Comprehensive Experimental Study of Affecting Factors on Rectangular Roadway Stability

In this paper, two methods of orthogonal numerical simulation test and similar material simulation test are used to study the influence of five factors on the stability of rectangular roadway: roadway width, roadway height, roadway buried depth, lateral pressure coefficient of surrounding rock, and comprehensive strength of surrounding rock.-e results show that five factors have influence on the stability of roadway, but the degree of influence is different.-e depth of the tunnel and the coefficient of the side pressure of the surrounding rock are positively correlated with the stability of the tunnel; the comprehensive strength of the surrounding rock is negatively correlated with the stability of the tunnel, but the correlation between the width and height of the tunnel and the stability of the tunnel is not obvious. -e results of orthogonal numerical simulation test and similar material simulation test verify each other. -e results of the field practice of the Fucun coal mine are basically consistent with the results of the two test methods, which shows that the research results have a certain guiding effect on the field roadway support.


Introduction
e factors influencing the roadway stability majorly arise from two aspects: (1) natural conditions which include the burial depth of roadway, the strength of surrounding rock, hydrological environments, etc.; (2) mining techniques, involving the roadway cross section shape, dimensions, roadway arrangement type, supporting method, etc. [1]. is paper presents a study on the effect of the abovementioned factors on the roadway stability. e ratio of width and height of rectangular roadway can directly influence the stress state of surrounding rock; the lateral pressure coefficient has an obvious effect on the distribution of the plastic zone of surrounding rock; and the closer the width-height ratio and the lateral pressure coefficient are, the smaller the stress concentration factor of roadway is [2,3]. From the perspective of Kang [4], the deformation and damage of the ribs of roadway are primarily subjected to the vertical stress, and the deformation and damage of roof and floor are determined by the horizontal stress which is the key factor. In the viewpoint of Li et al. [5], the range of plastic failure zone enlarges and the deformation increases with the increment of the burial depth of roadway. And the vertical stress zone of roof and floor expands, while the core of horizontal stress moves into the deeper rock mass. On the contrary, the horizontal stress zone of ribs expands and the core of vertical stress moves into the deeper rock. Jing et al. [6] hold the opinion that the strength of surrounding rock is composed of the peak strength and the residual strength of rock mass. When the residual strength is less than 5%∼10% of the peak strength, the plastic zone increases dramatically as the residual strength decreases. rough comprehensive analysis of the above literature, it can be found that, at present, the factors affecting the stability of the roadway are studied only from a single point of view, without comprehensive analysis and discussion of many factors affecting the stability of the roadway. In this paper, based on the principle of orthogonal test, a numerical simulation test and a similar material simulation test scheme are developed to comprehensively analyze the width, height, burial depth, and lateral pressure coefficient of the surrounding rock e influence of 5 factors of the comprehensive strength of the surrounding rock on the stability of the roadway and the comparison between the two test results and the field practice results put forward a new method to study the stability of the roadway for the reference of the field production of the coal mine.

Theoretical Analysis of the Roadway Stability
2.1. Mechanical Analysis of the Roof Stability. According to material mechanics, roof can be simplified as uniformly and axially loaded beam fixed at two ends, as shown in Figure 1.
Under the co-action of deadweight q and axial thrust N, the roof beam will be subjected to buckling failure. e approximate differential equation of deflection curve is where ω is the beam deflection; M x is the resultant moment of a certain section whose outward normal is the x-axis; E is the elastic modulus; I is the inertia moment of the cross section to neutral axis. In which where a is the span of beam AB. Substituting (2) into (1) and rearranging yield Solving differential equation (4), According to the boundary conditions, Substituting (6) into (7), Substituting (7) into (5), According to (8), the roof stability not only relates to deadweight q and axial thrust N, but also associates with the roof span a. While the axial thrust N is generated by horizontal stress which has a relation with burial depth H and lateral pressure coefficient λ, H and λ also have an effect on the roof stability.

Mechanical Analysis of the Rib Stability.
Coal seam is characterized by being inhomogeneous and stratified. Generally, the strength of roof and floor is harder than the strength of coal seam. For the reason of the cohesion and internal friction angle in the interface between coal seam and roof, floor (using interface for short in the following description) is smaller than that in the coal seam; the coal-body in the stress limiting equilibrium zone ABCD is going to move towards the void after excavating without providing any support. As a result, the movement will lead to the instability of rock mass (coal-body) of ribs [7]. e simplified mechanical model of coal-body in ribs is shown in Figure 2.
See Figure 3; a coal unit is taken from stress-limiting equilibrium zone ABCD.
According to static equilibrium conditions, where T (x) is the axial thrust at x of x-coordinate; τ is shear stress on the interface. Putting q � 2τ into (9) and rearranging yield where q is shear stress collection degree. According to Hooke's law, where b is the roadway width; λ is the lateral pressure coefficient; k x is the stress concentration factor at x of x-coordinate; c is the bulk density of rock; H is the burial depth of roadway; E is the elastic modulus of coal; and s is the displacement caused by axial thrust T (x).

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Substituting (11) into (10), Assuming that q is in linearity with s, then where A is the shear stiffness coefficient, which means the shear stress caused by unit displacement in the unit coalbody, of the interface. Putting α 2 � A/bE into simultaneous equations (12) and (13), Solving (14) yields According to the boundary conditions, Substituting (16) into (15) yields Substituting (17) into (15) yields According to (18), the ribs' displacement s is not only related to axial thrust T (x 0 ) and elastic modulus E, but also has a relationship with roadway height b. e bigger the height b is, the smaller the ribs' displacement s will be, with other variables being constant.

Comprehensive Strength of Surrounding Rock.
It is postulated that the roadway has a rectangular section and locates in the flat coal seam, roof and floor are constituted of hard strata like sandstones, etc., the rib is coal seam, additionally, there are no geological structures such as fault, etc., and the rock (coal) layers are well integrated.
Comprehensive strength of surrounding rock (using CSSR as abbreviation in the following text) is defined as the overall strength of roof, ribs, and floor rock mass of roadway, which reflects the general stability of surrounding rock. Specifically, CSSR is a weighted average of uniaxial compressive strength, tensile strength, and shear strength of rock, and its unit is MPa. CSSR is given by where σ i is CSSR; α T � (a 1 , a 2 , a 3 ) is the weight vector of each strength (uniaxial compressive strength, tensile strength, and shear strength) to the overall strength of a single rock layer; β � (b 1 , b 2 , b 3 ) T is the weight vector of each rock layer (roof, rib, and floor) to CSSR; and A � (1) is determined by AHP [8].Uniaxial compressive strength, tensile strength, and shear strength are served as the evaluation indexes of the overall strength of a certain stratum. e hierarchy diagram is shown in Figure 4.
According to a number of rock mechanical experiments, theoretical analysis, and numerical simulation [9,10], the 3order judgment matrix has been formulated, with the stratum overall strength evaluation indexes mentioned above with reference to the 1∼9 scaling law.

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e maximum characteristic value of (20) is λ max � 3. Calculating the feature vector and normalizing, it yields Since (20) is a consistent matrix, it surely satisfies the consistency condition. In terms of α T , the weight of evaluation index of overall strength of stratum is illustrated in Figure 5. e weight vector of each stratum to the overall strength of surrounding rock can also be calculated in the same way as the calculation of α T .

Evaluation Index.
Comprehensive deformation of roadway (CDR) is developed to evaluate the effect of roadway's width and height, burial depth, lateral pressure coefficient, and CSSR on the stability of roadway. e smaller the value of CDR is, the less effect on the roadway stability will be. Its unit is mm.
where D c is CDR; D � (d 1, d 2, d 3 ), the weight vector, is composed of displacements of roof, ribs, and floor.
According to Table 3, establishing 25 numerical simulation models, the 5 factors of each model are determined by the corresponding experiment no., and all other conditions are the same. CDR is served as the evaluation index, and the experiment results are shown in Table 3.

Analysis of Orthogonal Numerical Simulation Results
Extremum difference analysis, which is also known as intuitive analysis, is used in drawing any conclusions of the experiment by analyzing the range and trend chart. Extremum difference analysis is commonly used in orthogonal experiment, since it is straightforward and intuitive. According to the results from Table 3, the mean and range of different levels of each factor can be calculated. e visual analysis results of comprehensive deformation of roadway are shown in Table 4. According to the values in the last row of Table 4, arranging them in descending order is H > σ i > λ > a > b, which implies that burial depth is most influential, while CSSR and lateral pressure coefficient are less, and roadway width and height are the least.
According to Table 4, the range analysis diagram is illustrated in Figure 8, in order to analyze the trend more visually and reflect the effect more vividly.
It can be concluded from Figure 8 that roadway width, height, burial depth, lateral pressure coefficient, and CSSR all have effects on the stability of roadway. However, the significance is not the same. Burial depth and lateral pressure coefficient (when it is less than 1.0) are positively correlated with the roadway stability, while CSSR is negatively correlated with the roadway stability, and there is no obvious correlation between roadway width and height and roadway stability.
CDR increases sharply (from 26.28 mm to 138.74 mm) with the burial depth increase from 200 m to 1000 m. CDR decreases rapidly initially, subsequently changing moderately. CSSR adds from 8 MPa to 28 MPa, increased by 250%, and CDR decreases from 138.44 mm to 73.42 mm, decreasing by 47%. CSSR keeps increasing from 28 MPa to   Factors Index

Brief Introduction to Similar Materials Simulated
Experiments. Similar material simulation is a kind of scientific experiment. It is one of the ways for people to explore and understand the law of ground pressure. Artificial materials are used to simulate the physical and mechanical properties of natural rocks, and a mine model is made according to a certain scale. en, the tunnel is excavated in the model, and the deformation and damage of the model are recorded, so as to analyze and speculate the situation in the original mine prototype [31][32][33].
In order to make what happens in the model truly reflects what happens in the prototype, according to the nature of the problem, prototype and model similarity must have the following conditions.
(1) Geometric similarity: the geometry of the model should be comparable to that of the prototype. erefore, the size of the prototype, including length, width, and height, must be reduced or enlarged in a definite proportion to make the model (2) Similar motion: in the model and prototype, the motion of all corresponding points is comparable; that is, the velocity, acceleration, and time of each corresponding point are required to be proportional (3) Dynamic similarity: all forces acting on the model are to be similar to those of the prototype.

Experimental Instruments and Materials.
e main instruments used in this paper are three-dimensional similar material simulation testbed of East China University of Technology, as shown in Figure 9. Other instruments include displacement sensor, load sensor, balance weighing up to 1000 g, minimum 0.01 g, caliper accuracy of 0.02 mm, steel ruler, mixing pot, and measuring cylinder.
Similar materials used throughout this paper are cement mortar mixed with quartz sand, cement, gypsum, and water, with a density of about 2.0 g/cm 3 , and layered with mica powder.

Model Parameters.
e model parameter test is carried out on a three-dimensional parallel material simulation test bench. e size of the test bench is 1500 mm * 1500 mm m * m1500 mm (length m * mwidth m * height). e cramped space is composed of six pressure plates, i.e., upper, lower, front and rear, and left and right. e excavation openings are restricted to the front and rear pressure plates, and the openings are sealed by bolts and iron plates when loading.

Model Materials and Production.
According to the actual stratigraphic conditions, 25 models of similar materials were established through different material ratios, forming the surrounding rock of the rectangular roadway. e geometric similarity ratio of the model is 1 : 100. e  Advances in Civil Engineering bulk density similarity ratio is 1 : 1.25, and the stress similarity ratio is 1 : 125. According to the test requirements, there are five monitoring points on the roof of roadway, four on each side and three on the floor. e layout of monitoring points is shown in Figure 10. e physical model is fabricated by layered pouring. e fabrication process mainly includes weighing raw materials, full mixing, boundary treatment, spreading and compacting, and setting bedding surface according to the ratio of simulated rock layers. Due to the influence of temperature on moisture volatilization, this experiment was carried out in the summer. After production, the model should be placed for 10 days (about 30 days in the winter under constant temperature) to completely volatilize the moisture, so that the model can be fully consolidated, and then the subsequent loading and excavation work can be carried out [34][35][36][37][38][39][40][41].

Model Excavation and Pressurization.
Unloading the bolt and the iron plate, the hollow drill bit and twist drill pipe are used along the centreline at the distance of 100 mm from the bottom plate to simulate the excavation of the model, and the excavation is completed at one time. e experimental triaxial compression load is controlled by the oil circuit. Considering that the compaction process takes a certain time, in order to avoid the damage of the specimen and steel wire, the load is gradually exerted on the model. A curve diagram, which is shown in Figure 11, of the effect of roadway width, height, vertical pressure (burial depth), lateral pressure coefficient, and CSSR on the roadway stability was derived from the computer analysis and processing of the data collected by DataTaker515, and the data collecting and processing system is shown in Figure 12.
rough the analysis of the data in Figure 11, it can be found that the vertical stress is the key factor affecting the comprehensive deformation of the tunnel. In the similar material simulation test, with the increase of the vertical stress imposed by the three-dimensional similar material simulation test bench, the comprehensive deformation of the tunnel also shows a "steep rise." When the vertical stress increases from 0.05 MPa to 0.25 MPa, the comprehensive deformation of the tunnel increases from 2.7 mm to 17.3 mm; it increases by 540.74%. With the increase of the comprehensive strength of the surrounding rock, the change trend of the comprehensive deformation of the roadway is "sudden decrease" first, and then the change tends to be gentle. e comprehensive strength of surrounding rock increased from 0.1 MPa to 0.9 MPa, and the comprehensive deformation of surrounding rock decreased from 15 mm to 5.9 mm, 154.23%.
rough the comparative analysis of Figures 8 and 11, the influence trend of the five factors of similar material simulation test and numerical simulation test on the stability of the roadway is basically the same, and the results of the two simulation tests are basically the same. Advances in Civil Engineering limitation of mining conditions, the roadway test mainly explores the influence of the buried depth and the comprehensive strength of surrounding rocks on the comprehensive deformation of roadway. In this experiment, 9 representative test sites at 3 levels were selected. e burial depth and comprehensive strength of surrounding rocks of each test site are shown in Table 5, and the test results are shown in Figure 13. It can be seen from Figure 13 that under the same comprehensive strength of surrounding rock, the comprehensive deformation of roadway increases with the increase of buried depth. Under the same buried depth, the comprehensive deformation of the roadway decreases with the increase of the comprehensive strength of the surrounding rock, and when the comprehensive strength of the surrounding rock is less than 40 MPa, its impact on the comprehensive deformation of the roadway is relatively large; when the comprehensive strength of the surrounding rock is greater than 40 MPa, its impact on the comprehensive deformation of the roadway is relatively weak. e field test results are basically consistent with the two simulation results, but the comprehensive deformation of the roadway is larger than that of the numerical simulation results, which is mainly due to the lack of consideration of the influence of fracture and geological structure in the rock (coal) layer during the numerical simulation process.   Figure 11: e effect of each factor on the roadway stability in the similar material simulation experiment.

Conclusions
(1) e comprehensive strength of surrounding rock refers to the overall strength of the roof, two sides, and floor rock mass of the roadway, reflecting the overall stability of the surrounding rock of the roadway. rough the mechanical analysis, it can be seen that the span, depth, and lateral pressure coefficient of the roadway will affect the stability of the roof, and the height of the roadway will affect the stability of the two sides. erefore, there is a certain connection among the five factors of the roadway depth, roadway width, roadway height, lateral pressure coefficient, and comprehensive strength of the surrounding rock, which can be used as the factors to measure the stability of the roadway. (2) e results show that the width, height, buried depth, lateral pressure coefficient, and comprehensive strength of surrounding rock all have influence on the stability of roadway, but the influence size is not the same. e sequence of the effect in descending order is burial depth > CSSR > lateral pressure coefficient > roadway width > roadway height. e buried depth and lateral pressure coefficient of roadway are positively correlated with the comprehensive deformation of roadway, while the comprehensive strength of surrounding rock is negatively correlated with the comprehensive deformation of roadway, while the correlation between the width and height of roadway and the comprehensive deformation of roadway is not obvious. e research results can provide theoretical basis for roadway support, grouting reinforcement of surrounding rock, and roadway section design in deep mines. (3) Based on the principle of orthogonal test, the numerical simulation test and similar material simulation test schemes are developed, and the results of the two test methods are the same, and the field practice results are basically consistent with the test results. e study method is relatively mature, and the study results are more applicable to the study and practice of roadway stability in the coal mine site.

Data Availability
e authors declare that all data supporting the findings of this study are available within the article; the reader can find and use it. ere are no unavailable data.

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