Method for evaluating stable state of surrounding rock under cooling condition and application thereof

Abstract

The invention discloses a surrounding rock stable state evaluation method under a cooling condition and application thereof, and belongs to the technical field of underground engineering. The method specifically comprises the following steps: establishing a thermal-mechanical coupling model of an underground high-temperature cavern cooling process; a control equation of the heat conduction problem is established according to the thermal-mechanical coupling model, and rock mass thermal stress in the cavern cooling process is solved; the surrounding rock thermal coupling response in the whole cooling process of the high-temperature cavern is obtained; and calculating the relative relationship between the rock strength and the local stress state based on a point safety coefficient method, judging the stable state of each specific part of the surrounding rock of the cavern, and identifying a potential instability area. The method not only can quickly and accurately judge the stable state evolution law of the surrounding rock of the high-temperature cavern under the cooling effect, but also can reasonably predict the rock mass area where instability possibly occurs, and has the advantages of high calculation efficiency, short required time, small manpower and material resource consumption and the like; and theoretical guidance can be provided for engineering adaptive support design of the high-temperature roadway cavern.

Description

Technical Field

[0001] The invention belongs to the technical field of underground engineering, and in particular relates to a method for evaluating the stability state of surrounding rocks of an underground tunnel chamber under cooling conditions and an application thereof. Background Art

[0002] As mineral resources in the shallow crust are becoming increasingly depleted, resource exploration and mining activities around the world are continuously expanding into the deep earth. The available mineralization space inside the earth is distributed from the surface to 10,000 meters underground. Advancing into the deep earth is a strategic scientific and technological issue that we must solve. In the past 20 years, the mining depth of mineral resources in my country has gradually deepened and developed extremely rapidly. At present, there are dozens of mines in my country with a mining depth of more than 1,000 m. The rock temperature revealed has generally exceeded 35 °C, and the highest ground temperature is close to 50 °C; for mineral resources such as non-ferrous metals and oil and gas, the maximum mining depth can reach 7,500 m, and the ground temperature in some local areas can even reach more than 250 °C. The serious thermal damage caused by high ground temperature will directly lead to changes in the physical and mechanical properties of rocks, aggravate the deformation and destruction of surrounding rocks, significantly deteriorate the strength of lining structures, and change the stress field of surrounding rocks. It has gradually become one of the difficult problems faced by underground engineering construction.

[0003] For underground geotechnical engineering projects facing high temperature heat damage, cooling ventilation, low-temperature cold water and artificial ice making are usually used to reduce the working environment temperature after the excavation of the cavern, so as to ensure that construction personnel and mechanical equipment can smoothly enter the cavern to work. Taking the ventilation and cooling measures most commonly used in underground projects as an example, its main principle is to achieve the purpose of cooling the cavern through continuous heat exchange between cold air and high-temperature rock mass. In the early stage of cooling, the temperature of the surrounding rock of the cave wall drops sharply due to the intense heat exchange effect; as the ventilation time goes by, the influence range of the cold front gradually expands from shallow to deep into the rock mass. At the same time, due to the smaller temperature difference between the rock temperature and the cold wind, the temperature drop of the surrounding rock will gradually weaken in the later stage. On the other hand, the decrease in the temperature of the surrounding rock will cause the rock mass itself to shrink thermally, but due to the constraint effect inside the rock mass, the surrounding rock will generate thermal stress during the cooling process and cause the continuous deterioration of the secondary stress state, which will pose a great threat to the long-term stability of the underground tunnel cavern.

[0004] Therefore, establishing a method to evaluate the stability of surrounding rock under cooling has vital theoretical and engineering significance for improving the safety of mine tunnel construction and operation in high-temperature environments, and further promoting underground infrastructure construction and the development and utilization of deep resources.

[0005] At present, the main methods used to evaluate the stability of surrounding rock under cooling conditions are numerical simulation and in-situ monitoring. Numerical simulation method: For example, Yang Chaoshuai et al. established a surrounding rock parameter degradation model (CS model) that takes into account the influence of confining pressure and plastic strain and applied it to the numerical simulation of the project, thereby calculating the surrounding rock parameter degradation law, indicating that the closer to the tunnel wall, the higher the degree of surrounding rock parameter degradation and the worse the stability. Problems with numerical simulation methods: (1) Numerical calculations are usually limited by the grid division method. If the grid divided by the model is dense, the calculation efficiency is low and the time required is long; if the model grid is coarse, the accuracy of the calculation results cannot be effectively guaranteed; (2) The effects of surrounding rock temperature redistribution and secondary stress state degradation caused by cooling measures on surrounding rock stability are not considered, so it is impossible to accurately describe the surrounding rock stability law during the operation of high-temperature tunnels.

[0006] In-situ monitoring method: Jiang Quan et al. observed the evolution of the internal fracture of the basalt in the underground powerhouse of the Baihetan Hydropower Station through on-site drilling video, revealing the spatial discontinuity of rock fractures under high stress and the time-dependent growth of fracture depth and crack width, and proposed a stability optimization design method for large hard rock underground caverns under high stress. Problems with the in-situ monitoring method: (1) The layout of the in-situ monitoring instrument is relatively cumbersome, the monitoring process takes a long time, and consumes a lot of manpower and material resources; (2) The in-situ monitoring method can only obtain data such as surrounding rock displacement or stress under specific working conditions, and cannot reflect the co-evolution trend of rock temperature and stress during the cooling process, making it difficult to reasonably predict the long-term development law of the stability state of the surrounding rock of the high-temperature cavern. Summary of the invention

[0007] The first purpose of the present invention is to provide a method for evaluating the stability state of surrounding rock under cooling conditions. This method is based on the point safety factor method and the stress Mohr circle analysis method, and can accurately determine the evolution law of the stability state of surrounding rock under different geological environments and cooling methods. It overcomes the limitations of traditional numerical simulation and on-site monitoring methods, such as low calculation efficiency, long time required, large consumption of manpower and material resources, and inability to consider the cooling effect of surrounding rock.

[0008] The present invention adopts the following technical solution: a method for evaluating the stability of surrounding rock under cooling conditions, comprising the following steps: Step 1: establishing a thermal coupling model of the cooling process of an underground high-temperature cavern.

[0009] Obtain the basic parameters for thermal-mechanical coupling model analysis and calculation, including rock temperature T0, rock density ρ r , Young's modulus E, Poisson's ratio ν, cohesion c, friction angle ϕ, thermal expansion coefficient β T , thermal conductivity κ T and specific heat capacity C T .

[0010] Obtain the design parameters for high-temperature cavern cooling, including the heat transfer coefficient h between the cooling medium and the cavern wall T , chamber radius a, cooling medium temperature T b and cooling time t.

[0011] Step 2: The heat exchange between the cooling medium and the high-temperature surrounding rock will cause temperature redistribution of the rock mass and generate thermal stress. The control equation of the heat conduction problem is established based on the thermal-mechanical coupling model in step 1, and the Laplace transform method is used to solve the thermal stress of the rock mass during the cooling process of the cavern.

[0012] Step 3: On the basis of the initial geostress, the rock thermal stress determined in step 2 is superimposed to obtain the surrounding rock thermal-mechanical coupling response during the entire cooling process of the high-temperature cavern.

[0013] Step 4: Calculate the relative relationship between rock strength and its local stress state based on the point safety factor method, analyze the spatiotemporal evolution trend of surrounding rock stress and point safety factor under different geological environments and cooling conditions, determine the stability state of each specific part of the cavern surrounding rock and identify potential unstable areas.

[0014] Preferably, the process of establishing the thermal-mechanical coupling model in step 1 is as follows: a circular cavern with a radius of a is excavated in an infinite elastic homogeneous rock mass, the initial rock temperature of the rock mass is T0 and it is subjected to a horizontal ground stress P x and vertical ground stress P y After excavation is completed, a temperature of T is introduced within the cooling time t. b of cooling medium.

[0015] According to the principle of elastic stress superposition, the thermomechanical coupling model of the surrounding rock of the high-temperature cavern during the cooling process is obtained by superimposing the thermal stress induced by cooling and the initial ground stress.

[0016] In the horizontal ground stress P x and vertical ground stress P y Under the action, the initial ground stress is determined according to the Kirsch solution: (1).

[0017] (2).

[0018] (3).

[0019] (4).

[0020] Where: , , and The horizontal ground stress P x and vertical ground stress Py Static radial stress, hoop stress, shear stress and out-of-plane stress caused by is the distance of the rock unit from the center of the cave, is the radius of the cave, is the polar angle.

[0021] Preferably, step 2 specifically includes the following steps: Step 2.1: When the cooling medium is introduced into the cavern, the heat exchange between the cooling medium and the high-temperature surrounding rock will cause the rock temperature to be redistributed and generate thermal stress. The control equation of the heat conduction problem under polar coordinate conditions is: (5).

[0022] Where: T (r, t) represents the rock temperature redistribution function.

[0023] Introducing excess temperature function for: (6).

[0024] Substituting equation (6) into equation (5), the control equation of the heat conduction problem is: (7).

[0025] The initial and boundary conditions of the heat conduction problem can be written as: (8).

[0026] (9).

[0027] (10).

[0028] Where: H = h T / κ T ; is the excess temperature of the rock unit on the cave wall.

[0029] Step 2.2: Applying the Laplace transform to the heat conduction governing equation (7) yields: d 2 T ¯ * ( r , p ) dr 2 + 1 r d T ¯ * ( r , p ) dr = r r C T k T [ p T ¯ * ( r , p ) − ( T 0 − T b ) ] (11).

[0030] Where: , p is the Laplace transform parameter.

[0031] The solution of the second-order ordinary differential equation (11) is: T ¯ * ( r , p ) = T 0 − T b p [ 1 + HK 0 ( qr ) p K ′ 0 ( what ) − HK 0 ( what ) ] (12).

[0032] Where: , K0 is the 0th order modified Bessel function of the second kind.

[0033] Excess temperature function The solution in the time domain is obtained by inverse Laplace transform of equation (12): T * ( r , t ) = L − 1 [ T * ( r , p ) ] = 1 2 π i ∫ β − i ∞ β + i ∞ T * ( r , p ) e pt dp (13).

[0034] Finally, by combining equations (6), (12) and (13), we can obtain the temperature redistribution characteristics of the rock mass during the cooling process of the cavern: T ( r , t ) = T b − 2 H ( T 0 − T b ) π ∫ 0 ∞ e − k T u 2 t / r r C T u × J 0 ( ur ) [ uY 1 ( ua ) + HY 0 ( ua ) ] − Y 0 ( ur ) [ uJ 1 ( ua ) + HJ 0 ( ua ) ] you [ uY 1 ( ua ) + HY 0 ( ua ) ] 2 + [ uY 1 ( ua ) + HY 0 ( ua ) ] 2 (14).

[0035] Where u is the integral variable, J0, J1 and Y0, Y1 are the 0th and 1st order Bessel functions of the first and second kind respectively.

[0036] The thermal stress of rock mass induced by temperature change is obtained by the following formula: s r T ( r , t ) =− β T E ∫ a r [ T ( r , t ) − T 0 ] rdr r 2 ( 1 − n ) (15).

[0037] s i T ( r , t ) = β T E ∫ a r [ T ( r , t ) − T 0 ] rdr r 2 ( 1 − n ) − β T E [ T ( r , t ) − T 0 ] ( 1 − n ) (16).

[0038] (17);

[0039] s z T ( r , t ) =− β T E [ T ( r , t ) − T 0 ] ( 1 − n ) (18).

[0040] Where: , , , They represent radial stress, hoop stress, shear stress and out-of-plane stress induced by temperature change respectively.

[0041] Preferably, step 3 is specifically as follows: on the basis of formulas (1) to (4) of the initial geostress, the rock mass thermal stress obtained by formulas (15) to (18) is superimposed, thereby obtaining the surrounding rock thermal-mechanical coupling response during the entire cooling process of the high-temperature cavern: (19).

[0042] is the total radial couple stress on the rock unit in the cylindrical coordinate system, represents the total circumferential couple stress on the rock unit in the cylindrical coordinate system, is the total coupled shear stress, is the total out-of-plane normal direction couple stress on the rock element in the cylindrical coordinate system.

[0043] Preferably, step 4 specifically includes: converting the stress components in the cylindrical coordinate system into a Cartesian coordinate system: (20).

[0044] The Mohr-Coulumb yield criterion is used to define the rock shear strength: (twenty one).

[0045] Where: τ * is the shear strength, σ is the normal stress, c and φ are the cohesion and friction angle of the rock respectively.

[0046] By plotting the three-dimensional stress Mohr circle of the rock unit and the Mohr-Coulumb strength envelope simultaneously in the figure, it can be obtained that the most dangerous stress state of the rock depends only on the outermost stress Mohr circle represented by the maximum principal stress σ1 and the minimum principal stress σ3. Therefore, the point safety factor of the rock unit is defined as the ratio of the shear strength to the maximum shear stress, as shown in the following formula: LFS = t * t = | AC | | AB | = [ 2 c + ( s 1 + s 3 ) tan f ] cos f s 1 − s 3 (twenty two).

[0047] Where: AC is the distance from the center of the outermost Mohr circle to the intensity envelope, and AB is the radius of the outermost Mohr circle.

[0048] When the point safety factor is greater than 1, the outermost Mohr circle is within the strength envelope, and the rock remains stable; when the point safety factor is less than or equal to 1, the outermost Mohr circle intersects with the strength envelope, and the rock will become unstable.

[0049] The second object of the present invention is to provide an application of a method for evaluating the stability of surrounding rock under cooling conditions.

[0050] Specifically, it is an application of a surrounding rock stability evaluation method under cooling conditions in the cooling process of underground high-temperature caverns.

[0051] The beneficial effects of the present invention are as follows: (1) The present invention establishes a rigorous thermomechanical coupling model of the cooling process of a high-temperature cavern based on the rock heat conduction theory, and uses the Laplace transform and elastic stress superposition principle to accurately obtain the thermomechanical coupling response of the surrounding rock under different geological environments and cooling schemes.

[0052] (2) By adopting the point safety factor method and the stress Mohr circle analysis method, the present invention can quantitatively calculate the relative relationship between rock strength and local stress state, and then quantitatively determine the stability state of each specific part of the engineering rock mass and identify potential surrounding rock instability areas.

[0053] (3) Compared with numerical calculation or in-situ monitoring methods, the present invention can not only quickly and accurately determine the evolution law of the stable state of the surrounding rock of the high-temperature tunnel under the action of cooling, but also reasonably predict the rock mass area that may become unstable. At the same time, it has the advantages of high calculation efficiency, short time and low manpower and material resources. It can provide theoretical guidance for the engineering adaptability support design of high-temperature tunnel caverns. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Schematic diagram of the thermomechanical coupling model for the cooling process of a high-temperature cavern.

[0055] Figure 2 Define a graph for the point safety factor.

[0056] Figure 3 Point safety factor and stress evolution of cave wall unit under different ground stress conditions.

[0057] Figure 4 is the stress Mohr circle evolution of the cave wall unit during the cooling process.

[0058] Figure 5 This is a cloud diagram of the point safety factor distribution of the surrounding rock during the cooling process under different ground stresses.

[0059] Figure 6 The point safety factor distribution cloud diagram of the surrounding rock under different ground stresses and original rock temperatures after 15 days of cooling. DETAILED DESCRIPTION

[0060] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments:

[0061] Example 1 Combination Figure 1 to Figure 6 A method for evaluating the stability of surrounding rock under cooling conditions comprises the following steps: Step 1: Establish a thermomechanical coupling model for the cooling process of the underground high-temperature cavern.

[0062] Obtain the basic parameters for thermal-mechanical coupling model analysis and calculation, including rock temperature T0, rock density ρ r , Young's modulus E, Poisson's ratio ν, cohesion c, friction angle ϕ, thermal expansion coefficient β T , thermal conductivity κ T and specific heat capacity C T .

[0063] Obtain the design parameters for high-temperature cavern cooling, including the heat transfer coefficient h of the cooling medium and cavern wall T , chamber radius a, cooling medium temperature T b and cooling time t.

[0064] A circular cavern with a radius of a is excavated in an infinite elastic homogeneous rock mass. The initial rock temperature of the rock mass is T0 and it is subjected to a horizontal stress P. x and vertical ground stress P y After excavation is completed, a temperature of T is introduced within the cooling time t. b of cooling medium.

[0065] In this embodiment, a is 2 m, and the temperature of the cooling medium is T b The temperature is 15 °C and the cooling time t is 15 days. The basic parameters of the thermal coupling model and the heat transfer coefficient h of the cooling medium and the cave wall are calculated. T The specific values ​​are shown in Table 1.

[0066] Table 1 Basic parameters and heat transfer coefficients of thermomechanical coupling model analysis and calculation

[0067] Table 2 is the model calculation scheme table, including horizontal ground stress P x , vertical ground stress P y and the value of the initial rock temperature T0.

[0068] Table 2 Model calculation scheme

[0069] Assuming that the axis of the cavern is long enough, the cooling process of the high-temperature tunnel can be simplified to a plane strain problem. In addition, the cavern contour is set to the third type of heat transfer boundary condition with the same temperature as the cooling medium to simulate the heat exchange between the cooling medium and the high-temperature rock mass. According to the principle of elastic stress superposition, the thermal-mechanical coupling model of the high-temperature cavern surrounding rock under cooling conditions ( Figure 1 (a) Thermal stress induced by cooling ( Figure 1 (b)) and initial ground stress ( Figure 1 (c) is obtained by superposition.

[0070] In the horizontal ground stress P x and vertical ground stress P y Under the action, the initial ground stress is determined according to the Kirsch solution: (1).

[0071] (2).

[0072] (3).

[0073] (4).

[0074] Where: , , and The horizontal ground stress P x and vertical ground stress P y Static radial stress, hoop stress, shear stress and out-of-plane stress caused by is the distance of the rock unit from the center of the cave, is the radius of the cave, is the polar angle.

[0075] Step 2: The heat exchange between the cooling medium and the high-temperature surrounding rock will cause temperature redistribution of the rock mass and generate thermal stress. The control equation of the heat conduction problem is established based on the thermal-mechanical coupling model in step 1, and the Laplace transform method is used to solve the thermal stress of the rock mass during the cooling process of the cavern.

[0076] The specific steps include: Step 2.1: When the cooling medium is introduced into the cavern, the heat exchange between the cooling medium and the high-temperature surrounding rock will cause the temperature of the rock mass to be redistributed and generate thermal stress. The governing equation of this heat conduction problem under polar coordinate conditions is: (5).

[0077] Where: T (r, t) represents the rock temperature redistribution function.

[0078] To facilitate problem solving, the excess temperature function is introduced for: (6).

[0079] Substituting equation (6) into equation (5), the control equation of the heat conduction problem is: (7).

[0080] The initial and boundary conditions of the heat conduction problem can be written as: (8).

[0081] (9).

[0082] (10).

[0083] Where: H = h T / κ T , is the excess temperature of the rock unit on the cave wall.

[0084] Step 2.2: Applying the Laplace transform to the heat conduction governing equation (7) yields: d 2 T ¯ * ( r , p ) dr 2 + 1 r d T ¯ * ( r , p ) dr = r r C T k T [ p T ¯ * ( r , p ) − ( T 0 − T b ) ] (11).

[0085] Where: , p is the Laplace transform parameter.

[0086] The solution of the second-order ordinary differential equation (11) is: T ¯ * ( r , p ) = T 0 − T b p [ 1 + HK 0 ( qr ) p K ′ 0 ( what ) − HK 0 ( what ) ] (12).

[0087] Where: , K0 is the 0th order modified Bessel function of the second kind.

[0088] Excess temperature The solution in the time domain is obtained by inverse Laplace transform of equation (12): T * ( r , t ) = L − 1 [ T * ( r , p ) ] = 1 2 π i ∫ β − i ∞ β + i ∞ T * ( r , p ) e pt dp (13).

[0089] Finally, by combining equations (6), (12) and (13), we can obtain the temperature redistribution characteristics of the rock mass during the cooling process of the cavern: T ( r , t ) = T b − 2 H ( T 0 − T b ) π ∫ 0 ∞ e − k T u 2 t / r r C T u × J 0 ( ur ) [ uY 1 ( ua ) + HY 0 ( ua ) ] − Y 0 ( ur ) [ uJ 1 ( ua ) + HJ 0 ( ua ) ] you [ uY 1 ( ua ) + HY 0 ( ua ) ] 2 + [ uY 1 ( ua ) + HY 0 ( ua ) ] 2 (14).

[0090] Where u is the integral variable, J0, J1 and Y0, Y1 are the 0th and 1st order Bessel functions of the first and second kind respectively.

[0091] The thermal stress of rock mass induced by temperature change is obtained by the following formula: s r T ( r , t ) =− β T E ∫ a r [ T ( r , t ) − T 0 ] rdr r 2 ( 1 − n ) (15).

[0092] s i T ( r , t ) = β T E ∫ a r [ T ( r , t ) − T 0 ] rdr r 2 ( 1 − n ) − β T E [ T ( r , t ) − T 0 ] ( 1 − n ) (16).

[0093] (17).

[0094] s z T ( r , t ) =− β T E [ T ( r , t ) − T 0 ] ( 1 − n ) (18).

[0095] Where: , , , They represent radial stress, hoop stress, shear stress and out-of-plane stress induced by temperature change respectively.

[0096] Step 3: On the basis of the initial geostress, the rock thermal stress determined in step 2 is superimposed to obtain the surrounding rock thermal-mechanical coupling response during the entire cooling process of the high-temperature cavern.

[0097] Specifically, the thermal stress of the rock mass obtained by formulas (15) to (18) is superimposed on the initial geostress formulas (1) to (4), and the thermal-mechanical coupling response of the surrounding rock during the whole process of high-temperature cavern cooling is obtained: (19).

[0098] is the total radial couple stress on the rock unit in the cylindrical coordinate system, represents the total circumferential couple stress on the rock unit in the cylindrical coordinate system, is the total coupled shear stress, is the total out-of-plane normal direction couple stress on the rock element in the cylindrical coordinate system.

[0099] Step 4: Calculate the relative relationship between rock strength and its local stress state based on the point safety factor method, analyze the spatiotemporal evolution trend of surrounding rock stress and point safety factor under different geological environments and cooling conditions, determine the stability state of each specific part of the cavern surrounding rock and identify potential unstable areas.

[0100] Specifically: convert the stress components in the cylindrical coordinate system into the Cartesian coordinate system: (20).

[0101] The Mohr-Coulumb yield criterion is used to define the rock shear strength: (twenty one).

[0102] Where: τ * is the shear strength, σ is the normal stress, c and φ are the cohesion and friction angle of the rock respectively.

[0103] The three-dimensional stress Mohr circle and Mohr-Coulumb strength envelope of the rock unit are plotted simultaneously on Figure 2 In the equation, the most dangerous stress state of rock depends only on the outermost stress Mohr circle represented by the maximum principal stress σ1 and the minimum principal stress σ3. Figure 2 Where σ2 is the intermediate principal stress. Therefore, the point safety factor (LFS) of the rock unit is defined as the ratio of the shear strength to the maximum shear stress (i.e. the radius of the outermost Mohr circle), as shown in the following formula: LFS = t * t = | AC | | AB | = [ 2 c + ( s 1 + s 3 ) tan f ] cos f s 1 − s 3 (twenty two).

[0104] Where: AC is the distance from the center of the outermost Mohr circle to the intensity envelope, and AB is the radius of the outermost Mohr circle.

[0105] When the point safety factor is greater than 1, the outermost Mohr circle is located within the strength envelope, and the rock remains in a stable state at this time. When the point safety factor is less than or equal to 1, the outermost Mohr circle intersects the strength envelope, and the rock will become unstable at this time. Therefore, the point safety factor essentially characterizes the distance between the most dangerous stress state of the rock and the Mohr-Coulumb strength envelope.

[0106] Next, the evolution law of the stability of high-temperature caverns under different geological conditions and cooling conditions will be revealed by analyzing the spatio-temporal development process of the point safety factor of surrounding rock and the stress Mohr circle.

[0107] (1) Different in-situ stresses.

[0108] Figure 3 The calculation results of the stress and point safety factor of the rock units on the cavern wall under different in-situ stress conditions during the cooling process are shown. In the figure, t1 and t2 respectively refer to the critical moments when the out-of-plane and circumferential stresses decrease to less than 0, and Figure 4 the evolution law of the stress Mohr circle at different cooling moments is plotted (specifically referring to Figure 2 the outermost Mohr circle in Figure 5 The contour map of the point safety factor distribution of the high-temperature cavern under different confining pressure conditions at different cooling moments is shown. The dark black indicates the unstable area where the point safety factor is less than 1, and h is the depth of the unstable area.

[0109] It can be seen that when the in-situ stress level P0 = P x = P y = 10 MPa, that is, when the horizontal stress is equal to the vertical stress, P0 is used to characterize the magnitude of the in-situ stress, and the point safety factor of the cavern wall unit will first increase and then decrease with the cooling effect ( Figure 3 (a)). This change trend can be explained by the evolution characteristics of the principal stresses of the cavern wall unit at different cooling moments:

[0110] (i) t < t1, at this time, the maximum and minimum principal stresses of the cavern wall unit are the circumferential and radial stresses respectively ( Figure 3 (d)). Since the circumferential stress will gradually decrease with the stress relaxation effect induced by cooling, and the radial stress always remains 0, the principal stress difference and the principal stress sum of the cavern wall unit will gradually decrease, and then in the stress space, it is reflected as a cluster of Mohr circles with the origin of coordinates as the common tangent point and the radius gradually decreasing, as shown in Figure 4 (a). Therefore, the point safety factor of the cavern wall unit will gradually increase, indicating that the cooling effect in the initial stage of cooling will help to enhance the stability of the surrounding rock.

[0111] (ii) t1 < t < t2, the out-of-plane stress of the cavern wall unit develops into tensile stress under the cooling effect. At this time, the maximum and minimum principal stresses of the surrounding rock will change to the circumferential and out-of-plane stresses ( Figure 3(d)). Since the hoop stress and out-of-plane stress will decrease synchronously under the effect of cooling, the principal stress difference of the cave wall unit will remain constant, while the sum of the principal stresses will gradually decrease, which is reflected in the stress space as the size of the Mohr circle remains unchanged, while the center gradually moves to the left and approaches the rock yield surface ( Figure 4 (b)), which will eventually lead to a gradual decrease in the safety factor of the cave wall unit point ( Figure 3 (a)).

[0112] (iii) t>t2, the hoop stress of the cave wall unit also turns into tension under the action of continuous cooling. At this time, the maximum and minimum principal stresses of the cave wall unit will turn into radial and out-of-plane stresses ( Figure 3 (d)). Since the out-of-plane tensile stress will continue to increase (absolute value) under the effect of cooling, while the radial stress always remains at 0, the principal stress difference and the principal stress sum (absolute value) of the cave wall unit will gradually increase, and finally be reflected in the stress space as a cluster of Mohr circles with a common tangent point at the origin of the coordinate system and a gradually increasing radius ( Figure 4 (a)). At this time, the point safety factor of the cave wall unit will gradually decrease ( Figure 3 (a)), indicating that continued cooling will have a deteriorating effect on the stability of the surrounding rock.

[0113] When P0=20 and 40 MPa, Figure 3 It can be seen that the point safety factor of the cave wall unit will also show a trend of increasing first and then decreasing with the continuous cooling. However, since the higher ground stress level will inhibit the stress relaxation effect caused by cooling, the time when the out-of-plane tensile stress appears will be gradually delayed, which will lead to the continuous postponement of the critical time when the point safety factor changes from increasing to decreasing (P0=10 MPa, 20 MPa and 40 MPa correspond to t1=4.4 h, 10.0 h and 27.5 h respectively). In addition, since the cave wall unit under the confining pressure of 20 and 40 MPa is always kept in the annular compression state, it will only experience Mohr's circle shrinkage during the cooling period ( Figure 4 (a)) and translation to the left ( Figure 4 (a)) the first two stages, and will not go through the third stage where the Moore circle gradually expands ( Figure 4 (a)). Therefore, the decrease in the safety factor of the surrounding rock point under the confining pressure of 20 and 40 MPa will be weaker than that under the confining pressure of 10 MPa (see Figure 3 , when P0=10 MPa, LFS decreased from 1.80 to 0.41; when P0=20 MPa, LFS decreased from 1.18 to 0.63; when P0=40 MPa, LFS decreased from 0.88 to 0.79).

[0114] It can be seen that after 15 days of cooling, the surrounding rock of the caverns under the in-situ stress conditions of 10, 20, and 40 MPa will form unstable regions of 0.49 m, 0.42 m, and 0.37 m respectively due to the stress relaxation induced by cooling, indicating that a higher in-situ stress level will inhibit the disturbance of the surrounding rock caused by cooling and thus reduce the potential unstable range of the surrounding rock. In addition, it should be noted that since there is no initial unstable region in the rock mass when the in-situ stress level is low (P0 = 10 and 20 MPa), the strengthening effect of the surrounding rock stability in the initial stage of cooling (t < t1) will not cause a change in the unstable region (h is always 0). Until after a certain cooling time, an unstable region will begin to form near the contour surface of the cavern due to the point safety factor dropping below 1, and finally, the change in the unstable region of the surrounding rock under the low confining pressure condition will be reflected as gradually increasing with the cooling process Figure 5 (a) - (c), Figure 5 (d) - (f)). When the in-situ stress level is high (P0 = 40 MPa), the cavern will form an initial unstable region of 0.13 m due to the strong stress concentration effect, as shown in Figure 5 (g). After 1 day of cooling, the initial compressive stress stored in the high-temperature surrounding rock will be gradually released due to the cooling relaxation effect Figure 3 (f), so the stress state of the rock mass is improved, and the initial unstable region will gradually decrease Figure 5 (h), h = 0.08 m). However, as the cooling process continues, out-of-plane tensile stress will still be generated in the rock mass due to this cooling relaxation effect Figure 3 (f), so the point safety factor of the surrounding rock will begin to gradually decrease due to the left shift of the stress Mohr circle Figure 4 (b), which will in turn cause an increase in the unstable region of the surrounding rock Figure 5 (i), 0.37 m). Finally, the evolution of the unstable region of the surrounding rock under the high confining pressure condition will show a trend of first decreasing and then increasing with the cooling process Figure 5 (g) - (i))

[0115] (2) Different initial rock temperatures.

[0116] Figure 6 The contour maps of the point safety factor of the surrounding rock of the caverns under different in-situ stress and initial rock temperature conditions after 15 days of cooling are shown. It can be found that when the in-situ stress level is low (P0 = 10 and 20 MPa), since the decrease in the initial rock temperature will weaken the disturbance effect of cooling, the unstable region of the cavern will decrease accordingly. When the in-situ stress level is high (P0 = 40 MPa), the surrounding rock of the caverns under the conditions of 100 °C, 75 °C, and 50 °C will generate unstable regions of 0.37 m, 0.03 m, and 0.07 m respectively after the cooling ends, showing a trend of first decreasing and then increasing with the decrease in the initial rock temperature.

[0117] In summary, the present invention effectively reveals the evolution law of the stability of the surrounding rock of high-temperature caverns under different geological conditions and cooling conditions, and can provide theoretical and technical guidance for the engineering adaptability support design of high-temperature tunnels.

[0118] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for evaluating the stability of surrounding rock under cooling conditions, characterized in that: The following steps are involved: Step 1: Establish a thermomechanical coupling model for the cooling process of underground high-temperature caverns; Obtain the basic parameters for thermal-mechanical coupling model analysis and calculation, including rock temperature T0, rock density ρ r , Young's modulus E, Poisson's ratio ν, cohesion c, friction angle ϕ, thermal expansion coefficient β T , thermal conductivity κ T and specific heat capacity C T ; Obtain the design parameters for high-temperature cavern cooling, including the heat transfer coefficient h between the cooling medium and the cavern wall T , chamber radius a, cooling medium temperature T b and cooling time t; Step 2: The heat exchange between the cooling medium and the high-temperature surrounding rock will cause the temperature redistribution of the rock mass and generate thermal stress. The control equation of the heat conduction problem is established based on the thermal-mechanical coupling model in step 1, and the Laplace transform method is used to solve the thermal stress of the rock mass during the cooling process of the cavern; Step 3: On the basis of the initial geostress, the rock thermal stress determined in step 2 is superimposed to obtain the surrounding rock thermal-mechanical coupling response during the whole cooling process of the high-temperature cavern; Step 4: Calculate the relative relationship between rock strength and its local stress state based on the point safety factor method, analyze the spatiotemporal evolution trend of surrounding rock stress and point safety factor under different geological environments and cooling conditions, determine the stability state of each specific part of the cavern surrounding rock and identify potential unstable areas.

2. The method for evaluating the stability of surrounding rock under cooling conditions according to claim 1, characterized in that: The process of establishing the thermal-mechanical coupling model in step 1 is as follows: A circular cavern with a radius of a is excavated in an infinite elastic homogeneous rock mass. The initial rock temperature of the rock mass is T0 and it is subjected to a horizontal stress P. x and vertical ground stress P y After excavation is completed, a temperature of T is introduced within the cooling time t. b Cooling medium; According to the principle of elastic stress superposition, the thermal-mechanical coupling model of the surrounding rock of the high-temperature cavern during the cooling process is obtained by superimposing the thermal stress induced by cooling and the initial ground stress. In the horizontal ground stress P x and vertical ground stress P y Under the action, the initial ground stress is determined according to the Kirsch solution: （1）； （2）； （3）； （4）； Where: , , and The horizontal ground stress P x and vertical ground stress P y Static radial stress, hoop stress, shear stress and out-of-plane stress caused by is the distance of the rock unit from the center of the cave, is the radius of the cave, is the polar angle.

3. The method for evaluating the stability of surrounding rock under cooling conditions according to claim 2, characterized in that: Step 2 specifically includes the following steps: Step 2.1: When the cooling medium is introduced into the cavern, the heat exchange between the cooling medium and the high-temperature surrounding rock will cause the temperature of the rock mass to be redistributed and generate thermal stress. The governing equation of this heat conduction problem under polar coordinate conditions is: （5）； Where: T (r, t) represents the rock temperature redistribution function; Introducing excess temperature function for: （6）； Substituting equation (6) into equation (5), the control equation of the heat conduction problem is: （7）； The initial and boundary conditions of the heat conduction problem can be written as: （8）； （9）； （10）； Where: H = h T / κ T ; is the excess temperature of the rock unit on the cave wall; Step 2.2: Applying the Laplace transform to the heat conduction governing equation (7) yields: （11）； Where: , p is the Laplace transform parameter; The solution of the second-order ordinary differential equation (11) is: （12）； Where: , K0 is the 0th order modified Bessel function of the second kind; Excess temperature function The solution in the time domain is obtained by inverse Laplace transform of equation (12): （13）； Finally, by combining equations (6), (12) and (13), we can obtain the temperature redistribution characteristics of the rock mass during the cooling process of the cavern: （14）； Where: u is the integral variable, J0, J1 and Y0, Y1 are the 0th and 1st order Bessel functions of the first and second kind respectively; The thermal stress of rock mass induced by temperature change is obtained by the following formula: （15）； （16）； （17）； （18）； Where: , , , They represent radial stress, hoop stress, shear stress and out-of-plane stress induced by temperature change respectively.

4. The method for evaluating the stability of surrounding rock under cooling conditions according to claim 3, characterized in that: Step 3 is as follows: The thermal stress of the rock mass obtained by formulas (15) to (18) is superimposed on the initial geostress formulas (1) to (4), and the thermal-mechanical coupling response of the surrounding rock during the whole cooling process of the high-temperature cavern is obtained: （19）； is the total radial couple stress on the rock unit in the cylindrical coordinate system, represents the total circumferential couple stress on the rock unit in the cylindrical coordinate system, is the total coupled shear stress, is the total out-of-plane normal direction couple stress on the rock element in the cylindrical coordinate system.

5. The method for evaluating the stability of surrounding rock under cooling conditions according to claim 4, characterized in that: Step 4 is as follows: Convert the stress components in the cylindrical coordinate system to the Cartesian coordinate system: （20）； The Mohr-Coulumb yield criterion is used to define the rock shear strength: （21）； Where: τ * is the shear strength, σ is the normal stress, c and φ are the cohesion and friction angle of the rock respectively; By plotting the three-dimensional stress Mohr circle of the rock unit and the Mohr-Coulumb strength envelope simultaneously in the figure, it can be obtained that the most dangerous stress state of the rock depends only on the outermost stress Mohr circle represented by the maximum principal stress σ1 and the minimum principal stress σ3. Therefore, the point safety factor of the rock unit is defined as the ratio of the shear strength to the maximum shear stress, as shown in the following formula: （22）； Where: AC is the distance from the center of the outermost Mohr circle to the intensity envelope, AB is the radius of the outermost Mohr circle; When the point safety factor is greater than 1, the outermost Mohr circle is within the strength envelope, and the rock remains stable; when the point safety factor is less than or equal to 1, the outermost Mohr circle intersects with the strength envelope, and the rock will become unstable.

6. Application of a method for evaluating the stability of surrounding rock under cooling conditions, characterized in that: The application of the surrounding rock stability state evaluation method under cooling conditions according to any one of claims 1 to 5 in the cooling process of an underground high-temperature cavern.

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