A method for calculating influence range of carbon dioxide phase transition induced crack in deep vertical shaft

Abstract

The application discloses a method for calculating the influence range of carbon dioxide phase transition fracturing in a deep vertical shaft, which comprises the following steps: dividing the carbon dioxide phase transition fracturing process into a dynamic impact stage and a quasi-static fracturing stage, considering the initial geostress state and the pressure caused by the carbon dioxide phase transition in the two stages, respectively calculating the stress field distribution around the holes in the two stages, and respectively calculating the range of the crack initiation zone and the crack propagation zone based on the dynamic tensile stress and the crack intensity factor. The application provides a method for calculating the influence range of carbon dioxide phase transition fracturing in a deep hole, and the method considers the particularity of carbon dioxide phase transition fracturing, especially the stress characteristics of the rocks around the holes in different fracturing stages, thereby providing convenience for the engineering scheme design of carbon dioxide phase transition fracturing.

Description

Technical Field

[0001] This invention relates to the field of underground structure renovation and development, and in particular to a method for calculating the influence range of carbon dioxide phase transformation-induced cracking in deep vertical shafts. Background Technology

[0002] Blasting is a commonly used technique in deep-earth geotechnical engineering, particularly in the excavation of underground structures such as tunnels, adits, and shafts, as well as in the mining of underground resources like coal, unconventional oil and gas, and uranium. Traditional blasting, which uses explosives as an energy source, suffers from drawbacks such as high construction difficulty, stringent operating conditions, and low predictability. In recent years, carbon dioxide phase change fracturing, a novel non-explosive blasting technology, has gained increasing popularity and is being widely applied in deep-earth engineering due to its high controllability, safety, and environmental friendliness. By filling a specially designed carbon dioxide fracturing tube with liquid carbon dioxide, heat is released through an excitation tube, inducing a rapid phase change in the liquid carbon dioxide. The enormous energy generated by the expansion of the carbon dioxide during this phase change impacts the rock mass, causing it to fracture.

[0003] Calculating the impact range of blasting is fundamental to deep-earth rock blasting, directly affecting the design of the entire blasting scheme, especially the arrangement of blast holes. Currently, the calculation of the impact range of carbon dioxide phase transformation-induced fracturing still adopts blasting theory based on traditional explosive blasting, dividing the rock strata around the blast hole into fractured, fissure, and vibration zones from the inside out. The stress distribution of the rock strata is obtained based on the shock wave attenuation model, and then the range of the fractured and fissure zones is determined by combining the dynamic tensile strength of the rock. However, some experimental studies have found that the fracturing characteristics of carbon dioxide phase transformation in rock strata are significantly different from those of explosive blasting. Compared to the high peak pressure, short duration, and high frequency of explosive blasting, carbon dioxide blasting has a lower peak pressure, longer duration, and lower frequency. In particular, the pressure drop after the peak is more gradual. This results in the fracture zone not being obvious in many cases, and the development of the fracture zone also exhibits a phased characteristic. In the dynamic impact stage where the pressure rises rapidly, the shock wave generates several short radial cracks around the hole. In the quasi-static fracturing stage where the pressure drops slowly, carbon dioxide continues to expand into the cracks and generate a fracturing effect, causing some of the cracks to continue to propagate until they stop.

[0004] In summary, current methods for calculating the impact range of carbon dioxide phase transformation (CVT)-induced fracturing based on traditional explosive blasting theory do not consider the differences between CVT-induced fracturing and explosive blasting, and therefore fail to reflect the characteristics of CVT-induced fracturing. Therefore, there is an urgent need to provide a method for calculating the impact range of CVT-induced fracturing in deep vertical shafts, capable of calculating the extent of the initiation zone and crack propagation zone, taking into account the specific characteristics of CVT-induced fracturing. This is of great significance for the engineering design of CVT-induced fracturing solutions. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for calculating the influence range of carbon dioxide phase change fracturing in deep vertical shafts, which is beneficial for calculating the influence range of fracturing during deep hole blasting using a carbon dioxide phase change fracturing device.

[0006] The technical solution adopted by this invention to solve its technical problem is:

[0007] This invention provides a method for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts, including:

[0008] The carbon dioxide phase transformation fracturing process is divided into two stages: a dynamic impact stage and a quasi-static pressure fracturing stage. Considering the initial geostress state and the pressure caused by the carbon dioxide phase transformation in the two stages, the stress field distribution around the borehole in the two stages is calculated. Then, based on the dynamic tensile stress and the crack strength factor, the range of the crack initiation zone and the crack propagation zone are calculated.

[0009] Furthermore, the method of the present invention addresses the initial stress state prior to the dynamic impact stage, including a method for calculating the initial stress distribution:

[0010] Using the center of the deep borehole as the origin of the polar coordinate system and the direction of the maximum horizontal stress as the x-axis of the polar coordinate system, calculate the initial stress distribution around the borehole under the action of horizontal stress:

[0011]

[0012] Where, σ r0 (r, θ), σ θ0 (r, θ) represent the initial radial stress and initial circumferential stress at position (r, θ), respectively; τ rθ0 σ represents the initial shear stress at position (r, θ); H and σ h These represent the maximum and minimum horizontal in-situ stresses of the strata, respectively; r b θ is the radius of the deep hole; r and θ are the radius and angle in polar coordinates.

[0013] Furthermore, the specific methods for the dynamic impact phase in the method of the present invention include:

[0014] Calculate the impact pressure on the deep hole wall during the dynamic impact stage of carbon dioxide phase transformation-induced cracking;

[0015] Calculate the dynamic stress distribution around the hole caused by the stress wave generated by the impact pressure;

[0016] Based on the impact pressure and dynamic stress distribution, determine the conditions for crack initiation during the dynamic impact stage;

[0017] Based on the dynamic stress distribution, the crack initiation range around the hole during the dynamic impact stage is determined, and the distribution of the crack initiation range around the hole during the dynamic impact stage is plotted in polar coordinates.

[0018] Furthermore, the formula for calculating the impact pressure P1 on the deep hole wall during the dynamic impact stage caused by carbon dioxide phase transformation cracking is as follows:

[0019]

[0020] Where P1 is the impact pressure on the deep hole wall caused by carbon dioxide phase transformation during the dynamic impact stage; n is the pressure amplification factor; P c The pressure at which carbon dioxide causes the tube to rupture; d c d is the diameter of the carbon dioxide fracturing tube; b γ is the diameter of the deep hole; γ is the exponential parameter.

[0021] The formula for calculating the dynamic stress distribution around the hole caused by the stress wave generated by the impact pressure is:

[0022]

[0023] Where, σ rd σ θd These represent the dynamic radial stress and dynamic circumferential stress caused by the stress wave generated by the impact pressure at a distance r from the center of the deep hole, respectively; P1 is the impact pressure caused on the deep hole wall during the carbon dioxide phase transformation cracking stage of the dynamic impact phase; r b θ is the radius of the deep hole; r and θ are the radius and angle in polar coordinates.

[0024] Furthermore, the condition for determining the crack initiation stage during the dynamic impact phase in this invention is as follows:

[0025]

[0026] Where, σ θ1 (r, θ) represents the total radial stress around the hole during the dynamic impact phase; σ r0 (r, θ), σ θ0 (r, θ) represent the initial radial stress and initial circumferential stress at position (r, θ), respectively; σ H and σ h These represent the maximum and minimum horizontal in-situ stresses of the formation, respectively; P1 is the impact pressure generated on the borehole wall during the dynamic impact stage caused by carbon dioxide phase transformation fracturing; r b Let r be the radius of the deep hole; θ and r are the radius and angle in polar coordinates; σ t It represents the uniaxial tensile strength of the rock.

[0027] Furthermore, the specific methods for the quasi-static fracturing stage in the method of the present invention include:

[0028] Calculate the quasi-static pressure exerted by carbon dioxide on the borehole wall during the quasi-static fracturing stage;

[0029] Calculate the quasi-static radial stress and quasi-static circumferential stress caused by carbon dioxide phase transformation-induced cracking at a distance from the center of the deep hole;

[0030] Calculate the radial stress around the hole during the quasi-static fracturing stage;

[0031] The condition for determining crack propagation in the quasi-static fracturing stage is that the stress intensity factor of the crack is greater than the fracture toughness of the rock.

[0032] The formula for the condition of crack propagation in the static fracturing stage is transformed into an equation about the radius and angle in polar coordinates by using the Gauss-Legend de Gauss numerical integral formula. The range of crack propagation in the quasi-static fracturing stage is obtained and its distribution is plotted in polar coordinates, thus obtaining the range of carbon dioxide phase transformation-induced fracturing influence in deep vertical shafts.

[0033] Furthermore, the formula for calculating the quasi-static pressure P2 caused by carbon dioxide on the deep hole wall during the quasi-static fracturing stage in the method of the present invention is as follows:

[0034] P2 = KP c

[0035] Where P2 is the quasi-static pressure caused by carbon dioxide on the deep hole wall during the quasi-static fracturing stage; K is the carbon dioxide gas attenuation coefficient; P c This refers to the pressure at which carbon dioxide causes the tube to rupture.

[0036] The quasi-static radial stress and quasi-static circumferential stress caused by carbon dioxide phase transformation-induced cracking at a distance r from the center of the deep hole are calculated as follows:

[0037]

[0038] Where, σ rs (r), σ θs (r) represents the quasi-static radial stress and quasi-static circumferential stress caused by quasi-static pressure at a distance r from the center of the deep hole, respectively; P2 represents the quasi-static pressure caused by carbon dioxide on the deep hole wall during the quasi-static fracturing stage; r b θ is the radius of the deep hole; r and θ are the radius and angle in polar coordinates.

[0039] Furthermore, the formula for calculating the radial stress around the borehole during the quasi-static fracturing stage in the method of the present invention is as follows:

[0040]

[0041] Where, σ θ2 (r, θ) represents the radial stress around the borehole during the quasi-static fracturing stage; σ θ0(r, θ) represents the initial circumferential stress at position (r, θ); σ θs (r) represents the quasi-static circumferential stress caused by the quasi-static pressure at a distance r from the center of the deep hole; σ H and σ h These represent the maximum and minimum horizontal in-situ stresses of the strata, respectively; r b Let be the radius of the deep hole.

[0042] Furthermore, the specific conditions for crack propagation during the quasi-static fracturing stage in the method of the present invention are as follows:

[0043] Condition K for crack propagation in the quasi-static fracturing stage I The stress intensity factor of the crack is greater than the fracture toughness of the rock, and the formula is:

[0044]

[0045] Among them, K I The condition for crack propagation in the quasi-static fracturing stage; a = rr b σ is the total length of the crack; θ2 (r b +x,θ) is (r b The radial stress around the borehole during the quasi-static fracturing stage at position +x, θ; x is the distance between a point on the crack and the crack initiation point on the borehole wall; K IC For the fracture toughness of the rock, take C1, C2, and C3 are coefficients.

[0046] This invention provides a system for calculating the impact range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts, comprising:

[0047] Memory, used to store executable computer programs;

[0048] The processor, when executing an executable computer program stored in memory, implements the above-mentioned method for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts.

[0049] The beneficial effects of this invention are:

[0050] This invention provides a method for calculating the influence range of carbon dioxide phase transformation fracturing in deep vertical shafts. The method considers the influence of the initial geostress state while taking into account the special characteristics of carbon dioxide phase transformation fracturing. It divides the carbon dioxide phase transformation fracturing process into two stages: a dynamic impact stage and a quasi-static fracturing stage. Based on the stress field distribution around the borehole in these two stages, the range of the fracturing initiation zone and the crack propagation zone are calculated, providing a reference for the engineering design of carbon dioxide phase transformation fracturing. Attached Figure Description

[0051] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0052] Figure 1 This is a schematic diagram of the stress analysis around the borehole at each stage in the method for calculating the influence range of carbon dioxide phase transformation-induced cracking in a deep vertical shaft according to the present invention.

[0053] Figure 2 This is a schematic diagram showing the calculated range of carbon dioxide phase transformation-induced cracking in an embodiment of the present invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0055] Example 1

[0056] like Figure 1 As shown, the method for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts according to an embodiment of the present invention includes:

[0057] The carbon dioxide phase transformation fracturing process is divided into two stages: a dynamic impact stage and a quasi-static fracturing stage. Considering the initial geostress state and the pressure caused by the carbon dioxide phase transformation in both stages, the stress field distribution around the borehole in each stage is calculated. Then, based on the dynamic tensile stress and crack strength factor, the ranges of the crack initiation zone and crack propagation zone are calculated. Wherein:

[0058] First, take the center of the deep borehole as the origin of the polar coordinate system and the direction of the maximum horizontal stress as the x-axis of the polar coordinate system to calculate the initial stress distribution around the borehole under the action of horizontal stress.

[0059] The dynamic impact phase includes:

[0060] Calculate the impact pressure on the deep hole wall during the dynamic impact stage of carbon dioxide phase transformation-induced cracking;

[0061] Calculate the dynamic stress distribution around the hole caused by the stress wave generated by the impact pressure;

[0062] Based on the impact pressure and dynamic stress distribution, determine the conditions for crack initiation during the dynamic impact stage;

[0063] Based on the dynamic stress distribution, the crack initiation range around the hole during the dynamic impact stage is determined, and the distribution of the crack initiation range around the hole during the dynamic impact stage is plotted in polar coordinates.

[0064] Quasi-static fracturing stage:

[0065] Calculate the quasi-static pressure exerted by carbon dioxide on the borehole wall during the quasi-static fracturing stage;

[0066] Calculate the quasi-static radial stress and quasi-static circumferential stress caused by carbon dioxide phase transformation-induced cracking at a distance from the center of the deep hole;

[0067] Calculate the radial stress around the hole during the quasi-static fracturing stage;

[0068] The condition for determining crack propagation in the quasi-static fracturing stage is that the stress intensity factor of the crack is greater than the fracture toughness of the rock.

[0069] The formula for the condition of crack propagation in the static fracturing stage is transformed into an equation about the radius and angle in polar coordinates by using the Gauss-Legend de Gauss numerical integral formula. The range of crack propagation in the quasi-static fracturing stage is obtained and its distribution is plotted in polar coordinates, thus obtaining the range of carbon dioxide phase transformation-induced fracturing influence in deep vertical shafts.

[0070] Example 2

[0071] Based on Embodiment 1, this invention provides a more complete and specific calculation method, which specifically includes the following steps:

[0072] 1) Taking the center of the deep borehole as the origin of the polar coordinate system and the direction of the maximum horizontal stress as the x-axis of the polar coordinate system, the initial stress distribution around the borehole under the action of horizontal stress is calculated using equations (1) to (3). The formulas are as follows:

[0073]

[0074]

[0075] In equations (1) to (3), σ r0 (r, θ), σ θ0 (r, θ) represent the initial radial stress and initial circumferential stress at position (r, θ), respectively; τ rθ0 σ represents the initial shear stress at position (r, θ); H and σ h These represent the maximum and minimum horizontal in-situ stresses of the strata, respectively; r b Let r be the radius of the deep hole; θ and r are the radius and angle in polar coordinates.

[0076] 2) The impact pressure P1 caused on the deep hole wall during the carbon dioxide phase transformation cracking stage in the dynamic impact stage is calculated using formula (4). Formula (4) is:

[0077]

[0078] In equation (4), P1 is the impact pressure on the deep hole wall caused by carbon dioxide phase transformation during the dynamic impact stage; n is the pressure amplification factor; P c The pressure at which carbon dioxide causes the tube to rupture; d c d is the diameter of the carbon dioxide fracturing tube; bγ is the diameter of the deep hole; γ is an exponential parameter, taken as 3;

[0079] 3) The dynamic stress distribution around the hole caused by the stress wave generated by the impact pressure is calculated using formula (5). Formula (5) is:

[0080]

[0081] In equation (5), σ rd σ θd These represent the dynamic radial stress and dynamic circumferential stress caused by the stress wave generated by the impact pressure at a distance r from the center of the deep hole, respectively; P1 is the impact pressure caused on the deep hole wall during the carbon dioxide phase transformation cracking stage of the dynamic impact phase; r b Let r be the radius of the deep hole; θ and r are the radius and angle in polar coordinates.

[0082] 4) Formula (6) is the condition for crack initiation during the dynamic impact stage:

[0083]

[0084] In equation (6), σ θ1 (r, θ) represents the total radial stress around the hole during the dynamic impact phase; σ r0 (r, θ), σ θ0 (r, θ) represent the initial radial stress and initial circumferential stress at position (r, θ), respectively; σ H and σ h These represent the maximum and minimum horizontal in-situ stresses of the formation, respectively; P1 is the impact pressure generated on the borehole wall during the dynamic impact stage caused by carbon dioxide phase transformation fracturing; r b Let r be the radius of the deep hole; θ and r are the radius and angle in polar coordinates; σ t The uniaxial tensile strength of the rock;

[0085] 5) Based on the crack initiation range around the hole in the dynamic impact stage determined by equation (5), plot the distribution of the crack initiation range around the hole in the dynamic impact stage in polar coordinates.

[0086] 6) The quasi-static pressure P2 caused by carbon dioxide on the deep hole wall during the quasi-static fracturing stage is calculated using formula (7). Formula (7) is:

[0087] P2 = KP c (7)

[0088] In the formula, P2 is the quasi-static pressure caused by carbon dioxide on the deep hole wall during the quasi-static fracturing stage; K is the carbon dioxide gas attenuation coefficient; P c This refers to the pressure at which carbon dioxide causes the tube to rupture.

[0089] 7) The quasi-static radial stress and quasi-static circumferential stress caused by carbon dioxide phase transformation cracking at a distance r from the center of the deep hole are:

[0090]

[0091] In equations (8) and (9), σ rs (r), σ θs (r) represents the quasi-static radial stress and quasi-static circumferential stress caused by quasi-static pressure at a distance r from the center of the deep hole, respectively; P2 represents the quasi-static pressure caused by carbon dioxide on the deep hole wall during the quasi-static fracturing stage; r b Let r be the radius of the deep hole; θ and r are the radius and angle in polar coordinates.

[0092] 8) The radial stress around the borehole in the quasi-static fracturing stage is calculated using formula (10), which is:

[0093]

[0094] In equation (10), σ θ2 (r, θ) represents the radial stress around the borehole during the quasi-static fracturing stage; σ θ0 (r, θ) represents the initial circumferential stress at position (r, θ); σ θs (r) represents the quasi-static circumferential stress caused by the quasi-static pressure at a distance r from the center of the deep hole; σ H and σ h These represent the maximum and minimum horizontal in-situ stresses of the strata, respectively; r b θ is the radius of the deep hole; r and θ are the radius and angle in polar coordinates; P2 is the quasi-static pressure caused by carbon dioxide on the hole wall during the quasi-static fracturing stage.

[0095] 9) Condition K for crack propagation in the quasi-static fracturing stage I The stress intensity factor of the crack is greater than the fracture toughness of the rock, and the formula is:

[0096]

[0097] In the formula, K I The condition for crack propagation in the quasi-static fracturing stage; a = rr b σ is the total length of the crack; θ2 (r b +x,θ) is (r b Radial stress around the borehole during the quasi-static fracturing stage at positions +x, θ); r b π is the radius of the deep hole; x is the radius of a circle; k is the radius of a circle; π is the radius of a circle; x is the distance between a point on the crack and the crack initiation point on the hole wall; K is the radius of the hole. I For the fracture toughness of the rock, take C1, C2, and C3 are calculated using the following formula:

[0098]

[0099] In the formula, z r =log 10 (a / r b ), a = rr b r is the total length of the crack. b The radius of the deep hole;

[0100] 10) By using the Gauss-Legends numerical integral formula, equation (11) is transformed into an equation about r and θ, the range of fracture propagation in the quasi-static fracturing stage is obtained, and its distribution is plotted in polar coordinates. This is a method for calculating the range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts.

[0101] Example 3

[0102] Deep-pore carbon dioxide phase transformation fracturing was performed on a certain rock stratum, and the maximum horizontal in-situ stress of this rock stratum was σ. H =20MPa, minimum ground stress is σ h =15MPa, the measured uniaxial tensile strength is σ t =8MPa, the radius of the rupture hole is 0.15m. The parameters of the carbon dioxide fracturing tube used include the carbon dioxide fracturing tube rupture pressure P. c d, diameter of carbon dioxide fracturing tube c The pressure increase factor n, the exponential parameter γ, and the carbon dioxide gas attenuation coefficient K are shown in Table 1.

[0103] Table 1 Parameters of the carbon dioxide fracturing tube

[0104]

[0105] Using the proposed method for calculating the influence range of carbon dioxide phase transformation-induced cracking in deep-pore environments, the calculated influence range of carbon dioxide phase transformation-induced cracking is as follows: Figure 2 As shown in the figure. It should be noted that the five-node Gauss-Legend de Gauss numerical integral formula is used in step (8). As can be seen from the figure, the initiation zone and the crack propagation zone of the deep-hole carbon dioxide phase transformation cracking in this example are both elliptical, with the major axis corresponding to the direction of the minimum horizontal stress and the minor axis corresponding to the direction of the maximum horizontal stress. The major axis diameter of the initiation zone is 0.69m and the minor axis diameter is 0.59m, while the major axis diameter of the crack propagation zone is 5.89m and the minor axis diameter is 4.03m.

[0106] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0107] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts, characterized in that, include: The carbon dioxide phase change fracturing process is divided into two stages: dynamic impact stage and quasi-static pressure fracturing stage. Considering the initial geostress state and the pressure caused by the carbon dioxide phase change in the two stages, the stress field distribution around the hole in the two stages is calculated. Then, based on the dynamic tensile stress and crack strength factor, the range of the crack initiation zone and crack propagation zone is calculated. The specific methods for the dynamic impact phase in this method include: Calculate the impact pressure on the deep hole wall during the dynamic impact stage of carbon dioxide phase transformation-induced cracking; Calculate the dynamic stress distribution around the hole caused by the stress wave generated by the impact pressure; Based on the impact pressure and dynamic stress distribution, determine the conditions for crack initiation during the dynamic impact stage; Based on the dynamic stress distribution, the crack initiation range around the hole during the dynamic impact stage is determined, and the distribution of the crack initiation range around the hole during the dynamic impact stage is plotted in polar coordinates. The specific methods for the quasi-static fracturing stage in this method include: Calculate the quasi-static pressure exerted by carbon dioxide on the borehole wall during the quasi-static fracturing stage; Calculate the quasi-static radial stress and quasi-static circumferential stress caused by carbon dioxide phase transformation-induced cracking at a distance from the center of the deep hole; Calculate the radial stress around the hole during the quasi-static fracturing stage; The condition for determining crack propagation in the quasi-static fracturing stage is that the stress intensity factor of the crack is greater than the fracture toughness of the rock. The formula for the condition of crack propagation in the static fracturing stage is transformed into an equation about the radius and angle in polar coordinates by using the Gauss-Legend de Gauss numerical integral formula. The range of crack propagation in the quasi-static fracturing stage is obtained and its distribution is plotted in polar coordinates, thus obtaining the range of carbon dioxide phase transformation-induced fracturing influence in deep vertical shafts.

2. The method for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts according to claim 1, characterized in that, This method addresses the initial geostress state prior to the dynamic impact phase, including methods for calculating the initial stress distribution: With the center of the deep borehole as the origin of the polar coordinate system and the direction of the maximum horizontal stress as the polar coordinate system... x Calculate the initial stress distribution around the borehole under horizontal ground stress: in, , They are respectively Initial radial stress and initial circumferential stress at the location; τ rθ0 for Initial shear stress at the location; and These represent the maximum and minimum horizontal in-situ stresses of the strata, respectively. The radius of the deep hole; , The radius and angle are in polar coordinates.

3. The method for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts according to claim 1, characterized in that, Calculate the impact pressure on the deep hole wall during the dynamic impact stage of carbon dioxide phase transformation-induced fracturing. The formula is: in, The impact pressure generated on the deep hole wall during the dynamic impact stage of carbon dioxide phase transformation-induced cracking. This is the factor that increases the pressure. The pressure at which carbon dioxide causes pipe rupture; The diameter of the carbon dioxide rupture tube; The diameter of the deep hole; For exponential parameters; The formula for calculating the dynamic stress distribution around the hole caused by the stress wave generated by the impact pressure is: in, , The stress waves generated by the impact pressure are located at a distance from the center of the deep hole. The dynamic radial stress and dynamic circumferential stress caused at the location; The impact pressure generated on the deep hole wall during the dynamic impact stage of carbon dioxide phase transformation-induced cracking. The radius of the deep hole; , The radius and angle are in polar coordinates.

4. The method for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts according to claim 3, characterized in that, The conditions for determining crack initiation during the dynamic impact stage are: in, This represents the total radial stress around the hole during the dynamic impact phase. for Initial circumferential stress at the location; and These represent the maximum and minimum horizontal in-situ stresses of the strata, respectively. The impact pressure generated on the deep hole wall during the dynamic impact stage of carbon dioxide phase transformation-induced cracking. The radius of the deep hole; , The radius and angle are in polar coordinates; It represents the uniaxial tensile strength of the rock.

5. The method for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts according to claim 1, characterized in that, This method calculates the quasi-static pressure caused by carbon dioxide on the borehole wall during the quasi-static fracturing stage. P The formula for 2 is: in, P 2 represents the quasi-static pressure exerted by carbon dioxide on the deep hole wall during the quasi-static fracturing stage; The attenuation coefficient of carbon dioxide gas; The pressure at which carbon dioxide causes pipe rupture; Calculation of carbon dioxide phase transformation-induced fracturing in fractures at a distance from the center of deep borehole The quasi-static radial stress and quasi-static circumferential stress caused at the location are: in, , The quasi-static pressure at a distance from the center of the deep hole are respectively The quasi-static radial stress and quasi-static circumferential stress caused at the location; P 2 represents the quasi-static pressure exerted by carbon dioxide on the deep hole wall during the quasi-static fracturing stage; The radius of the deep hole; , The radius and angle are in polar coordinates.

6. The method for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts according to claim 5, characterized in that, The formula for calculating the radial stress around the borehole during the quasi-static fracturing stage in this method is: in, σ θ2 ( r , θ The radial stress around the borehole during the quasi-static fracturing stage; for Initial circumferential stress at the location; For quasi-static pressure at a distance from the center of the deep hole Quasi-static circumferential stress caused at the location; and These represent the maximum and minimum horizontal in-situ stresses of the strata, respectively. Let be the radius of the deep hole.

7. The method for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts according to claim 6, characterized in that, The specific conditions for crack propagation in the quasi-static fracturing stage of this method are as follows: Conditions for crack propagation in the quasi-static fracturing stage K I The stress intensity factor of the crack is greater than the fracture toughness of the rock, and the formula is: in, K I Conditions for crack propagation during the quasi-static fracturing stage; The total length of the crack; σ θ2 ( r b +x , θ )for( r b +x , θ Radial stress around the borehole during the quasi-static fracturing stage at the location; This is the distance between a point on the crack and the starting point of the crack on the hole wall; K IC For the fracture toughness of the rock, take , The uniaxial tensile strength of the rock; , , is a coefficient.

8. A system for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep vertical shafts, characterized in that, include: Memory, used to store executable computer programs; A processor, when executing an executable computer program stored in a memory, implements the method for calculating the influence range of carbon dioxide phase transformation-induced fracturing in deep shafts as described in any one of claims 1 to 7.

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