Considering the characteristics of the composite coal seam and the symmetry in numerical calculation, the numerical model containing the intercalated layer is established and shown in Figure 1A. It contains two intercalated layers and three coal seams. The size of the model is 6 m × 6 m × 6 m, where the thicknesses of the coal seam and the intercalated layer are set according to the experimental schemes. In the block distinct element method, the fracture needs to be preset. Therefore, a vertical preset joint was set along the center of the model. In addition, there was a horizontal bedding plane between the coal seam and the intercalated layer. As a result, this model contains four horizontal bedding planes and one vertical joint. The specific joint model is shown in Figure 1B. The injection point was set at the center of the model, and the flow boundary of the injection point was constant.

The composite coal seam consists of coal seams and intercalated layers. The combination of thicknesses affects the propagation of hydraulic fractures when encountering an intercalated layer, which in turn affects the fracture height (vertical characterization) and fracture length (horizontal characterization). In order to analyze the influence of the thickness of the intercalated layer and coal seam on the hydraulic fracture propagation, six schemes were designed, as shown in Table 1. When analyzing the influence of the thickness of the intercalated layer, the thickness of the coal seam is found to be 1 m. The thicknesses of the intercalated layers are 0.1–0.6 m in all six cases. When analyzing the influence of the thickness of the coal seam, the thickness of the intercalated layer is found to be 0.3 m, and the thicknesses of the coal seams are 0.6–1.1 m in a total of six cases.

Other parameters are set as follows: the injection rate is 0.001 m³/s. The viscosity of the fracturing fluid is 1 cp, and the fracturing time is 3,600 s. The cohesion of the joints is 2 MPa, the friction angle is 20°, and the tensile strength is 2 MPa. The Young’s modulus of the coal seam is 50 GPa, and that of the intercalated layer is 70 GPa. The Poisson’s ratio of both the coal seam and the intercalated layer is 0.25.

According to the experimental scheme shown in Table 1, the influence of coal seam thickness on fracture propagation is analyzed. The calculation results are shown in Figure 7. Since the thickness of the intercalated layer in this study is 0.3 m in all cases, the fractures are able to penetrate into the intercalated layer during the propagation. The effect of seam thickness on fracture propagation is the penetration behavior. The hydraulic fractures can penetrate the intercalated layer in all the cases with the thicknesses of 0.6–1.0 m of the coal seam. When the seam thickness was 1.1 m, the hydraulic fracture fails to penetrate the intercalated layer. In addition, hydraulic fractures can penetrate the intercalated layer in coal seams less than 1 m thick, but the degree of penetration varies. In conclusion, the thinner the coal seam, the smaller the hindering effect. As the coal seam thickens, the range of penetration of hydraulic fractures is smaller.

The thickness of the coal seam affects the penetration ability. Then, it affects the extent range of hydraulic fracture propagation. Figure 8A categorizes hydraulic fractures into the main zone, intercalated layer zone, and outward zone according to their location. The thickness of the coal seam directly determines the height of the main fracture zone. Figure 8B summarizes the fracture propagation length and height for different coal seam thicknesses. The results show that the length of hydraulic fractures remains generally consistent, but the height of hydraulic fractures is affected by the thickness of the coal seam. Hydraulic fracture height decreases gradually with the increase in the coal seam thickness. Low fracture height implies a reduction in the extent of fracturing.

In summary, the thickness of the coal seam mainly affects the ability of the hydraulic fracture to pass through the intercalated layer and the range of hydraulic fracture propagation. As the thickness of the seam increases in a composite seam, the hindering effect of the intercalated layer on the height of the fractures should be considered. When the coal seam is thin, the influence of the intercalated layer on the propagation of fractures is less. While the coal seam is thick, the influence of the intercalated layer on the vertical propagation of fractures is more, which should be emphasized in the design of fracturing.

The elastic modulus characterizes the deformability of rocks. Furthermore, the difference in the elastic modulus between the intercalated layer and coal seams has a significant effect on the penetration behavior of fractures. In order to analyze the effect of the elastic modulus on fracture propagation, the elastic moduli of the coal seam (Ec) are taken to be 20 GPa, 30 GPa, 40 GPa, and 50 GPa, and the moduli of the intercalated layer (Ei) are taken to be 40 GPa, 50 GPa, 60 GPa, and 70 GPa. Combined simulations are carried out for various scenarios, and a total of 16 sets of simulation scenarios are designed. The fracture propagation under each case is summarized in Figure 9.

First, the effect of the Ec is analyzed. Moreover, the same row shown in Figure 9 has the same Ei, and the Ec varies. With a small Ec, hydraulic fractures can penetrate the intercalated layer. As the Ec increases, the hindering effect of the intercalated layer on the vertical propagation of the fractures is enhanced. Second, the effect of Ei is analyzed. The same column in the figure has the same Ec and different Ei. The effect of Ei on hydraulic fracture propagation has different patterns at high and low Ec. In the low Ec (left first column), the Ei has little effect on fracture propagation. In the high Ec (50 GPa), hydraulic fractures can penetrate the intercalated layer when the Ei is low (40 GPa and 50 GPa). When the Ei is high (60 GPa and 70 GPa), the hydraulic fractures turn after encountering the intercalated layer, and the intercalated layer hinders the vertical propagation of the hydraulic fractures.

In summary, the influence of Ec on fracture propagation can be summarized. The hindering effect of the intercalated layer on fracture propagation increases with the increase in Ec. Furthermore, the influence of the Ei on the behavior of fracture propagation can be summarized. In low elastic modulus coal seams, the influence of the Ei on fracture propagation is small. Conversely, in high elastic modulus coal seams, the hindering effect of the intercalated layer on hydraulic fractures increases with the increase in the Ei.

According to Figure 9, as the Ec increases, it becomes more difficult for hydraulic fractures to pass through the intercalated layer. The elastic modulus characterizes the deformation. As shown in the figure, the hydraulic fracture with a small elastic modulus has a large aperture. Moreover, the aperture decreases with the increase in the Ec. The aperture determines the fracture volume. Furthermore, different fracture volumes under the same fluid injection volume determine the difference of pressure within the fracture. Different pressures ultimately cause differences in stress evolution. Figure 10 analyzes the stress evolution at the intersection of the hydraulic fracture and the intercalated layer for different Ec when the Ei is 70 GPa. The figure shows that the Ec affects the distribution of shear stresses on the bedding plane and normal stresses on the vertical joint.

First, the elastic modulus affects the change gradient in stress. As shown in Figures 10A, B, the stress curve for the coal seam with an elastic modulus of 20 GPa is on the leftmost side, which means that the stress change corresponding to this elastic modulus is earlier than that in the other cases. Whereas the stress evolution is related to fracture propagation, as the fracture approaches a certain point (numerical node), the stress profile at that point changes significantly. In addition, the sequence of stress curve changes in the figure characterizes the rate of hydraulic fracture propagation. Therefore, it can be known that hydraulic fractures expand fast when the Ec is small and expand slow when the Ec is large.

As shown in Figure 10A, the maximum shear stress increases with the increase in the Ec. Shear stress causes shear damage of the bedding plane. The shear stress increases with Ec, which subsequently increases the tendency of hydraulic fractures to turn toward the bedding plane and increases the hindering effect of the intercalated layer. However, it is worth noting that as shown in Figure 10A, the shear stress increases fastest at low Ec (the slope of the curve is the largest), but its maximum shear stress is at the lowest Ec. The paradox of a fast increase in the shear stress but a low maximum value needs to be explained in terms of the change in normal stress. From Figure 10B, it can be seen that the normal stress on the vertical joint surface decreases with injection time. The fastest rate of stress reduction occurs when the Ec is 20 GPa. When the stress decreases to −2 MPa, reaching the tensile strength of the joint, the hydraulic fracture expands vertically through the bedding plane. Now, the shear stress on the horizontal bedding plane reaches its peak. Due to the rapid decrease in normal stress, the shear stress does not increase. As the Ec increases, fracture propagation slows down, thus requiring more time for normal stress to decrease to tensile strength. Finally, the maximum shear stress increases. When the Ec is 50 GPa, the normal stress does not reduce to the tensile strength, and the shear stress reaches the shear strength of the bedding plane. Now, the bedding plane shear damage occurs, and the hydraulic fractures turn to the bedding plane.

Figure 10C shows the corresponding shear strength and shear stress curves of the bedding plane at different Ec. In the figure, the Sc curve represents shear strength, and the S curve represents shear stress. The shear strength (Sc) of the bedding plane gradually decreases with injection, while the shear stress (S) gradually increases. Finally, the two are gradually close to each other. Figure 10D shows the difference between the shear strength and shear stress (Dif-S) curves. According to the figure, Dif-S is gradually decreasing before the damage occurs at the intersection point. The minimum value of Dif-S decreases with the increase in the Ec. Actually, this difference can reflect the tendency of the shear damage of the bedding plane.

In summary, the mechanism of the Ec on the hindering effect of the intercalated layer is as follows: the influence of the elastic modulus on the deformation determines the fracture propagation rate and the stress distribution characteristics. The fracture propagates fast under low elastic modulus. So the normal stress on the vertical joint decreases fast. Then, the fracture is preferred to extend vertically through the intercalated layer. Under high elastic modulus, the fracture propagates slowly. So the normal stress on the vertical joint decreases slowly. Then, the shear stress on the bedding plane is preferred to reach the shear strength, and the bedding plane undergoes shear damage. The minimum value of Dif-S can be used to characterize the hindering effect of the intercalated layer. The smaller the Dif-S, the stronger the hindering effect. Therefore, with the increase in the elastic modulus, the minimum Dif-S decreases and the hindering effect of the bedding plane increases.

From Figure 9, it can be seen that the effect of Ei on the hydraulic fracture propagation pattern needs to consider the Ec. When the Ec is small (such as 20 GPa), changes in Ei have little effect on hydraulic fracture penetration. When the Ec is large (such as 50 GPa), the effect of Ei on hydraulic fracture penetration is significant. As shown in the figure, the fracture pattern changes from passing through the intercalated layer to being hindered by the intercalated layer with increase in Ei. Therefore, the effect of the intercalated layer on fracture patterns should be discussed for the classification of different Ec values.

Figure 11 shows the stress evolution curve corresponding to the Ec of 20 GPa. Since the coal seams have the same elastic modulus, the curves overlap before encountering the intercalated layer. As the fracture approaches the intercalated layer, the stress curves begin to differ. At this stage, the stress curve corresponding to 40 GPa is more to the left, indicating that stress changes occur earlier. The curve corresponding to 70 GPa is most to the right, indicating that stress changes occur later. Therefore, the effect of Ei on the stress change is mainly manifested in the following ways. The lower the Ei is, the earlier and faster the stress response at the fracture approaching. Although the effect of Ei on the stress evolution has been analyzed above, the overall influence of the interacted layer on the maximum shear stress and the minimum normal stress is very small. The stress curves shows that the normal stress reaches the tensile strength of the vertical joint and the hydraulic fracture directly penetrates the intercalated layer. Furthermore, the shear stress has not reached the shear strength at this point, so hydraulic fractures do not turn. In seams with low elastic modulus, Ei has little effect on the penetration behavior of hydraulic fractures.

Figure 12 shows the stress variation curves for the elastic modulus of 50 GPa. Combining the analysis in Figures 12A, B, the normal stress is shown to decrease to reach the tensile strength and the hydraulic fracture penetrates the intercalated layer at the Ei of 40 GPa and 50 GPa. The normal stresses do not reach the tensile strength at the Ei of 60 GPa and 70 GPa, so the hydraulic fractures fail to penetrate the intercalated layer.

All the shear stress curves shown in Figure 12A undergo a sudden vertical decrease. Combining the results of Zheng et al. (2022) and Figure 10, it can be seen that the vertical decrease in the shear stresses indicates that shear damage has occurred at this time. Although shear damage occurs in all horizontal bedding planes, the propagation patterns of hydraulic fractures at different Ei are different. In order to analyze the effect of Ei, the two cases of Ei of 50 GPa and 60 GPa are taken as examples to analyze the stress evolution. Their stress curves are plotted in Figures 12C, D. From Figure 12C, it can be seen that when the Ei is 50 GPa, the horizontal bedding plane can still withstand a certain amount of shear stress after shear failure. Thus, stresses and strains can be transferred from one side to the other side of the bedding plane. Therefore, the normal stresses on the vertical joint surface can continue to decrease. Finally, the normal stress is reduced to the tensile strength of the vertical joint, and the hydraulic fractures extend vertically through the bedding plane. When the Ei is 60 GPa, the stress and strain transfer between the two sides of the bedding plane is poor after the shear damage. So the normal stress does not reduce. As a result, the hydraulic fracture cannot pass through the bedding plane. Then, the hydraulic fracture can only continue to be extended along the bedding plane. Eventually, the fracture at this point opens up and loses its shear capacity, and both sides of the bedding plane lose the transfer ability of stress and strain. In summary, the mechanism of the intercalated layer on the penetration behavior in the high elastic modulus coal seam is as follows: Ei affects the reduction of the normal stress on the vertical joint. When Ei is lower, the normal stress can continue to decrease and the hydraulic fractures can penetrate the bedding plane. When Ei is higher, the normal stress cannot continue to decrease, and then hydraulic fractures cannot pass through the bedding plane.

The injection rate is one of the key construction parameters that can be artificially controlled in fracturing construction. In order to analyze the effect of injection rate on fracture propagation, eight injection schemes are developed as shown in Figure 13. The viscosity in the scheme is 1 cp. In order to unify the evaluation criteria, the total injection volume is used as the evaluation criterion in the simulation. Figure 13 shows the fracture propagation under the same injection volume. It can be seen from the figure that when the injection rate is 0.0005 m³/s (500 mL/s) and 0.001 m³/s (1000 mL/s), the hydraulic fracture is hindered after encountering the bedding plane, and the hydraulic fracture fails to pass through the intercalated layer. When the injection rate is 0.0015 m³/s, the hydraulic fracture passes through the intercalated layer. However, the hydraulic fractures on both sides of the intercalated layer are discontinuous. The intercalated layer has a strong hindering effect on the hydraulic fracture. With the increase in the injection rate, the hindering effect of the intercalated layer on the hydraulic fracture is reduced. Therefore, in the fracturing design, the injection rate should be designed according to the penetration behavior of the fracture, combined with the rock structure and rock property. The high injection rate is more conducive to the hydraulic fracture through the intercalated layer to ensure the fracture height. However, the high injection rate requires stronger power equipment, high injection pressure, and increased cost. Although the high injection rate is helpful for the fracture to penetrate the layer, the injection rate should be determined according to the actual situation of the reservoir.

Figure 14 shows the shear stress on the horizontal bedding plane and the normal stress on the vertical joint plane corresponding to the case shown in Figures 13A–D. Due to the different injection rates, the corresponding injection time is different at the same injection volume. In order to unify the evaluation criteria, the total injection volume is plotted along the x-axis in the figure. As shown in the figure, when the injection rate is low, the shear stress on the horizontal bedding increases slowly. With the increase in the injection rate, the shear stress rise rate increases (the curve moves to the left). When the injection rate is bigger than 0.0015 m³/s, the shear stress curve basically coincides. It can be seen from Figure 14A that the shear stress curves all show a vertical decline, which indicates that shear failure occurs on the horizontal bedding plane. It can be seen from Figure 14B that the normal stress of 0.0015 and 0.0020 m³/s can continue to decline after the shear failure of the horizontal bedding plane. As the normal stress decreases to the tensile strength, the vertical joint opens and the hydraulic fracture passes through the bedding plane. When the injection rate is low, the normal stress cannot continue to decrease, and the fractures can only expand along the bedding plane.

In summary, the influence of the injection rate on the penetration of hydraulic fractures is as follows. At a small injection rate, the normal stress on the vertical joint cannot reach its tensile strength, and the hydraulic fracture cannot expand vertically. Therefore, the hydraulic fractures tend to expand along the horizontal bedding plane. With the increase in the injection rate, the normal stress on the vertical joint can reach the tensile strength, and the hydraulic fracture can extend along the vertical direction, weakening the trend of extending along the horizontal bedding plane. As a result, the hindering effect of the intercalated layer fractures decreases, and hydraulic fractures tend to expand directly through the intercalated layer.

The fluid viscosity is another key construction parameter that can be artificially controlled in fracturing construction. In order to analyze the influence of fluid viscosity on fracture propagation, eight viscosity schemes are designed as shown in Figure 15. In the scheme, the fixed injection rate is 0.001 m³/s. Figure 15 shows the fracture morphology under different viscosities.

As shown in the figure, the hydraulic fracture is hindered by the bedding plane with the viscosities of 50 cp and 100 cp. It means that the hindering effect of the intercalated layer on hydraulic fractures increases with the increase in fluid viscosity. This conclusion is inconsistent with the previous understanding of the influence of construction parameters on the penetration behavior (Zheng et al., 2022). In the previous studies, the research on the penetration behavior of the hydraulic fracture was mainly aimed at the weak plane of bedding, while we establish the actual intercalated layer considering the thickness. Different from the above simulation, the hydraulic fracture penetrated the internal bedding plane and entered the intercalated layer but failed to penetrate the external bedding plane. In order to analyze this process, the hydraulic fracture propagation process with the injection viscosity of 100 cp is given in Figure 16. Before 1,600 s, the hydraulic fracture expands in the main zone, and the hydraulic fracture is penny-shaped. At 1,600 s, the hydraulic fracture reaches the inner bedding plane of the intercalated layer. Subsequently, hydraulic fractures can pass through the bedding plane into the intercalated layer (Figure 16B), which is consistent with the previous understanding of the influence of construction parameters on the fracture penetration behavior. However, this paper considers the thickness of the actual intercalated layer, so the intercalated layer is divided into two layers. Hydraulic fractures can enter the intercalated layer, but they are hindered by the outer bedding plane coming out of the intercalated layer (Figure 16C). Subsequently, the internal bedding plane reached the shear failure condition, and the hydraulic fracture turned to expand along the internal bedding plane (Figure 16D). The propagation process of fractures under high fluid viscosity is as follows: first, the hydraulic fractures pass through the bedding plane and enter the intercalated layer. Then, the hydraulic fractures are hindered when they pass through the intercalated layer. Finally, the hydraulic fractures turn to expand along the internal bedding plane. In this process, although the hydraulic fracture expands along the internal bedding plane, the fracture first passes through the bedding plane, but it turns to the bedding plane due to obstruction. This is different from the direct offset of hydraulic fractures after encountering bedding planes in the previous studies.

In summary, when considering the two bedding planes and the thickness of the intercalated layer, the viscosity of the fracturing fluid has a significant effect on the penetration of the hydraulic fracture through the intercalated layer. Figure 17 shows the details of fracture propagation under different viscosities for the analysis of the propagation characteristics of hydraulic fractures under different viscosities. For clarity, only the top half of the fractures is shown. As shown in the figure, although the hydraulic fracture passes through the intercalated layer, the shear failure occurs on the internal bedding plane when the viscosity is 4 cp and 5 cp. The shear failure range at low viscosity is greater than that at high viscosity. Furthermore, the shear range characterizes the hindrance of the bedding plane. The larger the shear failure range is, the greater the hindrance effect. It means that in this viscosity range, the hindering effect of the bedding plane decreases as the viscosity increases. When the viscosity is 10 cp, the hydraulic fracture passes through the intercalated layer, and no shear failure occurs on the bedding plane. When the viscosity is 20 cp, the hydraulic fracture passes through the intercalated layer, but the shear failure area appears on the horizontal bedding plane. When the viscosity is 50 cp, the hydraulic fracture can pass through the intercalated layer, but it fails to expand vertically after passing out. In addition, the hydraulic fracture expands along the horizontal bedding plane.

Figure 18 shows the stress evolution curve corresponding to Figure 17. In order to facilitate the marking, the shear stress on the horizontal bedding plane is represented by S-H, and the normal stress on the vertical joint plane is represented by N-V. The position of the intersection point between the internal bedding plane and the vertical joint plane is denoted by in. The position of the intersection point between the outer bedding plane and the vertical joint is denoted by out. As shown in the figure, when the viscosity is 4 cp and 5 cp, the horizontal bedding plane first undergoes shear failure. Then, the N-V can continue to decrease to the tensile strength, so the hydraulic fracture eventually expands vertically. When the viscosity is 10 cp, no shear failure occurs on the horizontal bedding plane. As the viscosity continues to increase, under the conditions of 20 cp, 50 cp, and 100 cp, the vertical joint first undergoes tensile failure. Then, the internal bedding surface undergoes shear failure. Therefore, the viscosity of the fracturing fluid affects the order of failure of the horizontal bedding plane. Under the condition of low viscosity, the shear failure of the horizontal bedding plane precedes the tensile failure of the vertical joint. In a word, the viscosity affects whether the hydraulic fracture can penetrate the intercalated layer by the shear failure of the horizontal bedding plane. At this time, the greater the viscosity, the easier it is for hydraulic fractures to enter the intercalated layer.

In summary, this study considers the thickness of the intercalated layer. High viscosity increases the tendency for fractures to enter the intercalated layer. Furthermore, the difficulty of passing out through the intercalated layer increases. This understanding is different from the existing understanding of the impact of construction parameters on the penetration behaviors. During fracturing operations, it is not advisable to blindly increase the viscosity of fracturing fluids, but rather to consider the increased difficulty of penetrating the interlayer caused by increased viscosity of fracturing fluids.