A microseismic positioning method for a rectangular cross-section single-hole tunnel

Abstract

The application relates to a microseismic positioning method for a rectangular-section single-hole tunnel, belonging to the technical field of microseismic positioning of underground tunnels, and establishes a fitness function for eliminating the influence of wave velocity, deduces the shortest propagation path of microseismic signals to sensors in a seismic source point in the surrounding rock of a rectangular-section single-hole tunnel through an analytical method, iteratively optimizes the fitness function by using a differential evolution method, and finally takes the seismic source coordinates corresponding to the minimum value of the fitness function as the microseismic positioning result. The method can quickly obtain the actual shortest propagation path of microseismic signals under the assumption of a uniform wave velocity model, and improves the precision and efficiency of microseismic positioning.

Description

Technical Field

[0001] This invention belongs to the field of microseismic positioning technology in underground tunnel engineering, specifically relating to a microseismic positioning method for a single-bore tunnel with a rectangular cross-section. Background Technology

[0002] Rectangular cross-section tunnels are widely used in roadways of various mining projects. With the research and development and promotion of rectangular shield tunneling machines, rectangular cross-section tunnels are also gradually being applied in urban underground transportation, underground space development and utilization, and other fields. For the current challenges of population growth and land resource shortages, projects such as integrated utility tunnel systems and underground storage spaces constructed using rectangular tunnels can play a vital role.

[0003] During the construction of deep-buried tunnels under high ground stress, rocks are prone to fracturing, leading to engineering accidents such as rock bursts and collapses, which can cause significant casualties and property damage in severe cases. Before macroscopic fracturing occurs in rocks, there are often precursory failures such as the generation, propagation, convergence, and penetration of microcracks within the rock mass. When rocks undergo microfracture under external loads, some strain energy is released in the form of elastic waves, which are excellent sources of acoustic emission signals. By analyzing these acoustic emission signals, information about rock damage and fracturing behavior can be obtained, allowing for the inversion of rock failure mechanisms.

[0004] Microseismic monitoring technology utilizes the elastic waves released during the stress, deformation, and failure of rock masses to monitor the stability of engineering rock masses. Sensor arrays are deployed in the area requiring microseismic monitoring to receive acoustic emission signals generated when rock microfractures occur. Data processing software identifies, retrieves, and reduces noise from the acquired signals to obtain the microseismic event signal. Then, parameters such as the location of the seismic source, the time of occurrence, and the released energy are derived through inversion. Based on the size, concentration, and density of microfractures and other relevant source data, and according to certain evaluation criteria, the development trend of rock fractures from microfractures to macroscopic fractures can be predicted, and early warnings can be issued.

[0005] In practical engineering applications, microseismic location calculations often assume that microseismic signals propagate in a straight line. However, for projects containing underground chambers, such as tunnels, this assumption is often unreasonable and prone to significant errors. Therefore, a method is needed to calculate the shortest path for microseismic signals to propagate around tunnel cavities for microseismic location. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes a microseismic positioning method for a single-tunnel with a rectangular cross-section, comprising the following steps:

[0007] (1) Based on the wave velocity residual, establish a fitness function to eliminate the influence of wave velocity, which is used to characterize the fitness of the potential solution of the source.

[0008] (2) For the source point existing in the surrounding rock of a single-hole tunnel with a rectangular cross section, calculate the shortest propagation path length of the microseismic signal from the potential solution of the source to a certain sensor;

[0009] (3) Microseismic location calculation is performed by differential evolution method, and the potential solution with the highest fitness during the optimization process is output as the source location result.

[0010] The beneficial effects of this invention are as follows:

[0011] (1) The case of the microseismic signal propagation path bypassing the tunnel cavity was considered, and the shortest path length of the microseismic signal propagation under the uniform wave velocity model was calculated, thereby improving the accuracy of microseismic location.

[0012] (2) The shortest path length of microseismic signal propagation is obtained by analytical method. The calculation speed is fast and it is suitable for batch calculation of a large number of microseismic events in actual engineering.

[0013] (3) The calculation process avoids the influence of wave velocity estimation. Under the assumption of a uniform wave velocity model, only the tunnel cross-sectional dimensions, sensor coordinates and relative positions of the tunnel face need to be known to perform the calculation, which has high versatility. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the sensor layout around the tunnel;

[0015] Figure 2 It is a schematic diagram of a two-dimensional plane projection;

[0016] Figure 3 This is a schematic diagram of the propagation path of microseismic signals in a tunnel. Figure 1 ;

[0017] Figure 4 This is a schematic diagram of the propagation path of microseismic signals in a tunnel. Figure 2 ;

[0018] Figure 5 This is a flowchart of the microseismic location calculation using the differential evolution method;

[0019] Figure 6 This is a comparison chart of the positioning results. Detailed Implementation

[0020] A single-tunnel microseismic location method for a rectangular cross-section tunnel includes: a fitness function to eliminate the influence of wave velocity, calculation of the shortest propagation path length of the microseismic signal from the potential solution of the seismic source to a certain sensor, and microseismic location calculation based on the differential evolution method.

[0021] Furthermore, a microseismic location method for a single-tube tunnel with a rectangular cross-section includes the following steps:

[0022] (1) When the sensors at the engineering site detect micro-seismic events. Sensors such as... Figure 1 As shown by the red dots, they are installed in the surrounding rock of the tunnel by drilling.

[0023] (2) Based on the wave velocity residual, establish a fitness function to eliminate the influence of wave velocity, which is used to characterize the fitness of the potential solution of the seismic source. The specific steps include:

[0024] (2.1) Calculate the time required for the sensor to calculate the potential solution of a seismic source. Specifically, calculate the theoretical time required for the P-wave to travel from the location of the potential solution of the seismic source to the location of the sensor using the known parameters in formula (1).

[0025]

[0026] Where: c con Let T0 be the constant P-wave velocity in the surrounding rock, T0 be the seismic source initiation time, n be the total number of sensors, and l be the velocity of the P-wave. u (u = 1, 2, ..., n) represents the shortest path length from the sensor to the seismic source. This is the theoretical time required for a P-wave to travel from the location of the potential solution at the seismic source to the location of the sensor.

[0027] (2.2) Calculate the calculated arrival times of any two sensors i and j (i≠j) and then subtract them. Specifically, obtain the result of subtracting the calculated arrival times of the two sensors using formula (2), and obtain the calculated wave velocity c using formula (3). con .

[0028]

[0029]

[0030] (2.3) Calculate the wave velocity residual and sum the squares to construct the optimization target. Specifically, for each set of data consisting of two different sensors, the wave velocity is obtained by the method in step (2.2) and used to construct the wave velocity residual optimization target as shown in equation (4). Theoretically, when the positioning is completely accurate, f = 0.

[0031]

[0032] (3) Calculating the shortest propagation path length of the microseismic signal from the potential solution of the seismic source to a certain sensor specifically includes the following steps:

[0033] (3.1) Calculate the number of intersections between the line connecting the sensor and the potential solution of the seismic source and the tunnel cavity. Specifically, establish the expression for the line connecting the sensor using equation (5), establish the expression for the tunnel cavity wall using equations (6)-(9), and solve for the number of intersections w by combining the equations.

[0034]

[0035] Where: (x a ,y a ,z a (a = 1, 2, ..., n) represents the coordinates of the sensor in three-dimensional space, (x... b ,y b ,z b ) represents the coordinates of the potential solution of the earthquake source in three-dimensional space.

[0036]

[0037]

[0038]

[0039]

[0040] Where: p is the side length of the rectangular section parallel to the x-axis, q is the side length of the rectangular section parallel to the z-axis, the tunnel axis is parallel to the y-axis, and y = h is the plane where the tunnel face is located.

[0041] (3.2) Based on the value of w and y b The calculation is divided into three cases based on the different values ​​of w. Specifically: Case 1, w = 0, calculate according to step (3.3); Case 2, w ≠ 0 and y b If ≤h, calculate according to steps (3.4)-(3.7); Case 3, w≠0 and y b >h, calculate according to steps (3.8)-(3.12). And express the plane where the shortest propagation path of the microseismic signal is located through equation (10).

[0042] (xx a )+M(yy a )+N(zz a )=0 (10)

[0043] Where (1, M, N) is the normal vector of the plane containing the shortest path for the microseismic signal propagation, and N can be expressed through M as follows:

[0044] (3.3) When w = 0, its two-dimensional plane projection is as follows Figure 2 As shown in (a), the shortest propagation path length of the microseismic signal from the potential solution of the seismic source to the sensor is calculated. Specifically, when w = 0, the microseismic signal propagates in a straight line, and the shortest propagation path length L is calculated using equation (11). min .

[0045]

[0046] (3.4) w≠0 and y b When h ≤ h, determine whether the potential solutions of the sensor and the source can be directly connected to the corner points of the rectangular cross-section of the tunnel, and count them separately. Specifically, project the potential solutions of the sensor and the source onto the two-dimensional plane containing the tunnel cross-section. Any point outside the rectangle can be directly connected to at most three corner points of the rectangle without passing through it. Let the set R be the set of corner points that can be directly connected to the sensor. a The set R is the number of corner points of the elements that can be directly connected to the potential solution of the earthquake source. b The element. Case 1, Perform the calculation according to step (3.5); Case 2, R a ∩R b ={p i}, calculate according to step (3.6); Case 3, R a ∩R b ={p i ,p j}(i≠j), calculate according to step (3.7).

[0047] (3.5) Calculate the shortest propagation path length of the microseismic signal from the potential solution of the seismic source to the sensor. Specifically: At that time, its two-dimensional planar projection diagram is as follows: Figure 2 As shown in (b), the equation for the shortest propagation path length L(M) is established using equation (12), and M = m is solved using equation (13). Substituting this into equation (12) yields the shortest path length L. min =L(m).

[0048] L(M)=L AH +L HK +L KB (12)

[0049] Where: L AH L is the length of the line segment between the sensor and point H. HK L is the length of the line segment between point H and point K. KB H(x) is the length of the line segment between point K and the potential solution of the earthquake source; h ,y h ,z h ) is a point located on the edge of the tunnel wall near the sensor, x h z h Given that y h It can be represented by the unknown M; K(x) k ,y k ,z k (x) is a point located on the edge of the tunnel wall column near the potential solution of the seismic source. k z k Given that y kIt can be represented by the unknown M.

[0050]

[0051] (3.6) Calculate the shortest propagation path length of the microseismic signal from the potential solution of the seismic source to the sensor. Specifically: R a ∩R b ={p i When there is a point in the intersection, its two-dimensional plane projection diagram is as follows: Figure 2 As shown in (c), the equation for the shortest propagation path length L(M) is established using equation (14), and M = m is solved using equation (15). Substituting this into equation (14) yields the shortest path length L. min =L(m).

[0052] L(M)=L AH +L HB (14)

[0053] Where: H(x) h ,y h ,z h (x) is a point located on the edge of the tunnel wall column. h z h With p i Same, y h It can be represented by the unknown M.

[0054]

[0055] (3.7) Calculate the shortest propagation path length of the microseismic signal from the potential solution of the seismic source to the sensor. Specifically: R a ∩R b ={p i ,p j When (i≠j), there are two points in the intersection set, and its two-dimensional planar projection diagram is as follows. Figure 2 As shown in (d), the equation for the shortest propagation path length L(M) is established through equation (16), and M = m is solved through equation (17). Substituting into equation (16), the shortest path length L is obtained. min =L(m).

[0056] L(M)=L AH +L HB (16)

[0057] Where: H(x) h ,y h ,z h (x) is a point located on the edge of the tunnel wall column. h z h With p i or p j Same, yh It can be represented by the unknown M.

[0058]

[0059] (3.8) w≠0 and y b When h > h, project the sensor and the potential solution of the seismic source onto the two-dimensional plane containing the tunnel cross-section, and determine whether the potential solution of the seismic source is located within the rectangular area. Case 1: The potential solution of the seismic source is located within the rectangular area, and calculate according to steps (3.9)-(3.10); Case 2: The potential solution of the seismic source is located outside the rectangular area, and calculate according to step (3.11).

[0060] (3.9) Find the intersection point of the shortest path and the tunnel face. Specifically: when the potential solution of the seismic source is located within the tunnel face, the shortest path is formed by splicing two line segments. The common point of the two line segments is located on the edge of the tunnel face. Project the sensor and the potential solution of the seismic source onto the two-dimensional plane containing the tunnel cross-section, and denote the intersection point of the line connecting the two and the rectangle as (x... h ,z h ), whose corresponding point in three-dimensional space is H(x) h ,h,z h Its path diagram is as follows: Figure 3 As shown.

[0061] (3.10) Calculate the shortest propagation path length of the microseismic signal from the potential solution of the seismic source to the sensor. Specifically, establish the equation L(M) for the shortest propagation path length using equation (18), and solve for M = m using equation (19). Substitute this into equation (18) to obtain the shortest path length L. min =L(m).

[0062] L(M)=L AH +L HB (18)

[0063]

[0064] (3.11) Calculate the shortest propagation path length of the microseismic signal from the potential solution of the seismic source to the sensor. Specifically, calculate the path length L through steps (3.4)-(3.7). a The path diagram is as follows Figure 4 As shown; the path length L is calculated through steps (3.9)-(3.10). b The path diagram is as follows Figure 3 As shown. The shortest path length is obtained through equation (20).

[0065] L min =min{L a ,L b} (20)

[0066] (4) Microseismic location calculations are performed using the differential evolution method. The latent solution with the highest fitness during the optimization process is output as the source location result. The flowchart is as follows: Figure 5 As shown, the specific steps include:

[0067] (4.1) Establishing the initial population. Specifically, N initial solutions are randomly generated within a certain range to form the initial population, and the i-th potential source solution is denoted as X. i = (x,y,z,t) (i = 1,2,...,N), where (x,y,z) are the coordinates of the potential source solution, and t is the initiation time of the potential source solution.

[0068] (4.2) Calculate the fitness of each potential source solution. Specifically, for each potential source solution, calculate the shortest path length of the microseismic signal from its coordinates to each sensor using the method in step (3), and calculate its velocity difference as the fitness using the fitness function established in step (2). The fitness of the i-th potential source solution is denoted as f(X). i The lower the fitness, the better.

[0069] (4.3) Generate the mutation vector. Specifically, three potential source solutions are randomly selected from the population and sorted according to their fitness from best to worst to obtain X. i X j With X k The mutation vector is generated by equation (21).

[0070] V = X i +F(X j -X k ) (twenty one)

[0071] Where F is the adaptive scaling factor.

[0072] (4.4) Generate the crossover vector using the population and mutation vectors. Specifically, the crossover vector is generated for the i-th potential source solution X. i Crossover is performed using equation (22). A random number between 0 and 1 is generated. When the crossover probability CR is greater than or equal to the random number, the crossover vector U is... i The j-th dimension U i,j Equal to the mutation vector V i The j-th dimension V i,j Otherwise, it equals the j-th dimension X of the potential source solution X. i,j .

[0073]

[0074] Where: j (j=1,2,3,4) represents the j-th dimension of the vector, CR is the crossover probability, and rand(0,1) is a random number between 0 and 1.

[0075] (4.5) Update the population. Specifically, the solution X of the i-th potential seismic source. i The update is performed using equation (23). When the cross vector U i Its fitness is better than X i When considering the fitness of the i-th potential source solution X i Updated to U i Otherwise, it remains unchanged.

[0076]

[0077] (4.6) When f(X) i When the convergence condition is met, or the number of iterations reaches its maximum value, X is... i Output the source solution as the source solution; otherwise, repeat steps (4.2)-(4.5).

[0078] (1) When the sensors at the engineering site detect micro-seismic events. Sensors such as... Figure 1 As shown by the red dots, they are installed in the surrounding rock of the tunnel by drilling.

[0079] (2) Based on the wave velocity residual, establish a fitness function to eliminate the influence of wave velocity, which is used to characterize the fitness of the potential solution of the source.

[0080] (3) Calculate the shortest propagation path length of the microseismic signal from the potential solution of the seismic source to a certain sensor.

[0081] (4) Microseismic location calculations are performed using the differential evolution method, and the potential solution with the highest fitness during the optimization process is output as the source location result. For example... Figure 6 As shown, the grid nodes represent the actual locations of the seismic source points, the red dots represent the positioning results of the method of this invention, and the points connected to the red dots by a straight line represent the positioning results when the microseismic signal propagates along a straight line.

[0082] In summary, this positioning method, based on a uniform wave velocity model, solves for the shortest propagation path of microseismic signals while considering the presence of tunnel cavities, thus improving the accuracy of microseismic positioning. Furthermore, by obtaining the shortest path length of microseismic signals analytically, the calculation speed is fast, making it suitable for batch calculations of a large number of microseismic events in practical engineering projects.

[0083] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A microseismic positioning method for a single-tunnel with a rectangular cross-section, characterized in that, Includes the following steps: (1) Based on the wave velocity residual, establish a fitness function to eliminate the influence of wave velocity, which is used to characterize the fitness of the potential solution of the source. (2) For the source point existing in the surrounding rock of a single-tunnel with a rectangular cross-section, calculate the shortest propagation path length of the microseismic signal from the potential solution of the source to a certain sensor, including: (2.1) Calculate the number of intersections between the line connecting the sensor and the potential solution of the seismic source and the tunnel cavity. ; (2.2) According to Value and The calculation is divided into three cases based on the different values: Case 1, Perform the calculation according to step (2.3); Case 2, and Perform the calculations according to steps (2.4)-(2.7); Case 3, and The calculation is performed according to steps (2.8)-(2.11); and the plane containing the shortest propagation path of the microseismic signal is expressed by equation (10): (10) in: The coordinates of the sensor in three-dimensional space. ; It is the normal vector of the plane containing the shortest propagation path of the microseismic signal. pass Expressed as ,in, The coordinates of the potential solution of the earthquake source in three-dimensional space; (2.3) When the microseismic signal propagates in a straight line, the shortest propagation path length is calculated using equation (11). : (11)； (2.4) and At that time, determine whether the potential solutions of the sensor and the source can be directly connected to the corner points of the rectangular cross-section of the tunnel, and count them separately: Project the potential solutions of the sensor and the source onto the two-dimensional plane containing the tunnel cross-section. Any point outside the rectangle can be directly connected to at most three corner points of the rectangle without passing through the rectangle. The set of corner points that can be directly connected to the sensor is denoted as the set. The elements that can be connected by a straight line to the potential solution of the earthquake source are the set of points. Element; (2.5) Then, the equation for the shortest propagation path length is established using equation (12). Solve using equation (13) Substituting into equation (12) yields the shortest propagation path length. : (12) in: It is the length of the line segment between the sensor and point H. It is the length of the line segment between point H and point K. It is the length of the line segment between point K and the potential solution of the earthquake source; It is a point located on the edge of the tunnel wall near the sensor. , It is known that It can be represented by the unknown M; It is a point located on the edge of the tunnel wall near the potential solution of the seismic source. , It is known that It can be represented by the unknown M; (13) (2.6) When there is a point in the intersection, the equation for the shortest propagation path length can be established using equation (14). Solve using equation (15) Substituting into equation (14) yields the shortest propagation path length. : (14) in: It is a point located on the edge of the tunnel wall. , and same, It can be represented by the unknown M; （15） (2.7) When there are two points in the intersection, the equation for the shortest propagation path length is established using equation (16). Solve using equation (17) Substituting into equation (16) yields the shortest propagation path length. : (16) in: It is a point located on the edge of the tunnel wall. , and or same, It can be represented by the unknown M; (17) (2.8) and When the potential solution of the source is projected onto the two-dimensional plane of the tunnel cross section, it is determined whether the potential solution of the source is located within the rectangular area; Case 1: The potential solution of the source is located within the rectangular area, and the calculation is performed according to steps (2.9)-(2.10); Case 2: The potential solution of the source is located outside the rectangular area, and the calculation is performed according to step (2.11). (2.9) Solving for the intersection of the shortest propagation path and the tunnel face: When the potential solution of the seismic source is located within the tunnel face, the shortest propagation path is formed by splicing two line segments. The common point of the two line segments is located on the edge of the tunnel face. Project the sensor and the potential solution of the seismic source onto the two-dimensional plane containing the tunnel cross-section, and denote the intersection of the line connecting the two and the rectangle as... Its corresponding point in three-dimensional space is ; (2.10) The equation for the shortest propagation path length is established using equation (18). Solve using equation (19) Substituting into equation (18) yields the shortest propagation path length. : (18) (19) (2.11) Calculate the shortest propagation path length through steps (2.4)-(2.7). The shortest propagation path length is calculated through steps (2.9)-(2.10). The shortest propagation path length can be obtained through equation (20): (20) (3) Microseismic location calculation is performed by differential evolution method, and the source potential solution with the highest fitness during the optimization process is output as the source location result.

2. The microseismic positioning method for a single-tunnel with a rectangular cross-section according to claim 1, characterized in that, The step (1) of establishing a fitness function to eliminate the influence of wave velocity based on the wave velocity residual includes the following steps: (1.1) Calculate the time required for the sensor to calculate the potential solution for a seismic source. Using the known parameters in formula (1), calculate the theoretical time required for the P-wave to travel from the location of the potential solution to the location of the sensor: (1) in: For a constant P-wave velocity in the surrounding rock, The time of earthquake origin. , where is the shortest propagation path length from the sensor to the potential solution from the earthquake source. , which is the theoretical time required for a P-wave to travel from the location of the potential solution at the seismic source to the location of the sensor; (1.2) Calculate any two sensors After calculating the time, subtract the two values ​​to obtain the result of subtracting the calculated time from the two sensors using formula (2), and obtain the calculated wave velocity using formula (3). : (2) (3) (1.3) Calculate the wave velocity residual, sum the squares to construct the optimization target. For each set of data consisting of two different sensors, the wave velocity is obtained by the method in step (1.2), and the wave velocity residual is used to construct the wave velocity residual optimization target as shown in equation (4). Theoretically, when the positioning is completely accurate, , (4).

Images