1 Introduction

With the increase of energy demand and the depletion of shallow coal resources, the exploitation of coal resources in China is increasing at a rate of 10–50 m per year to the deep (Liu et al. 2014; Zhang et al. 2018). The gas content and gas pressure are at a high level under the conditions of increasing mining depth and intensity, and the geological structure and geo-stress state are becoming increasingly complex, which exacerbates the danger of CGO (Soleimani et al. 2023; Tang et al. 2022; Zhang et al. 2022b). As we all know, CGO is one of the major dynamic disasters that affect the global mine safety production, and China is the country with the most serious CGO problem in the world (Liu et al. 2021; Zheng et al. 2022). During the period of CGO, the coal and rock around the coal mining face are rapidly broken and ejected, and a large amount of gas is released from the pulverized coal, which causes the pulverized coal and gas flow with huge energy, resulting in casualties and property losses (Zhou et al. 2018). Therefore, the research on the dynamic disaster mechanism of outburst fluid in the roadway during CGO is of great significance for underground disaster prevention and control and underground rescue.

At present, some scholars have studied the mechanism of CGO, and the comprehensive effect hypothesis has been widely recognized by many scholars. That is, CGO is the result of the combined action of geo-stress, gas pressure and physical and mechanical properties of coal (Zhou et al. 2019b; Zhao et al. 2020; Tian et al. 2021). Some scholars have also explored the source of outburst energy, believing that gas expansion energy is the most important energy source for outburst (Wang et al. 2018b; An et al. 2019; Lei et al. 2020), and put forward the prediction and prevention measures of outburst (Rudakov and Sobolev 2019; Hou et al. 2021; Wang et al. 2022). Outburst equipment and numerical models are constantly improving over time (Xue et al. 2011; Cao et al. 2019b, 2020; Zhou et al. 2019a), many scholars have studied the dynamic disaster-causing process of outburst in roadways. Zhang et al. (2022a) analyzed the evolution process of shock wave static pressure in straight roadway through the self-developed visual simulation system of CGO, and concluded that the peak static pressure increased first and then decreased during the gradual approach to the outburst mouth, and the propagation of the shock wave front needs to go through the process of first accelerating, then slowly decelerating and finally rapidly decelerating. Zhou et al. (2020a, 2020b, 2021a, 2021b) established the outburst shock wave model through numerical simulation, explored the transmission mode of CGO shock wave in near-field and far-field, and analyzed the factors affecting the two-phase flow dynamics characteristics of CGO. Wang et al. (2021) carried out experimental studies under downwind, upwind, windless and different local resistance conditions, and the migration law of outburst shock wave and airflow in mine ventilation network was also discussed. Cao et al. (2019a) explored the influence of gas adsorption on the dynamic effect of CGO, and concluded that the evolution of static pressure increased first and then decreased rapidly in the roadway near the outburst source, and the peak static pressure showed a downward trend along the roadway. The peak static pressure under CO2 conditions was larger than that under air conditions. Zhou et al. (2021c) studied the influence of different gas pressures on the movement characteristics of pulverized coal, outburst intensity and the impact characteristics of CGO two-phase flow. It is concluded that higher gas pressure will lead to higher outburst intensity, and the impact force will intermittently appear strong and weak disturbances during the attenuation process. Cheng et al. (2022) analyzed the influence of gas pressure on the evolution of gas pressure drop in the coal seam during the CGO process and the characteristics of outburst impact airflow in the roadway. It was concluded that the pulse characteristics of the CGO process had only a weak impact on the evolution process of roadway static pressure.

To sum up, although domestic and foreign scholars have carried out extensive discussions on the static pressure propagation characteristics and disaster-causing of the outburst fluid in the roadway, due to the limitation of experimental methods, the influence of roadway shape on the evolution of static disaster-causing and the role of pulverized coal in the process of static disaster-causing are rarely discussed. Therefore, based on the self-developed multi-field coupling coal mine dynamic disaster large-scale physical simulation test system, this paper carried out large-scale physical simulation tests of gas outburst and CGO under different roadway conditions. The influence of roadway shape on the evolution law of static pressure in the process of outburst was analyzed. At the same time, the difference of static pressure evolution during the process of gas outburst fluid and CGO fluid migration was compared and analyzed. The obtained research results are of reference significance for understanding the dynamical disaster-causing laws of fluids in CGO processes, and guiding the rational arrangement of disaster prevention and anti-disaster facilities in outburst mines.

2 Experimental system and method

2.1 Experimental system

In this experiment, the self-developed multi-field coupling large-scale physical simulation test system for coal mine dynamic disaster was used for experimental research (Zhou et al. 2019a), the system is shown in Fig. 1 and consisted of power subsystem, gas injection subsystem, integrated data acquisition subsystem, and roadway subsystem. Among them, the power subsystem includes stress loading device and specimen chamber, which can truly reproduce the stress state of coal seam under triaxial stress in coal mine. Considering the safety factors of the laboratory, the inflatable system used carbon dioxide instead of methane to provide a preset gas occurrence state for the simulated coal seam. The integrated data acquisition subsystem can real-time collect the evolution process of static pressure in the roadway and gas pressure in the specimen chamber. The forming work of the coal seam inside the specimen chamber is mainly completed by the forming machine. The simulated coal seam size is 400 mm × 400 mm × 1050 mm, and the total coal demand is about 220 kg. The roadway subsystem includes pressure relief device, straight-through roadway, cross roadway and sensor support, which can simulate the migration process of roadway fluid during outburst.

Fig. 1
figure 1

Coal and gas outburst dynamic disaster test system

2.2 Experimental scheme

Domestic and foreign scholars have extensively explored the propagation characteristics and disaster mechanism of outburst fluid in roadways, and have achieved certain results. The research shows that the dynamic disaster effect of CGO fluid in roadway is mainly related to static pressure and dynamic pressure (Cheng et al. 2022). Therefore, most scholars have made a detailed study on the problem of shock wave overpressure (static pressure) (Wang et al. 2012b; Sun et al. 2018; ** et al. 2018). The influence of roadway shape on the evolution of static pressure disaster and the role of pulverized coal in the process of static pressure disaster are rarely discussed due to the limitation of experimental methods. In summary, under the condition of gas pressure of 2.0 MPa and outburst mouth diameter of 30 mm, three kinds of roadway shapes were designed, and two kinds of outburst tests of gas outburst and CGO were completed. The detailed test scheme is shown in Table 1.

Table 1 Experimental scheme

The shape of the roadway includes "straight" roadway, "L-shaped" roadway and "T-shaped" roadway. Figure 2 shows the layout of the roadway and sensors. Each two straight-through roadways are connected by a cross roadway, and the static pressure sensors are arranged on the central wall of the straight-through roadway. Six, eight and eight static pressure sensors are respectively arranged in straight, L-shaped and T-shaped roadways, and the distance between the two static pressure sensors was 2 m. The detailed sensor numbers are shown in Fig. 2. The static pressure sensor used a piezoresistive sensor with a sampling rate of 20000 Hz.

Fig. 2
figure 2

Roadway shape and static pressure sensor layout diagram

2.3 Experimental procedure

Experimental procedure of gas outburst:

  1. (1)

    The gas pressure sensors were preset inside the specimen chamber to monitor the gas occurrence state in real time.

  2. (2)

    Under the condition of good air tightness, the specimen chamber was hoisted to the stress loading device, and connected with the roadway subsystem through the pressure relief device, and static pressure sensors in the roadway were detected and arranged.

  3. (3)

    Started the integrated data acquisition subsystem and inflated the interior of the specimen chamber until the gas pressure inside the specimen chamber reached 2.0 MPa.

  4. (4)

    Through the pressure relief device to induce the outburst, the test was completed. That is, the gas was rapidly filled into the explosion relief device, breaking through the rupture disc on the roadway side, so that its pressure was immediately reduced to atmospheric pressure. The pressure difference between the coal seam gas and the outside gas made the coal seam side of the rupture disc rupture instantly, realizing rapid pressure relief.

Experimental procedure of CGO:

  1. (1)

    The coal was crushed, dried and sieved to the expected particle size ratio, stirred evenly and adjusted the moisture content. Table 2 presents the particle size distribution of pulverized coal when coal briquette is proportioned (Zhou et al. 2021c).

  2. (2)

    The coal samples with uniform stirring were put into the specimen chamber in batches for forming work, and gas pressure sensors were preset in the coal seam to monitor the gas occurrence in the coal seam in real time.

  3. (3)

    Under the condition of good air tightness, the specimen chamber was hoisted to the stress loading device and connected with the roadway subsystem through the pressure relief device, and static pressure sensors in the roadway were detected and arranged.

  4. (4)

    Started the integrated data acquisition subsystem, vacuum the specimen chamber to 0.1 MPa, and then started the adsorption work in stages until the coal seam gas pressure adsorption equilibrium to 2.0 MPa. The entire adsorption process lasted > 40 h.

  5. (5)

    After the geo-stress was loaded to a preset value (Zhou et al. 2021c), the test was completed by inducing the outburst through the pressure relief device.

Table 2 Coal briquette particle-size distribution

3 Experimental results and analysis

3.1 Time history evolution of roadway static pressure during gas outburst process

Studies have shown that underground coal seam gas is the main energy source of CGO (Wold et al. 2008; wang et al. 2018a). The dynamic behavior of CGO two-phase fluid is directly determined by the impact airflow formed by the high-pressure gas in the coal seam in the CGO process to a certain extent. At the same time, the dynamic effect of CGO is very intense and complex, which is a major research difficulty in the field of multiphase flow engineering. Therefore, in order to simplify the analysis of the dynamic process of CGO fluid, gas outburst test was designed to more clearly understand the static pressure evolution process of CGO impact airflow in the roadway under severe dynamic phenomena.

Figure 3 is the static pressure time history evolution process in different roadways during gas outburst. On the whole, the duration of gas outburst was within 2000 ms, and the duration of straight roadway was less than that of T-shaped and L-shaped roadway in turn. The static pressure in the three shapes of roadways showed a fluctuating downward evolution trend, but the attenuation was different. When the pressure is suddenly released, the compressed gas in the prominent cavity expands violently, and the high-pressure gas produces a compression wave superposition to form a shock wave during the rapid outward movement of the high-pressure gas. When the shock wave front reaches the position of the static pressure sensor, the peak static pressure increases rapidly and then decays immediately, forming a positive phase pressure. The peak static pressure at different positions in the three types of roadways all appeared within the first 100 ms after the outburst started, and the peak response time of static pressure in the L-shaped roadway was slightly longer than that in the straight and T-shaped roadways. It was worth noting that the maximum values of static pressure in straight, L-shaped and T-shaped roadways all appeared at the P2 measuring point 3.5 m away from the outburst mouth, which were 5.79 kPa, 5.75 kPa and 5.66 kPa respectively. It showed that the area near the outburst mouth was not the maximum static pressure disaster area, but had a certain distance along the roadway. At the same time, it was also confirmed that the static pressure distribution was not a decreasing process along the way, but a process of increasing first.

Fig. 3
figure 3

Time history evolution of static pressure of gas outburst. a Straight roadway; b L-shaped roadway; c T-shaped roadway

By comparing the different static pressure wave peaks at the same measuring point, the attenuation of static pressure at measuring points in roadway with time was deeply explored. Therefore, the static pressure attenuation coefficient was defined as the ratio of the previous wave peak to the adjacent latter wave peak. The formula is as follows (Wang et al. 2012a):

$$K_{i} = F_{i} /F_{i + 1}$$

where Ki is the static pressure attenuation coefficient; Fi is the i static pressure wave peak at the measuring point; Fi+1 is the i + 1 static pressure wave peak at the measuring point.

The evolution process of static pressure attenuation coefficient of measuring points under three roadway shapes was shown in Fig. 4. It can be seen from the figure that the difference in shape affected the attenuation process of static pressure, resulted in different disaster-causing effects. In the straight roadway, the attenuation of static pressure at P1 showed an evolutionary trend of weakening, strengthening and weakening. The attenuation of static pressure at P2 and P3 showed an evolution trend of slow fluctuation and rising, and the number of static pressure peaks was the largest. The P4 position had a similar static pressure attenuation trend with the P1 position, but the fluctuation degree was much smaller than that of P1. The attenuation of static pressure at P5 and P6 showed two trends of concave rise and convex rise respectively, and the two are cross-symmetric distribution. In the L-shaped roadway, evolutionary trend of the static pressure attenuation coefficient at P1-P4 was similar to that of the straight roadway, but the maximum attenuation coefficient at P1 lagged behind the straight roadway. The attenuation of static pressure at P5-P8 showed an evolutionary trend of "steep increase-steep decrease" alternately. It can be seen that the influence of the turning structure on the static pressure evolution at P5 and P6 at the end of the straight section was much greater than that at the middle and front ends of the straight section, and the turning section and the end of the straight section had similar evolution trends. Moreover, the turning structure obviously delayed the attenuation of static pressure at P1. The static pressure attenuation at P1-P5 in the T-shaped roadway showed an evolution trend of increasing–decreasing-increasing, and the increase and decrease range was relatively gentle; the attenuation of static pressure at P6, P7 and P9 between the first two peaks was very large, and then the evolution trend of "weakening-enhancing" alternating fluctuation was presented. The bifurcation structure changed the attenuation law of the static pressure of each measuring point in the straight section, among which P1 and P6 were the largest. The bifurcation section and the straight section end (P6) had similar evolution trend. In summary, there were great differences in the attenuation law of static pressure in different shapes of roadways. The attenuation of static pressure in the turning section and the bifurcation section was similar to the attenuation of static pressure at the end of the corresponding straight section. Moreover, the attenuation of static pressure before and after the tail structure of both L-shaped and T-shaped roadways showed an alternating fluctuation trend, but the maximum attenuation coefficients were located in K2 and K1 in turn.

Fig. 4
figure 4

Attenuation coefficient of static pressure in gas outburst. a Straight roadway b L-shaped roadway c T-shaped roadway

3.2 Spatial evolution of roadway static pressure during gas outburst process

From Fig. 3, it can be seen that the most serious stage of static pressure disaster in the process of gas outburst was in the first peak period. Therefore, the spatial distribution trend of static pressure in the roadway 100 ms before outburst was drawn, as shown in Fig. 5. In the straight roadway, the static pressure at P1 and P2 increased rapidly in the first 20 ms of gas outburst, and P1 was greater than P2. When the gas outburst was 40 ms, the static pressure in the whole roadway had an upward trend, and its maximum value was located at P2, shown a distribution trend of increasing first and then decreasing. At 60 ms of gas outburst, the static pressure at P1 began to decrease, and the middle end of the straight section roadway (P2-P4) showed a high static pressure distribution. When the gas outburst was 80 ms, the static pressure inside the whole roadway showed an attenuation trend, and it was found that the attenuation degree of the front and middle ends of the roadway was significantly higher than that of the end. L-shaped and T-shaped roadways had similar static pressure distribution trend with straight section roadway, and it increased first and then decreased within 20–100 ms of gas outburst, indicated that the most serious area of static pressure disaster during the gas outburst process was in the middle and front parts of the roadway. The difference was that the duration and range of high static pressure disaster in roadway showed L-shaped > T-shaped > straigh. In addition, the static pressure in the turning roadway (P7, P8) and the bifurcation roadway (P7, P9) responded after 40 ms of gas outburst, and the rising and decay rates were very rapid. It is worth noting that when the gas outburst was 60 ms, the static pressure at P5, P6 and P7 of the L-shaped roadway reached 5.11 kPa, 4.92 kPa and 3.52 kPa respectively, while the static pressure at P5, P6 and P7 of the T-shaped roadway were 3.96 kPa, 3.38 kPa and 2.18 kPa respectively, indicated that the turning roadway was more conducive to the accumulation of static pressure in the roadway than the bifurcated roadway, resulted in more serious disaster consequences. When the gas outburst was 80 ms, the bifurcated roadway was no longer subject to static hazards, but there was still a risk of static pressure disaster in the turning roadway, indicated that the static pressure attenuation of the bifurcated roadway was faster than that of the turning roadway, which was easier to evacuate the gas, thus helped to reduce the risk of static pressure disaster.

Fig. 5
figure 5

The spatial evolution of static pressure gas outburst. a Straight roadway; b L-shaped roadway; c T-shaped roadway

3.3 Time history evolution of roadway static pressure during CGO process

CGO is one of the most complex and serious dynamic disasters in coal mine, which involves engineering rock mass dynamics, adsorption and desorption dynamics, gas-coal two-phase coupling disaster dynamics and other multidisciplinary fields. The flow of coal–gas two-phase flow after outburst is a multiphase turbulence problem, and the process of CGO has unique pulse characteristics, which makes it very difficult to study the hydrodynamic disaster in the process of CGO. In this paper, the mechanism of CGO static pressure disaster was explored by experimental means, and the difference of static pressure evolution in L-type and T-type roadways was analyzed, which provided a certain reference for further understanding the dynamic disaster mechanism of outburst disaster.

Figure 6 is the static pressure time history evolution process in L-shaped and T-shaped roadways during CGO. Similar to gas outburst, the static pressure in the two shapes of roadway showed an evolutionary trend of fluctuating decline. The difference was that the peak value of static pressure wave rised after 800 ms of CGO, indicated that CGO had the phenomenon of intermittent energy release compared with gas outburst. It showed the pulse characteristics of CGO. Rapid destructive processes in the coal seam and the blocking state of the gas flow are the main factors in the creation of the outburst pulse phenomenon. The maximum static pressure in the L-shaped and T-shaped roadways was similar and appeared in the initial peak, but the position was different. In addition, the peak static pressure at different positions increased and decreased alternately along the L-shaped roadway, while the T-shaped roadway increased first and then decreased. The peak static pressure of L-shaped roadway appeared at P2, reached 3.03 kPa. The peak static pressure of the T-shaped roadway appeared at P3, reached 2.79 kPa.

Fig. 6
figure 6

Time history evolution of static pressure of CGO. a L-shaped roadway; b T-shaped roadway

Figure 7 shows the evolution process of static pressure attenuation coefficient of each measuring point under L-shaped and T-shaped roadway conditions. It should be noted that the static pressure was a single peak evolution process at P1, P2 of the L-shaped roadway and at P1 of the T-shaped roadway. Therefore, there was no static pressure attenuation coefficient of these three measuring points in Fig. 7. In the L-shaped roadway, the attenuation coefficient of the static pressure except P3 showed a wave-shaped downward evolution trend of cyclic "decrease-increase". Among them, the number of "decrease-increase" cycles of P4-P8 was 3, 1, 2, 2 and 1 in turn. The static pressure at P3 showed a cyclic "increase–decrease" wavy downward evolution trend, and the number of cycles was 2 times. In the T-shaped roadway, the static pressure at P2 had only one attenuation process. The attenuation trend of static pressure at P3-P5 was similar to that of P3 in L-shaped roadway, shown a cyclic "increase–decrease" wave-shaped downward evolution trend, and the number of cycles was 3,4 and 2 times respectively. The attenuation process of static pressure at P6, P7 and P9 was similar, shown an evolution trend of steep dropped first, then steep increased and then slow decreased. In summary, the static pressure in the near-outburst source area during the CGO process showed a single-peak evolution, and gradually evolved into a multi-peak attenuation evolution with the increase of distance. From near to far, the maximum value of static pressure attenuation coefficient changed from K2 to K1. In addition, the attenuation of static pressure in the bifurcation section was obviously more severe than that in the turning section, indicated that the bifurcation roadway was more conducive to gas expansion. The reason for the above phenomenon is that the increase of the transportation section of the bifurcation roadway is more obvious, which is beneficial to the rapid release and pressure relief of the two-phase flow of coal and gas, and the reflection of the shock wave in the bifurcation roadway is not obvious, while the diffraction effect is prominent.

Fig. 7
figure 7

Attenuation coefficient of static pressure in CGO. a L-shaped roadway; b T-shaped roadway

3.4 Spatial evolution of roadway static pressure during CGO process

Figure 8 shows the spatial evolution process of roadway static pressure within 100 ms after CGO. In the L-shaped roadway, the static pressure at P1 and P2 increased rapidly within 20 ms of CGO. When the CGO was 40 ms, the static pressure at P1 and P2 showed a downward trend, and the static pressure of the straight section was large in the middle and small at both ends, with the highest value at P4 and P5. When the CGO was 60 ms, the static pressure propagated to the whole roadway and the value was relatively small, and the static pressure of the straight section showed a downward trend. At 80 ms of CGO, only the middle and front ends of the straight section had static pressure distribution. The overall distribution trend of static pressure in T-shaped roadway and L-shaped roadway was similar. The difference was that when the outburst was 60 ms, the distribution of static pressure in T-shaped roadway was small in the middle and large at both ends. Intuitively, the static pressure decay rate of the T-shaped roadway was faster. For example, when the CGO was 80 ms, there was no static pressure disaster in the T-shaped roadway. This phenomenon further showed that the bifurcated roadway was more conducive to reducing the risk of static pressure disaster than the turning roadway.

Fig. 8
figure 8

Spatial evolution of static pressure of CGO. a L-shaped roadway; b T-shaped roadway

4 Discussion

4.1 Influence analysis of roadway shape on roadway static pressure during outburst process

4.1.1 Comparison of static pressure evolution in different roadways during gas outburst process

The layout of underground roadway in coal mine is complex and changeable. It can be considered that it is mainly composed of turning roadway and bifurcation roadway arrangement. It can be seen from the above that the static pressure evolution law of outburst fluid in two shapes of roadways is quite different. Therefore, in order to investigate the influence of the shape of the roadway on the evolution of static pressure, the comparative analysis diagrams of static pressure of gas outburst and CGO in different shapes of roadways within 1000 ms were drawn, and the differences of static pressure characteristic parameters were discussed, as shown in Figs. 9, 10, 11, 12.

Fig. 9
figure 9

Influence of roadway shape on static pressure of gas outburst. a Comparison of three conditions at P1 b Comparison of three conditions at P2 c Comparison of three conditions at P3 d Comparison of three conditions at P4 e Comparison of three conditions at P5 f Comparison of three conditions at P6 g Comparison of three conditions at P7

Fig. 10
figure 10

Influence of roadway shape on static pressure characteristic value of gas outburst fluid. a Comparison of peak static pressure b Comparison of impulse c Comparison of the number of peaks

Fig. 11
figure 11

Influence of roadway shape on static pressure of CGO. a Comparison of two conditions at P1 b Comparison of two conditions at P2 c Comparison of two conditions at P3 d Comparison of two conditions at P4 e Comparison of two conditions at P5 f Comparison of two conditions at P6 g Comparison of two conditions at P7

Fig. 12
figure 12

Influence of roadway shape on static pressure characteristic value of CGO fluid. a Comparison of peak static pressure b Comparison of impulse c Comparison of the number of peaks

Figure 9 is a comparative evolution diagram of static pressure in straight, L-shaped and T-shaped roadways during gas outburst. At P1, the maximum static pressure of straight, L-shaped and T-shaped roadways were 5.25 kPa, 5.04 kPa and 5.31 kPa, respectively. The static pressure disaster hazards of L-shaped and T-shaped roadways decreased by 4.00% and increased by 1.14% compared with straight roadway. After the first wave peak, all three showed the evolution trend of intermittent wave attenuation, and the order of the occurrence of the sub-peaks and their subsequent peaks was straight, T-shaped, and L-shaped. At P2-P4 in the middle end of the straight section roadway, compared with the straight roadway, the static pressure disaster hazard of the L-shaped roadway decreased by 0.52%, 1.96% and increased by 3.58%, while the static pressure disaster hazard of T-shaped roadway decreased by 2.08%, 2.31% and 2.64% respectively. After the first peak, the number of static pressure fluctuations of the three was significantly increased compared with P1, and the complexity of the static pressure evolution process was improved. At P5-P6 at the end of the straight section roadway, the static pressure hazard of the L-shaped roadway increased by 15.33% and 85.02% compared with the straight roadway, while the static pressure hazard of the T-shaped roadway decreased by 7.34% and increased by 26.59% compared with the straight roadway. Due to the influence of outlet pressure and tail structure, the static pressure decayed rapidly, which made the complexity of the static pressure evolution process of the three after the first peak gradually decrease. At the P7 of the turning (right bifurcation) roadway, the peak static pressure at each peak of the L-shaped roadway was greater than that of the T-shaped roadway, indicated that the bifurcation structure was more conducive to the attenuation of static pressure than the turning structure, thus helped to reduce the harm of static pressure disaster. The static pressure duration of the L-shaped roadway at P1-P7 was significantly longer than that of the straight and T-shaped roadways, indicated that the L-shaped roadway helped to prolong the static pressure disaster time, thereby increased its disaster hazard. In addition, the time sequence of the sub-peaks and subsequent peaks of the three shapes of roadways at P1-P7 was straight, T-shaped, and L-shaped in turn, indicated that the turning structure and bifurcation structure affected the reflection, refraction, and superposition of compression-expansion waves during fluid migration, resulted in static pressure hysteresis, and the turning structure had the greatest influence. At the same time, it can be found from Fig. 9 that the complexity of the static pressure evolution increased first and then decreased along the roadway.

Drawing on research in the field of gas explosion (Jiang et al. 2011), the main characteristic parameters to measure the static dynamic hazard are the peak static pressure and its action time, and the impulse is used to measure the cumulative static pressure action in time to cause the hazard. Therefore, in order to more intuitively explore the differences of static dynamic hazards in straight, L-shaped and T-shaped roadways, the comparison graphs of peak static pressure, impulse and number of wave peaks for the three shapes were drawn, as shown in Fig. 10. As shown in Fig. 10a, when gas outburst occurred, the static pressure peaks in the three shapes of roadways increased first and then decreased along the roadway. At the front end of the straight roadway at P1, the peak static pressure was T-shaped > straight > L-shaped; compared with other shapes of roadways, the peak static pressure in the T-shaped roadway decreased to the minimum at the front end P2-P3 in the straight section roadway; at the P4-P5 of the middle and rear end of the straight section roadway, the peak static pressure of straight and T-shaped roadway decreased rapidly, shown L-shaped > straight > T-shaped; at the end of the straight section roadway and the turning (right bifurcation) roadway P6-P7, the peak static pressure in the L-shaped roadway was much larger than that in the straight and T-shaped, and the peak static pressure in the straight roadway dropped steeply and was lower than that in the T-shaped roadway. From Fig. 10b, the evolution trend of the impulse in the three shapes of roadways was consistent with the peak static pressure, and all of them increased first and then decreased. When the static pressure value and its action time were measured simultaneously, the static dynamic hazard in L-shaped and T-shaped roadways was significantly greater than that in straight roadway, and the hazard of L-shaped was higher than that of T-shaped in general, especially at P1 near the outburst mouth and at P5-P7 in the middle and rear end of the roadway. Figure 10c showed that the number of static pressure peaks in the straight roadway increased first and then decreased along the roadway. However, when there was a turning or bifurcation structure, the distribution of the number of peaks changed greatly, shown a fluctuating distribution trend. At the same time, the difference between L-shaped and T-shaped in the number of peaks was mainly reflected in P1 and P5, and there was little difference in other positions.

In summary, the peak static pressure and impulse of the three shapes of the roadway had similar distribution trend, all of which showed an increasing trend followed by a decreasing trend, indicated that the most hazardous area for static dynamics in the roadway was at P2 in the front end of the straight roadway, rather than showing a decreasing distribution along the roadway. In addition, the variability of the peak static pressure, impulse and the number of peeks at P1, P5 and P6 was much larger than that at P2-P4, indicated that the different shapes of the roadway mainly affected the static dynamic hazard at the front and rear ends of the straight section roadway, and the hazard was L-shaped > T-shaped > straight. The hazard of T-shaped roadway after straight roadway was less than that of L-shaped due to the diversion effect. It is worth noting that when only the peak static pressure was measured, the difference between the straight hazard and the other two was small; however, when both the static pressure value and its action time were measured, the static dynamic hazard in the L-shaped and T-shaped roadways was significantly greater than that of the straight one.

4.1.2 Comparison of static pressure evolution in different roadways during CGO process

Figure 11 shows the comparative evolution of static pressure in L-shaped and T-shaped roadways during CGO. At P1, both L-shaped and T-shaped roadways had only one static pressure peak, with peaks of 2.68 and 2.73 kPa, respectively, and the static pressure hazard in T-shaped roadway increased by 1.87% compared with L-shaped roadway. At P2-P4 in the middle of the straight section roadway, the static pressure hazard in T-shaped roadway decreased by 8.58%, increased by 2.57% and decreased by 9.09% compared with L-shaped roadway; after the first peak, the appearance of static pressure peaks in L-shaped roadway lagged behind that in T-shaped roadway. In P5-P6 at the end of the straight section roadway, the static pressure hazard in T-shaped roadway decreased by 1.56% and 24.91% compared with that in L-shaped roadway. At P7 of the turning roadway, the static hazard of T-shaped roadway decreased by 38.43% compared with L-shaped roadway. Similar to the gas outburst, the peak of each wave in the L-shaped roadway at P7 was larger than that in the T-shaped roadway, which further indicated that the roadway shape had a non-negligible effect on the decay of static pressure. It is worth noting that the second wave peak of the L-shaped roadway at P3-P7 consisted of two wave peaks, indicated a more complex static pressure-causing effect. In addition, the peak static pressure in a T-shaped roadway decayed faster along the roadway than in an L-shaped roadway.

Figure 12 shows the comparison of the peak static pressure, impulse and the number of wave peaks in L-shaped and T-shaped roadways. From Fig. 12a, it can be seen that the peak static pressure in the L-shaped roadway fluctuated up and down along the roadway, while that in T-shaped roadway showed an increasing and then decreasing distribution trend. The peak static pressure of each measurement point in T-shaped roadway was higher than that in L-shaped roadway only at P1 and P3, and there was a steep drop at the end of the straight section roadway and the P6-P7 of the turning (right bifurcation) roadway. Figure 12b showed that the impulse in the two shapes of roadways increased first and then decreased, in which the maximum value of impulse in T-shaped roadway was at P3, 176.07 kPa ms, and the maximum value of impulse in L-shaped roadway was at P4, 214.89 kPa ms. Except for P5, the impulse in L-shaped roadway was larger than that in T-shaped roadway. This indicated that when the static pressure value and its action time were measured at the same time, the hazard of L-shaped roadway was generally higher than that of T-shaped roadway from the overall point of view. From Fig. 12c, it can be seen that the number of static pressure peaks of the two shapes of roadways increased first, then decreased and then increased along the roadway, and all the locations except P2 showed a well consistency.

As mentioned above, the peak static pressure was an important indicator to judge the static pressure causing disaster. When this factor was considered alone, the main disaster-causing range of the T-shaped roadway was on the side near the outburst source, and the disaster-causing intensity at the bifurcation structure had a steep drop phenomenon. The distribution of disaster-causing intensity of L-shaped roadway was relatively uniform, shown a fluctuating and slow decline distribution state. It is worth noting that the static pressure action time was also an evaluation index to be considered in specific cases. When considered the static pressure value and its action time at the same time, the disaster-causing intensity in the two roadways had changed, shown a distribution state of large in the middle and small at both ends, and its main disaster-causing range was in the middle of the straight section. Moreover, the static pressure dynamic disaster hazard in the L-shaped roadway was significantly greater than that in the T-shaped roadway.

4.2 Influence of pulverized coal on static pressure during outburst process

CGO is a process in which a large amount of broken coal carried by high-pressure gas is rapidly ejected from the coal seam to the mining space, and finally formed a coal–gas two-phase flow. Therefore, the static pressure dynamic disaster in the roadway is mainly affected by the pressure drop of coal seam gas and the effect of pulverized coal on gas in two-phase flow. Among them, the pressure drop of coal seam gas is related to gas desorption and coal crushing (Wang et al. 2015; Zhao et al. 2016). Pulverized coal plays an important role in CGO, and it is particularly important to explore its influence on the hazard of static pressure dynamic disaster. Therefore, by comparing the static pressure characteristic parameters such as peak static pressure, impulse and number of peaks of gas outburst and CGO fluid, the effect of pulverized coal on static pressure dynamic disaster was analyzed, as shown in Fig. 13.

Fig. 13
figure 13

Comparison diagram of static pressure characteristics of gas outburst and CGO. a Comparison of peak static pressure in L-shaped roadway b Comparison of impulse in L-shaped roadway c Comparison of the number of peaks in L-shaped roadway d Comparison of peak static pressure in T-shaped roadway e Comparison of impulse in T-shaped roadway f Comparison of the number of peaks in T-shaped roadway

Figure 13a, d are the peak static pressure comparison of gas outburst and CGO fluid. The peak static pressure of each measuring point of gas outburst was higher than that of CGO, and the decrease rate of peak static pressure was greater. The maximum peak static pressure of gas outburst fluid was about 2 times of that of CGO. Figure 13b, e are the comparison of the impulse of gas outburst and CGO fluid. The impulse of gas outburst fluid near the outburst mouth was much larger than that of CGO. The maximum impulse of gas outburst fluid was about 4–5 times that of CGO. After the impulse of gas outburst and CGO fluid reached the maximum value, the difference gradually decreased. Gas outburst and CGO fluid static pressure wave peak number comparison, as shown in Fig. 13c, f. The number of static pressure peaks of gas outburst fluid was greater than or equal to that of CGO, and the greatest difference in the number of peaks near the outburst source.

In summary, the maximum value of the peak static pressure of the gas outburst in the two kinds of roadways was about 2 times that of the CGO, and the maximum impulse was about 4–5 times that of the CGO, indicated that the existence of pulverized coal reduced the hazard of static pressure dynamic disaster. The analysis suggests that some of the energy from the rapid expansion of the gas is used for the crushing and moving of the coal. Therefore, the loss of part of the energy makes the static pressure lower. In addition, the desorption of gas in the coal seam affects its expansion and release. It is worth noting that the maximum impulse of gas outburst fluid was located in the middle front end of the roadway, while that of CGO was located in the middle end of the roadway. The existence of pulverized coal made the static pressure dynamic disaster-causing harm greatly reduced, and also extended the location of the greatest disaster-causing harm from the front end of the roadway to the middle end of the roadway, indicated that the existence of pulverized coal prolonged the process of energy release, further indicated that paroxysmal is the characteristic of CGO (Zhou et al. 2020c).

4.3 Outburst shock wave front velocity

The average propagation velocity of the outburst shock wave front between the two measuring points can be obtained by the response time of the static pressure and the spacing between the measuring points. As shown in Fig. 14. Figures 14a, b show the propagation velocities of shock wave fronts of different roadway shapes under gas outburst and CGO conditions, respectively.

Fig. 14
figure 14

Outburst shock wave front propagation velocity. a Gas outburst b Coal and gas outburst

Under gas outburst, the maximum propagation velocities of the shock wave fronts were 487.8, 430.1, and 459.8 m/s for straight, L-shaped, and T-shaped roadways, respectively. Among them, the velocity evolution laws of straight and L-shaped roadway conditions are approximated in the straight section. It shows the evolution trend of decreasing first and then increasing. In the L-shaped roadway condition, the shock wave velocity showed a decreasing trend after the turning structure. In the T-shape roadway condition, the shock wave velocity shows a fluctuating decreasing trend in the straight section and an increasing trend after the bifurcation structure.

Comparing the gas outburst conditions, the maximum shock wave front propagation velocities of L-shaped and T-shaped roadways with coal and gas outburst conditions were 481.9 and 444.4 m/s, respectively. The same as in the case of the gas outburst, the initial trend of the shock wave velocity of the L-shape is decreasing whereas that of the T-shape is increasing. Moreover, the L-shape roadway still shows a decreasing trend after the turning structure, while the T-shape has a small increase. Unlike in the case of the gas outburst, the shock wave velocity has a great change in the middle and back of the straight section of the roadway, which increases in the middle and then decreases at the end of both the L-shaped and T-shaped roadways.

5 Conclusions

Using the self-developed large-scale physical simulation test system of multi-field coupling coal mine dynamic disaster, the influence of different roadway shapes on the evolution of static pressure of gas outburst and CGO was studied. The evolution law of static pressure in straight roadway, L-shaped roadway and T-shaped roadway after outburst was explored, and the influence of tail structure on static pressure was compared and analyzed. The test conclusions are as follows:

  1. (1)

    During the process of gas outburst, the static pressure in the three roadway shapes showed a fluctuating downward evolution law. The peak static pressure, impulse and the complexity of static pressure evolution process increased first and then decreased along the roadway. The most serious area of static pressure disaster was located in the middle and front part of the roadway. The static pressure attenuation of the turning section and the bifurcation section was similar to the end of the corresponding straight section.

  2. (2)

    In the process of CGO, the static pressure in the two roadway shapes showed a fluctuating downward trend, and the static pressure evolution along the roadway changed from single peak to multi-peak attenuation evolution. The peak static pressure of each measuring point in the L-shaped roadway showed an alternating distribution law of increase–decrease along the roadway, while the T-shaped showed a distribution trend of increasing first and then decreasing. When only considering the peak value of static pressure, the main disaster area of T-shaped roadway was near the side of the outburst source, and the disaster intensity at the bifurcation structure was obviously reduced. The disaster-causing intensity distribution of the L-shaped roadway was relatively uniform, shown a fluctuating and slow decline distribution state. When the static pressure value and its action time were considered at the same time, the disaster-causing intensity in the two roadways showed a distribution state of large in the middle and small at both ends, and its main disaster-causing range was in the middle of the straight section.

  3. (3)

    In the process of gas outburst, the static pressure duration of L-shaped roadway at P1-P7 measuring points was larger than that of T-shaped and straight in turn. The turning and bifurcation structure affected the migration and propagation process of fluid, which led to the phenomenon of static pressure hysteresis. The different shapes of the roadway mainly affected the static pressure dynamic disaster at the front and back ends of the straight section roadway. When only the static pressure peak was measured, the hazard of straight roadway was less different from the other two. However, when the static pressure value and its action time were measured at the same time, the degree of static pressure dynamic disaster in L-shaped and T-shaped roadways was significantly greater than that of straight roadway, and the hazard of L-shaped was higher than that of T-shaped. The disaster duration and disaster range of high static pressure showed L-shaped > T-shaped > straight, indicated that the turning roadway was more conducive to the accumulation of static pressure than the bifurcation roadway, resulted in more serious disaster consequences. In the process of CGO, the peak static pressure of the T-shaped roadway decayed faster along the roadway than the L-shaped roadway. When the static pressure value and its action time were considered at the same time, the static pressure dynamic disaster hazard in L-shaped roadway was significantly greater than that in T-shaped roadway.

  4. (4)

    The maximum peak static pressure and impulse of gas outburst fluid were 2 times and 4–5 times that of CGO respectively. The existence of pulverized coal reduced the hazard of static pressure dynamic disaster and prolonged the time for energy release, which resulted in the most serious position of static pressure dynamic damage changed from the front end of the roadway to the middle end of the roadway. Compared with gas outburst, CGO had the phenomenon of intermittent energy release, which showed the pulse characteristics of CGO.