Method for constructing a calculation model for dynamic stress concentration factor of surrounding rock of elliptical tunnel induced by P wave

Abstract

The present invention discloses a method for constructing a calculation model of dynamic stress concentration coefficient of surrounding rock of an elliptical tunnel induced by P wave, including obtaining a calculation model of dynamic stress concentration coefficient of surrounding rock of an elliptical tunnel induced by P wave, wherein the calculation model of dynamic stress concentration coefficient of surrounding rock of an elliptical tunnel induced by P wave is constructed by a construction method; data of a target elliptical tunnel is brought into the calculation model of dynamic stress concentration coefficient of surrounding rock of an elliptical tunnel induced by P wave, and the distribution of dynamic stress concentration coefficient of surrounding rock of an elliptical tunnel induced by P wave of the target elliptical tunnel is obtained. The calculation of dynamic stress concentration coefficient of surrounding rock of an elliptical tunnel of the present invention is more accurate; the present invention theoretically derives the dynamic stress concentration coefficient of surrounding rock of an elliptical tunnel by using mathematical and physical methods such as complex variable functions and conformal mapping, and provides an analytical solution of dynamic stress concentration coefficient, and the calculated value is more accurate, and the distribution of dynamic stress concentration coefficient and time domain evolution law can be explained from a theoretical aspect.

Description

Technical Field

[0001] The invention relates to a method for constructing a calculation model of dynamic stress concentration coefficient of surrounding rock of an elliptical tunnel induced by a P wave, and belongs to the technical field of geotechnical engineering. Background Art

[0002] With the rapid development of my country's economy, the demand for mineral resources is increasing. In mining projects, underground tunnels play an important role in the mining and transportation of minerals. At present, the elliptical cross-section has a unique advantage in reducing stress concentration due to the lack of edges and corners. Therefore, tunnels with this cross-section are gradually being adopted by a large number of underground projects. At the same time, the drilling and blasting method is often used for blasting construction in underground engineering construction due to its advantages such as flexible construction and wide application conditions. The surrounding rock of the elliptical cavern will inevitably be subjected to different forms of impact disturbances. These impact stress waves will be reflected and scattered at the free boundary of the elliptical tunnel, resulting in uneven force on the surrounding rock of the elliptical tunnel, leading to the destruction of the surrounding rock of the elliptical tunnel. Therefore, it is necessary to establish a theoretical model for evaluating the stability of the surrounding rock of the elliptical tunnel under the incidence of stress waves.

[0003] Although many prevention and stabilization measures for tunnel surrounding rock failure under dynamic disturbance loads have been summarized based on engineering experience, most studies are mainly focused on the numerical simulation and model test research of elliptical tunnel surrounding rock, and are mainly aimed at the analysis of the destructive behavior of elliptical tunnel surrounding rock under static loads. At present, there is no relevant theoretical model to conduct theoretical analysis on the dynamic stress concentration state of elliptical tunnel surrounding rock under dynamic loads, especially for the theoretical derivation of the wave function equation of stress wave incidence and other problems. Summary of the invention

[0004] In order to overcome the defects in the prior art, the present invention aims to provide a method for constructing a calculation model for the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by P waves.

[0005] The technical solution provided by the present invention to solve the above technical problems is: a method for constructing a calculation model of dynamic stress concentration factor of surrounding rock of an elliptical tunnel induced by P wave, comprising the following steps:

[0006] S1. Use Cartesian rectangular coordinates and polar coordinates to analyze elliptical tunnels simultaneously;

[0007] S2. Based on the two-dimensional elastic wave diffraction theory, write the corresponding Lame motion equation using the horizontal displacement u and vertical displacement v of any point in the two-dimensional elastic wave propagation medium;

[0008] S3. According to the theory of complex functions, conjugate complex variables are introduced, and the expression of displacement is written according to the chain rule. According to Hook's law, the conjugate complex variables are substituted to deduce the stress expression and displacement boundary conditions;

[0009] S4. When the incident P wave reaches the free boundary of the elliptical tunnel, it is decomposed into scattered waves inside the elliptical cavity. and ψ i and reflected waves and ψ r , and write the corresponding wave function;

[0010] S5, through the hoop stress σ θ The ratio of the dynamic stress concentration factor to the maximum incident wave stress σ0 is used to obtain the dynamic stress concentration factor calculation formula. Then the displacement boundary conditions and wave function are substituted into the dynamic stress concentration factor calculation formula to obtain the stress concentration factor calculation model.

[0011] A further technical solution is that the coordinates of the rectangular coordinate system in step S1 are (x, y), and the coordinates of the polar coordinate system are (r, θ).

[0012] A further technical solution is that the equation in step S2 is:

[0013]

[0014]

[0015] Where: α = ω / C p , β=ω / C s , represent the compression wave number and the shear wave number respectively, and ω represents the circular frequency of the wave function.

[0016] A further technical solution is that the expression of the displacement in step S3 is:

[0017]

[0018] Where: Θ represents the angle between the normal vector of the boundary point and the horizontal x-axis.

[0019] A further technical solution is that the stress expression is

[0020]

[0021]

[0022] Where: λ and μ are the Lame constants of rocks.

[0023] A further technical solution is that the displacement boundary condition is

[0024]

[0025]

[0026] Where: ξ is the factor function that maps the ellipse to a circle.

[0027] A further technical solution is that the stress concentration factor calculation model in step S5 is:

[0028]

[0029]

[0030] Where: is the incident compression wave; λ and μ are the Lame constants of the rock; where: κ is a constant related to the Lame constant, α n represents the imaginary quantity, Re represents the real part of the imaginary number, represents the Hanker function, ω(η) represents the mapping function, |ω(η)| represents the modulus of the mapping function, represents the incident wave function, e -iωt A time-variant factor representing the dynamic stress concentration factor.

[0031] A method for calculating the dynamic stress concentration factor of surrounding rock of an elliptical tunnel induced by P waves, comprising:

[0032] Obtaining a P-wave induced elliptical tunnel surrounding rock dynamic stress concentration factor calculation model, wherein the P-wave induced elliptical tunnel surrounding rock dynamic stress concentration factor calculation model is constructed using the above method;

[0033] The data of the target elliptical tunnel is brought into the P-wave induced elliptical tunnel surrounding rock dynamic stress concentration factor calculation model to obtain the P-wave induced elliptical tunnel surrounding rock dynamic stress concentration factor distribution of the target elliptical tunnel.

[0034] An electronic device comprises: a memory, a processor and a computer program stored in the memory and executable by the processor, characterized in that when the processor executes the computer program, the above-mentioned construction method is implemented, or a method for calculating the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by a P wave.

[0035] A computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores computer instructions, wherein the computer instructions are used to enable the computer to execute the above-mentioned construction method, or a method for calculating the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by a P wave.

[0036] The present invention has the following beneficial effects: the dynamic stress concentration coefficient of the surrounding rock of an elliptical tunnel is calculated more accurately; the present invention theoretically derives the dynamic stress concentration coefficient of the surrounding rock of an elliptical tunnel by using mathematical and physical methods such as complex functions and conformal mapping, and provides an analytical solution to the dynamic stress concentration coefficient. The calculated value is more accurate, and the distribution and time domain evolution law of the dynamic stress concentration coefficient can be explained theoretically. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Schematic diagram of an elliptical tunnel subjected to plane P wave incidence;

[0038] Figure 2 Schematic diagram of mapping an elliptical tunnel to a unit circle;

[0039] Figure 3 Schematic diagram of the theoretical value of dynamic stress concentration factor under different ellipse major semi-axes;

[0040] Figure 4 This is a schematic diagram comparing the theoretical value and the simulated value of the stress concentration factor of the elliptical tunnel;

[0041] Figure 5 Schematic diagram of simulated values ​​of dynamic stress concentration factor of tunnel surrounding rock under different impact directions;

[0042] Figure 6 Schematic diagram of the simulated value of the dynamic stress concentration factor of the tunnel surrounding rock at 90 degrees. DETAILED DESCRIPTION

[0043] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0044] The method for constructing a calculation model for dynamic stress concentration factor of surrounding rock of an elliptical tunnel induced by a P wave of the present invention comprises the following steps:

[0045] Step 1: First, use Cartesian coordinates and polar coordinates to analyze the elliptical tunnel simultaneously. For example, the coordinates of point M in the rectangular coordinate system are (x, y) and in the polar coordinate system are (r, θ). Figure 1 As shown;

[0046] Step 2: Through the two-dimensional elastic wave diffraction theory, the corresponding Lame motion equation can be written using the horizontal displacement u and vertical displacement v of any point in the two-dimensional elastic wave propagation medium.

[0047]

[0048] Where: λ and μ are the Lame constants of the rock, ρ is the density of the rock, is the Laplace operator, and we have;

[0049]

[0050] Where: θ represents the volume strain rate. According to the above formula, the wave function of P wave incident can be introduced: and ψ, and separate the time factor as;

[0051]

[0052] and ψ satisfy the following wave equations respectively:

[0053]

[0054] Where: Respectively represent the wave speeds of compression waves and shear waves in rocks.

[0055] Substituting (3) into the above formula, we can write:

[0056]

[0057] Where: α = ω / C p , β=ω / C s , represents the compression wave number and the shear wave number, and ω represents the circular frequency of the wave function.

[0058] Step 3: According to the theory of complex functions, conjugate complex variables are introduced, and the expression of displacement can be written according to the chain rule:

[0059]

[0060] Where: Θ represents the angle between the normal vector of the boundary point and the horizontal x-axis. According to Hook's law, by substituting the conjugate complex variables, the stress expression can be deduced as follows;

[0061]

[0062] The displacement boundary conditions are G1 and G2, which can be written as;

[0063] u ρ +iu θ =G1+iG2 (7)

[0064] In the steady-state wave problem, the time factor is not considered so:

[0065] (G1,G2)=Re(g1,g2)e -iωt (8)

[0066] Substituting equation (5) and equation (8) into equation (7), we can get the final displacement boundary condition:

[0067]

[0068] Step 4: When the incident P wave reaches the free boundary of the elliptical tunnel, it can be decomposed into scattered waves inside the elliptical cavity. and ψ iand reflected waves and ψ r , so the corresponding wave function can be written as:

[0069]

[0070] The reflected wave also satisfies the corresponding steady-state wave equation:

[0071]

[0072] The conformal mapping function ω(η) is introduced to map the curve Г in the ξ plane to the unit circle in the η plane. Figure 2 , formula (11) can be written as:

[0073]

[0074] Step 5: By separation of variables, function It can be written as:

[0075]

[0076] Substituting formula (13) into formula (12), we can obtain:

[0077]

[0078] Where: κ is an unknown constant. By integrating formula (14), we can get:

[0079]

[0080] Substituting (15) into (13), the function It can be written as:

[0081]

[0082] Where: C represents any integral path in the η plane that makes equation (16) converge.

[0083] ω(η)=|ω(η)|e iδ ,δ=argω(η),κ=e -it

[0084] Formula (16) can be rewritten as:

[0085]

[0086] make Formula (17) can be written as:

[0087]

[0088] Where a nis the unknown coefficient, and it can be found that removing a n e inδ The remaining part in formula (17) is the first-kind Hanker function. From the mathematical physics equations, we know that:

[0089]

[0090] Substituting formula (19) into formula (18), we can get:

[0091]

[0092] Similarly, another wave function is:

[0093]

[0094] Where b n is also an unknown coefficient, a n 、b n It can be obtained from the boundary conditions, for the reflected wave function and When the reflected wave reaches infinity, it should vanish and satisfy the Sommerfeld condition, as shown below:

[0095]

[0096] Step 6: In order to analyze the local damage of the surrounding rock of the elliptical tunnel when the steady-state P wave enters the tunnel, the dynamic stress concentration factor is introduced to explain the dynamic stress concentration phenomenon of the surrounding rock. The dynamic stress concentration factor can be calculated by the hoop stress σ θ The ratio of the maximum incident wave stress σ0 is calculated as follows:

[0097]

[0098] In the formula and ψ0 is the amplitude of the incident wave. According to equation (9), when σ ρ When it is equal to 0, there is

[0099] σ θ =-2α 2 (λ+μ)Φ (24)

[0100] Where Φ is the incident wave function and the incident compression wave Related to the incident shear wave ψ, the incident wave function and ψ i It can be written as:

[0101]

[0102] Substituting equation (24) into equation (23), we have:

[0103]

[0104] When the incident wave is a P wave, ψ0=0, substituting equation (10) into equation (26) we have:

[0105]

[0106] Where: is a constant related to the Lamé constant, is the incident compression wave; λ and μ are the Lame constants of the rock, α n represents the imaginary quantity, Re represents the real part of the imaginary number, represents the Hanker function, ω(η) represents the mapping function, |ω(η)| represents the modulus of the mapping function, represents the incident wave function, e -iωt A time-variant factor representing the dynamic stress concentration factor.

[0107] Apply the matrix to solve the coefficient a n and b n for

[0108]

[0109] Where:

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116] (s=0,±1,±2,±3,···)

[0117] From formula (28), we get:

[0118]

[0119] As we can see from the previous section, the factor function for mapping an ellipse into a circle is:

[0120]

[0121] Where:

[0122] The dynamic stress concentration factor of the elliptical tunnel when P wave is incident can be obtained by formula (27).

[0123] A method for calculating the dynamic stress concentration factor of surrounding rock of an elliptical tunnel induced by P waves, comprising:

[0124] Obtain the calculation model of dynamic stress concentration factor of surrounding rock of elliptical tunnel induced by P wave,

[0125] The data of the target elliptical tunnel is brought into the P-wave induced elliptical tunnel surrounding rock dynamic stress concentration factor calculation model to obtain the P-wave induced elliptical tunnel surrounding rock dynamic stress concentration factor distribution of the target elliptical tunnel.

[0126] Example 1

[0127] The elastic modulus is 13.58 GPa, the Poisson's ratio is 0.25, and the rock density is 2265 kg / m 3 , C p =2682.3m / s, C s =1548.6m / s, a=10m, b is 10m and 15m respectively, the calculated theoretical value of dynamic stress concentration factor is shown in Figure 3 It can be seen from the figure that when the stress wave incident direction is perpendicular to the long semi-axis of the elliptical tunnel, the compressive stress concentration phenomenon mainly occurs on both sides of the long semi-axis of the elliptical tunnel, while the tensile stress concentration phenomenon occurs on both sides of the short semi-axis of the elliptical tunnel and cracking is prone to occur, causing disasters such as tunnel collapse.

[0128] Example 2

[0129] The AUTODYN software was used to conduct numerical analysis and verification of the theoretical formula of dynamic stress concentration factor. A numerical model of a rectangular plate with a size of 300mm×350mm was established. The dimensions of the tunnel were a=50mm, b=50mm. A steady-state P wave was input at the upper boundary of the plate to simulate the damage of the tunnel surrounding rock under the impact load. The incident P wave was a sine half wave with an amplitude of 1, and the global mesh was divided using triangular units.

[0130] The theoretical solution of the dynamic stress concentration factor is calculated by formula (26), and the result is as follows: Figure 4 As shown in (a), Gaussian points (Gauge points) with an interval of 15° are set on the elliptical surrounding rock boundary of the numerical model to calculate the simulated value of the dynamic stress concentration factor. The calculation results are shown in Figure 4 (b) Put the theoretical value and numerical simulation value in the same polar coordinate system to analyze the error, such as Figure 4 (c). Figure 4 (c) It can be seen that the theoretical value and the simulated value have the same trend and are in good agreement, which can illustrate the correctness of the theoretical calculation. The reasons for the errors between the two are due to the meshing errors and parameter setting errors in the numerical model.

[0131] Example 3

[0132] The size of the elliptical tunnel is a=50mm, b=25mm, the specimen size is 300mm×350mm, and the global grid is divided by triangular units. The specific numerical grid model, the elliptical inclination angles are 0°, 15°, 30°, 45°, 60°, 75° and 90°, which can also cause different incident directions of the shock wave. The incident P wave of the impact load adopts a sine half wave with an amplitude of 1. Gaussian points with an interval of 15° are set at the boundary of the surrounding rock of the elliptical tunnel to monitor and theoretically calculate the dynamic stress concentration factor of the surrounding rock of the elliptical tunnel. The calculation results are shown in the figure. Figure 5 , 6 shown.

[0133] according to Figure 5 , 6 The calculation results show that a positive dynamic stress concentration coefficient indicates tensile stress concentration, and a negative dynamic stress concentration coefficient indicates compressive stress concentration. The larger the absolute value, the more obvious the dynamic stress concentration phenomenon. By applying impact loads in different directions to the elliptical tunnel, it is found that when the impact direction is perpendicular to the major axis of the ellipse, the compressive stress concentration coefficient on both sides of the major axis of the ellipse is the largest and reaches 5. Figure 5 (a) When the impact direction is perpendicular to the minor semi-axis of the ellipse, the tensile stress concentration factor on both sides of the major semi-axis of the ellipse is the largest and reaches 0.515, as shown in Figure 6 As shown in the figure, therefore, more attention should be paid to the two sides of the long semi-axis of the elliptical tunnel during the construction of the underground elliptical tunnel. When the impact direction changes from 0° to 45°, the compressive stress concentration phenomenon on both sides of the long semi-axis of the ellipse is obvious; when the impact direction changes from 60° to 90°, the compressive stress concentration phenomenon on both sides of the long semi-axis of the ellipse gradually disappears and turns into tensile stress concentration. On the contrary, the tensile stress concentration phenomenon on both sides of the short semi-axis of the elliptical tunnel turns into compressive stress concentration phenomenon.

[0134] The memory, processor and computer program stored in the memory and executable by the processor provided in the embodiments of the present invention implement the above-mentioned construction method or a method for calculating the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by P waves when the processor executes the computer program.

[0135] An embodiment of the present invention also provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the method for constructing a calculation model of the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by a P-wave or the method for calculating the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by a P-wave is implemented in any embodiment.

[0136] The computer storage medium of the embodiment of the present invention may adopt any combination of one or more computer-readable media. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples (non-exhaustive list) of computer-readable storage media include: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory, a read-only memory), an erasable programmable read-only memory, an optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination of the above. In this document, a computer-readable storage medium may be any tangible medium containing or storing a program, which may be used by or in combination with an instruction execution system, device or device.

[0137] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, which carry computer-readable program code. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. Computer-readable signal media may also be any computer-readable medium other than a computer-readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0138] The program code embodied on the computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0139] Computer program code for performing the operations of the present invention may be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as C or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network or a wide area network, or may be connected to an external computer.

[0140] The above description is not intended to impose any form of limitation on the present invention. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A calculation method for the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by P waves. It is characterized in that include: The global grid is divided by triangular elements. In the specific numerical grid model, the ellipse inclination angles are 0º, 15º, 30º, 45º, 60º, 75º and 90º respectively. The incident P wave of the impact load adopts a half-sine wave with an amplitude of 1. Obtain a calculation model for the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by P waves; specifically, it is constructed through the following steps: S1. Use Cartesian rectangular coordinates and polar coordinates to analyze elliptical tunnels simultaneously; S2. Through the two-dimensional elastic wave diffraction theory, in the two-dimensional elastic wave propagation medium, the horizontal displacement of any point is u and vertical displacement v Write down the corresponding Lame equation of motion; S3. According to the theory of complex functions, conjugate complex variables are introduced, and the expression of displacement is written according to the chain rule. According to Hook's law, the conjugate complex variables are substituted to deduce the stress expression and displacement boundary conditions; S4. When the incident P wave reaches the free boundary of the elliptical tunnel, it is decomposed into scattered waves inside the elliptical cavity. φ i and ψ i and reflected waves φ r and ψ r , and write the corresponding wave function; S5, through hoop stress σ θ and the maximum incident wave stress σ 0 The ratio of is used to obtain the dynamic stress concentration factor calculation formula, and then the displacement boundary conditions and wave function are substituted into the dynamic stress concentration factor calculation formula to obtain the stress concentration factor calculation model; Where: φ is the incident compression wave; λ and μ is the Lame constant of the rock; is a constant related to the Lamé constant, α n represents the imaginary quantity, Re represents the real part of the imaginary number, represents the Hanker function, represents the mapping function, | | represents the modulus of the mapping function, represents the incident wave function, A time-variable factor representing the dynamic stress concentration factor; Gauss points with an interval of 15° were set at the boundary of the surrounding rock of the elliptical tunnel to monitor and theoretically calculate the dynamic stress concentration factor of the surrounding rock of the elliptical tunnel; The time domain evolution law of the elliptical tunnel is analyzed based on the calculation results; According to the calculation results, after applying impact loads in different directions to the elliptical tunnel, when the impact direction is perpendicular to the major semi-axis of the ellipse, the compressive stress concentration factor on both sides of the major semi-axis of the ellipse is the largest and reaches 5; when the impact direction is perpendicular to the minor semi-axis of the ellipse, the tensile stress concentration factor on both sides of the major semi-axis of the ellipse is the largest and reaches 0.

515. During the construction of underground elliptical tunnels, attention should be paid to both sides of the major semi-axis of the elliptical tunnel; when the impact direction changes from 0º to 45º, the compressive stress concentration phenomenon on both sides of the major semi-axis of the ellipse is obvious; When the impact direction changes from 60º to 90º, the compressive stress concentration phenomenon on both sides of the major semi-axis of the ellipse gradually disappears and turns into tensile stress concentration, and the tensile stress concentration phenomenon on both sides of the minor semi-axis of the elliptical tunnel turns into compressive stress concentration phenomenon.

2. According to claim 1, a method for calculating the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by P waves, It is characterized in that The coordinates of the rectangular coordinate system in step S1 are ( x , y ), the coordinates of the polar coordinate system are ( r , θ ).

3. According to claim 2, a method for calculating the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by P waves, It is characterized in that The equation in step S2 is: Where: α = ω / C p , β = ω / C s , represent the compression wave number and the shear wave number, respectively. ω Represents the circular frequency of the wave function.

4. According to claim 3, a method for calculating the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by P waves, It is characterized in that The expression of displacement in step S3 is: Where: Θ Represents the normal vector of the boundary point and the horizontal x The angle of the axis.

5. The method for calculating the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by P waves according to claim 1, It is characterized in that The stress expression is Where: λ and μ is the Lame constant of the rock.

6. The method for calculating the dynamic stress concentration factor of the surrounding rock of an elliptical tunnel induced by P waves according to claim 1, It is characterized in that The displacement boundary condition is Where: The factor function that maps an ellipse to a circle.

7. An electronic device, It is characterized in that include: A memory, a processor, and a computer program stored in the memory and executable by the processor, wherein the processor implements the calculation method according to any one of claims 1 to 6 when executing the computer program.

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