1 INTRODUCTION OF UNDERGROUND SUPPORT STRUCTURES

As one of the main energy sources in China, for a long time, over 60% of the total energy consumption has been from coal. In China, the total amount of available coal resources is 5059.2 billion tons, of which 53% are buried below 1000 m and 78% are buried below more than 600 m (Peng, 2017). With increasing mining depth, the mining conditions become increasingly complex. Due to high compression stress, high pore pressure, high temperature, and intensive mining disturbance, cracks develop in the surrounding rock of roadways, leading to an enlarged plastic zone with potential large deformation. Supported by conventional anchor, cable, truss anchor, anchor-with-grouting, and other techniques, the roadway can easily collapse when severe deformation of the surrounding rock occurs. The large deformation in the surrounding rock triggers roof fall and other disasters, resulting in a large number of casualties and roadway damage (He et al., 2014). Classical rock mechanics theory and conventional support techniques are facing new challenges.

Previous studies have been conducted on roadway surrounding rock stability and support technology, and some theories have been established on roadway surrounding rock support, such as the suspension support theory, the composite beam theory, the composite arch theory, the surrounding rock strengthening theory of anchor-supported roadway, the surrounding rock loose zone theory, and the combined support theory (Dong, 2001; Hou & Gou, 2000; Lang & Bischoff, 1982; Li, 2008; Meng et al., 2015; Panek, 1962). According to the deformation of surrounding rock and the applicable conditions of anchors, the above-mentioned surrounding rock support theories can be divided into three categories. The first category of theories is based on the assumption that the surrounding rock of roadway is in an elastic state, and includes the suspension support theory and the composite beam theory. The second category of theories gives full consideration to the elastic–plastic mechanical properties of roadway surrounding rock and the residual strength of cracked rock mass. The representative theories of this category are the surrounding rock strengthening theory and the broken rock zone theory. The third category of theories in essence includes a methodology that emphasizes the scientific nature of engineering applications, and the representative theory is the combined support theory. However, with increasing complexity of mining conditions, increasing mining depth, and increasing service time of roadway, many deep roadways designed according to the traditional support theory develop some problems, such as severe deformation, maintenance difficulty, and frequent instability disasters, which leads to decreased safety in coal mines and considerably affects the efficiency of mining.

On the other hand, with the continuous development of underground engineering, roadway surrounding rock support technologies have also been continuously developed. At present, the widely used technologies mainly include anchor and shotcreting support, anchor mesh and shotcreting support, and U-shaped retractable metal support. However, the above support technologies fail to consider the classification of the surrounding rock of deep roadway, and the specific construction measures are often unclear. To ensure the safety and stability of deep roadways, many new support technologies have been developed in recent years to prevent the deformation of the surrounding rock of deep roadways. Specifically, these technologies mainly focus on the following two aspects: (1) improvement of strength and (2) improvement of the yield capacity. In terms of the first aspect, Kang et al. (2007) developed a high prestress and strong support system for deep coal mines and complex and difficult roadway conditions, and applied it to the kilometer-deep roadway in the Xinwen Mining Area. Aiming to address the problems of large surrounding rock deformation and difficult roadway support in a large cross-section soft rock inclined shaft, Li et al. (2013) developed the support technology of high-strength concrete-filled steel tubular support, which has the advantages of good supporting strength, remarkable bending and torsion resistance, and so on. However, it should be pointed out that the above support technologies make the pressure energy absorption capacity slightly insufficient. Xiao et al. (2011) put forward a new three-dimensional anchor cable support technology, which improves the overall stability and bearing capacity of roadway surrounding rock by applying active compressive stress. As for the second aspect, He et al. (2014) developed constant resistance and large deformation anchors/anchor cables, which can provide constant working resistance and stable deformation, thus meeting the requirements of large deformation of roadway surrounding rock. Focusing on the problem of deep dynamic pressure roadway support, Zhang et al. (2012) developed a “high resistance-yield” support system with a high strength yield anchor and a ribbed anchor cable as the core. He et al. (2023) developed negative Poisson's ratio (NPR) anchors/anchor cables as the core of the development of large deformation restriction technology. NPR anchors/anchor cables can effectively improve the deformation capacity up to 1000 mm, but the deformation of the perimeter rock between the anchors in the state of tensile stress has limited effect on deformation restriction. Based on the possible types of failure that can occur in the roadway, Zang et al. (2020) proposed a combined support “anchor-cable-mesh-steel beam.”

The mode of occurrence of deep roadway disasters is dynamic, but its gestation process is relatively static, and the deformation and failure of surrounding rock show obvious time-varying characteristics (He et al., 2008; Liu, 2018). At present, roadway support technology is mostly based on rock strength while ignoring the influence of rock rheological properties (Ansell, 2005; He et al., 2014; Li, 2010, 2012; Tao et al., 2016; Zhang et al., 2015). Therefore, on the basis of previous studies and taking the influence of rheological properties of surrounding rock into consideration, this study applied four-dimensional (4D) support technology to exert extrusion force on roadway surrounding rock in the circumferential, radial, and axial dimensions. Therefore, under 4D support, roadway surrounding rock was in a three-dimensional compressive state in the new equilibrium structure. Given that the compressive strength of brittle materials such as coal and rock is higher than the tensile strength, a spatial network-bearing structure was constructed. In this way, prevention and control of surrounding rock instability disasters in three spatial dimensions and one time dimension (four dimensions in total) could be achieved.

2 THEORY OF THE 4D SUPPORT STRUCTURE

Generally, roadway depth is considered to be the main reason for severe deformation of surrounding rocks because the roadway service life used to be short as reported in previous studies on coal mining (Meng et al., 2015). However, with the increase of the service life of the roadway, the influence of service time on the deformation needs to be considered (He et al., 2008, 2014). 4D support has been launched to investigate the effect of creep deformation time on roadway deformation. Given that conventional support cannot exert effective extrusion force on surrounding rock between anchors/anchor cables to restrict roadway deformation, 4D anchor cable (anchor) support technology has been developed (Liu, 2018). Technically, this support technology is implemented by the following steps: first, the anchor cable exposed in the roadway is broken into multiple strands; second, a protective bowl lock is installed at the anchor cable orifice; third, two steel strands are twisted into one strand; fourth, this strand is connected with adjacent steel strands (or corner anchors) through special locks along the axial and circumferential directions of the roadway; fifth, force transmission cushion blocks are set between the steel strands and the surface of coal and rock mass; and finally, pretightening force is applied to the steel strands connected along different directions. With the use of 4D support, the force transmission cushion blocks are close to the surface of coal and rock mass, and the whole support structure forms an organic integral spatial structure on the roadway surface. The schematic diagram of a 4D anchor cable (anchor) support structure is shown in Figure 1. Liu (2018) performed an indoor 4D support structure-bearing capacity test, which was consistent with the experimental results of numerical simulations. Cui (2018) conducted on-site deformation monitoring to verify the applicability of the 4D support technique in engineering practice, and it was consistent with the indoor experimental results and numerical simulation results.

Specifically, through the force transmission block, the tension forces of the flexible steel strand connected to and stretched with each other are converted into the circumferential and axial extrusion force and the radial anchor supporting force on the surrounding rock (Liu, 2018). After that, the radial anchoring force converts the tensile zone into the compressive zone in the common support of shallow roof strata. Also, as shown in Figure 2, the thickness of the supporting bearing shell increases, and extrusion force improves the stability and integrity of the surrounding rock. Therefore, the surrounding rock of the roadway remains under three-dimensional compression in the new equilibrium structure. Meanwhile, since brittle materials such as coal and rock can bear certain plastic deformation when the three-dimensional compressive stress state is achieved, this phenomenon is given full consideration as well (Li, 2010; Zhang et al., 2015). The mechanism of the overall supporting structure can be explained by the composite arch theory, which is shown in Figure 2 (He et al., 2014; Liu, 2018).

As can be seen from Figure 2, after the anchor is established in the shallow broken area of the roadway surrounding rock, an abacus-bead-shaped cone compression zone (Figure 2) is formed at an angle of about 45° on the left and right sides of the coal and rock mass at both ends of the anchor (He et al., 2008, 2014; Liu, 2018). When enough anchors are arranged along the circumferential direction of the roadway, the abacus-bead-shaped cone compression zone formed by each anchor will overlap with each other, and finally create a uniform and continuous composite arch compression strip (referred to as composite arch for short) in the surrounding rock. Meanwhile, the thickness of this composite arch is far greater than that of conventional support. Once the surrounding rock of the roadway is deformed, the composite arch can actively bear the radial load from the overlying broken rock mass, and improve the stability of the surrounding rock. The surrounding rock in the composite arch is under pressure in both radial and tangential directions, so the stress state of the surrounding rock is spread toward three directions and the bearing capacity is obviously improved, which can provide better capability to withstand the increase of surrounding rock stress with the increase of roadway depth. Meanwhile, as shown in Figure 2, each anchor cable (anchor) in the traditional anchor cable (anchor) support works independently. When the stress of the surrounding rock increases, the group of cables (anchors) cannot coordinate well to restrict the deformation of the surrounding rock. The new 4D support connects adjacent cables or anchors through force transmission blocks, steel strands, and dedicated locks to increase the coordination capability of anchor cables against deformation, thus improving the stability of the support structure under long-time mining conditions.

Liu (2018) pointed out that better withstand the high stress and long-term high-intensity disturbance of deep mining, the new 4D support theory needs to be further studied in terms of the support effect of roadway surrounding rock under conditions of large roadway depth and long-term service, so as to obtain the design parameters and engineering indexes of the 4D support theory. As revealed by the review of previous studies, there are relatively few studies on the influence of the increase of roadway depth and creep deformation time on roadway surrounding rock deformation under different support modes, and more detailed studies are needed to promote the application of new technologies (Ansell, 2005; Freeman, 1978; He et al., 2014, 2023; Kang et al., 2013; Kilic et al., 2002; Kim et al., 2007; Li, 2010, 2012; Ma et al., 2023; Tao et al., 2016; Yang et al., 2008; Zhang et al., 2015). In this study, the influence of roadway depth and time effect on the energy development of 4D supported surrounding rock is discussed in detail. Meanwhile, the supporting effects of 4D support and conventional support were compared. This study provides the theoretical basis for the application of 4D support in the future.

3 ESTABLISHMENT OF A NUMERICAL SIMULATION MODEL OF 4D SUPPORT FOR ROADWAY SURROUNDING ROCK

3.1 Mechanical constitutive relation of roadway surrounding rock with time effect

Based on the 4D support mechanism and the actual engineering geological conditions of a mining area, this study simulated the creep deformation of the surrounding rock of a roadway using the finite difference method and the Cvisc viscoelastic–plastic model in the software FLAC3D. The creep deformation and plastic zone distribution of the surrounding rock with different roadway depths were explored under 4D support and conventional support conditions.

By utilizing the Cvisc model, this study further examined the time effect on stress distribution and deformation of surrounding rock. Cvisc is a viscoelastic–plastic model combined with the Maxwell model, the Kelvin model, and the M-C plastic body, and its component model is shown in Figure 3 and Equation (1) (Liu, 2018). In Figure 3, $�$ is the compression stress imposed in the Cvisc model; ${�}_{\mathrm{M}}$ and ${�}_{\mathrm{M}}$ denote the mechanical properties of the Maxwell body; ${�}_{\mathrm{K}}$ and ${�}_{\mathrm{K}}$ represent the mechanical properties of the Kelvin body; and ${�}_{\mathrm{M}–\mathrm{C}}$ , c, and $�$ are the compressive yield strength, the cohesive force, and the internal friction angle of the M–C plastic body, respectively.

The creep deformation equation corresponding to this model is as follows:

$�\left(�\right)=\frac{�}{{�}_{\mathrm{M}}}+\frac{�}{{�}_{\mathrm{M}}}�+\frac{�}{{�}_{\mathrm{K}}}\left[1-\text{exp}\left(-\frac{{�}_{\mathrm{K}}}{{�}_{\mathrm{K}}}�\right)\right]+{�}_{\mathrm{p}},$ (1)

where t is the creep deformation time; ${�}_{\mathrm{M}}$ and ${�}_{\mathrm{K}}$ denote the elastic module of the Maxwell body and the Kelvin body, respectively; ${�}_{\mathrm{M}}$ and ${�}_{\mathrm{K}}$ represent the viscosity coefficient of the Maxwell body and the Kelvin body; and ${�}_{\mathrm{p}}$ is the plastic strain of the M-C plastic body.

In addition, the elastic strain energy model was established in FLAC3D by Fish language to explore the energy development of the surrounding rock. Considering that there is a certain gap between the rock samples taken in the test and the engineering practice, it is necessary to reduce the physical and mechanical test data of standard coal rock samples in the selection of rock mechanical parameters of a numerical model. The empirical method was adopted for reduction. The physical and mechanical parameters of coal and rock used for calculation are shown in Table 1. According to the mechanical properties of coal and rock layers, rock deformation shows obvious elastic–plastic characteristics. In view of this, the Mohr–Coulomb elastic–plastic constitutive model can effectively reflect the strength of the rock. The rock mechanical parameters shown in Table 1 are based on the research results of Jiang (2014).

Table 1. Physical and mechanical parameters of coal and rock layers.

Lithology	Density (kg/m3)	Bulk modulus (GPa)	Shear modulus (GPa)	Cohesive force (MPa)	Tensile strength (MPa)	Compressive yield strength (MPa)	Internal friction angle (°)	Poisson's ratio
Fine sandstone	2300	2.48	1.85	3.15	9.86	60.11	30	0.14
Mudstone	1600	1.40	1.10	2.25	3.88	36.21	27	0.18
Coal	1350	0.50	0.10	0.60	3.50	30.46	22	0.31
Mudstone	2000	1.40	1.10	2.25	3.88	36.24	27	0.18
Medium sandstone	2200	2.38	1.80	3.00	7.51	45.22	29	0.20

3.2 Dimensioning and meshing of a numerical simulation model

The geological conditions of the mining working face were simplified, and the influence of geological conditions, such as faults and coal seam inclination, on the simulation was neglected. According to the actual situation of the mining area, the model size was set to 100 m × 70 m × 50 m (length × width × height). The x-direction is the layout direction of the mining working face and the y-direction is the advancing direction of the working face; the z-direction is the direction of gravity. The roadway section is 4.5 m × 3.2 m (width × height). To improve the accuracy and computational efficiency of numerical calculations, a proper dense meshing was placed near the roadway, and the gradient ratio near and away from the roadway was 0.9 and 1.1, respectively. To represent clearly the stress field distribution in the surrounding rock of roadway caused by the change of supporting parameters in the actual model, the influence of the original rock stresses was not considered in the calculation model. The constructed three-dimensional calculation model is shown in Figure 4.

Considering a coal mine located at north-central China, the depth of the roadway ranges from 220 to 620 m (Cui, 2018). The roadway depth used as a reference was set to be 320 m. The roadway was simulated in the numerical model with a depth ranging from 220 to 620 m. Therefore, based on the in situ situation, the influence of roadway depth on the surrounding rocks of roadway can be investigated accordingly.

3.3 Simulation method of a roadway supporting structure in the numerical model

3.3.1 Selection of a structural unit

Considering that in the actual situation, the roadway roof generally needs to be reinforced, 4D support is applied to the roadway roof. Meanwhile, conventional support is applied to the roadway sides, and no support is applied on the floor in the finite element model. In the process of numerical simulation, because only the axial strength is considered, the anchor and the part driven into rock stratum (including traditional cable and 4D cable) are simulated by cable elements. For the steel strands connected in pairs, not only the axial strength but also the shear capacity should be considered. Accordingly, the pile element is used for simulation in that it could simulate the tangential and normal forces of the structure. For the load-transfer block on the surface of a rock mass, the model element attribute is set as an “isotropic elastic model” to simulate its stress and deformation.

3.3.2 Simulation of bowl-shaped hole guard lock and pretightening force (refer to Figure 1)

For a traditional anchor cable (anchor), the anchoring section, the free section, and the end of the anchor cable (anchor) are assigned different attributes to simulate their stress state. The anchoring parameters of the end of the anchor cable are set to a maximum value to simulate the role of a bowl-shaped hole guard lock. Specific parameters of pretightening force are assigned to the free section of cables or anchors. For a 4D cable, the pretightening force of the 4D cable is realized by applying pressure along the axis direction of each cable.

3.3.3 4D supporting structure combination (refer to Figure 1)

Interactions between structural elements (cable elements) and between structural elements and rock are achieved by connection. In view of the specific characteristics of 4D cable support, the connection between nodes is set as a free connection and that between nodes and structural elements is set as an elastic connection (especially steel strands exposed in the roadway). The mechanical connections between structural elements (cable elements) and rock in 4D support are shown in Figure 5.

4 TIME EFFECT OF STRESS AND DEFORMATION OF ROADWAY SURROUNDING ROCK UNDER 4D SUPPORT

4.1 Distribution of the plastic zone

This study used a numerical model to explore the stress and corresponding deformation of roadway surrounding rock at different roadway depths. Considering the restriction effect of 4D support and conventional support on surrounding rock deformation, the change of the roadway plastic zone at different roadway depths and the change of roadway surrounding rock deformation with creep deformation time were analyzed. According to the stress distribution of the surrounding rock, the elastic strain energy distribution of the surrounding rock was further calculated, and the influence of roadway depth and different supporting methods on elastic strain energy was examined. On the basis of the above analysis, the support effect of 4D support in the roadways with large roadway depth and long service life was compared with that of conventional support.

4.1.1 Change of the plastic zone under the influence of different roadway depths

Figure 6 shows the diagram of the plastic zone distribution in the surrounding rock with 4D support at different roadway depths. As can be seen from the diagram, with a gradual increase in the roadway depth from 220 to 620 m, the depth and area of the plastic zone of the surrounding rock increase correspondingly. The type of failure of the surrounding rock is mainly shear failure. By comparing the two interfaces of roadway walls (roof side, side floor), it can be seen that the roof-side plastic zone is not connected with that of the side floor, showing obvious boundaries. Also, the plastic zone of the surrounding rock gradually extends deeper in a stepwise manner.

From Figure 6c–e, it can be seen that with the increase of roadway depth, the plastic zone of the roadway roof shows no obvious increase after the roadway depth exceeds 320 m, demonstrating that 4D support technology used at the roadway roof can effectively restrain the deformation and failure of the surrounding rock.

Table 2 shows the distribution of the plastic zone of the surrounding rock at different roadway depths. Combined with Figure 6, it is clear that when the roadway depth is less than 520 m, the area and depth of the plastic zone in the roof increase with increasing roadway depth. After that, when the roadway depth exceeds 520 m, the area and depth of the plastic zone in the roadway roof and sides remain stable with increasing roadway depth. Specifically, when the roadway depth is over 520 m, the plastic area in the roof and roadway side is stabilized at 5.76 and 3.52 m2, respectively.

Table 2. Area and depth of the plastic zone under the influence of roadway depth.

	Plastic zone distributed in roadway surrounding rock
	Roof		Floor		Side
Roadway depth (m)	Area (m2)	Depth (m)	Area (m2)	Depth (m)	Area (m2)	Depth (m)
220	2.56	0.8	4.16	0.8	1.92	0.8
320	4.48	0.8	5.76	1.2	2.56	0.8
420	5.44	1.2	6.08	1.6	3.52	1.2
520	5.76	1.2	6.40	1.6	3.52	1.2
620	5.76	1.2	7.04	1.6	3.52	1.2

With the increase of roadway depth, the area and depth of the plastic zone in the floor are larger than that of the roof and roadway side, and the area shows a rising trend. This is because 4D support is applied to the roof and the conventional support is applied to the roadway side. Consequently, the plastic zone failure in the roof and sides of roadway is restricted to varying degrees, and the support effect on the roof and sides is more obvious. This phenomenon shows the coordinated deformation of the surrounding rock, which reflects the integrity of the roof and sides of the roadway. Meanwhile, because no support is applied to the floor, the plastic deformation of the floor fails to coordinate with the roof and roadway side.

When the roadway depth exceeds 520 m, the depth of plastic zones in the roof and side remains stable (1.2 m) with the increase of roadway depth. This further shows that the combined support form (4D support in the roof and conventional support in the roadway sides) is suitable for stability control of the surrounding rock in deep roadways with roadway depth exceeding 520 m, and can effectively restrain the area and depth of plastic deformation of roadway surrounding rock.

4.1.2 Time dependence of the plastic zone of surrounding rock developed with increasing creep deformation time

Based on the case information of a mine with a depth of 320 m, the time dependence of the plastic zone distribution of roadway surrounding rock under different support modes was studied. The creep deformation time of surrounding rock was analysed as 1, 2, 3, 4, 5 and 6 months to show the development of plastic zone. The creep deformation model shown in Equation (1) is applied in this simulation.

Figure 7 show the plastic zone of roadway surrounding rock with time (1–6 months) with different support modes (4D support and conventional support). Table 3 shows the plastic zone area of roadway surrounding rock (roof, sides, and floor) with creep deformation time under different support modes. From Figure 7 and Table 3, it can be seen that most of the plastic zones of the surrounding rock under 4D support and conventional support are consistently shear failure.

Table 3. Plastic zone area in roadway surrounding rock at different creep deformation times and under different support modes of the roof.

	Roof (m2)		Side (m2)		Floor (m2)
Creep deformation time (month)	Conventional support	4D support	Conventional support	4D support	Conventional support	4D support
1	1.92	1.92	1.28	1.28	1.92	1.92
2	1.92	1.92	1.60	1.28	3.52	3.52
3	2.24	2.24	2.08	2.40	3.52	4.48
4	4.16	3.52	2.56	2.56	5.44	5.76
5	5.12	3.84	2.72	2.56	5.76	5.76
6	5.12	3.84	2.88	2.56	5.76	5.76

• Abbreviation: 4D, four dimensional.

At the initial stage of creep deformation (1 month), the plastic zone area of the surrounding rock under the two support modes is basically the same. When the creep deformation lasts for 2 months, the area of the plastic zone in the roadway sides with conventional support (1.60 m2) is slightly larger than that with 4D support (1.28 m2). Also, the distribution area of the plastic zone in the roof and floor is the same under two support modes.

After 2 months of creep deformation, with increasing deformation time, the plastic zone area of the surrounding rock with conventional support is larger and increases faster than that with 4D support. When the creep deformation lasts from 5 to 6 months, the plastic zone distribution of the surrounding rock is basically stable under 4D support. However, the plastic zone of roadway sides still slowly expands under conventional support (increasing from 2.72 to 2.88 m2). It can be seen that 4D support can effectively restrict the development of surrounding rock failure with increasing creep deformation time. In particular, it can obviously reduce the plastic zone area in the roadway roof and sides, thus ensuring the long-term safety and stability of roadway surrounding rock.

4.2 Variation of roadway surrounding rock deformation with different creep deformation times under conventional support and 4D support

4.2.1 Variation of roadway surrounding rock deformation with different creep deformation times at different roadway depths

Tables 4 and 5 and Figure 8 show the variation of surrounding rock deformation with different creep deformation times at different roadway depths. From Table 4 and Figure 8, it can be seen that with the increase of creep deformation time, the deformation of the roof, sides, and floor gradually increases and tends to remain stable, and the deformation rate gradually decreases after a period of rapid deformation accumulation. This rapid accumulation of deformation under the action of 4D roof support and conventional side support can generate dislocation in the surrounding rock, which leads to the closure of cracks in the surrounding rock. With the increase of contact surface, the cohesion and internal friction angle between rock particles gradually increase, resulting in a gradual increase of rock strength and a corresponding decrease of the creep deformation rate.

Table 4. Creep deformation time needed for achieving stable deformation of roadway surrounding rock at different roadway depths.

Roadway depth (m)	Creep deformation time of roadway surrounding rock (day)
	Roof subsidence	Side convergence	Floor heave
220	24	26	28
320	28	31	35
420	33	36	41
520	39	42	49
620	43	47	55

Table 5. Displacement of roadway surrounding rock at different roadway depths after 180 days.

Roadway depth (m)	The displacement of roadway surrounding rock after 180 days (mm)
	Roof subsidence	Side convergence	Floor heave
220	115	131	110
320	156	203	175
420	213	273	227
520	275	328	288
620	331	403	373

On the other hand, as shown in Table 5, with the increase of roadway depth (220–620 m), the deformation of roadway roof, sides, and floor approximately increases linearly in 180 days. At the same time, as shown in Table 4, with the increase of roadway depth, the time required for the deformation of the surrounding rock to reach stability gradually increases. In addition, as shown in Table 4, due to the application of 4D support to the roof, the time required for the roof to reach stable deformation is the shortest at the roadway depth of 320 m, which is about 9.7% and 20.0% less than that in the sides and floor, respectively. Because the two sides are supported by traditional anchors, it takes a long time for the deformation to reach stability, and the deformation of the roadway side reaches up to 203 mm.

Because there is no support for the floor, it takes the maximum time for its deformation to reach stability. Specifically, it takes 35 days to reach stable deformation when the roadway depth is 320 m. As shown in Figure 8, with the increase of the deformation time of rock strata, the growth rate of floor deformation after reaching the stable stage is higher than that of roof and sides. The measured results in the field verify the results in Figure 8 that there is a continuous increase in the deformation of the roadway with the increase of the creep deformation time (Cui, 2018).

4.2.2 Variation of roadway surrounding rock deformation with time under different support modes

To explore the influence of support modes on the deformation time dependence of roadway surrounding rock, this study set the roadway depth to 320 m and the vertical stress around roadway to 8 MPa. On the premise of maintaining the support mode of two sides and the floor unchanged, the influence of different roof support modes (conventional support and 4D support) on the time-dependent creep deformation of roadway surrounding rock was analyzed.

Figure 9 shows the displacement of roadway surrounding rock changing with creep deformation time when different roof support modes are adopted. As can be seen from Figure 9a, when conventional support is applied, the roadway surrounding rock is in the state of slow creep deformation in the early stage of support (9–30 days). Then, after a short period of creep deformation (9–30 days), the strength of the rock gradually decreases with the expansion and penetration of roadway cracks. Besides, the deformation of roadway surrounding rock gradually accelerates after 30 days, showing the trend of accelerated creep deformation. In addition, in the whole supporting period, roof subsidence is the largest, followed by the convergence of roadway sides (pillars) and floor heave. After 180 days of roadway deformation, the deformation rate of roadway surrounding rock under conventional support still remains at a high level, and the displacement in the roof, sides, and floor is 351, 276, and 226 mm, respectively.

As can be seen from Figure 9b, with the increase of the creep deformation time, the deformation of the roadway roof and sides (pillars) under 4D support gradually increases and tends to remain stable within 45 days, and increases slightly (less than 10 mm) after 45 days. However, due to the lack of effective support, the floor heave gradually deteriorates with the increase of the creep deformation time, rising from 125 to 170 mm after reaching the stable stage. After 180 days of deformation, the convergence of roadway sides (pillars) is the largest (201 mm), followed by floor heave (170 mm), and roof subsidence is the smallest (161 mm).

According to Figure 9a,b,d, support can reduce the continuous increase of creep deformation of the surrounding rock after reaching the stable deformation stage. Meanwhile, the deformation in this case is relatively small (less than 200 mm), which is beneficial to the long-term safety and stability of the roadway.

5 DEVELOPMENT OF ELASTIC STRAIN ENERGY OF ROADWAY SURROUNDING ROCK WITH THE INCREASE OF THE CREEP DEFORMATION TIME AND ROADWAY DEPTH

5.1 Calculation method of elastic strain energy of roadway surrounding rock

Due to the disturbance of underground mining activities, the initial stress equilibrium state of the coal and rock mass may be disrupted. This will lead to stress redistribution of the surrounding rock. Energy accumulation and release of surrounding rock often occur together in the excavation process. According to the law of thermodynamics, energy dissipation reflects the essential property of rock deformation and failure (He et al., 2014; Liu, 2018). It manifests the whole process of continuous development of internal defects, the constant attenuation, and final loss of strength. Considering the deformation of rock element volume under external load and assuming that there is no heat exchange with the outside, according to the first law of thermodynamics (Tao et al., 2016; Zhang et al., 2015),

${�}^{\mathrm{d}}=�-{�}^{\mathrm{e}},$ (2)

where $�$ denotes the total input energy under the action of external force; ${�}^{\mathrm{e}}$ represents the elastic strain energy accumulated in the element volume; and ${�}^{\mathrm{d}}$ denotes the dissipation energy of the element body, which reflects the attenuation degree of rock mass strength.

Figure 10 shows the loading and unloading stress–strain correlation of rock samples. For rock loaded and unloaded in the $�$ direction, σi and ${�}_{�}$ are defined as the stress and strain in this direction, respectively. The directions include x-, y-, and z-direction. When the load reaches up to the stress level of ${�}_1$ with the strain of ${�}_1$ , the elastic strain energy density accumulates per element volume in this direction. Then, the rock unloads to zero stress with plastic strain of ${�}_2$ . ${�}_{�}^{\mathrm{e}}$ can be determined by the area between the unloading curve and the abscissa. The dissipation energy ${�}_{�}^{\mathrm{d}}$ can be determined by the area between the loading and unloading curves, namely,

${{�}_{�}}^{\mathrm{d}}={\int }_0^{{�}_1}{�}_{�}\mathrm{d}{�}_{�}-{\int }_{{�}_2}^{{�}_1}{�}_{�}\mathrm{d}{�}_{�},$ (3)

${{�}_{�}}^{\mathrm{e}}={\int }_{{�}_2}^{{�}_1}{�}_{�}\mathrm{d}{�}_{�}=\frac{1}{2}{�}_{�}{{�}_{�}}^{1,2},$ (4)

where ${�}_1$ denotes the strain value corresponding to ${�}_1$ and ${�}_2$ is the residual strain value corresponding to the stress unloading from ${�}_1$ to 0.

According to the theory of elasticity, the strain energy density equation of an elastic body expressed by stress and strain under three-dimensional stress is as follows:

${�}^{\mathrm{e},\text{rock}}=\frac{1}{2}\left({�}_{�}{�}_{�}+{�}_{�}{�}_{�}+{�}_{�}{�}_{�}+{�}_{\mathit{yz}}{�}_{\mathit{yz}}+{�}_{\mathit{zx}}{�}_{\mathit{zx}}+{�}_{\mathit{xy}}{�}_{\mathit{xy}}\right),$ (5)

where ${�}^{\mathrm{e},\text{rock}}$ denotes the elastic strain energy density of rock; σi( i =  x, y, z) and ${�}_{\mathit{ij}}\left(�,�=�,�,�\right)$ are the axial and shear stresses of rock, respectively, and ${�}_{�}(�=�,�,�)$ and ${�}_{\mathit{ij}}\left(�,�=�,�,�\right)$ are the axial and shear strains of the rock, respectively.

Assuming that the elastic body is isotropic, its constitutive equation can be expressed as follows:

$\{\begin{array}{l}{�}_{\mathit{�}}=\frac{1}{�}\left[{�}_{\mathit{�}}-�\left({�}_{�}+{�}_{\mathit{�}}\right)\right],{�}_{��}=\frac{1}{�}{�}_{��},\\ {�}_{�}=\frac{1}{�}\left[{�}_{\mathit{�}}-�\left({�}_{�}+{�}_{\mathit{�}}\right)\right],{�}_{��}=\frac{1}{�}{�}_{��},\\ {�}_{�}=\frac{1}{�}\left[{�}_{\mathit{�}}-�\left({�}_{�}+{�}_{\mathit{�}}\right)\right],{�}_{��}=\frac{1}{�}{�}_{��},\end{array}$ (6)

where $�$ and $�$ denote the elastic modulus and Poisson's ratio of the elastic body, respectively, and $�$ represents the shear modulus of the elastic body. The relationship between the three is as follows:

$�=\frac{�}{2(1+�)}.$ (7)

When Equations ( 5) and ( 6) are introduced into Equation ( 4), the elastic strain energy expressed by stress components can be obtained as follows:

$�=\left[{\left({�}_{�}+{�}_{�}+{�}_{�}\right)}^2-2\left(1+�\right)\left({�}_{\mathit{�}}{�}_{\mathit{�}}+{�}_{\mathit{�}}{�}_{\mathit{�}}+{�}_{\mathit{�}}{�}_{\mathit{�}}-{�}_{��}^2-{�}_{��}^2-{�}_{��}^2\right)\right]/2�.$ (8)

According to Equation (8), the model to calculate the distribution of elastic strain energy density of a rock mass can be obtained by introducing FISH language into FLAC3D. Then, the influence of roadway depths and support modes on the energy distribution of roadway surrounding rock is explored to reveal the energy development of roadway surrounding rock under 4D support.

5.2 Influence of roadway depth on energy distribution of surrounding rock under 4D support

Figure 11 shows the isoline distribution of elastic strain energy of roadway surrounding rock under different roadway depths and 4D support with a creep deformation time of 6 months. The elastic strain energy on the roadway surface of any depth is distributed in an elliptical pattern, and the elastic strain energy of two sides appears to be axisymmetric around the central axis of roadway cross-section. The farther the distance from the roadway surface, the larger the radius of the ellipse, and the smaller the elastic strain energy value. This is mainly because the roadway excavation destroys the initial stress state of the surrounding rock, and the stress on the surrounding rock changes from a three-dimensional stated to an approximately two-dimensional state, which leads to the redistribution and local stress concentration of the surrounding rock.

Accordingly, the bearing capacity of the surrounding rock decreases greatly. Affected greatly by the disturbance of excavation, the roadway surface appears to be a fracture zone. At this time, the rock mass is under high stress, and the elastic strain energy accumulated in it is comparatively large. Inward from the surface lies the plastic zone and the elastic zone, where the stress on the rock mass gradually decreases, as does the elastic strain energy density. In the elastic state, the surrounding rock still has its bearing capacity so that it can stabilize itself. However, once fractured, the surrounding rock would lose its self-supporting capacity. Accordingly, the fracture zone is highly pivotal for effective support. In particular, reasonable support should be provided on an urgent basis in the roof and sides of the surrounding rock where elastic strain energy accumulates (Figure 11).

As shown in Figure 11, the corresponding peak density of elastic strain energy is 95 000, 305 000, 635 000, 1 005 000, and 1 475 000 J/m3 for roadways with depths of 220, 320, 420, 520, and 620 m, respectively. It can be seen that with the increase of roadway depth, the elastic strain energy density of the roadway gradually increases. The increasing amplitude of elastic strain energy (from 210 000 to 470 000 J/m3) and the accumulation range of strain energy are positively correlated with the roadway depth.

5.3 Influence of support mode on the time effect of energy distribution in roadway surrounding rock

Figure 12 show the variation of the elastic strain energy isoline of roadway surrounding rock with creep deformation time under different roof support modes at a roadway depth of 320 m. As can be seen, with the increase of the distance from the roadway surface, the elastic strain energy increases first and then decreases, and the distribution gradient shows a gradual downward trend. The peak energy is mainly concentrated in the range of 0.5–2.0 m from the roadway side. This is mainly because the excavation of roadway leads to the vertical loss of bearing capacity of the surrounding rock. In this case, the overlying strata pressure is mainly borne by the two sides, resulting in considerable energy accumulation in the roadway sides.

With time, the elastic strain energy of the roadway surface increases gradually. In the case of creeping deformation for 1–6 months, the peak value of the elastic strain energy of roadway surrounding rock under 4D support is 250 000, 300 000, 350 000, 400 000, 450 000, and 450 000 J/m3, respectively. The increase in rate in the first 5 months is about 50 000 J/m3 per month, and the peak value of the elastic strain energy tends to become stable in the sixth month. The peak value of the elastic strain energy of the surrounding rock under conventional support is 350 000, 450 000, 550 000, 650 000, 750 000, and 950 000 J/m3, respectively. Also, its rate of increase is 100 000 J/m3 per month in the first 5 months, which is twice that of 4D support. In the sixth month, the rate of increase is 200 000 J/m3, and the energy accumulation rate of the surrounding rock further increases. Further analysis shows that when the energy accumulation of conventional support reaches the critical value, it is easily released instantly; consequently, a large amount of energy directly acts on the surrounding rock support system. In this case, instability of the support system may occur easily, which may induce serious collapse accidents, and even rock burst.

Therefore, compared with conventional support, 4D support at the roadway roof can optimize the stress state of the surrounding rock and limit the rate and range of energy accumulation on the surface of the surrounding rock. By providing lasting and effective roadway support, 4D support ensures safe mining conditions for a longer time, which can help prevent the occurrence of sudden roof fall and other uncontrollable instability disasters.

Moreover, as shown in Figures 11, 12, the plastic zone distribution of the surrounding rock under 4D roof support is still affected by roadway depth and creep deformation time. With the increase of roadway depth, the plastic zone in the roadway sides develops slightly faster than that in the roof, while the plastic zone in the unsupported floor is the largest among the three.

6 CONCLUSIONS

CONFLICT OF INTEREST STATEMENT

The authors declare no conflict of interest.