Experimental Study on Deformation Law of Rectangular Roadway in Horizontal Layered Rock Mass

In order to analyze the characteristics and mechanism of roadway deformation caused by high stress in horizontal strata, a physical model with rectangular roadway was designed. ­e model was constructed by the so-called “Physically Finite Elemental Slab Assemblage (PFESA)” to bring about the structural eect of the deep strata. In the experiment, the vertical and horizontal pressures were increased step-by-step to simulate high stress. ­e deformation characteristics of surrounding rock in layered rock roadway were observed by video image and digital image correlation method (DIC). ­e strain and stress characteristics of surrounding rock of roadway in layered rock mass were obtained by using the strain gauge test method, and compared with the deformation characteristics. For the sake of analyzing the deformation and failure mechanism of layers, the mechanical model of layered rock structure was established, and the experimental phenomenon and mechanism were veried. ­rough systematic study, this paper enriches the research methods of model experiment and provides an experimental basis for practical engineering of similar conditions.


Introduction
With the exploitation of shallow resources, the mining industry began to focus on the exploitation of deep underground resources. e environment makes the deep rock mechanical characteristics and engineering responses very distinctive [1][2][3][4]. Due to the high stress of deep rock stratum, its strength is weaker than that of shallow rock stratum, which is prone to large deformation and failure. e large deformation of surrounding rock in deep roadway will lead to narrow road, hinder transportation, a ect normal production and cause casualties [5][6][7][8].
Physical model experiment is an important research method of roadway deformation and failure. Reference [9] reproduced the zonal fracture process of surrounding rock in deep roadway through three-dimensional geomechanical model test of similar materials. Reference [10] used similar material simulation test to study the deformation and failure characteristics of roadway surrounding rock under di erent horizontal stress. Reference [11] studied the response characteristics of transient electromagnetic eld of mine water rich abnormal body through physical model experiment. Reference [12] developed variable temperature similar materials, and carried out failure test on the model by combining overload and strength reduction. Reference [13] developed a large geomechanical model test system and carried out model tests on the anchor cable box girder support system. Reference [14] used similar materials of transparent rock mass to physically simulate the excavation process of rock mass.
In the process of physical model experiment, the deformation and failure characteristics of roadway surrounding rock can be obtained by means of displacement, infrared and strain measurement [15][16][17][18][19][20][21], physical modeling plays an indispensable and key role in understanding the deformation and failure mechanism of deep roadway [22,23]. Constructing large-scale physical model experiment can avoid the scaling problem of parameters and variables, but it is expensive [24]. In recent years, a new physical modeling technique, that is, the Physically Finite Elemental Slab Assemblage (PFESA) has been proposed to construct large-scale geological physical models for mimicking stratified rock masses [25,26]. Although the Elemental Slabs are made of artificial materials, the physical and mechanical properties are similar to the real rocks. It can be put into mass production at low cost, and the cost of building a largescale physical model is greatly reduced.
Based on the similarity theory, a physical model is established by using the PFESA technique to simulate the deep horizontal layered rock mass. Using camera, digital image correlation system and strain gauge, the deformation and strain of rock stratum are simulated by physical model under load, and the deformation and failure mechanism of surrounding rock of rectangular roadway in layered rock mass under high stress is analyzed.

Physical Model Prototype.
e physical model experimental prototype is located in the −510 m horizontal roadway with a buried depth of about 1000 m in Datai mine, Mentougou District, Beijing. e study area is monoclinic structure without large-scale geological structure. Diabase, green mudstone, and coal rock are distributed in the stratum where the roadway is located. According to the in situ stress test, the maximum principal stress of the studied stratum is 39.7 MPa, the included angle with the horizontal plane is −2.11°, and the minimum principal stress is 19.2 MPa. e direction of the maximum principal stress is basically consistent with the dip direction of the stratum, which is unfavorable to the stability of the surrounding rock of the roadway. According to the mechanical test, it is found that the bedding of roadway surrounding rock is developed, and the uniaxial strength along the bedding is greater than that perpendicular to the bedding, which has obvious anisotropic characteristics.

Similarity Principle and Materials.
Based on the similarity proportion relationship, when studying the similarity of stress, deformation, and failure characteristics of roadway surrounding rock, the prototype and physical model should meet the similarity index [27,28].
In equations (1) and (2), Cl is the geometric similarity factor, C σ is the stress similarity factor, CE is the elastic modulus similarity factor, C c is the gravity similarity factor, I σ is the stress similarity index, IE is the elastic modulus similarity index. e dimensions of the physical model are 1600 × 1600 × 400 mm 3 and the roadway is designed as a rectangular space in the center of the physical model with the length and width of 200 × 300 mm 2 . e geometric similarity factor is selected empirically as Cl � 15, which meets the requirements in experimental system operating instruction of physical models in deep mine engineering. In addition, the physical model should also satisfy other similarity theories, including the stress similarity factor, defined as C σ � 9. e prototype rock mass to be simulated in this paper is diabase, green mudstone, and coal rock, and its mechanical parameters are given in Table 1. e PFESA technique is employed here. is method utilizes the assembly of rectangular plates which are made of artificial materials according to "similarity theory." e elementary slabs are produced based on different ratio of water-gypsum. e material properties of the elementary slabs simulating the different rock masses are given in Table 2.

Model Design and Production.
e elementary slabs are made through the process of pouring, demolding, and curing as shown in Figures 1(a)-1(c). In order to simulate the inclined rock strata, large numbers of these slabs are arranged at the specified orientation, which is 0°in this case, as shown in Figure 1(d). Different types of elementary slabs simulate different prototype rock masses. According to the on-site stratigraphic structure and geometric similarity factor, the type and range of rock mass simulated by physical model are shown in Figure 1(e).

Loading Scheme.
e experimental loading scheme mainly simulates the stress conditions of rock mass, the process of roadway excavation and the deformation and failure process of roadway caused by high stress. e "Geological Disaster Simulation Testing Machine whose model type is YDMC-C" was equipped with a host machine, specimen mold, truck, hydraulic control system, and data collection system. By using YDMC-C, the top and two side boundaries were imposed uniform load, respectively; the bottom of the model was fixed on the basement of the machine, the loading boundary pressure conditions are shown in Figure 2. e loading process can be divided into 23 load levels, and the loading scheme of model experiment is shown in Table 3. At load levels 1-4, vertical and horizontal pressures increase at the same time, resulting in stress conditions in the rock mass. After load level 4 loading, roadway excavation is carried out. e horizontal pressure of load levels 5-14 is maintained at 0.8 MPa, and the vertical pressure is increased to 2.8 MPa step-by-step. e simulated vertical stress value reaches the condition of 1000 m buried depth. e vertical pressure of load levels 15-24 is maintained at 2.8 MPa, and the horizontal pressure increases step-by-step until the model is damaged. In this paper, the roadway is deformed and damaged under 23 load level, and the experiment is stopped. e physical model and the prototype rock stress condition accord with the similarity theory.

Displacement Test. Digital image correlation (DIC)
technology is a non-contact displacement measurement method [29,30]. In this paper, MTI-2D digital image correlation measurement system is used to measure the surface displacement eld of physical model in real time [31]. When using DIC technology, it is necessary to arrange randomly distributed spots on the surface of the measured object. e spots arrangement is shown in Figure 3(a). ese arti cial random spots are used as the carrier of deformation information to realize the whole eld displacement measurement. In the measurement, set the positive direction of vertical displacement downward and the positive direction of horizontal displacement to the right. During the measurement, real-time displacement monitoring points are set for the roof, oor, left and right sides of the roadway surrounding rock, as shown in Figure 3(b).

Strain Test.
e strain of the model is measured by strain gauge. BA120-3BA strain gauge was used in the experiment, and the sensitive grid size of strain gauge is 3 mm × 2 mm, the sensitivity coe cient is 2.10 ± 1%. A groove with a depth of about 2 mm shall be excavated in the thickness direction   of the elementary slabs. When the strain gauge is bonded in the groove, it shall be flat and firm, and it shall be cured for ten mins. Because the rock stratum is horizontal and the loading direction is vertical and horizontal, two right angle strain flowers are adopted, and the strain measurement range is shown in Figure 1(e).     level 23, the two sides move integrally into the roadway, and there are horizontal displacement staggered zones in the roadway oor and roof strata, resulting in shear deformation.

Displacement Analysis of Measuring Points.
When the cumulative duration of the experiment is 541 to 544 mins, it is the roadway failure stage. Extract the displacement data of roof, oor, left side, and right side monitoring points in the failure stage and adjacent time of roadway surrounding rock. e layout of monitoring points is shown in Figure 3(b). e vertical displacement curve of roadway surrounding rock measuring points with a cumulative duration of 539-550 mins and a total of 660 sec is shown in Figure 7. In the failure stage, the F01 monitoring point of roadway oor rst produces oor heave, and the vertical displacement is 120 mm, then the R01 monitoring point of roadway roof sinks, and the nal vertical displacement is 44 mm. During the vertical change of roadway oor and roof, the vertical displacement of left and right sides uctuates slightly. e horizontal displacement curve of roadway surrounding rock measuring points with a cumulative duration of 539-550 mins and a total of 660 sec is shown in Figure 8. In the failure stage, the monitoring point F01 of the roadway oor moves 25 mm horizontally to the roadway, and the movement amount of F02 and F03 is lower than F01. R01 monitoring point of roadway roof moves horizontally to the right by 16 mm, and R02 and R03 monitoring points move horizontally to the left. e monitoring points LS01, LS02, and LS03 on the left side of the roadway move horizontally into the roadway, with a displacement of about 20 mm. e monitoring points RS01, RS02, and RS03 on the right side of the roadway move about 20 mm into the roadway. By analyzing the deformation characteristics of the model, it can be concluded that the surrounding rock of the roadway can be divided into stable stage, failure stage, and post-failure stage, and the displacement in the failure stage appears sudden change. e failure form of roadway surrounding rock is roof collapse, oor heave, and the two sides slide into the roadway as a whole.

Strain Field Analysis.
e vertical and horizontal strain values of the measuring points during the experiment can be obtained by sticking the strain gauge. Based on Kriging interpolation algorithm, calculate the strain values of each strain monitoring point to obtain the evolution of vertical strain eld of physical model, as shown in Figure 9.
At the level 4 load, the vertical compressive strain is distributed in the lower part of the model, and the tensile strain is distributed in the upper part of the model and the surrounding rock of the roadway. e range of vertical compressive strain and strain value of the model increase under level 14 load. Under the 23 level load, the surrounding rock of the roadway enters the failure stage, and the vertical tensile strain area is concentrated in the roof and oor of the roadway. e evolution of horizontal strain eld under di erent loads is shown in Figure 10. Under level 4 load, the roof and oor of the roadway are horizontal compressive strain, and the two sides of the roadway are horizontal tensile strain. ere is horizontal strain concentration on the left and right sides of the roadway surrounding rock under level 14 load. After entering the failure stage under level 23 load, the strain concentration area appears in the roof, then the strain concentration occurs in the oor, and nally the compressive strain also occurs in the two sides of the roadway surrounding rock.

Strain Analysis of Measuring Point.
When the cumulative duration is 539-550 mins, the vertical strain of the measuring points is shown in Figure 11. In the failure stage, the vertical tensile strain of R01 and R02 monitoring points suddenly increases, and the vertical compressive strain at R03 monitoring suddenly decreases. e vertical tensile strain at F01 monitoring decreases, and the vertical compressive strain at F02 and F03 monitoring points increases.
e vertical tensile strain values of the monitoring points on the left side of the roadway are increased. RS01 on the right side of the roadway changes from vertical compressive strain to tensile strain, and the vertical compressive strain of RS02 and RS03 increases.
When the cumulative duration is 539-550 mins, the horizontal strain at the measuring points is shown in Figure 12. In the failure stage, the horizontal compressive strain at the monitoring points R01 and R02 increases and then falls back to close to the original value, and the horizontal strain at the monitoring point R03 does not change signi cantly. e horizontal tensile strain at F01 monitoring point decreases, and the horizontal compressive strain at F02 and F03 monitoring points increases. e horizontal compressive strain of LS01 and ls03 monitoring points decreases, and the strain of LS02 monitoring point approaches zero. e horizontal compressive strain of RS01 monitoring point is gradually transformed into tensile strain, the horizontal tensile strain of RS02 monitoring point rises and then falls, and the horizontal compressive strain of RS03 monitoring point drops suddenly.
rough the analysis of the strain characteristics of the model, it can be concluded that the vertical tensile strain area in the failure stage is concentrated in the roof and oor of the roadway, and the horizontal compressive strain is concentrated in the left and right sides. When the surrounding rock of the roadway is unstable, the strain changes abruptly, accompanied by the transformation of tension and compression strain.  horizontal stress σ H . e elastic modulus of the physical model material is E, and the Poisson's ratio is μ. Vertical strain of strain measuring point ε V and horizontal strain ε H can be expressed as: Formula (3) is transformed to obtain After the vertical strain and horizontal strain values of the measuring points are obtained through strain monitoring, the vertical stress σ V and horizontal stress σ H can be calculated according to formulas (3) and (4) [32]. Using Kriging interpolation algorithm, according to the location and value of stress monitoring points, the evolution diagrams of vertical and horizontal strain fields of physical model can be obtained.

Stress Field Analysis.
e evolution of vertical stress field under different loads is shown in Figure 13. e surrounding rock of roadway is mainly subjected to vertical tensile stress under level 4 and 14 loads. When the load is level 23, the roadway enters the failure stage, the surrounding rock of the roadway is mainly affected by the vertical tensile strain, and there is an obvious concentration of tensile strain on the roof and floor. e evolution of horizontal stress field under different loads is shown in Figure 14. Under level 4 load, the roof and floor of the roadway are horizontal compressive stress, and the two sides are horizontal tensile stress. Under level 14 load, there is horizontal compressive stress concentration on the left and right sides of the roadway surrounding rock. Under the level 23 load, the roadway enters the failure stage. At the beginning of the failure, the surrounding rock of the roadway produces compressive stress, and then the stress concentration area of the roof and floor appears. e roof and floor of the roadway are mainly subject to horizontal compressive stress, and the left and right sides are mainly subject to horizontal compressive stress.

Stress Analysis of Measuring Point.
When the cumulative duration is 539-550 mins, the vertical stress at the measuring points is shown in Figure 15. In the failure stage, the vertical tensile stress of R01 and R02 monitoring points increases, and the vertical compressive stress of R03 suddenly decreases. e vertical tensile stress of F01 monitoring point drops suddenly, the vertical stress of F02 monitoring point changes from compressive stress to tensile stress, and the vertical stress of F03 monitoring point changes from tensile stress to compressive stress. e vertical tensile stress values of the monitoring points on the left side of the roadway are increased.
e vertical stress of RS01 monitoring point changes from compressive to tensile, and the vertical compressive stress of RS02 and RS03 monitoring points increases. e horizontal stress of measuring points when the cumulative duration is 539-550 mins is shown in Figure 16.
e horizontal compressive stress of roof R01 monitoring point increases and then decreases, the compressive strain of R02 monitoring point increases, and the horizontal tensile stress of R03 monitoring point remains stable. e horizontal tensile stress at F01 monitoring point decreases, and the horizontal compressive stress at F02 and F03 monitoring points increases.
e horizontal compressive stress of monitoring points LS01 and LS03 decreases, and tensile stress of monitoring point LS02 occurs, and then the tensile stress decreases to zero. e horizontal compressive stress of RS01 monitoring point is gradually transformed into tensile stress, the horizontal tensile stress of RS02 monitoring point rises and then falls back, and the horizontal compressive stress of RS03 monitoring point drops suddenly.
In the failure stage of roadway surrounding rock, the tensile strain concentration appears in the roof and floor, the horizontal compressive stress concentration mainly occurs in the left and right sides, and the stress of roadway surrounding rock suddenly changes, accompanied by the transformation of tensile and compressive stress. e stress and displacement of roadway roof measuring points when the cumulative duration is 539-550 mins is shown in Figure 17. R1 is horizontally compressed and vertically tensioned, moving horizontally to the right and vertically downward. R2 monitoring point is horizontally compressed and vertically tensioned, moving horizontally to the left and vertically downward. R3 monitoring point is horizontally compressed, vertically compressed, horizontally moved to the left and vertically moved upward. It can be seen that in the deformation and failure area of roadway roof, the rock stratum is pulled vertically, sinks into the roadway, and is pressed horizontally, resulting in interlayer sliding.
e stress and displacement of roadway floor measuring points when the cumulative duration is 539-550 mins is shown in Figure 18. F1 monitoring point is horizontally compressed and vertically tensioned, moving horizontally to the right and vertically upward. F2 monitoring point is horizontally compressed and vertically tensioned, moving horizontally to the left and vertically upward. F3 monitoring point is horizontally compressed and vertically compressed, moving horizontally to the left and vertically downward. It can be seen that the deformation and failure mode of roadway oor is that the rock stratum is vertically tensioned, bulged into the roadway, and horizontally compressed, resulting in interlayer sliding. e stress and displacement of roadway left side measuring points when the cumulative duration is 539-550 mins is shown in Figure 19. LS1 monitoring point is horizontally compressed and vertically tensioned, moving horizontally to the right and vertically downward. LS2 monitoring point is horizontally compressed and vertically tensioned, moving horizontally to the left and vertically downward. LS3 monitoring point is horizontally compressed and vertically tensioned, moving horizontally to the left and vertically downward. It can be seen that the left side of the roadway slides into the roadway as a whole and sinks in the sliding. e stress and displacement of roadway right side measuring points when the cumulative duration is 539-550 mins is shown in Figure 20. RS1 monitoring point is tensioned horizontally and vertically, moving horizontally to the left and vertically to the down. RS2 monitoring point is horizontally tensioned and vertically compressed, moving horizontally to the left and vertically downward. RS3 monitoring point is pressed horizontally and vertically, moving horizontally to the left and vertically to the down. It can be obtained that the right side of the roadway moves integrally into the roadway and sinks in sliding. It can be seen that in the stage, the strata on the left and right sides of the roadway continue to slide toward the interior of the roadway, the displacement values of the two monitoring points continue to rise, and the strata around the roof and oor of the roadway are subject to shear sliding. With the increase of sliding value, the roof and oor strata are sheared and destroyed. At this time, the displacement of roof monitoring points and oor monitoring points increases abruptly, and the surrounding rock of the roadway is damaged.

Mechanism of Deformation and Failure of the Model.
Taking advantage of rock structural mechanics, combining the situation of the model test, the rock structural mechanics    Figure 21(a). For the same rock stratum, the elastic deformation of rock is an elastic constraint condition. Q V and Q N are the loading provided by the constraints, Q H is the loading provided by hydraulic system. For the same layer, the mechanical model of left side is shown in Figure 21(b), and the mechanical model of right side is shown in Figure 21(c), the mechanical analysis is where F x is the horizontal resultant force; F y is the vertical resultant force; P H is the horizontal load; P V is the vertical load; f is the frictional force; F n is the axial force along the stratum; N is the interlayer pressure. It can be concluded that horizontal load P H and vertical load P V have the same e ect on the left and right strata. In no excavated area, the sliding should conquer f and F n and the sliding space is necessary, which comes from the construction gap and elastic deformation of rock itself.
e value of f and F n is as the equation, respectively: f F y × tan β, where β is the frictional angle of rock interface; E is the elasticity modulus of stratum along the layers; Δl is the deformation of the rock in the actuating range of P H . When F x > f + F n , the sliding would happen. In the horizontal rock stratum, the left and right sides of the mechanical model are the same, so their sliding characteristics are consistent. e order of elastic modulus from small to large is coal seam, green mudstone, and diabase. erefore, the order of model rock sliding from easy to di cult is also coal seam, green mudstone, and diabase. After excavation, it turned into bidirectional compression stress state along the tangent direction of the roadway from triaxial stress state in a certain range of surrounding rock. Because there is no supporting measure for the tunnel, F n equals zero, when the friction f between layers was overcome, and the strata move toward the tunnel along the inclined direction of strata. Under the action of horizontal load, the rock strata on both sides of the roadway are easy to slide to the interior of the roadway. e roof and oor strata of the roadway are easy to produce shear failure with the sliding, so they are easy to damage areas. e roof rock of the roadway is green mudstone, and coal seams are distributed  in the oor of the roadway, which has low shear modulus and is easier to slide.
According to the mechanical model analysis, in the 1-4 loading stage, the horizontal load P H and vertical load P V increase at the same time, P H promotes the rock strata on the left and right sides of the roadway to slide into the roadway, P V makes the rock strata more denser. In the 5-14 loading stage, the horizontal load remains unchanged, the vertical load increases, and the rock stratum is more denser. In the 15-23 loading stage, the vertical load remains unchanged and the horizontal load increases, which promotes the rock strata on the left and right sides of the roadway to slide into the roadway. e roof and oor strata of the roadway are easy to produce shear failure under the action of shear sliding, while the shear modulus of the coal seam of the roadway oor is lower than that of the roof green mudstone strata, which is more prone to deformation and failure. During the 23 loading, the balance was broken, the surrounding rock of the roadway is deformed and damaged.

Veri cation of Results By On-Site Monitoring.
e deformation of the prototype roadway of the physical model experiment is monitored and analyzed to verify the accuracy of the physical model experiment. Displacement monitoring was carried out on multiple sections of the prototype roadway during the mining process ( Figure 22). e plane position of the prototype roadway is shown in Figure 22(a). Each roadway monitoring section is arranged with four displacement monitoring points to measure the displacement of roof, oor, left side, and right side respectively. Figure 22(b) shows the layout of roadway displacement monitoring points.
During the mining process, instability failure occurred at the No. 1 monitoring section of the roadway, and the displacement curve of the failure section with time is statistically obtained, as shown in Figure 23. With the instability of roadway surrounding rock, the maximum value of roof subsidence is 0.67 m, the maximum value of oor heave is 0.94 m, and the maximum value of two sides moving into the roadway is 0.45 m.
rough the comparison of the displacement monitoring data of the physical model Advances in Materials Science and Engineering experiment and the prototype roadway, it can be seen that the displacement changes of the two show the same change trend, which are the roof sinking, the oor bulging, the two sides sliding into the roadway, and the displacement change value basically conforms to the similarity theory. e photographs after the instability of the No. 1 section of the prototype roadway are shown in Figure 24. e destruction form of the roadway surrounding rock is roof collapse, oor heave (Figure 24(a)), and the two sides move into the roadway as a whole (Figure 24(b)). e failure form of the prototype roadway is consistent with the physical model experiment. By comparing the physical model experiment with the prototype roadway displacement on-site monitoring and failure forms, it can be concluded that the roadway deformation characteristics obtained from the physical model experiment are consistent with the engineering practice, and the roadway deformation law obtained from the physical model experiment in this paper is reliable.

Conclusions
is paper analyzed the characteristics and mechanisms of deformation based on the physical model test on deep rectangular roadway in layered rock. e main conclusions were summarized as follows.
(1) e physical model experiment process can be divided into three stages: stable stage, failure stage, and post-failure stage. In the stable stage, the physical model is compressed, the cracks between slabs are closed, and the model is gradually dense. After entering the load of failure stage, first the floor of the roadway heaves, then the roof sinks greatly, then the surrounding rocks of the two sides of the roadway slide into the roadway, and finally the surrounding rocks of the roadway are deformed and damaged. (2) e deformation and failure of roadway surrounding rock occurs under the vertical load of 2.8 MPa and horizontal load of 4.4 MPa. After the surrounding rock of the roadway is damaged, the roof sinks 75.9 mm, the floor bulges 118.7 mm, the left side slides 39.7 mm horizontally into the roadway, and the right side slides 36.2 mm horizontally into the roadway. After similar calculation, the loading conditions are close to the field original rock stress after conversion, and the test results are in good agreement with the field test results of mine roadway surrounding rock. (3) e failure stage of roadway surrounding rock is sudden, and the deformation and failure characteristics are greatly affected by the layered structure of horizontal strata. In the failure stage, the floor rock stratum is compressed horizontally and tensioned vertically, resulting in interlayer sliding and floor heave. e roof strata of the roadway are pulled vertically, sinking into the roadway, compressed horizontally and sliding along the layer. e roof and floor strata of roadway are easy to produce shear failure under the action of shear sliding. e rock strata on both sides of the roadway are easy to slide along the layer under horizontal load.

Data Availability
e data used to support the findings of this study are included within the paper.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.