A method for solving the plastic zone of surrounding rock in tunnels under the influence of repeated mining

Abstract

The present application discloses a method for solving the plastic zone of tunnel surrounding rock under the influence of repeated mining, which relates to the field of tunnel surrounding rock, including: obtaining rock mechanics parameters, tunnel size parameters and three-dimensional stress values ​​of tunnel surrounding rock under the influence of one mining; obtaining implicit equations of the boundary of the plastic zone of tunnel surrounding rock under the influence of one mining according to the obtained parameters, and solving to obtain the plastic zone size ρ of the tunnel surrounding rock under the influence of one mining; obtaining the three-dimensional stress values ​​of tunnel surrounding rock under the influence of repeated mining through field measurements; calculating the new radius of any point under the influence of repeated mining according to the boundary of the plastic zone of tunnel surrounding rock under the influence of one mining; obtaining implicit equations of the boundary of the plastic zone of tunnel surrounding rock under the influence of repeated mining according to the new radius, and solving to obtain the plastic zone size τ of the tunnel surrounding rock under the influence of repeated mining. In view of the low accuracy of solving the plastic zone of tunnel surrounding rock under the influence of repeated mining in the prior art, the present application improves the calculation accuracy.

Description

Technical Field

[0001] The present application relates to the field of tunnel surrounding rock, and in particular to a method and system for solving the plastic zone of tunnel surrounding rock under the influence of repeated mining. Background Art

[0002] As coal mining extends to deeper areas, the geostress environment of the tunnels is becoming increasingly severe, and it is becoming more and more common for the tunnels to be affected by mining multiple times during their service life. During the entire service life from excavation to scrapping, the surrounding rock of the tunnel will continue to experience the process of surrounding rock stress redistribution caused by mining, and the deformation and damage of the surrounding rock will also continue to change. Taking the tunnels affected by adjacent section mining as an example, the surrounding rock deformation usually goes through five stages: the excavation impact stage, the excavation impact stabilization stage, the primary mining impact stage, the primary mining impact stabilization stage, and the repeated mining impact stage. When the tunnel is in the repeated mining impact stage, the tunnel surrounding rock stress will change rapidly, and the plastic zone will expand sharply, seriously threatening the normal use of the tunnel and the life safety of the workers.

[0003] At present, domestic and foreign scholars mainly use theoretical analysis and numerical simulation methods to study the stress distribution and plastic zone range of tunnel surrounding rock under the influence of mining. Theoretical analysis methods are mostly based on certain classical mechanical models, and analytical or semi-analytical solutions are given after simplifying the calculation conditions; numerical simulation methods use numerical methods such as finite element, discrete element, boundary element, etc. to simulate and analyze the mechanical behavior of tunnel surrounding rock under conditions closer to actual engineering. However, most of the existing research focuses on the situation under the influence of a single mining, and few scholars have systematically analyzed the evolution law of the plastic zone of tunnel surrounding rock under the influence of repeated mining.

[0004] In addition, the expansion of the plastic zone of the tunnel surrounding rock under the non-uniform stress field shows obvious asymmetry, which makes the effective excavation section of the tunnel asymmetrically deformed after a mining event, and finally no longer presents a circular shape; at the same time, after a mining event, the tunnel surrounding rock will yield and form a certain range of plastic zone, and the rock will lose its structural integrity during the process of fracture and fragmentation, so the bearing effect of the internal friction and cohesion of the rock is relatively small. When solving the theory of the plastic zone of the tunnel surrounding rock under the influence of repeated mining, the small bearing capacity of the rock in the plastic zone after a mining event is usually not considered, and the original tunnel size is still used as the calculation radius, which makes the results biased and cannot reflect the actual problems of the project well. Summary of the invention

[0005] In response to the problem of low accuracy in solving the plastic zone of tunnel surrounding rock under the influence of repeated mining in the prior art, the present application provides a method and system for solving the plastic zone of tunnel surrounding rock under the influence of repeated mining. Based on the plastic zone of the tunnel under the influence of one mining, the implicit equation of the boundary of the plastic zone of the tunnel surrounding rock under the influence of repeated mining is obtained through three-dimensional stress state yield criterion analysis, and then the size and shape of the plastic zone under the influence of repeated mining are solved.

[0006] The purpose of this application is achieved through the following technical solutions.

[0007] One aspect of the present application provides a method for solving the plastic zone of tunnel surrounding rock under the influence of repeated mining, including: determining the rock mechanics parameters of the tunnel surrounding rock including cohesion, internal friction angle and Poisson's ratio through rock mechanics tests; determining the tunnel size parameters through field measurements; obtaining the three-dimensional stress values ​​of the tunnel surrounding rock under the influence of one mining through field measurements, including the horizontal stress σ x , stress σ parallel to the tunnel axis y , vertical stress σ of tunnel surrounding rock z ; According to the rock mechanics parameters, tunnel size parameters and the three-dimensional stress values ​​of the tunnel surrounding rock under the influence of primary mining, the tunnel is subjected to elastoplastic mechanics analysis to obtain the implicit equation of the plastic zone boundary of the tunnel surrounding rock under the influence of primary mining; the implicit equation of the plastic zone boundary of the tunnel surrounding rock under the influence of primary mining is solved to obtain the plastic zone size ρ of the tunnel surrounding rock under the influence of primary mining, and a plastic zone morphological size diagram is drawn according to the plastic zone size ρ through a drawing software to obtain the plastic zone boundary of the tunnel surrounding rock under the influence of primary mining; wherein, the mathematical software may be MATLAB, Mathematica, Maple, etc.; the obtained plastic zone size of the tunnel surrounding rock under the influence of primary mining is input into the drawing software, and a morphological size diagram of the plastic zone is drawn with the tunnel center as the center of the circle and the plastic zone size as the radius, so as to realize the visualization of the plastic zone boundary of the tunnel surrounding rock under the influence of primary mining; wherein, the drawing software may be Origin, MATLAB, Maple, etc.

[0008] The three-dimensional stress values ​​of the tunnel surrounding rock under the influence of repeated mining were obtained through field measurements, including the horizontal stress σ of the vertical tunnel side. x ', stress σ parallel to the tunnel axis y ', vertical stress σ of tunnel surrounding rock z'; Discretize the boundary of the plastic zone of the tunnel surrounding rock under the influence of one mining into multiple points at equal intervals along the surrounding rock contour, establish a polar coordinate system with the tunnel center as the center of the circle and the plastic zone size ρ as the radius, and use the plastic zone size ρ of each discrete point as the new calculated radius of any point under the influence of repeated mining; According to the rock mechanics parameters and tunnel size parameters, as well as the new radius of any point in the plastic zone of the tunnel surrounding rock under the influence of repeated mining, perform elastic-plastic mechanics analysis on the tunnel, and obtain the implicit equation of the boundary of the plastic zone of the tunnel surrounding rock under the influence of repeated mining; Solve the implicit equation of the boundary of the plastic zone of the tunnel surrounding rock under the influence of repeated mining, and obtain the plastic zone size τ of the tunnel surrounding rock under the influence of repeated mining, and draw the plastic zone morphological size diagram according to the plastic zone size τ through drawing software to obtain the plastic zone boundary of the tunnel surrounding rock under the influence of repeated mining.

[0009] Furthermore, according to the rock mechanics parameters, tunnel size parameters and the three-dimensional stress values ​​of the tunnel surrounding rock under the influence of primary mining, an elastic-plastic mechanical analysis is performed on the tunnel to obtain the implicit equation of the plastic zone boundary of the tunnel surrounding rock under the influence of primary mining, including: according to the generalized plane strain problem model, through the equilibrium equation and the geometric equation, the stress expression of any point around the tunnel in the polar coordinate system is obtained; the judgment criterion for the yield and failure of the surrounding rock is selected; the judgment criterion includes at least one of the Mohr-Coulomb criterion, the Mogi-Coulomb criterion, the Drucker-Prager criterion and the Lade-Duncan criterion; through the average stress σ m , the second deviatoric stress invariant J2, the third deviatoric stress invariant J3 and the stress Lode angle θ σ , the selected judgment criterion is expressed as a function of the principal stress; the stress expression of any point around the tunnel in the polar coordinate system is substituted into the function of the principal stress, and the implicit equation of the plastic zone boundary of the tunnel surrounding rock under the influence of primary mining is obtained. The implicit equation is a function of the tunnel size parameters, rock mechanics parameters and the three-dimensional stress values ​​of the tunnel surrounding rock under the influence of primary mining.

[0010] Among them, the Mohr-Coulomb (MC) criterion is a classic yield criterion for geotechnical materials, proposed by Mohr and improved by Coulomb. This criterion assumes that the material yields under the action of shear stress, and the yield condition is related to the normal stress. The MC criterion is expressed as an irregular hexagonal yield surface in the principal stress space. The Mogi-Coulomb (MC) criterion is an improved yield criterion proposed by Mogi based on the MC criterion. This criterion takes into account the effect of the intermediate principal stress of the surrounding rock, and introduces the quadratic terms of the octahedral shear stress and the mean stress to describe the yield behavior of the rock. The Drucker-Prager (DP) criterion is a yield criterion developed by Drucker and Prager based on the MC criterion. The DP criterion uses stress invariants to express the yield condition, and is expressed as a conical yield surface in the principal stress space. Compared with the MC criterion, the DP criterion can better describe the compression and shear characteristics of rock. The Lade-Duncan (LD) criterion is another yield criterion proposed by Lade and Duncan that takes into account the effect of the intermediate principal stress. The LD criterion establishes a yield function based on stress invariants and introduces material parameters related to rock mechanical properties. The LD criterion presents a smooth non-circular yield surface in the principal stress space. The second deviatoric stress invariant J2: a second-order invariant that characterizes the deviatoric stress tensor, reflecting the magnitude of the deviatoric stress of the surrounding rock. The third deviatoric stress invariant J3: a third-order invariant that characterizes the deviatoric stress tensor, reflecting the direction of the deviatoric stress of the surrounding rock. Stress Lode angle θ σ : Characterizes the angular coordinate of the surrounding rock stress state on the π plane, reflecting the influence of the relative size of the principal stress on the yield behavior of the material.

[0011] Furthermore, when the Mohr-Coulomb criterion is selected as the judgment criterion, the stress expression of any point around the tunnel in the polar coordinate system is as follows:

[0012]

[0013] Among them, σ r Represents the radial stress at any point, MPa; σ θ Represents the hoop stress at any point, MPa; σ v Indicates the axial stress of the tunnel, MPa; τ rθ Represents the shear stress at any point, MPa; σ x Indicates the horizontal stress of the vertical tunnel side, MPa; σ y Represents the stress parallel to the tunnel axis, MPa; σ z represents the vertical stress of the tunnel surrounding rock, MPa; v represents the Poisson's ratio of the tunnel surrounding rock; R represents the radius of the circular tunnel, m; (r,θ) represents the polar coordinates of any point;

[0014] Furthermore, the functional form of the principal stress is:

[0015]

[0016] in: represents the internal friction angle of the surrounding rock, MPa; c represents the cohesion of the surrounding rock, MPa;

[0017] σ m , J2, J3 and θ σ The expressions are:

[0018]

[0019] J3=(σ r -σ θ )(σ r -σ r )(σ θ -σ v )

[0020]

[0021] Furthermore, the stress expression of any point around the tunnel in the polar coordinate system is substituted into the function form of the principal stress, and the implicit equation of the boundary of the plastic zone of the tunnel surrounding rock under the influence of a single mining is obtained. The implicit equation is a function of the tunnel size parameters, rock mechanics parameters and the three-dimensional stress value of the tunnel surrounding rock under the influence of a single mining, including: The implicit equation expression of the boundary of the plastic zone of the tunnel surrounding rock under a single mining is as follows: Among them, ρ represents the size of the plastic zone of the roadway after a mining operation; R0 represents the radius of the circular roadway, m. Among them, the implicit equation is an equation that does not explicitly express the relationship between the dependent variable and the independent variable. In the implicit equation of the boundary of the plastic zone of the roadway surrounding rock, the dependent variable is usually the radius of the plastic zone ρ, and the independent variables include the roadway radius R0, the Poisson's ratio of the surrounding rock v, the cohesion c, and the internal friction angle Three-dimensional normal stress σ of surrounding rock under the influence of primary mining x , σ y , σ z And the angular coordinates θ of the current point, etc.

[0022] Furthermore, the total number of discrete points n is determined. The value of n should be weighed according to the requirements of calculation accuracy and efficiency. Calculate the angle interval Δθ between adjacent discrete points. For the i-th discrete point, its angular coordinate θi can be expressed as: θ i =(i-1)×Δθ, where i=1, 2, ..., n. According to the implicit equation of the plastic zone under the influence of a mining event, the size of the plastic zone corresponding to each discrete point is calculated. i , that is, the coordinates of the discrete points are (ρ i ,θ i). Select the center of the roadway as the origin O of the polar coordinate system. Define the polar radius ρ and polar angle θ, where ρ represents the distance from the point to the origin O, and θ represents the angle between the point and the positive x-axis. In the polar coordinate system, the plastic zone size ρ of each discrete point is i is the new calculated radius of any point under repeated mining influence, ρ i The expression is

[0023] Furthermore, according to the rock mechanics parameters and the tunnel size parameters, as well as the new radius of any point in the plastic zone of the tunnel surrounding rock under the influence of repeated mining, the tunnel is subjected to elastic-plastic mechanical analysis, and the implicit equation of the boundary of the plastic zone of the tunnel surrounding rock under the influence of repeated mining is obtained, including: in the polar coordinate system, according to the stress parameters, rock mechanics parameters, tunnel size parameters and the new radius of discrete points in the plastic zone under the influence of repeated mining Establish the stress component expression of any point within the preset range of the tunnel under the influence of repeated mining:

[0024]

[0025] Where: r ' represents the radial stress at any point under the influence of repeated mining, MPa; σ θ ' represents the hoop stress at any point under the influence of repeated mining, MPa; σ v ' represents the axial stress of the tunnel under the influence of repeated mining, MPa; τ rθ ' represents the shear stress at any point under the influence of repeated mining, MPa; σ x ' represents the horizontal stress of the vertical tunnel side under the influence of repeated mining, MPa; σ y ' represents the stress parallel to the tunnel axis under the influence of repeated mining, MPa; σ z ' represents the vertical stress of the tunnel surrounding rock under the influence of repeated mining, MPa; v represents the Poisson's ratio of the tunnel surrounding rock; R0 represents the radius of the circular tunnel, m; (r, θ) represents the polar coordinates of any point; It represents the size of the plastic zone of the surrounding rock of the roadway under the influence of a mining operation, m;

[0026] The Mohr-Coulomb criterion is selected as the criterion for judging the yield and failure of the surrounding rock. m ', the second deviatoric stress invariant J2', the third deviatoric stress invariant J3' and the stress Lode angle θ σ ', establish the Mohr-Coulomb criterion expression under three-dimensional stress state:

[0027]

[0028] Where: θ' represents the hoop stress at any point under the influence of repeated mining, MPa; σ r ' represents the radial stress at any point under the influence of repeated mining, MPa; σ v ' represents the axial stress of the tunnel under the influence of repeated mining, MPa; τ rθ ' represents the shear stress at any point under the influence of repeated mining, MPa;

[0029] σ m ', J2', J3' and θ σ The expressions of ' are:

[0030]

[0031] J3′=(σ r ′-σ θ ′)(σ r ′-σ r ′)(σ θ ′-σ v ′)

[0032]

[0033] Furthermore, the stress expression of any point around the tunnel in the polar coordinate system under the influence of repeated mining is substituted into the analytical expression of the Mohr-Coulomb criterion under the three-dimensional stress state, and the plastic zone size of the tunnel is traversed in all directions, and the implicit equation expression of the plastic zone boundary of the tunnel surrounding rock under the influence of repeated mining is obtained as follows:

[0034]

[0035] Another aspect of the present application also provides a system for solving the plastic zone of tunnel surrounding rock under the influence of repeated mining, which is used to execute a method for solving the plastic zone of tunnel surrounding rock under the influence of repeated mining of the present application.

[0036] Compared with the prior art, the advantages of this application are:

[0037] The real triaxial stress values ​​of the tunnel surrounding rock under the influence of single and repeated mining are obtained through on-site measurements. Combined with the rock mechanics parameters determined by indoor rock mechanics tests, it is possible to more accurately reflect the actual stress state of the tunnel and the physical and mechanical properties of the surrounding rock, providing a reliable parameter basis for the subsequent plastic zone solution.

[0038] When solving the plastic zone of the tunnel surrounding rock under the influence of primary mining, the non-uniformity of the stress field of the tunnel surrounding rock and the anisotropy of the surrounding rock yield criterion are fully considered. By establishing the stress expression of any point in the surrounding rock in the polar coordinate system and combining it with the Mohr-Coulomb criterion, the implicit equation of the plastic zone boundary is derived. After solving it, the true shape and range of the plastic zone can be obtained, avoiding the calculation deviation caused by the assumption of isotropy of surrounding rock stress in previous studies.

[0039] When determining the plastic zone under the influence of repeated mining, this method innovatively proposes to discretize the boundary of the plastic zone after the first mining into multiple calculation points, and use the size of the plastic zone at each point as the new calculation radius for the second mining. This processing method can objectively reflect the changes in the cross-sectional shape of the tunnel and the damage to the integrity of the surrounding rock caused by the first mining, making the calculation model closer to engineering practice.

[0040] By re-establishing the surrounding rock stress expression in the new polar coordinate system and substituting the Mohr-Coulomb yield criterion under the three-dimensional stress state, the plastic zone size is traversed and solved in all directions, and finally the implicit equation of the plastic zone boundary under the influence of repeated mining is obtained. This equation fully reflects the mutual influence of factors such as the scope of the plastic zone of a single mining, rock mechanics parameters, tunnel geometry, and repeated mining stress level. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flow chart of a method for solving the plastic zone of surrounding rock of a roadway under the influence of repeated mining provided by the present invention;

[0042] Figure 2 It is a schematic diagram of the plastic zone of the tunnel surrounding rock under the influence of single mining and repeated mining provided by the present invention.

[0043] Reference numerals:

[0044] 1. The boundary of the plastic zone under the influence of single mining; 2. The boundary of the plastic zone under the influence of repeated mining; 3. The boundary of the tunnel. DETAILED DESCRIPTION

[0045] The method and system provided in the embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0046] Figure 1 The present invention provides a flow chart of a method for solving the plastic zone of tunnel surrounding rock under the influence of repeated mining, including: determining the rock mechanics parameters of tunnel surrounding rock including cohesion, internal friction angle and Poisson's ratio through rock mechanics tests; determining tunnel size parameters through field measurements; obtaining the three-dimensional stress values ​​of tunnel surrounding rock under the influence of one mining through field measurements, including the horizontal stress σ x , stress σ parallel to the tunnel axis y , vertical stress σ of tunnel surrounding rockz ; According to the rock mechanics parameters, tunnel size parameters and the three-dimensional stress values ​​of the tunnel surrounding rock under the influence of one mining, the tunnel is subjected to elastoplastic mechanics analysis to obtain the implicit equation of the plastic zone boundary of the tunnel surrounding rock under the influence of one mining; the implicit equation of the plastic zone boundary of the tunnel surrounding rock under the influence of one mining is solved to obtain the plastic zone size ρ of the tunnel surrounding rock under the influence of one mining, and the plastic zone morphological size diagram is drawn according to the plastic zone size ρ through the drawing software to obtain the plastic zone boundary of the tunnel surrounding rock under the influence of one mining; the three-dimensional stress values ​​of the tunnel surrounding rock under the influence of repeated mining are obtained through field measurements, including the horizontal stress σ of the vertical tunnel side. x ', stress σ parallel to the tunnel axis y ', vertical stress σ of tunnel surrounding rock z '; Discretize the boundary of the plastic zone of the tunnel surrounding rock under the influence of one mining into multiple points at equal intervals along the surrounding rock contour, establish a polar coordinate system with the tunnel center as the center of the circle and the plastic zone size ρ as the radius, and use the plastic zone size ρ of each discrete point as the new calculated radius of any point under the influence of repeated mining; According to the rock mechanics parameters and tunnel size parameters, as well as the new radius of any point in the plastic zone of the tunnel surrounding rock under the influence of repeated mining, perform elastic-plastic mechanics analysis on the tunnel, and obtain the implicit equation of the boundary of the plastic zone of the tunnel surrounding rock under the influence of repeated mining; Solve the implicit equation of the boundary of the plastic zone of the tunnel surrounding rock under the influence of repeated mining, and obtain the plastic zone size τ of the tunnel surrounding rock under the influence of repeated mining, and draw the plastic zone morphological size diagram according to the plastic zone size τ through drawing software to obtain the plastic zone boundary of the tunnel surrounding rock under the influence of repeated mining.

[0047] In order to obtain the mechanical parameters of the tunnel surrounding rock, several in-situ rock samples were first taken from the tunnel periphery to make standard rock mechanics test samples. Then, a series of indoor rock mechanics tests were carried out using the rock mechanics test system in accordance with relevant standards such as "Rock Compressive Strength Test Method", "Rock Tensile Strength Test Method", and "Rock Direct Shear Test Method". By testing the uniaxial compressive strength, uniaxial tensile strength, cohesion, internal friction angle and other parameters of multiple groups of samples and taking the average value, the cohesion of the tunnel surrounding rock c = 2.5MPa, the internal friction angle At the same time, the rock sonic tester was used to measure the longitudinal and transverse wave velocities of the rock, and the Poisson's ratio v=0.225 of the surrounding rock was calculated based on the wave velocity ratio.

[0048] While determining the mechanical parameters of the tunnel surrounding rock, it is also necessary to measure the actual excavation section size of the tunnel. Using measuring equipment such as a laser rangefinder or a total station, select several representative measuring points along the axial direction of the tunnel, accurately measure the width and height of the tunnel, and then average the data of multiple measuring points to obtain a tunnel section size of 5.2m×3.8m. Considering that the actual tunnel section is not a standard circle, it needs to be equivalent to a circular section for calculation. Take the average value of the major and minor axes as the equivalent circle radius, then the tunnel equivalent radius r = (5.2 + 3.8) / 4 = 2.25m.

[0049] In order to obtain the true stress state of the tunnel surrounding rock under the influence of primary mining, it is necessary to arrange stress monitoring sections around the tunnel and use stress monitoring equipment for on-site measurements. Commonly used stress monitoring methods include hydraulic fracturing, borehole strain method and acoustic emission method. Taking the borehole strain method as an example, firstly, several stress measuring points are arranged on the side and top and bottom plates of the tunnel, and a force measuring borehole with a diameter of 130 mm is drilled at the measuring point location, and the drilling depth is not less than 1.5 times the hole diameter. Then, a strain sensor is installed in the borehole, and the sensor is tightly fitted to the hole wall by grouting. After the sensor is initialized and stabilized for a period of time, an independent digital switching strain gauge is used to collect strain data and convert it into stress values. By analyzing and counting the stress monitoring data of multiple measuring points, the three-dimensional average principal stress values ​​of the tunnel surrounding rock under the influence of primary mining are obtained, which are σ x =27MPa,σ v =9MPa and σ z =18MPa, where x, y, and z represent the horizontal, axial, and vertical directions of the tunnel, respectively.

[0050] According to the obtained mechanical parameters of tunnel surrounding rock and primary mining stress value, combined with the generalized plane strain problem model, the elastic-plastic mechanical analysis of the tunnel is carried out, and the implicit equation expression of the plastic zone boundary of the tunnel surrounding rock under primary mining is derived.

[0051] First, the stress expression of any point (r, θ) around the tunnel is established in the polar coordinate system. According to the theory of elastic mechanics, considering the existence of stress σ in the axial direction of the tunnel v , and σ v ≠0, so it belongs to the generalized plane strain problem. The stress component at any point (r, θ) can be expressed as:

[0052]

[0053] Among them, σ r Represents the radial stress at any point, MPa; σ θ Represents the hoop stress at any point, MPa; σ v Indicates the axial stress of the tunnel, MPa; τ rθ Represents the shear stress at any point, MPa; σx Indicates the horizontal stress of the vertical tunnel side, MPa; σ y Represents the stress parallel to the tunnel axis, MPa; σ z represents the vertical stress of the tunnel surrounding rock, MPa; v represents the Poisson's ratio of the tunnel surrounding rock; R represents the radius of the circular tunnel, m; (r, θ) represents the polar coordinates of any point.

[0054] When studying the destruction of tunnel surrounding rock, it is necessary to select appropriate yield and destruction judgment criteria. Commonly used judgment criteria include Mohr-Coulomb criterion, Mogi-Coulomb criterion, Drucker-Prager criterion and Lade-Duncan criterion. This embodiment uses the Mohr-Coulomb criterion (MC criterion for short) applicable to three-dimensional stress state. The MC criterion under three-dimensional stress state can be expressed by the mean stress σ m , the second deviatoric stress invariant J2, the third deviatoric stress invariant J3 and the stress Lode angle θ σ To express, that is:

[0055]

[0056] Where: —Internal friction angle of surrounding rock, °; c—Internal cohesion of surrounding rock.

[0057] σ m , J2, J3 and θ σ The expressions are:

[0058]

[0059] J3=(σ r -σ θ )(σ r -σ r )(σ θ -σ v )

[0060]

[0061] Substituting the stress expression of any point in the polar coordinate system into the analytical expression, the implicit equation expression of the plastic zone boundary of the tunnel surrounding rock under primary mining can be obtained as follows:

[0062] After obtaining the implicit equation of the plastic zone boundary of the tunnel surrounding rock under primary mining, it is difficult to directly obtain an explicit solution through analytical methods due to the complex form of the equation. Therefore, it is necessary to use mathematical software for numerical calculation and programming to solve it. Taking Maple software as an example, the basic steps of writing a solution program are as follows: define the known parameters, including the tunnel radius R, the Poisson's ratio v of the surrounding rock, the cohesion c, and the internal friction angle And the primary mining stress σ x , σ y , σ z Etc., and assign specific values. Define the discretized vector of angle θ, enter the stress function and strength criterion in the polar coordinate system in a programming language, and use loop statements to call the solve function to solve the octonic equation about r for each angle value in the θ vector. The positive real root is the radius of the plastic zone at the θ angle. It should be noted that since the quartic equation is being solved, there may be complex solutions or negative real roots, and the results must be screened. According to the calculation result table given, take θ = [0, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 66, 72, 78, 84, 90]. Store the plastic zone radius obtained at each θ angle in an array to complete the calculation in the first quadrant. Using symmetry, mirror the results of the first quadrant to the other three quadrants to obtain the full range of plastic zone size data for the tunnel. The solution results are plotted in polar coordinates to generate a cloud map of the plastic zone distribution, and necessary legends, axis labels and other elements are added to intuitively display the shape and size of the plastic zone. The size of the plastic zone of the tunnel surrounding rock under the influence of a single mining operation is as follows (unit: m):

[0063] Angle / ° Plastic zone size / m Angle / ° Plastic zone size / m 0 4.277466 49 4.488965 7 4.294263 55 4.300188 13 4.335518 61 4.082842 19 4.400765 66 3.912729 25 4.484525 72 3.741085 31 4.569668 78 3.609004 37 4.622362 84 3.519969 43 4.602290 90 3.486878

[0064] It can be seen that under the influence of mining, the plastic zone as a whole presents an elliptical distribution characteristic extending along the vertical direction of the tunnel axis. Based on the obtained results, the morphological size diagram of the plastic zone is drawn as shown in Figure 2 shown.

[0065] In order to obtain the real stress state of the tunnel surrounding rock under repeated mining disturbance, on-site measurement is required. This embodiment uses the stress sensor method to determine the three-dimensional stress value of the tunnel surrounding rock. According to the geological conditions, support methods and the influence range of secondary mining in the tunnel, several measuring points are arranged in the tunnel surrounding rock. The measuring points should cover the top and bottom plates and both sides of the tunnel to reflect the spatial distribution characteristics of the surrounding rock stress. At each measuring point, a measuring hole with a diameter slightly larger than the stress sensor is drilled, and the hole depth should be greater than 1.5 times the width of the tunnel to minimize the influence of the unloading effect of tunnel excavation. Clean the measuring hole to ensure that the hole wall is intact and not broken. Select a three-dimensional stress sensor suitable for the on-site lithological conditions, such as a CSIRO hollow coated sensor or a USBM deformation sensor. Install the sensor on a special installation tool and slowly push it into the measuring hole so that the sensor is close to the hole wall. Adjust the sensor posture to ensure that the sensor main axis is parallel to the tunnel axis. Use quick-hardening cement to fill the annular gap between the sensor and the hole wall. After the cement solidifies, the sensor can form a whole with the surrounding rock mass, and the stress and deformation are synchronized with the surrounding rock. Connect the sensor wires to the data acquisition instrument, debug the system, and ensure normal data transmission. Set the acquisition frequency and duration, and start monitoring. When the repeated mining face advances to the vicinity of the monitoring point, pay close attention to the changes in the monitoring data. When the mining stress wave reaches the monitoring point, it can be judged by the sudden change of stress data that the surrounding rock begins to be disturbed. As the mining face gradually moves away, the surrounding rock stress undergoes a dynamic change process until it reaches a state of equilibrium again. Take the stable stress value after equilibrium as the actual measurement result of the measuring point. The monitoring data of different measuring points are summarized and compared and analyzed to obtain the spatial distribution law of the three-dimensional stress of the tunnel surrounding rock. The principal stress values ​​of each measuring point are transformed into coordinates to obtain a unified vertical normal stress σ z , horizontal normal stress σ x and axial normal stress σ y According to the field measurement results, the average triaxial stress value of the tunnel surrounding rock under repeated mining disturbance is: vertical normal stress σ z ′=13.5MPa; horizontal normal stress σ x ′=40.5MPa; axial normal stress σ y ′=27.0MPa. It can be seen that due to repeated mining, the surrounding rock of the tunnel is generally in a state of stress concentration. The horizontal stress is significantly greater than the vertical stress, which is related to the initial ground stress state of the rock layer and the additional stress induced by mining. The axial normal stress is between the horizontal stress and the vertical stress.

[0066] On the basis of considering the influence of the first mining, the effect of repeated mining on the expansion of the plastic zone of the tunnel surrounding rock is further analyzed. The boundary curve of the plastic zone formed after the first mining is discretized into countless calculation points. These points are used as the new stress equilibrium boundary. The stress calculation model under repeated mining is established to obtain the redistribution law of the surrounding rock stress in the plastic zone, and then the secondary expansion range of the plastic zone boundary is obtained. The plastic zone boundary curve ρ = f (θ) obtained under the influence of the first mining is discretized into n calculation points in the polar coordinate system. The coordinates of each point are (ρ i ,θ i ), where i = 1, 2, ..., n. ρi is the radial distance of the point from the center of the tunnel, and θi is the angular coordinate corresponding to the point. A local coordinate system is established at each calculation point with the center of the tunnel as the origin and ρi as the radius. The radial direction of the local coordinate system is the r axis, the tangential direction is the θ axis, and the axial direction is parallel to the axis of the tunnel. In the local coordinate system of each calculation point, a similar equilibrium equation is established to describe the equilibrium relationship of the surrounding rock stress at this point under repeated mining disturbance. Unlike a single mining operation, the far-field stress term in the equilibrium equation is no longer the initial ground stress, but the current stress state after repeated mining. Combined with the field measurement of the three-dimensional normal stress value σ of the tunnel surrounding rock under repeated mining x ′=40.5MPa,σ y ′=27MPa,σ z ′=13.5MPa, substitute into the above equilibrium equation, and solve each calculation point (ρ i ,θ i ). Substitute the current stress component at the calculation point into the same Mohr-Coulomb yield criterion as step (4) to determine whether the surrounding rock at that point has reached the yield state. For the calculation point that has reached the yield state, its position is the boundary point of the plastic zone under the influence of repeated mining, and the secondary expansion range of the plastic zone of the surrounding rock is obtained based on this. For the calculation point that has not reached the yield state, it is used as the new stress boundary point and the calculation is repeated until the stress state of all calculation points meets the yield criterion, and the final plastic zone boundary curve is obtained, which is recorded as ρ i =f(θ i , σ x ′,σ y ′,σ z ′, R0, v, c). The calculated boundary curve of the plastic zone under the influence of repeated mining is ρ i Substituting the equilibrium equation and yield criterion in step (3), the stress equilibrium relationship at any point (r, θ) in the plastic zone of the surrounding rock is established, and the expression of the stress component is obtained:

[0067]

[0068] Where: r′ represents the radial stress at any point under the influence of repeated mining, MPa; σ θ ′ represents the hoop stress at any point under the influence of repeated mining, MPa; σ v ′ represents the axial stress of the tunnel under the influence of repeated mining, MPa; τ rθ ′ represents the shear stress at any point under the influence of repeated mining, MPa; σ x ′ represents the horizontal stress of the vertical tunnel side under the influence of repeated mining, MPa; σ y′ Represents the stress parallel to the tunnel axis under the influence of repeated mining, MPa; σ z ′ represents the vertical stress of the surrounding rock of the tunnel under the influence of repeated mining, MPa; v represents the Poisson's ratio of the surrounding rock of the tunnel; R0 represents the radius of the circular tunnel, m; (r, θ) represents the polar coordinates of any point; Represents the size of the plastic zone of the tunnel surrounding rock under the influence of primary mining, m;.

[0069] When studying the destruction of the tunnel, it is necessary to apply the criterion for the yield and destruction of the surrounding rock. Here, the MC criterion under the three-dimensional stress state is used. m , the MC criterion under the three-dimensional stress state represented by the second deviatoric stress invariant J2, the third deviatoric stress invariant J3 and the stress Lode angle θσ is:

[0070]

[0071] Where: —Internal friction angle of surrounding rock, °; c—Internal cohesion of surrounding rock.

[0072] σ m The expressions of ′, J2′, J3′ and θσ′ are:

[0073]

[0074] J3′=(σ r ′-σ θ ′)(σ r ′-σ r ′)(σ θ ′-σ v ′)

[0075]

[0076] Substituting the stress expression of any point in the polar coordinate system into the analytical expression, the implicit equation expression of the plastic zone boundary of the tunnel surrounding rock under secondary mining can be obtained as follows:

[0077]

[0078] After obtaining the implicit equation of the boundary of the plastic zone of the tunnel surrounding rock under the influence of repeated mining, the numerical calculation method similar to that of single mining can be used to solve the shape and range of the plastic zone with the help of mathematical software. Taking Maple software as an example, the basic steps of writing the solution program are as follows: define the known parameters, including the tunnel radius R0, the Poisson's ratio v of the surrounding rock, the cohesion c, the current three-dimensional normal stress σ after repeated mining, and the x ′、σ y ′、σ z ′, etc. Define the discretization vector of the angle θ, take n discrete values ​​in the range of 0°≤θ≤90°, and form θ=[θ1,θ2,...,θ n ]. Take n=16, and the θ vector is [0, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 66, 72, 78, 84, 90]. Using the loop statement, for each angle value in the θ vector, call the solve function to solve the problem about ρ. i A high-order equation. Since the degree of the equation is high, there may be multiple positive real roots, and the solution results need to be screened and analyzed to obtain a plastic zone radius value with reasonable physical meaning. The plastic zone radius obtained at each angle θ is stored in an array to complete the calculation in the first quadrant. Using symmetry, the results of the first quadrant are mirrored to the other three quadrants to obtain the full range of plastic zone size data of the tunnel under the influence of repeated mining. The solution results are plotted in polar coordinates to generate a spatial distribution cloud map of the plastic zone under the influence of repeated mining, and necessary legends, coordinate axis labels and other elements are added to intuitively display the secondary expansion of the plastic zone. The size of the plastic zone of the tunnel surrounding rock under the influence of repeated mining is as follows (unit: m):

[0079] Angle / ° Plastic zone size / m Angle / ° Plastic zone size / m 0 5.960529 49 7.031820 7 6.024081 55 6.390003 13 6.183878 61 5.686100 19 6.447167 66 5.171333 25 6.803104 72 4.693389 31 7.185080 78 4.360033 37 7.445341 84 4.155073 43 7.415999 90 4.083460

[0080] It can be seen that compared with the results of a single mining operation, repeated mining has caused the plastic zone to expand to varying degrees in all directions. The maximum value of the plastic zone size appears in the θ=37° direction, reaching 7.445m, and the minimum value appears in the θ=90° direction, which is 4.083m. The overall shape of the plastic zone shows a trend of extending in the horizontal direction. The above calculation results are plotted in the polar coordinate plane to obtain the distribution diagram of the plastic zone under the influence of repeated mining as shown in the figure. Figure 2 As shown in the figure, the secondary expansion effect of the plastic zone of the tunnel surrounding rock under repeated mining disturbance is intuitively demonstrated. Compared with the results of the first mining, it can be seen that the expansion amplitude of the plastic zone in the horizontal direction is significantly greater than that in the vertical direction. Affected by the dynamic disturbance of repeated mining, the uneven distribution of the plastic zone is further aggravated.

Claims

1. A method for solving the plastic zone of surrounding rock of a tunnel under the influence of repeated mining, characterized by: The rock mechanics parameters of the tunnel surrounding rock, including cohesion, internal friction angle and Poisson's ratio, are determined through rock mechanics tests; the tunnel size parameters are determined through field measurements; The three-dimensional stress values ​​of the tunnel surrounding rock under the influence of mining were obtained through field measurements, including the horizontal stress σ of the vertical tunnel side. x , stress σ parallel to the tunnel axis y , vertical stress σ of tunnel surrounding rock z ; According to the rock mechanics parameters, tunnel size parameters and the three-dimensional stress values ​​of the tunnel surrounding rock under the influence of primary mining, the tunnel is subjected to elastoplastic mechanical analysis, and the implicit equation of the plastic zone boundary of the tunnel surrounding rock under the influence of primary mining is obtained. Solve the implicit equation of the plastic zone boundary of the tunnel surrounding rock under the influence of primary mining, obtain the plastic zone size ρ of the tunnel surrounding rock under the influence of primary mining, and use the drawing software to draw the plastic zone morphology size diagram according to the plastic zone size ρ to obtain the plastic zone boundary of the tunnel surrounding rock under the influence of primary mining; The three-dimensional stress values ​​of the tunnel surrounding rock under the influence of repeated mining were obtained through field measurements, including the horizontal stress σ of the vertical tunnel side. x ', stress σ parallel to the tunnel axis y ', vertical stress σ of tunnel surrounding rock z '; The boundary of the plastic zone of the tunnel surrounding rock under the influence of one mining operation is discretized into multiple points at equal intervals along the surrounding rock contour. A polar coordinate system is established with the tunnel center as the center of the circle and the plastic zone size ρi as the radius. The plastic zone size ρi of each discrete point is used as the new calculated radius of any point under the influence of repeated mining operation. According to the rock mechanics parameters and the size parameters of the roadway, as well as the new radius ρi of any point in the plastic zone of the roadway surrounding rock under the influence of repeated mining, the roadway is subjected to elastic-plastic mechanical analysis, and the implicit equation of the boundary of the plastic zone of the roadway surrounding rock under the influence of repeated mining is obtained; Solve the implicit equation of the plastic zone boundary of the tunnel surrounding rock under the influence of repeated mining, obtain the plastic zone size τ of the tunnel surrounding rock under the influence of repeated mining, and use the drawing software to draw the plastic zone morphology size diagram according to the plastic zone size τ to obtain the plastic zone boundary of the tunnel surrounding rock under the influence of repeated mining; Obtain the new radius of each discrete point in the plastic zone of the tunnel surrounding rock under the influence of repeated mining, including: The boundary of the plastic zone of the tunnel surrounding rock under the influence of a mining operation is discretized into n points along the surrounding rock contour at equal intervals. The coordinates of each discrete point are (ρ i ,θ i ), where ρ i is the plastic zone size of the ith discrete point, θ i is the angular coordinate of the i-th discrete point; With the center of the laneway as the origin, a polar coordinate system is established; In the polar coordinate system, the plastic zone size ρ of each discrete point is i is the new calculated radius of any point under repeated mining influence, ρ i The expression is Obtain the implicit equation of the plastic zone boundary of the tunnel surrounding rock under the influence of repeated mining, including: In the polar coordinate system, according to the stress parameters, rock mechanics parameters, tunnel size parameters and the new radius of discrete points in the plastic zone under the influence of repeated mining, Establish the stress component expression of any point within the preset range of the tunnel under the influence of repeated mining: That Medium: σ r ' represents the radial stress at any point under the influence of repeated mining; σ θ ' represents the hoop stress at any point under the influence of repeated mining; σ v ' represents the axial stress of the tunnel under the influence of repeated mining; τ rθ ′ represents the shear stress at any point under the influence of repeated mining; σ x ' represents the horizontal stress of the vertical tunnel side under the influence of repeated mining; σ y ' represents the stress parallel to the tunnel axis under the influence of repeated mining; σ z ' represents the vertical stress of the tunnel surrounding rock under the influence of repeated mining; v represents the Poisson's ratio of the tunnel surrounding rock; It indicates the size of the plastic zone of the tunnel surrounding rock under the influence of a mining operation; The Mohr-Coulomb criterion is selected as the criterion for judging the yield and failure of the surrounding rock. m ', the second deviatoric stress invariant J2', the third deviatoric stress invariant J3' and the stress Lode angle θ σ ', establish the Mohr-Coulomb criterion expression under three-dimensional stress state: Where: θ ' represents the hoop stress at any point under the influence of repeated mining; σ r ' represents the radial stress at any point under the influence of repeated mining, MPa; σ v ' represents the axial stress of the tunnel under the influence of repeated mining; τ rθ ′ represents the shear stress at any point under the influence of repeated mining; σ m ', J2', J3' and θ σ The expressions of ' are: J3′=(σ r ′-σ θ ′)(σ r ′-σ v ′)(σ θ ′-σ v ′) The implicit equation expression of the plastic zone boundary of the tunnel surrounding rock under the influence of repeated mining is obtained as follows:

2. The method for solving the plastic zone of surrounding rock of tunnel under the influence of repeated mining according to claim 1 is characterized in that: Obtain the implicit equation of the plastic zone boundary of the tunnel surrounding rock under the influence of primary mining, including: According to the generalized plane strain problem model, the stress expression of any point around the tunnel in the polar coordinate system is obtained through equilibrium equations and geometric equations. Select the judgment criteria for yield and failure of surrounding rock; the judgment criteria include at least one of the Mohr-Coulomb criterion, Mogi-Coulomb criterion, Drucker-Prager criterion and Lade-Duncan criterion; The mean stress σ m , the second deviatoric stress invariant J2, the third deviatoric stress invariant J3 and the stress Lode angle θ σ , the selected criterion is expressed as a function of the principal stress; Substituting the stress expression of any point around the tunnel in the polar coordinate system into the function form of the principal stress, the implicit equation of the boundary of the plastic zone of the tunnel surrounding rock under the influence of primary mining is obtained. The implicit equation is a function of the tunnel size parameters, rock mechanics parameters and the three-dimensional stress values ​​of the tunnel surrounding rock under the influence of primary mining.

3. The method for solving the plastic zone of surrounding rock of tunnel under the influence of repeated mining according to claim 2 is characterized in that: When the Mohr-Coulomb criterion is selected as the judgment criterion, the stress expression of any point around the tunnel in the polar coordinate system is as follows: Among them, σ r Represents the radial stress at any point; σ θ represents the hoop stress at any point; σ v Represents the axial stress of the tunnel; τ rθ represents the shear stress at any point; σ x Represents the horizontal stress of the vertical tunnel side; σ y Represents the stress parallel to the tunnel axis; σ z represents the vertical stress of the tunnel surrounding rock; v represents the Poisson's ratio of the tunnel surrounding rock; R represents the radius of the circular tunnel, m; (r,θ) represents the polar coordinates of any point.

4. The method for solving the plastic zone of surrounding rock of tunnel under the influence of repeated mining according to claim 3 is characterized in that: Function form of principal stress: in: represents the internal friction angle of the surrounding rock; c represents the cohesion of the surrounding rock; σ m , J2, J3 and θ σ The expressions are: J3=(s r -s θ )(s r -s v )(s θ -s v ) 5. The method for solving the plastic zone of surrounding rock of tunnel under the influence of repeated mining according to claim 4 is characterized in that: The implicit equation expression of the plastic zone boundary of the tunnel surrounding rock under primary mining is as follows: Among them, ρ represents the size of the plastic zone of the tunnel after one mining; R0 represents the radius of the circular tunnel.

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