1 Introduction

Layered rock mass structure is common in engineering rock mass. Different layers of rock have different mechanical properties, which makes the layered rock mass with heterogeneity have strong anisotropy (Wang et al. 2019; Tavallali et al. 2010; Meng et al. 2021; Yang et al. 2021a, b; Du et al. 2018). As a result, its mechanical behavior and response characteristics in engineering rock mass become complex and unpredictable, and the interface between rock layers has become a key area for rock mass failure and sliding. Especially under the action of external disturbances such as excavation unloading, the internal stress of layered rock mass is redistributed, which can easily cause the expansion and connection of internal primary fissures, joints and other defects. It further reduces the overall stability of layered rock mass, and even induces geological disasters such as mine slope landslide, mine and tunnel collapse (Cao et al. 2016a, b; Cao et al. 2016a, b; Zhao et al. 2018; Wang et al. 2023; Li et al. 2020). Therefore, it is of great significance to study further the mechanical behavior and fracture mode of fissured layered rock mass for reducing engineering risk.

In order to reveal the failure behavior of rock mass with defects, and understand the internal mechanism of its failure, many scholars have conducted in-depth research on it (Chen et al. 2020a, b; Xia et al. 2020; Liu et al. 2022). Chen et al. (2020a, b) reproduced the 3D cracking behavior of non-persistent joints specimen by a numerical method, and identified five types of fracture patterns and 12 types of failure modes of jointed rocks. Hu et al. (2020) found that the mechanical parameters and final failure mode of fissured layered rock samples were affected by rock strength and fissure angle, and the failure modes were divided into two major categories of coalescence mode and no-coalescence mode. Xu et al. (2017) established the elastic–plastic model of layered rock mass, and proposed a damage index reflecting the damage and failure degree of interlayered rock and bedding plane. Yuan et al. (2023) studied the influence of fracture length and inclination angle on the mechanical properties and failure characteristics of composite rock mass, and found that fracture inclination angle and rock material would interfere with its failure type, and fracture length was the main factor determining its fragmentation degree. Zhang et al. (2023) conducted triaxial compression tests on mudstone samples containing weak-interlayer, and found that their shear strength gradually decreased with the increase of thickness and dip angle of weak interlayer, and different dip angle and thickness of weak interlayers would affect its final failure modes.

The above scholars have focused on the crack propagation process and final failure mode of fissured rock mass, but the research on revealing its internal damage, and the evolution law of macroscopic cracks is not sufficient. As a technique for non-destructive monitoring of acoustic signals generated inside the sample, AE can reflect the process of progressive damage of rock (Cheon et al. 2011; Kong et al. 2017; Li et al. 2019; Shi et al. 2019). In recent years, researchers have conducted in-depth analysis of rock failure by using AE signal characteristics (Zhao et al. 2023; Pan et al. 2018; Yang et al. 2019), and achieved some meaningful results. Zhao et al. (2020) analyzed the distribution characteristics of AE signals of different frequency bands and amplitudes during rock deformation and failure based on the relationship between the loading stress corresponding to the minimum average frequency centroid of AE signals and peak stress. Li et al. (2021) obtained the structural characteristics of coal rock masses associated with damage at different loading stages by analyzing the AE waveforms, indicating that the AE energy is concentrated at low-frequency in the critical stage of instability and failure. Zhou et al. (2021) analyzed the AE source location distribution characteristics and frequency variation law of rock crack evolution process under different rock combination modes and prefabricated fissures with different orientation. Zhang et al. (2018) explored the mechanical properties and damage modes of shale at different bedding angles, and found that the sudden drop of AE time sequence correlation dimension values can be used as an early warning of imminent instability. Ma et al. (2023) studied the influence of fissure angles, lengths and positions on microcrack evolution and rock bursting of layered and heterogeneous rock masses, and found that among prefabricated fissures in strong rock mass, the number of AE events at peak strength of fissured layered rock mass is the largest. Wang et al. (2021) used AE location technique to explore the failure process of rock samples with different crack inclination angles, and found that the initial damage and damage rate of rock samples with a crack angle of 45°were the largest. Yang et al. (2021a, b) explored the crack evolution of fissured rock. Based on the AE source location, it was found that the variation of rock bridge inclination angle would affect the main damage zone formed by the accumulation of high-energy AE events and the mechanism driving internal cracking. He et al. (2009) conducted dynamic unloading tests on sedimentary limestone samples, obtained the frequency-amplitude relationship figures of AE signals during the rock burst stage, and found that high amplitude and low frequency events could be observed near the rock burst failure stage.

At present, the research on crack propagation and failure mode of fissured rock mass is mostly concentrated on homogeneous rock mass or homogeneous rock mass with different bedding dip angles. The research results have certain significance for understanding the crack propagation process and final failure mode of rock mass with defects. However, there are few reports on the heterogeneous layered rock mass with fissures, and the research on the internal damage and crack propagation evolution of layered rock mass with multiple fissures is not sufficient. In reality, most of the rock mass is this layered structure, and its crack propagation evolution law and failure mode are more complex. Therefore, this study explores the mechanical properties of fissured layered rock mass with different dip angle under uniaxial compression and the characteristics of AE parameters during fracture process. The influence of fissure dip angle on progressive damage and macroscopic fracture of layered rock mass is explored. The fracture mode, local stress variation characteristics and stress field evolution law of fissured layered rock mass are analyzed from the microscopic point of view.

2 Test scheme and process

2.1 Specimen preparation

Based on the ISRM classification of uniaxial rock compressive strength (Brown 1981), ordinary Portland cement (P.O42.5) and quartz sand with particle size of 0.6 mm ~ 1.18 mm and water were used to prepare rock-like materials A and B in accordance with the properties of sandstone and marl respectively according to the mass ratio of 1: 4: 0.33 and 3: 1: 1. The prepared rock-like material was poured into a rectangular mold inserted into an intermediate baffle and a stainless-steel sheet to prepare a layered rock mass with two sets of parallel fissures. The size of the layered rock mass is 150 mm × 75 mm × 30 mm. The dimensions of rock-like materials A and B in layered rock mass are both height × width × thickness = 75 mm × 75 mm × 30 mm. The width and length of the fissures are 1.5 mm and 20 mm, respectively. The center spacing of the same set of fissures is 15 mm, as shown in Fig. 1. The fissure dip angle is the inclination of the fissure relative to the horizontal plane. Based on the fissure dip angle of the layered rock mass, the specimens are numbered by L-α, and α is the fissure dip angle, ranging from 0 to 90°. Three parallel specimens were made at each angle, and a total of 21 specimens were made.

Fig. 1
figure 1

Testing procedures a layered rock mass dimension and fissure arrangement; b uniaxial loading control system; c AE monitoring device and AE sensor arrangement; d industrial camera

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2.2 Experimental system and scheme

The uniaxial compression test was carried out by using YAW-2000kN microcomputer controlled electro-hydraulic servo pressure testing machine, as shown in Fig. 1b. This test adopts displacement loading, and the loading rate is 0.01 mm s−1 to ensure that the test is in a quasi-static loading state. The DS2 AE system is used to monitor AE events. The sampling frequency is 1 MHz, and the acquisition threshold is set to 40 dB, as shown in Fig. 1c. At the beginning of the experiment, the AE monitoring system and the loading system were turned on at the same time, and the test data were collected in real time. The whole failure process of the sample was recorded by industrial camera, as shown in Fig. 1d.

The stress–strain curves of specimens A, B and intact layered rock mass AB are shown in Fig. 2. The basic physical and mechanical parameters are shown in Table 1. The peak stress, elastic modulus and peak strain of specimen AB are between specimen A and specimen B, indicating that the combination of rock A and rock B changes the physical and mechanical properties of a single lithology, increasing and decreasing their respective strengths respectively.

Fig. 2
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Axial stress–strain curves of Layer A, Layer B and intact layered rock mass under uniaxial compression

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Table 1 Basic physical and mechanical parameters of rock-like material
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3 Results and discussion

3.1 Mechanical properties

The peak strength and elastic modulus of prefabricated fissured layered rock mass with different dip angles are shown in Fig. 3. Considering the discreteness of the data, the average values of the peak strength and elastic modulus of the specimens are used to represent the overall trend in the study. Owing to the intact layered rock mass is not weakened by fissures, its peak strength and elastic modulus are the highest. With the increase of fissure dip angle α, the peak strength and elastic modulus of each specimen show a trend of decreasing first and then increasing. Because the fissures with different dip angles control the development and propagation path of the cracks, the change of the dip angle of the fissures reduces the mechanical properties of the layered rock mass to varying degrees. Compared with the intact layered rock mass, the peak strength and elastic modulus of the L-30 specimen are the most seriously weakened, which are reduced by 51.87% and 30.01%, respectively. This is mainly due to the cracks generated at the tip of each group of fissures in the L-30 specimen gradually propagation and coalescence during the loading process, the cracks at the two fissure tips near the interface also propagation and coalescence, resulting in rock swelling phenomenon at the interface. This greatly reduces the bearing capacity of the specimen, making the 30°fissure angle the dominant angle for the failure of the fissured layered rock mass. However, the fissures in the L-90 specimen are parallel to the loading direction, and the stress concentration at the crack tip is not obvious, which makes it significantly less affected by fissure weakening than other specimens, that is, its peak strength and elastic modulus are higher than those of the other fissured layered rock mass, indicating that the fissure dip angle α has obvious influence on the mechanical parameters of the layered rock mass. For example, the peak strength and elastic modulus of the L-90 specimen are about 25.06 MPa and 5.66 GPa, which are about 1.55 times and 1.12 times that of the L-30 specimen.

Fig. 3
figure 3

The peak stress and elastic modulus of layered rock mass with different fissure dip angles

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In order to quantitatively study the relationship between α and peak strength and elastic modulus, polynomial fitting is performed on the peak strength and elastic modulus of fissured layered rock mass specimens. The red dotted line in Fig. 3 is a polynomial fitting curve. The polynomial fitting equations of peak strength and elastic modulus are as follows:

$$\sigma_{c} = {18}.{26548} - 0.{13426}\alpha + 0.00{24}\alpha^{{2}}$$
(1)

Goodness of fit R2 = 0.95624,

$$E = {5}.{4881} - 0.0{1855}\alpha + 0.000{232275}\alpha^{{2}}$$
(2)

Goodness of fit R2 = 0.90585.where σc is the peak strength of the specimen in MPa; E is the elastic modulus of the specimen in GPa; α is the dip angle of fissure. From the fitting characteristic curve of mechanical parameters, it can be clearly seen that the peak strength and elastic modulus decrease first and then increase with the increase of α.

3.2 AE characteristics

3.2.1 AE counts and cumulative AE counts characteristics

Figure 4 shows the AE counts and cumulative AE counts of fissured layered rock mass with different dip angles. According to the stress–strain curve and the cumulative counts characteristics of AE, four stress feature points are determined (Cai 2010). The progressive failure stage of fissured layered rock mass under uniaxial compression is divided into five stages I ~ V (Zhao et al. 2020; Moradian et al. 2016). They are crack closure stage (a–b), linear elastic deformation stage (b–c), stable crack growth stage (c–d), unstable crack growth stage (d–e) and post-peak failure stage (e–f), respectively. The stresses corresponding to point b–e are crack closure stress σcb, crack initiation stress σcc, crack damage stress σcd and peak stress σc, respectively. At the initial stage of loading, the original cracks inside the layered rock mass are gradually compacted, resulting in a small number of AE events, and the cumulative AE counts are relatively flat. In the I stage, the AE counts are not significantly affected by the fissure dip angle α. The AE counts of L-45 and L-90 specimens at the II stage increase significantly compared with other specimens, indicating that the primary cracks in the specimens are further compacted and accompanied by the formation of new cracks. However, the AE counts distribution of L-90 specimen are more uniform at this stage. This is mainly due to the fact that when the fissure dip angle is 90°, the stress distribution concentration at the fissure tip is weakened, and the microcracks gradually increase inside the specimen, showing the progressive failure characteristics. With the increase of axial load, the stress reaches the crack initiation stress. The number of AE counts of L-0, L-75 and L-90 specimens increases gradually, and the density also increases. Owing to the AE counts are proportional to the number of microcracks generated (Moradian et al. 2016; Lockner et al. 1993), it shows that the microcracks inside the specimen in stage III begin to generate in large quantities. Near the peak stress of stage IV, the generation and further propagation of new cracks lead to severe damage of the specimen. The number of AE counts of specimens with different dip angles α showed a surge phenomenon. The large amount of elastic energy accumulated in the rock mass can be released quickly. The AE counts reach the maximum value, and the cumulative AE counts show a short vertical growth. It is worth noting that the maximum AE counts of specimens with different fissure dip angle are slightly different. The maximum AE counts of L-15 and L-60 are about 3300. Compared with other specimens, the maximum AE counts are higher. This may be due to the influence of two macroscopic shear cracks produced by L-15 and L-60 specimens. Owing to the formation and propagation of shear cracks are usually accompanied by a large number of small friction and local displacement, more elastic waves will be released, so that the maximum AE counts are higher. At stage V, the stress begins to decrease rapidly. Because the specimen still has a certain bearing capacity at this time, a small number of cracks further initiate and propagate. The cumulative AE is further increased.

Fig. 4
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AE counts and cumulative AE counts of fissured layered rock mass with different dip angles

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Figure 4h demonstrates that with the increase of fissure dip angle α, the cumulative AE counts number of each specimen decreases first and then increases. It shows an oblique V-shaped distribution. This is consistent with the change trend of peak strength and elastic modulus in Fig. 3. Owing to the internal damage degree of the final failure of the specimen can be qualitatively characterized by the cumulative AE counts (Kong et al. 2019; Geng et al. 2017). Therefore, from the cumulative AE counts monitored, it can be seen that the internal damage degree of L-30 specimen is the lowest, and that of L-90 specimen is the highest. This is because when the fisuure dip angle is 90°, the internal stress distribution of the specimen is more uniform, the bearing capacity is higher, and the microcracks in the rock mass are more fully developed. The peak strength and elastic modulus of fissured layered rock mass are positively correlated with the degree of internal damage.

3.2.2 AE amplitude-frequency characteristics

In order to study the macroscopic crack development of fissured layered rock mass under uniaxial compression. Here, only the L-0 specimen is taken as an example to draw the relationship between the peak frequency and amplitude of AE, as shown in Fig. 5. The peak frequency of the AE signal is mainly concentrated in 0–120 kHz, while the AE signal at 120–300 kHz is less, and the amplitude is mainly distributed between 60 and 90 dB, as shown in Fig. 5a. In order to further study the distribution characteristics of AE peak frequency and amplitude, the fewer points with higher peak frequency in the figure are not displayed, as shown in Fig. 5b. It can be seen that the peak frequency and amplitude of the processed AE signal have obvious stratification. Therefore, the amplitude and peak frequency of the fissured layered rock mass are divided into three stages, that is, low amplitude (60–70 dB), medium amplitude (70–80 dB), high amplitude (80–90 dB) and low frequency (0–40 kHz), medium frequency (40–80 kHz) and high frequency (80–120 kHz). The characteristics of AE peak frequency, amplitude and stress–strain curve after processing are shown in Fig. 6.

Fig. 5
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The relationship between the peak frequency and amplitude of AE when the fissure dip angle is 0°

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Fig. 6
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AE amplitude-frequency of fissured layered rock mass with different dip angles

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From Fig. 6, it can be seen that the AE signals of each fissured layered rock mass specimen in stage I and II are mainly distributed in the low frequency band (20–40 kHz) and mainly low amplitude signals. During this period, the stress–strain curve showed a "concave" growth, and the original microcracks in the specimen are compacted. With the gradual increase of stress, the low frequency signal is more active when entering the stage III and IV. In addition, the medium amplitude signals of L-0, L-15 and L-60 samples begin to gather in the low frequency band, and the small-scale rupture gradually expands. The distribution of medium frequency signals in L-30 and L-45 is relatively uniform, while the remaining specimens are mainly concentrated at 40–60 kHz. The fissure dip angle has little effect on the distribution of high frequency signals, which is mainly concentrated in 80–100 kHz. It is worth noting that macroscopic crack propagation and penetration are observed in the III and IV stages of each fissured layered rock mass specimen. And the peak frequency of the high amplitude signal is low, mainly concentrated in the low frequency band. This is consistent with the research results of Santis and Tomor that the high amplitude is concentrated in the low frequency region, suggesting the release of high energy, which is accompanied by the generation and development of macroscopic cracks, that is, the LF-HA signal represents the larger scale microcracks (Santis et al. 2013). By analyzing the line graph of the ratio of the number of LF-HA signals every 5 s to the total number of signals during that period, it can be found that LF-HA signals are mainly concentrated in stages III and IV. The fluctuation range of the proportion of LF-HA signals is 1.43–24.29%, concentrated in 7.14–15.71%, and the maximum proportion occurs near the peak stress. The LF-HA signals of L-30, L-45 and L-90 specimens show obvious fluctuating rise or fall in stage IV. This shows that during this period, the evolution characteristics of internal cracks in the specimen are a large number of small scale cracks initiation, propagation and interpenetration, and ultimately lead to macroscopic fracture.

The frequency and first occurrence time of internal large scale cracks in the specimen can be determined by the proportion of LF-HA signals and the time node of the first occurrence of LF-HA signals. With the increase of fissure dip angle α, the ratio of LF-HA signals of fissured layered rock mass specimens increases first, then decreases and then increases again, and the proportion of LF-HA signals has obvious stage characteristics. The crack frequency of L-30 is the highest when the final instability occurs, and from the time node of the first occurrence of LF-HA signal, it is later than that of the other specimens to generate macroscopic cracks. This reflects that the internal microcrack propagation degree of L-30 is not severe, which confirms from another perspective that the internal damage degree of L-30 is lower than that of other specimens.

4 Numerical simulation results and analysis

4.1 Establishment of numerical model and parameter calibration

A numerical model of fissured layered rock mass is established by using particle fow code (PFC), and prefabricated fissures are created by removing particles. The stress measurement circle is set up above and below the interface between the four fissure tips and the layered rock mass. The diameter of the measurement circle is 1.5 mm, and each measurement circle contains 14–18 particles. It can accurately measure the stress at the fissure tip and the interface, as shown in Fig. 7. In the numerical simulation study, appropriate mesoscopic parameters can accurately reflect the basic mechanical properties of rock. Therefore, on the basis of laboratory experiments, we carried out a large number of numerical simulation experiments similar to the laboratory experimental conditions. The mesoscopic parameters of rock-like materials A and rock-like materials B are repeatedly checked and compared by "trial and error method". In this study, in order to ensure the accuracy of the mesoscopic parameters, the calibration of the mesoscopic parameters in PFC mainly considers three principles, peak strength, elastic modulus and failure mode (Huang et al. 2017). The data of peak stress, elastic modulus and peak strain output in numerical simulation are compared with experimental data. The numerical model evaluated by this process can accurately simulate the results of the experiment. Based on this principle, the mesoscopic parameters are calibrated according to the basic physical and mechanical parameters of rock-like materials A and B obtained from laboratory experiments. The mesoscopic parameters of rock-like materials A and B are shown in Table 2, and the comparison of the basic physical and mechanical parameters of the experimental and numerical simulation specimens is shown in Table 3.

Fig. 7
figure 7

Establishment of numerical model of fissured layered rock mass and arrangement of stress measurement circle

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Table 2 Microscopic parameters of Layer A and Layer B
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Table 3 Comparison between the experimental results and the numerical simulation results for Layer A and B (Numerical peak strain has been corrected)
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4.2 Comparison of experimental results with numerical simulation results

Figure 8 shows the comparison of peak stress and elastic modulus between numerical simulation results and experimental results of fissured layered rock mass with different dip angles. The peak stress and elastic modulus of both decrease first and then increase with the increase of fissure dip angle, showing an inclined “V” type distribution. However, owing to the heterogeneity of the experimental material or the randomness of the particle distribution in the numerical simulation, and the particles in the numerical model are materials composed of 2D disks. However, the fissured layered rock mass in the experiment is 3D, which also causes a certain difference between the numerical simulation results and the experimental results (Cao et al. 2016a, b). Although the numerical simulation results do not fully match the experimental results, the stress–strain curve, peak strength and elastic modulus considered in the calibration process of the specimen are similar to the experimental results. This shows that the numerical model can better reflect the mechanical behavior of fissured layered rock mass specimens with different dip angles.

Fig. 8
figure 8

Comparison of peak stress and elastic modulus in numerical simulation with experimental results

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4.3 Displacement vector pattern

Affected by the difference of lithology, owing to the low strength and relatively weak bearing capacity of rock layer A, the microcracks produced in the failure process are much more than that of rock layer B (The black lines in the numerical simulation failure diagram are shear cracks, and the purple lines are tensile cracks). The failure mode of rock layer A is more complicated, mainly showing shear failure, while that of rock layer B is mainly tensile failure. The final failure mode is similar to that of laboratory experimental.

From a microscopic perspective, the formation of cracks is the relative motion of the particles to change the force of the bonding bond (Zhao et al. 2018). When the stress of the specimen reaches the initial crack initiation stress, the bond between the particles breaks, and the continuous fracture of the bond indicates the continuous generation of new cracks. Therefore, the analysis of the displacement field of fissured layered rock mass is helpful to understand the influence of fissures and their dip angles on crack propagation characteristics. Based on the displacement characteristics generated by particle motion, the crack modes in this study are divided into three types: tensile failure, shear failure and tensile-shear mixed failure. Tension failure is divided into direct tension (DT) and relative tension (RT). Shear failure is divided into direct shear (DS) and relative shear (RS). Tension-shear mixed failure is divided into four types: MF-1, MF-2, MF-3 and MF-4. Eight types of mesoscopic displacement field models are proposed. The length of the arrow line represents the size of the particle displacement, and the direction of the arrow represents the direction of motion, as shown in Fig. 10.

  1. (1)

    Direct tension. The two particles move in the opposite direction along the normal direction of the bond surface, resulting in the separation of the two particles, which is manifested as direct tensile failure.

  2. (2)

    Relative tension. The two particles move in the same direction along the normal direction of the bond surface. If the displacement of one particle is greater than that of the other particle, resulting in the separation of the two particles, it is manifested as relative tensile failure.

  3. (3)

    Direct shear. The two particles move in the opposite direction along the tangential direction of the bond surface, resulting in the separation of the two particles, which is manifested as direct shear failure.

  4. (4)

    Relative shear. The two particles move in the same direction along the tangential direction of the bond surface. If the displacement of one particle is greater than that of the other particle, resulting in the separation of the two particles, it is manifested as relative shear failure.

  5. (5)

    Mixed failure. The two particles move in different directions. One particle moves along the normal direction of the bond surface, and the other particle moves along the tangential direction of the bond surface. Tensile displacement and shear displacement exist at the same time. According to the different vector relations, it is further divided into four types: MF-1, MF-2, MF-3 and MF-4.

Figure 9 is the schematic diagram of the displacement field after the final failure of the fissured layered rock mass, and the displacement vector enlarged view of the six regions around the fissure is shown on the right side, which is represented by red numbers 1–6 respectively. Figure 9a is the displacement field of the L-0 specimen. The crack mode at region 1 is driven by the tensile-shear mixed mode (MF-4), and the crack near the left side of the rock mass is related to the RT type displacement field. Both regions 2 and 3 produce cracks that are approximately parallel to the axial compression direction, but their formation mechanisms are different, which are driven by DT type and MF-3 type, respectively. The tensile cracks initiate at the left and right ends of fissure ③, which is related to the RT type displacement field. It is worth noting that the right crack in region 4 and the left crack in region 5 are caused by mixed failure (MF-2, MF-3 and MF-4), which indicates that the crack mode in the middle region of fissure ③ is more complex, mainly tensile shear mixed failure.

Fig. 9
figure 9figure 9

The final failure diagram and displacement vector distribution of fissured layered rock mass

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The displacement field of the L-15 specimen is shown in Fig. 9b. The cracks begin to initiate from the upper left end of fissure ① and the left and right tips of fissure ③ driven by the MF-3 type displacement field. The displacement field of crack initiation at the right tip of fissure ③ is different from that of crack propagation. The crack mode of crack propagation is tensile failure driven by RT type displacement field. The crack modes of regions 2 and 5 are more complex, including shear cracks and tensile cracks, and are related to DT, RT, RS, MF-1 and MF-2 displacement fields.

With the increase of fissure dip angle, the displacement field of L-30 specimen is shown in Fig. 9c. Regions 1, 2 and 5 demonstrate that the cracks initiated upward at the fissure tip are driven by MF-2 type displacement field, while the crack propagation is mainly affected by DT type displacement field. The cracks that coalesce between fissure ② and ③ are mainly driven by MF-4 type displacement field. The cracks in region 4 initiate downward driven by the MF-3 type displacement field and gradually become RT type displacement field during the process of propagation and extension.

Figure 9d is the displacement field of L-45 specimen. Different from the MF type displacement field of L-15 and L-30, the initiation of the left lower end of the fissure ① is driven by the horizontal displacement field (RT) caused by the tensile crack (Chen et al. 2020a, b). There are two different types of coalescence at the tips of fissures ② and ③. The left crack is driven by the MF-3 type displacement field, while the right crack is driven by the MF-2 type and DT type together, as shown in region 3.

The displacement field of the L-60 specimen is shown in Fig. 9e. The cracks at the upper and lower tips of fissure ① begin to initiate and evolve driven by the mixed displacement fields MF-2 and MF-3. Owing to the change of fissure dip angle, the stress is redistributed, which narrows the distance between the two cracks shown in region 3, and the displacement field is completely opposite to that of L-45. The crack initiation in region 4 is driven by MF-4 displacement field, and then transformed into RT type driven propagation.

The displacement field of L-75 specimen is shown in Fig. 9f. The increase of tensile cracks at the tip of fissure ① and fissure ③ is related to the RT type displacement field. For the two cracks generated in region 2, the right crack is driven by RT type displacement field, and the left crack is driven by mixed type displacement field, that is, MF-2 and MF-3. The cracks in region 6 are related to the RT, MF-2 and MF-3 type displacement fields.

Figure 9g is the displacement field of L-90 specimen. Serious damage occurs on the left side of fissures ① and ③, mainly MF-2, MF-3, MF-4 and tensile displacement fields. It is worth noting that except for the L-90 specimen, the other specimens produce a relatively significant crack downward in the fissure ④, and the displacement field mode is affected by the fissure dip angle. For L-0–L-45 specimens, the cracks are driven by mixed MF-2 type displacement field, L-60 is driven by DT type, and L-75 is driven by both MF-2 type and MF-3 type (Fig. 10).

Fig. 10
figure 10

Displacement field types of fissured layered rock mass with different dip angles

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4.4 Fissure tip stress and interface stress

The layered rock mass with fissure dip angle α of 0°, 45°and 90°is selected to analyze the stress in the Y-direction of the fissure tip and the interface (positive value is compressive stress; negative value is tensile stress). The strain–stress curves of fissure tip and interface of fissured layered rock mass with different dip angle are shown in Fig. 11. Since there is no compaction stage in the simulation curve, the stress is divided into four stages based on the microcrack derivation process of fissured layered rock mass. In the stress stage I, because there is no microcrack initiation at this time, the stress curve of the interface and the tip is relatively smooth. Then entering the stress stage II, the change of fissure dip angle changes the stress concentration area, which makes the initial crack initiation stress different. When α is 45°, the stress is the smallest, and its value is 2.06 MPa. Moreover the local stress curve began to fluctuate upward trend, the cracks grew slowly. The stress release of L-0 specimen is caused by the coalescence of fissure ② and ③ near the interface, which leads to the stress drop in the early stage of stress stage III. Moreover the stress at measuring points 1 and 4 on the left side of the interface decreased, the stress at measuring points 3 and 6 on the right side increased, and the tensile stress appeared at measuring points 2 and 5 in the middle. The sharp increase and decrease of stress at the tip also indicate the initiation of crack propagation. This phenomenon is not obvious for specimens with α of 45°and 90°. It is worth noting that the stress of measuring points 2 and 5 in the middle of the interface is affected by the fissure dip angle, and its change is obvious. When α is 0°, the tensile and compressive stresses appear alternately. With the increase of dip angle, the tensile stress gradually disappears and the compressive stress gradually increases. In the stress stage IV, the stress at the interface and tip of each dip angle fluctuates and decreases rapidly. This reflects the release of local stress in the rock mass at this stage, and the rapid growth of microcracks.

Fig. 11
figure 11

The stress of fissure tip and interface of fissured layered rock mass with different dip angles

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Figure 12 shows the peak stress in the Y-direction at the fissure tip and interface of rock mass with different fissure dip angles. The magnitude of local peak stress in Y-direction in the rock mass can reflect whether rock mass is prone to local fracture when subjected to external loads, thus helping to predict the tendency of fracture. Figures 9 and 12 demonstrate that the greater the peak stress in the local Y-direction, the higher the degree of rupture there. The measuring points at the interface of Fig. 12a are axisymmetrically distributed, and the black dotted line represents the magnitude of the stress. The stress distribution in the corresponding area of A and B layers at the interface is approximately symmetrical. Because the B layer is hard rock, it is not easy to destabilize and destroy under higher stress, so the stress of measuring point 4, measuring point 5 and measuring point 6 at the interface B layer is slightly larger than that of measuring point 1, measuring point 2 and measuring point 3 at the A layer. When the fissure dip angle is small, the stress on both sides is generally larger than the stress in the middle, and the stress shows a rectangular distribution, indicating that the left and right sides of the interface are prone to damage. The stress at measuring point 2 and measuring point 5 in the middle area of the interface increases gradually with the increase of α, the stress is approximately hexagonal distribution, and the damage degree of the specimen also increases gradually, which is consistent with the results shown in Fig. 9. Figure 12b and c demonstrate that with the increase of α, the stress at the fissure tip as a whole presents a tendency of fluctuating downward. The peak stress difference in the Y-direction at the fissure tip (Under the same dip angle, the maximum Y-direction peak stress at the fissure tip subtracts the minimum Y-direction peak stress) increases first and then decreases with the increase of the dip angle α. This is negatively correlated with the change trend of peak stress and elastic modulus, indicating that the greater the peak stress difference in the Y-direction, the more serious the deterioration of the mechanical properties of the fissured layer rock mass.

Fig. 12
figure 12

The variation characteristics of local Y-direction stress in fissured layered rock mass and the relationship between local peak stress difference and peak stress

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4.5 Evolution characteristics of stress field

Figure 13 shows the crack propagation and stress field evolution process of L-45 specimen. The tensile stress in the Y-direction stress field is positive, and the compressive stress is negative. The black dotted line drawn in the figure is the A-B layer interface. When the stress is in stage a, there is no crack because the specimen does not reach the crack initiation stress. The maximum principal stress concentration area is mainly distributed in the upper left and lower right areas of the fissure. The tensile stress concentration area is distributed near the fissure tip along the inclined direction of the fissure. The compressive stress concentration area is distributed on the left and right sides of the fissure tip. The shear stress concentration area is mainly distributed at the fissure tip near the boundary in a “butterfly” shape. With the increase of axial load, because the tensile strength of the rock is less than the compressive strength of the rock, the crack first initiates at the fissure tip, and gradually expands and coalesces. The initial crack initiation induces the development and propagation of other cracks, thereby changing the propagation characteristics of subsequent cracks. Owing to the influence of fissures and interfaces, the distribution of stress at the interface shows a certain discontinuity, but the range of stress concentration area and the magnitude of stress gradually increase. As the loading continues, the microcracks further develop, expand and penetrate. The stress in the penetration area is instantaneously reduced, owing to the bond fracture between the particles after the crack coalescence, and the support effect is lost, so that the model begins to gradually destroy. With the gradual destruction of the model, part of the stress inside the rock layer is released. The range of the maximum principal stress, compressive stress and shear stress concentration area near the fissure end is gradually reduced, while the tensile stress concentration range is increased. When the model is gradually destroyed, the particles on the right side still have a certain bearing capacity, which plays a certain supporting role in the whole model, especially in the right side of the B layer, there is a large stress concentration area, which indicates that the B layer is the main bearing area at this time.

Fig. 13
figure 13

Crack propagation and stress field evolution process of L-45 specimen

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5 Conclusions

  1. (1)

    With the increase of fissure dip angle, the peak strength and elastic modulus of layered rock mass decrease first and then increase. The control effect of fissure dip angle on the peak strength of layered rock mass is more significant. The peak strength and elastic modulus of L-30 specimen are most seriously weakened by fissures.

  2. (2)

    The variation of damage based on the cumulative AE counts is consistent with the variation of mechanical parameters. The LF-HA signals of AE mainly appear in the stable crack growth stage, the unstable crack growth stage and the post-peak failure stage. With the increase of fissure dip angle, the signal ratio increases first, then decreases and then increases.

  3. (3)

    Owing to the influence of fissure dip angle and lithology, rock layer A is mainly shear failure, and rock layer B is mainly tensile failure. The fissure layered rock mass as a whole shows tensile-shear mixed failure. The cracks around the prefabricated fissures are composed of eight types displacement field modes. With the increase of fissure dip angle, the crack is obviously driven by a single displacement field, and the cracking process of the specimen tends to be simple.

  4. (4)

    The existence of the interface makes in a certain discontinuity in the distribution of stress at the interface. During the failure process of the model, the tensile stress concentration in the rock layer gradually increases, while the range of the maximum principal stress, compressive stress and shear stress concentration area gradually decreases. Moreover there is a large stress concentration area on the right side of the B layer with higher strength, and the B layer becomes the main bearing area.