Stability fluid-solid coupling analysis method for shaft wellbore based on aquifer hydrophobicity

Abstract

The present application belongs to the field of well and roadway stability analysis, and particularly relates to a vertical shaft stability fluid-solid coupling analysis method based on aquifer hydrophobicity; the method comprises calculating the equivalent stress on the shaft wall under the sliding limit condition based on the shaft wall limit additional axial stress, shaft wall initial axial stress and tangential stress on the inner side of the shaft wall; calculating the shaft wall limit bearing strength based on the compressive strength of concrete and steel in the shaft wall and the steel content of the shaft wall vertical reinforcement; if the equivalent stress on the shaft wall under the sliding limit condition is less than the shaft wall limit bearing strength, calculating the overburden stratum free subsidence amount critical value under the critical state of relative sliding between the overburden stratum and the shaft wall, otherwise, calculating the overburden stratum free subsidence amount as the overburden stratum free subsidence amount critical value when the shaft wall is damaged; taking the smaller value of the sum as the final critical value. The present application provides a vertical shaft stability analysis method with the overburden stratum free subsidence amount as an index, and realizes the quantitative evaluation of the vertical shaft stability.

Description

Technical Field

[0001] This invention belongs to the field of shaft stability analysis, specifically a fluid-structure interaction analysis method for vertical shaft stability based on the hydrophobicity of aquifers. Background Technology

[0002] Vertical shafts serve vital functions such as transporting equipment and providing ventilation, acting as crucial passageways in coal mining. These shafts pass through aquifers within loose strata. During construction and operation, external factors can cause aquifer drainage, leading to a decrease in pore water pressure and subsequent aquifer compression, resulting in overlying strata subsidence. During this subsidence, the shaft walls exert constraints, creating interaction forces that generate additional stress on the shaft walls. This additional stress, combined with the shaft wall's own weight, ground pressure, and other stresses, can easily trigger instability accidents such as shaft wall rupture. Current vertical shaft stability analysis methods often consider only ground pressure, neglecting stress changes and strata subsidence caused by aquifer drainage. They also fail to adequately consider fluid-structure interaction effects and lack quantitative logical relationships between various physical quantities, resulting in significant errors in the analysis results and hindering effective guidance for practical engineering projects. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes a fluid-structure interaction analysis method for vertical shaft stability based on aquifer hydrophobicity, comprising: Calculate the equivalent stress on the wellbore under the slip limit condition:

[0004] In the formula, This represents the equivalent stress on the wellbore under the sliding limit condition. Apply axial stress to the ultimate wellbore; This represents the initial axial stress of the wellbore. This represents the tangential stress on the inner side of the well wall; all units are in MPa. Calculate the ultimate bearing strength of the wellbore Unit: MPa; like The critical value of free settlement of the overlying strata under the critical state of relative sliding between the overlying strata and the wellbore is calculated based on the following formula. :

[0005] In the formula, K is the comprehensive settlement coefficient of the overlying strata. R is the outer radius of the well wall, in meters; R0 is the inner radius of the well wall, in meters; H is the thickness of the overlying strata, in meters. Es is the average compressive modulus of the aquifer, MPa, and h is the thickness of the aquifer, m. Represents the average long-term shear modulus of the overlying strata, in MPa; , Let be the long-term shear modulus of the i-th soil layer in the overlying strata, in MPa; The thickness of the i-th soil layer in the overlying strata is m; n represents the number of layers. The ratio can be obtained by looking up the Bessel function table; 'a' is the well wall stiffness conversion factor, which is taken by comprehensively considering the differences in elastic modulus of different layers of the well wall. like ≥ ,make Solving the following equation for the free settlement of the overlying strata gives the critical value of the free settlement of the overlying strata at the point of wellbore failure. :

[0006] In the formula, The free subsidence of the overlying strata is expressed in meters (m); the corresponding... , The unit is m; The equivalent stress on the well wall when the well wall fails is expressed in MPa.

[0007] Preferably, the formula for calculating the initial axial stress of the wellbore is:

[0008] In the formula, N is the total weight of the well wall and its auxiliary facilities, in tons.

[0009] Preferably, the formula for calculating the tangential stress on the inner side of the well wall is as follows:

[0010] In the formula, P is the lateral ground pressure acting on the outer wall of the well, in MPa.

[0011] The preferred formula for calculating the ultimate additional axial stress of the wellbore is as follows:

[0012] In the formula, The earth pressure acting on the well wall, in MPa; θ is the internal friction angle of the overlying strata, °; C is the cohesion of the overlying strata, MPa.

[0013] The preferred formula for calculating the ultimate bearing strength of the wellbore is as follows:

[0014] In the formula, R a R g , respectively, represent the compressive strength of concrete and steel in the well wall, in MPa; μ is the steel content of the vertical reinforcement in the well wall.

[0015] Preferably, the formula for calculating the wellbore stiffness conversion factor is as follows:

[0016] In the formula, A1, A2, and A3 are the cross-sectional areas of the 1st, 2nd, and 3rd well walls from the inside out, respectively, in meters. 2 E1, E2, and E3 are the elastic moduli of the 1st, 2nd, and 3rd well walls from the inside out, respectively, in MPa.

[0017] The beneficial technical effects of the present invention are as follows: (1) The present invention comprehensively considers various factors affecting the stability of the vertical shaft, analyzes in detail the stress of the shaft wall during the settlement of the overlying strata, and provides a method for analyzing the stability of the vertical shaft with the free settlement of the overlying strata as an indicator, thereby realizing the quantitative evaluation of the stability of the vertical shaft, and the evaluation indicators are easy to obtain.

[0018] (2) This invention takes the change in pore water pressure caused by the hydrophobicity of the aquifer as the starting point, links the change in the aquifer head with the deformation of the overlying strata, establishes the coupling relationship between water flow and stress, and gives a direct relationship formula between the additional axial stress of the well wall and the change in the aquifer head height, thus solving the problem of the existing method separating hydrological and mechanical effects.

[0019] (3) This invention fully considers the possible states of the shaft during the settlement of the overlying strata, analyzes two situations: plastic sliding between the shaft wall and the overlying strata and shaft wall failure, and provides calculation methods for the critical settlement amount of each situation, so as to eliminate the influence of different overlying strata characteristics as much as possible, and has a wide range of engineering applications. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the radial force analysis of the fluid-structure interaction for the stability of the vertical shaft according to the present invention; Figure 2 This is a schematic diagram of the axial force analysis of the stability of the vertical shaft under fluid-structure interaction according to the present invention. Detailed Implementation

[0021] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0022] This invention proposes a fluid-structure interaction analysis method for vertical shaft stability based on aquifer hydrophobicity, such as... Figures 1-2 As shown, it includes the following steps: S1: Determine the aquifer compression rate like Figure 1As shown, when an aquifer becomes hydrophobic, its thickness decreases due to compression. In coal mines, aquifer hydrophobicity is mainly caused by the fractures created during mining, which allow water to flow through these fractures into the goaf. The total stress borne by the aquifer originates from the gravity of the overlying strata and its own weight, and is a constant value. This stress is borne by the soil skeleton and the pore water within the soil skeleton. The pore water bears the pore water pressure, while the soil skeleton bears the effective soil stress. The pore water pressure can be considered as hydrostatic pressure, which is the product of the unit weight of water and the water head. Taking the unit weight of water as 10 kN / m³, the effective soil stress after hydrophobicity is:

[0023] In the formula, The total stress borne by the aquifer, in MPa; The effective stress of the soil is expressed in MPa. Pore ​​water pressure, MPa; The water head height of the aquifer is in meters (m).

[0024] Calculate the change in effective stress in the soil when the aquifer is drained:

[0025] In the formula, The effective stress change in the soil is expressed in MPa. The change in aquifer head height is expressed in meters (m); H w0 H we These are the aquifer head heights before and after drainage, respectively, in meters (m).

[0026] After the aquifer is drained, the pore water pressure decreases significantly, while the effective stress of the soil increases. The decrease in pore water pressure equals the increase in effective soil stress. This increase in effective soil stress leads to overall compression of the aquifer. Under conditions without wellbore constraint, the free compressibility of the aquifer is:

[0027] In the formula, is the free compressibility of the aquifer, which is also the free subsidence of the overlying strata, in meters; Es is the average compressibility modulus of the aquifer, in MPa; h is the thickness of the aquifer, in meters.

[0028] S2: Determine the shear stress of the overlying formation near the wellbore. After the aquifer is drained, the stress conditions of the wellbore itself and the surrounding overlying strata change. For example... Figure 1 As shown, in the overlying strata, an annular unit A with a width of dr and a thickness of H is extracted radially from the shaft at a distance r from the shaft centerline. The shear stress acting on the inner side of the annular unit A due to overlying strata subsidence is... Upward; the shear stress acting on the outside of the annular unit A is Downward; the supporting reaction force of the aquifer on the annular unit A is Q. z Upward; based on the equilibrium condition that the total force on the annular element A in the vertical direction is zero, we can obtain:

[0029] In the formula, r is the distance from the centerline of the vertical shaft, in meters; H is the thickness of the overlying strata, in meters. The shear stress acting on the inner side of the annular element A is expressed in MPa. Q is the shear stress acting on the outside of the annular element A, in MPa; z ρ represents the supporting reaction force of the aquifer on annular unit A, in MPa.

[0030] Assuming the overlying strata are a standard viscoelastic body, and neglecting the rate of change of shear stress and shear strain over time, then

[0031] In the formula, The long-term shear modulus of the overlying strata represents the stiffness of the overlying strata under long-term shear stress and reflects the ability of the overlying strata to resist shear deformation over a long period of time, in MPa. The shear strain is located inside the annular unit A; w is the vertical displacement of the overlying strata confined by the wellbore, which is equal to the free settlement of the overlying strata. Subtract the actual settlement of the overlying strata, S, m, under the constraint of the wellbore.

[0032] Determine the supporting reaction force of the aquifer on annular unit A:

[0033] Substituting formulas (5) and (6) into formula (4), ignoring the higher-order terms of dr and simplifying, we get:

[0034] In the formula, , This represents the average long-term shear modulus of the overlying strata, expressed in MPa.

[0035] Formula (7) is the Bessel equation, and its general solution is as follows:

[0036] In the formula, , These are the zeroth-order, type I and type II dummy variables, respectively, Bessel functions. and These are constants to be determined.

[0037] If the wellbore's constraint on the distant overlying strata is negligible, then... Assuming there is no vertical relative sliding between the wellbore and the overlying formation, then ; The value is the actual settlement of the overlying strata at the wellbore, in meters; from this, we can conclude that:

[0038] In the formula, K1(gr) is a first-order type II dummy variable Bessel function.

[0039] Due to the actual subsidence of the overlying strata at the well wall Much smaller than the free subsidence of the overlying strata Therefore, the actual settlement of the overlying strata at the wellbore can be ignored. Formula (9) can be simplified to:

[0040] The overlying strata are in an elastic state during the early stages of subsidence, with shear stress... Less than its limit value As the subsidence of the overlying strata increases, the shear stress... As shear stress increases, Increase to ultimate shear stress At that time, shear stress Reaching the limit state, thereafter shear stress The pressure will no longer increase, and at the wellbore, the subsequent phenomenon will be relative sliding between the wellbore and the overlying strata. This relative sliding can be considered as being caused by plastic failure of the soil. According to the Mohr-Coulomb strength criterion, the ultimate shear stress between the wellbore and the overlying strata is obtained. for:

[0041] In the formula, The earth pressure acting on the well wall, in MPa; θ is the internal friction angle of the overlying strata, °; C is the cohesion of the overlying strata, MPa.

[0042] S3: Determine the additional axial stress on the wellbore. Along the axial direction (Z direction) of the vertical shaft, on the outer surface of the shaft wall, at a distance from the ground surface If a circular infinitesimal element B of thickness dz is taken out, then the additional axial force acting on the circular infinitesimal element B is:

[0043] In the formula, This represents the additional axial force acting on the circular infinitesimal segment B, in units of MN. Let B be the depth of the circular infinitesimal segment. ≤H, m; R is the outer radius of the well wall, m.

[0044] Simultaneous formulas (10), (12), It is a constant value at r=R, and does not change with the depth of the overlying strata, but the long-term shear modulus of the overlying strata... It may vary with the depth of the overlying strata, so we retain the integral sign and get:

[0045] To more accurately reflect the differences in overlying strata at different depths, the average long-term shear modulus of the overlying strata is introduced. In this case, the long-term shear modulus of the overlying strata can be extracted from the integral, yielding:

[0046] In the formula, From the surface to the deep The average long-term shear modulus of the overlying strata, in MPa.

[0047] Determine the additional axial stress :

[0048] In the formula, R0 is the cross-sectional area of ​​the well wall; R0 is the inner radius of the well wall, in meters; a is the well wall stiffness reduction factor, which is taken to comprehensively consider the differences in elastic modulus of different layers of the well wall, and the calculation method is as follows:

[0049] In the formula, A1, A2, and A3 are the cross-sectional areas of the 1st, 2nd, and 3rd well walls from the inside out, respectively, in meters. 2 E1, E2, and E3 are the elastic moduli of the 1st, 2nd, and 3rd well walls from the inside out, respectively, in MPa.

[0050] S4: Vertical Shaft Stability Analysis Whether a vertical shaft becomes unstable depends on the ultimate bearing capacity of the shaft wall and the equivalent stress acting on the shaft wall; shear stress. Free compressibility of aquifer The shear stress increases with the increase of the shear stress. Increase to ultimate shear stress At this point, the limiting state is reached, and thereafter it will not increase further, manifesting as relative sliding between the wellbore and the overlying formation. Therefore, under shear stress... During the increase of shear stress, there are two situations. The first situation is shear stress. Increase to ultimate shear stress At this time, the equivalent stress borne by the wellbore is still less than the bearing capacity of the wellbore, which manifests as relative sliding between the wellbore and the overlying formation. The second situation is under shear stress. Increase to ultimate shear stress Previously, the equivalent stress on the wellbore exceeded its bearing capacity, causing it to collapse. In this situation, shear stress control is essential. The critical value at which wellbore failure occurs. This affects shear stress. The core factor is the free compressibility of the aquifer. This refers to the free subsidence of the overlying strata. The subsidence of the overlying strata can be obtained through measurement, thus allowing the determination of a specific free subsidence of the overlying strata. Critical values ​​indirectly determine shear stress Critical value.

[0051] S41: Calculate the equivalent stress on the wellbore under the slip limit condition. (1) Calculate the tangential stress at the well wall The initial stress on the wellbore caused by lateral ground pressure can be determined according to the theory of thick-walled cylinders in elasticity. According to Lamé's formula, for a thick-walled cylinder subjected only to lateral ground pressure P, the stress includes radial stress. and tangential stress At the most dangerous inner side of the well wall, i.e., where r=R0, the radial stress is... The tangential stress is 0, and the tangential stress is:

[0052] In the formula, P represents the tangential stress on the inner side of the well wall, in MPa, and P represents the lateral ground pressure acting on the outer wall of the well, in MPa.

[0053] (2) Calculate the axial stress of the well wall The stress acting on the well wall includes additional axial stress and initial axial stress; before the aquifer is drained, the weight of the well wall itself and its auxiliary facilities (such as well towers, well equipment, etc.) already act on the well wall, resulting in the following initial axial stress:

[0054] In the formula, The initial axial stress of the well wall is MPa; the coefficient 0.01 is the result of unit conversion; N is the total weight of the well wall and its auxiliary facilities, t.

[0055] By combining formulas (11) and (15), the ultimate additional axial stress of the wellbore can be determined:

[0056] In the formula, The ultimate additional axial stress on the wellbore is measured in MPa.

[0057] (3) Calculate the equivalent stress on the wellbore under the sliding limit condition. According to the von Mises stress calculation formula = + , = ≈0, so the equivalent stress is calculated as follows:

[0058] In the formula, The equivalent stress on the wellbore under the sliding limit condition is expressed in MPa.

[0059] S42: Calculate the ultimate bearing strength of the wellbore.

[0060] In the formula, R represents the ultimate bearing strength of the wellbore, in MPa; a R g , respectively, represent the compressive strength of concrete and steel in the well wall, in MPa; μ is the steel content of the vertical reinforcement in the well wall.

[0061] S43: Determine the critical value of free subsidence of the overlying strata. Compare the equivalent stress on the wellbore under the slip limit condition. Ultimate bearing capacity of the well wall ,like ≥ This indicates that before plastic sliding occurred between the wellbore and the overlying strata, the ultimate bearing capacity of the wellbore was insufficient to support the additional stress caused by the subsidence of the overlying strata, and the wellbore had already been crushed. At this point, it is necessary to determine the amount of free subsidence of the overlying strata at the time that caused the wellbore failure. Critical value; if This indicates that during the settlement of the overlying strata, the wellbore will not be crushed; instead, plastic sliding will occur between the wellbore and the overlying strata. However, although the wellbore is not crushed, it is in a very dangerous state. Under the influence of other external factors, the wellbore may become unstable at any time. At this point, it is necessary to determine the amount of free settlement of the overlying strata at the critical state of relative sliding between the overlying strata and the wellbore. Critical value.

[0062] (1) Establish the relationship between additional axial stress and free settlement of overlying strata. According to formula (15), take , ,have to

[0063] In the formula, K is the comprehensive settlement coefficient of the overlying strata. , Let be the long-term shear modulus of the i-th soil layer in the overlying strata, in MPa; The thickness of the i-th soil layer in the overlying strata is m; n represents the number of layers. The ratio can be obtained by looking up the Bessel function table.

[0064] (2) Calculate the critical settlement of the strata under the two conditions. like Calculate the free settlement of the overlying strata under the critical state of relative sliding between the overlying strata and the wellbore. critical value When the additional axial stress reaches the limit, the additional axial stress... When the wellbore and the overlying formation are in a critical state of relative sliding, then:

[0065] like ≥ Calculate the free settlement of the overlying strata when the wellbore fails. critical value ,make have to:

[0066] Solve for this free subsidence of the overlying strata. The equation has a positive root that represents the critical value of free subsidence of the overlying strata when the wellbore fails. ;in, The equivalent stress on the well wall when the well wall fails is expressed in MPa.

[0067] Subsequent measurements of free settlement of the overlying strata And keep it below the final critical value, and take reinforcement measures when it approaches the final critical value.

[0068] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A fluid-structure interaction analysis method for vertical shaft stability based on aquifer hydrophobicity, characterized in that, include: Calculate the equivalent stress on the wellbore under the slip limit condition: ； In the formula, This represents the equivalent stress on the wellbore under the sliding limit condition. Apply axial stress to the ultimate wellbore; This represents the initial axial stress of the wellbore. This represents the tangential stress on the inner side of the well wall; all units are in MPa. Calculate the ultimate bearing strength of the wellbore Unit: MPa; like The critical value of free settlement of the overlying strata under the critical state of relative sliding between the overlying strata and the wellbore is calculated based on the following formula. : ； In the formula, K is the comprehensive settlement coefficient of the overlying strata. R is the outer radius of the well wall, in meters; R0 is the inner radius of the well wall, in meters; H is the thickness of the overlying strata, in meters. Es is the average compressive modulus of the aquifer, MPa, and h is the thickness of the aquifer, m. Represents the average long-term shear modulus of the overlying strata, in MPa; , Let be the long-term shear modulus of the i-th soil layer in the overlying strata, in MPa; The thickness of the i-th soil layer in the overlying strata is given in meters (m). n represents the number of layers; The ratio can be obtained by looking up the Bessel function table; 'a' is the well wall stiffness conversion factor, which is taken by comprehensively considering the differences in elastic modulus of different layers of the well wall. like ≥ ,make Solving the following equation for the free settlement of the overlying strata gives the critical value of the free settlement of the overlying strata at the point of wellbore failure. : ； In the formula, The free subsidence of the overlying strata is expressed in meters (m); the corresponding... , The unit is m; The equivalent stress on the wellbore when it fails is expressed in MPa.

2. The fluid-structure interaction analysis method for vertical shaft stability based on aquifer hydrophobicity as described in claim 1, characterized in that, The formula for calculating the initial axial stress of the wellbore is: ； In the formula, N is the total weight of the well wall and its auxiliary facilities, in tons.

3. The fluid-structure interaction analysis method for vertical shaft stability based on aquifer hydrophobicity as described in claim 2, characterized in that, The formula for calculating the tangential stress on the inner side of the well wall is as follows: ； In the formula, P is the lateral ground pressure acting on the outer wall of the well, in MPa.

4. The fluid-structure interaction analysis method for vertical shaft stability based on aquifer hydrophobicity as described in claim 3, characterized in that, The formula for calculating the ultimate additional axial stress in the wellbore is as follows: ； In the formula, The earth pressure acting on the well wall, in MPa; θ is the internal friction angle of the overlying strata, °; C is the cohesion of the overlying strata, MPa.

5. The fluid-structure interaction analysis method for vertical shaft stability based on aquifer hydrophobicity as described in claim 4, characterized in that, The formula for calculating the ultimate bearing strength of the well wall is as follows: ； In the formula, R a R g , respectively, represent the compressive strength of concrete and steel in the well wall, in MPa; μ is the steel content of the vertical reinforcement in the well wall.

6. The fluid-structure interaction analysis method for vertical shaft stability based on aquifer hydrophobicity as described in claim 5, characterized in that, The formula for calculating the wellbore stiffness conversion factor is as follows: ； In the formula, A1, A2, and A3 are the cross-sectional areas of the 1st, 2nd, and 3rd well walls from the inside out, respectively, in meters. 2 E1, E2, and E3 are the elastic moduli of the 1st, 2nd, and 3rd well walls from the inside out, respectively, in MPa.

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