in spalling failure. This phenomenon is mainly due to the fact that rockburst is caused by large-scale cracks, which hinder the propagation of elastic waves generated by micro-cracks in the rock, resulting in only AE signals with high amplitude being received.

Table 2 Characteristic parameter of acoustic emission (AE)

The relationship between average frequency (AF) and RA (the ratio of rise time to amplitude) can further be used to classify micro-cracks in rocks (Ohno and Ohtsu 2010). Figure 12 shows the schematic illustration of the method to classify microcracks based on the scatters of AF–RA. A boundary line with slope k (AF/RA) is used to distinguish shear and tensile cracks, assuming k is equal to 1.2 (Wang et al. 2019a). Figures 13 and 14 show the kernel density of AF and RA at different stages of rockburst and spalling failure, and Fig. 15 shows the proportional change of shear (tensile) cracks. From Fig. 13 it can be seen that due to the closure of primary cracks, a large number of AE signals are generated in stage I₁, which are concentrated in the tension region. With the increase of stress, AE signals generated in I₂ and I₃ stages are less, but tensile cracks are still dominant. It can be seen from Fig. 15a that the proportion of tensile cracks in stages I₁, I_2, and I₃ of rockburst is greater than 60%, which is much larger than the proportion of shear cracks. In stage III, the concentrated area of AE gradually shifts from the tension region to the shear region, indicating that shear cracks are dominant during rockburst, however, a large number of tensile cracks are still present (shear cracks account for 58% and tensile cracks account for 42%). Figure 14 shows that AE signals are always concentrated in the tension region during spalling failure, and in stage III, tensile failure is dominant (70% tensile crack and 30% shear crack). It can be inferred from the above observations that the mechanism of rockburst is complex, which includes coupling of tension-shear cracks, while the mechanism of spalling failure is simple, including only tensile cracks.

Fig. 12

Schematic of crack type classification by AF and RA values

Fig. 13

Kernel density of AF and RA of rockburst

Fig. 14

Kernel density of AF and RA of spalling failure

Fig. 15

The ratio of shear (tensile) cracks to total cracks

4.3 Fragments Characteristics

After the experiment, rock fragments were collected, screened, and measured. Figures 16 and 17 show the fragments of rockburst and spalling failure, respectively. It can be seen from Figs. 16 and 17, that the amount of fragments of rockburst is much more than that of spalling failure. Furthermore, the morphological characteristics of fragments differ, with rockburst fragments being in long strips and spalling failure fragments being as flakes or plates. Figure 18 and Table 3 present the number of fragments and the ratio of width to length of fragments. Average number of fragments generated in rockburst is 39, which is far more than the number of fragments generated by spalling failure, indicating that the energy released by rockburst is greater than that released by spalling failure. Moreover, the average ratio of width to length of fragments in rockburst and spalling failure is 0.58 and 0.63, respectively, which proves that the rockburst is more violent than spalling failure.

Fig. 16

Classification of fragments of rockburst

Fig. 17

Classification of fragments of spalling failure

Fig. 18

Characteristics of width-to-length ratio

Table 3 Number of fragments and characteristics of width-to-length ratio

Fractal theory can be used to quantitatively describe various complex morphologies of different materials’ surfaces. Rock failure goes through the process of crack initiation, propagation, and penetration, during which a lot of energy is dissipated. Previous studies have demonstrated that the rock fragments possess the property of statistical self-similarity and the fractal dimension of fragments can reflect the severity of rock failure and energy consumption. The fractal dimension can be calculated in form of granularity–quantity, perimeter–quantity, and area–quantity by using the area, perimeter, length, and width of fragments.

The area of fragments is converted into equivalent side length L_eq, and the fractal dimension of granularity–quantity is expressed as:

$$\left\{ {\begin{array}{*{20}l} {N = N_0 \left( {L_{{\text{eq}}} /L_{{\text{eqmax}}} } \right)^{ - D} } \hfill \\ {L_{{\text{eq}}} = \sqrt[2]{l \times w}} \hfill \\ \end{array} } \right.$$

(4)

where N is the number of fragments whose equivalent side length is greater than L_eq, N₀ is the number of fragments whose equivalent side length is L_eqmax (N₀ = 1), D is the fractal dimension, w and l are width and length of fragments, respectively. The logarithmic relationship between L_eqmax/L_eq and N/N₀ is shown in Fig. 19a. The absolute value of the slope of the linear fitting curve in Fig. 19a is the fractal dimension of granularity–quantity. The fractal dimension of perimeter–quantity and area–quantity can be calculated using a similar method.

Fig. 19

Characteristics of fractal dimension

The fractal dimensions are summarized in Table 4 and Fig. 19. For rockburst, the average fractal dimensions of granularity–quantity, perimeter–quantity, and area–quantity are 2.43, 2.15, and 1.35, respectively. For spalling failure, the average fractal dimensions of granularity–quantity, perimeter–quantity, and area–quantity are 2.41, 2.12, and 1.33, respectively. Although fractal dimensions obtained by different calculation methods are different, in general, the fractal dimensions of spalling failure are smaller than those of rockburst. The fractal dimension reflects the severity of rock failure. The larger the fractal dimension, the more violent rock failure. Therefore, the results further indicate that the rockburst is more violent than spalling failure.

Table 4 Fractal dimensions of fragments

4.4 Morphology Characteristics of V-shaped Notch

Figures 20 and 21 show the overall and local damage suffered by the samples after rockburst and spalling failure. It can be seen that rockburst and spalling failure occurred on both sidewalls of the hole, along with the formation of V-shaped notches. However, there is a large difference in the morphology characteristics of V-shaped notches between rockburst and spalling failure. Rock samples of rockburst experience violent damage which is in contrast to the spalling failure. A lot of tensile cracks can be observed around the middle of the hole, and two dominant shear cracks can be seen along the diagonal of the rock samples (see Fig. 20). Whereas, rock samples of spalling failure are intact and just a few tensile cracks can be seen in the V-shaped notches (see Fig. 21). Therefore, the rockburst is characterized by shear-tensile failure, whereas the spalling failure is characterized by tensile failure. Furthermore, both the rockburst and the spalling failure produce multilayer rock slabs, demonstrating that the rockburst and spalling failure evolve layer by layer from the surface of the tunnel to the deep surrounding rock. The V-shaped notches boundary of rockburst is jagged, which is more complex than the spalling failure, whereas the V-shaped notches boundary of spalling failure is parallel to the axis of the hole. Figure 22 shows the failure mode of the tunnel in the engineering site, which is consistent with the experimental result presented in Figs. 20 and 21. This indicates that the experimental result in this paper is reliable and effective to simulate the rockburst and spalling failure.

Fig. 20

Photos of specimens after rockburst

Fig. 21

Photos of specimens after spalling failure

Fig. 22

On-site failure model of surrounding rock

The rock sample photos are imported into the image processing software, and the outline is sketched with smooth curves, as shown in Fig. 23. The depth and angle of V-shaped notches are calculated as suggested by Wang et al. (2019a) (see Fig. 24) and are presented in Table 5 and Fig. 25. The result shows that the average angles of the left and right V-shaped notch of rockburst are 84.3° and 89.7°, respectively, and the average depths are 5.12 mm and 6.62 mm, respectively. Whereas, the average angles of the left and right V-shaped notch of spalling failure are 102.3° and 103.7°, and the average depths are 2.78 mm and 3.23 mm, respectively. In contrast, V-shaped notches of rockburst are narrow and deep, while V-shaped notches of spalling failure are wide and shallow, which demonstrates that the damage scope of rockburst is smaller, and energy is released in a small area, leading to the violent ejection of rock fragments. However, the damage scope of spalling failure is large, and the energy is gradually released in a large area. The energy release is relatively slow, and there is no fragment ejection with high speed. It should be noted that the angles and depths on both sidewalls should be symmetrically distributed, however, the experimental results do not show the feature of symmetrical distribution, which may be caused by the heterogeneity of the rock.

Fig. 23

Schematic diagram of V-shaped

Fig. 24

Schematic diagram of V-shaped notch

Table 5 Morphological characteristics of V-shaped notch

Fig. 25

Depth and angle of V-shaped notch

5 Discussion

5.1 Influence of Scale Effect

The scale effect is a common concern in the experimental studies of rock mechanical properties in the laboratory. Generally, to satisfy 3–5 times the excavation radius, a large-scale physical model experiment is usually used (seen Fig. 26). Furthermore, the experimental sample was made using similar materials, such as gypsum and concrete, which although have similar mechanical behavior, are different from the rock material. Reproducing the rockburst process is a challenging task. If a large-scale rock block is used to simulate a rockburst, two primary problems will encounter. One is the difficulty of sampling on site, and the other is the high requirement of the loading capacity of the experimental machine. Therefore, some scholars, such as (i) Gong et al. (2018); (ii) Luo et al. (2020); (iii) Wang et al. (2019b) employed small-scale rock samples with a circular hole in the center to simulate rockburst (seen Fig. 27). In addition, Martin (1997) conducted compression test on granite with different hole diameters. The result shows that the ratio of tangential stress to uniaxial compression strength will increase sharply when the hole diameters are less than 50 mm, which will result in an inaccurate experiment result. Based on the above reason, in this study, a circular hole with 50 mm diameters was adopted in the experimental tests considering the available testing conditions. Though the size of rock specimens used in this paper cannot satisfy 3–5 times the excavation radius, the experiment result can help enhance the understanding of rockburst and spalling failure.

Fig. 26

Large-scale physical model experiment

Fig. 27

Small-scale rock block physical model experiment

5.2 Influence of Loading Mode on Failure Process

Figure 28 is a schematic diagram showing the evolution of rock failure of rockburst and spalling failure. As mentioned in Sect. 3.2, the failure process of rockburst and spalling failure can be divided into four stages, i.e., quiet period, particle ejection period, rock slabbing period, and rockburst or spalling failure period. The characteristics of each stage can be stated as follows:

• 1. The quiet period: The tangential stress reaches σ_θ1. No macroscopic damage can be seen on the sidewall, but micro-cracks have begun to propagate in the surrounding rock (see Fig. 28a).

• 2. The particle ejection period: During this period, no visible buckling deformation appears on the sidewall and the tensile crack propagates along the direction of the tangential stress. The tangential stress reaches σ_θ2 and particle ejection from the center of the sidewalls initiates (see Fig. 28b). This demonstrates that some micro-cracks have intersected each other on the sidewall, but there is no visible accumulation of fragments in the bottom of the hole because the ejected particles are small.

• 3. The rock slabbing period: As the tangential stress reaches σ_θ3, the sidewall begins to deform and the rock near the surface splits into small rock plates, which continuously open outward (see Fig. 28c). A large number of micro-cracks intersect and coalesce to form a larger-scale crack, and visible rock slabbing occurs.

• 4. The rockburst or spalling failure period: The tangential stress reaches (σ_θ3 + Δ1), buckled rock plates instantaneously fracture and separate from the sidewall, triggering the rockburst. The elastic energy stored in these rock plates is suddenly released, part of the energy converts into dissipative energy by rock breaking, and part of the energy converts into the ejection kinetic energy of fragments, resulting in rock fragments being thrown into the hole space at high speed (see Fig. 28d). However, when the tangential stress reaches (σ_θ3 + Δ2) (noting that the Δ2 is less than Δ1), the spalling damage is further evolved, and the tensile crack gradually propagates toward the inside of the sidewall. Multiple cracks propagate and penetrate simultaneously, resulting in the frizzy rock plates to continuously open and slip from the sidewalls with no abrupt ejection (see Fig. 28e).

Fig. 28

Schematic diagram of the four stages of rockburst and spalling failure

It can be inferred that if the tangential stress is increasing when the spalling failure occurs, i.e., Δ2 comes closer to Δ1 gradually, a rockburst will occur accompanied by violent ejection of rock fragments. Previous studies have shown that spalling failure is an inevitable and precursor phenomenon for rockburst in intact rocks around deep tunnels (He et al. 2010; Gong et al. 2019). Historically, spalling failure has often been used as an indicator to provide a warning for rockburst. However, it should be noted that spalling failure does not imply that the occurrence of rockburst is inevitable. Although every rockburst is accompanied by spalling failures.

Comparison of rockburst and spalling failure at σ_v = 55 MPa and σ_v = 60 MPa, as presented in Fig. 29, has been done to study the failure characteristics of surrounding rock under static load and dynamic disturbance load. When σ_v = 55 MPa, a visible failure phenomenon occurs on the left sidewall with a large number of rock fragments peeling off from the parent rock, while the right sidewall remains intact (see Fig. 29a). Compared with rockburst, the severity of spalling failure is significantly less when σ_v = 55 MPa. There is no apparent failure on either of the sidewalls, however, a small bulging of rock slabs on the right sidewall is seen in Fig. 29b.

Fig. 29

Failure characteristics of the sidewalls

When σ_v = 60 MPa, both sidewalls are damaged severely, a large number of rock fragments buckle and bulge steadily, and even some rock fragments are ejected at a high speed (see Fig. 29a). However, for spalling failure, although the left and right sidewalls are similarly damaged to a large extent when σ_v = 60 MPa, with multiple layered rock fragmentation, no ejection of fragments happens. The rock fragments only slide slowly under the action of gravity. Therefore, the severity of spalling failure is slight than rockburst.

This indicates that the failure of surrounding rock under dynamic disturbance load is more apparent than spalling failure under the same vertical stress, and high-speed rock fragment ejection is more likely to occur. Therefore, in deep underground rock engineering, it is necessary to avoid the generation of dynamic disturbance load or reduce the rate of dynamic disturbance load.

5.3 Strain Energy of the Surrounding Rock

Rock masses can store a large amount of strain energy under high-stress conditions. Once the stored strain energy exceeds the strain energy required for rock failure, the strain energy inside the rock releases quickly, resulting in serious disasters. Before the onset of rock failure, it is assumed that the rock element is a continuous and uniform elastic body. The elastic strain energy in the rock can be calculated according to the Eq. (5)

$$\left\{ {\begin{array}{*{20}l} {W = \int {F_X } {\text{d}}L_X + \int {F_Y } {\text{d}}L_Y + \int {F_Z } {\text{d}}L_Z } \hfill \\ {V_\varepsilon = \frac{W}{V} } \hfill \\ \end{array} } \right.$$

(5)

where W is the strain energy, i.e., the work done by external force; F_X, F_Y, F_Z and L_X, L_Y, L_Z are the forces and displacements in the direction of X, Y, Z, respectively; V is the rock specimen volume (V = 5.07 × 10^–4 m³); and V_ε is the strain energy density.

The forces and displacements in the X, Y, and Z directions were measured when the rockburst or spalling failure occurred. The strain energy in all three directions and the strain energy density of the specimen was calculated. The results are summarized in Table 6. The result in Table 6 shows that the average strain energy density of rockburst is 798.80 kJ/m³, and that of spalling failure is 739.13 kJ/m³. The strain energy released by the surrounding rock of the roadway under dynamic disturbance load is higher than that released under static load, thus the severity of rockburst is higher than spalling failure as well, which is consistent with the previous research conclusions.

Table 6 Strain energy and strain energy density of specimens

Rockburst or spalling failure will happen only when the strain energy accumulated in the rocks exceeds the energy that is necessary for rock failure, and there is enough excess energy (ΔE) that can be released in the form of kinetic energy or other forms. In the uniaxial compression test, it is assumed that the critical maximum principal strain before the rockburst or spalling failure is equal to the axial strain at the peak stress. The excess energy stored in the sample is mainly released, which induces the rockburst or spalling failure (He et al. 2012). The energy calculation model is shown in Fig. 30.

Fig. 30

Energy calculation model (He et al. 2012)

The mechanism of the rockburst and spalling failure can be analyzed according to the failure process discusses in Sect. 5.2, from the viewpoint of energy, as illustrated in Fig. 31.

Fig. 31

Schematic illustration of the energy evolution

Firstly, it is assumed that the required energy for rock failure under the uniaxial compression test is $E_0$.

Secondly, significant elastic strain energy is stored in the surrounding rocks during the quiet period of rockburst and spalling failure. Since the stress is less than the strength of the rocks, the stored strain energy $E_1^{\prime}$ and $E_2^{\prime}$ is lower than $E_0$ ($E_1^{\prime}$ and $E_2^{\prime}$ are stored strain energy during the quiet period of rockburst and spalling failure, respectively).

Thirdly, both sidewalls begin to exhibit initial failure in both rockburst and spalling failure after the quiet period, i.e., the stored strain energy $E_1^{\prime\prime}$ and $E_2^{\prime\prime}$ is higher than $E_0$ ($E_1^{\prime\prime}$ and $E_2^{\prime\prime}$ are stored strain energy of rockburst and spalling failure when the initial failure occurred, respectively). However, $E_1^{\prime\prime}$ and $E_2^{\prime\prime}$ is not large enough to cause violent particle ejection and excess energy is just dissipated by the cracks propagation and plastic deformation.

Finally, when the rockburst or spalling failure occurs, the stored strain energy $E_1$ and $E_2$ surpasses $E_0$, as shown in Fig. 31, resulting in serious failure on both left and right sidewalls. However, the excess energy $\Delta E_1$ of spalling failure is lower than the excess energy $\Delta E_2$ of a rockburst. This indicates that the excess energy $\Delta E_1$ is all consumed by the cracks propagation, resulting in multiple rock plate exfoliation and no violent particle ejection. The excess energy $\Delta E_2$ is consumed not only by the cracks propagation but also part of $\Delta E_2$ is converted to kinetic energy, resulting in violent particle ejection.

6 Conclusions

Rockburst caused by the dynamic disturbance load and the spalling failure caused by the static load was investigated using a cubic red sandstone with a circular hole. Simultaneously, the AE signals and failure process was monitored and collected by the AE system and miniature camera. The experiment results were analyzed and discussed in detail. The main conclusions are as follows:

• 1. The evolution process of rockburst and spalling failure was reproduced. Rockburst failure was a dynamic phenomenon and usually occurred suddenly and violently. The process of rockburst could be divided into four stages: quiet period, particle ejection, rock slabbing, and rockburst. The spalling failure was a slow and progressive static failure, which included four stages: quiet period, particle ejection, rock slabbing, and spalling failure. Thus, spalling failure can be regarded as a precursor phenomenon of rockburst failure.

• 2. The final failure strength of the surrounding rock under dynamic disturbance load was higher than that under static load. However, under dynamic disturbance load, the initial failure stress of the surrounding rock was lower than that under static load, indicating that the surrounding rock was more prone to failure under dynamic disturbance load.

• 3. The AE signals with high amplitude generated during the rockburst were distributed in the range of 100–200 kHz. However, the AE signals of spalling failure were distributed in the range of 100–350 kHz, wherein, all of the AE signals were of low amplitude, indicating that the spalling failure was caused by the expansion of small-scale cracks. Tensile cracks predominate in the early stages of rockburst, however, when rockburst occurs, a substantial number of shear cracks were formed. Furthermore, the proportion of tensile cracks in the entire spalling failure process was always higher than that of shear cracks.

• 4. Rockburst produced a greater number of fragments than spalling failure. The fragments of rockburst were in form of long strips, while fragments of spalling failure were in form of flakes or plates. Furthermore, the rockburst pieces had a bigger fractal dimension than the spalling failure fragments, indicating that the rockburst was more severe.

• 5. Both rockburst and spalling failure generated visible V-shaped notches, but their morphological characteristics were different. The angle of rockburst V-shaped notches was smaller than that of spalling failure, but the depth was greater. Rockburst had a narrow and deep V-shaped notch, whereas spalling failure had a wide and shallow V-shaped notch.