A method for calculating long-distance rock jacking force in stable rock mass

Abstract

This invention discloses a method for calculating the jacking force of long-distance rock jacking in stable rock masses. The method includes analyzing the buoyancy of the slurry per unit length of the pipe section, calculating the resultant pressure in the contact zone under pipe-rock and pipe-slag contact conditions, determining the side friction resistance per unit length of the pipe section under pipe-rock contact conditions, determining the side friction resistance per unit length of the pipe section when the pipe is in contact with slag, and finally obtaining the jacking force. Considering the buoyancy effect of the slurry, the contact pressure changes caused by slag at the bottom of the pipe section, and the distribution range of the slag along the pipeline, the method determines the jacking force of long-distance rock jacking under stable surrounding rock conditions. Because the influence of both slurry and slag on the side friction resistance of the jacking pipe is considered simultaneously, this invention can more accurately calculate the jacking force of long-distance rock jacking under stable surrounding rock conditions, improving the efficiency of pipe jacking equipment and achieving safe and economical production.

Description

Technical Field

[0001] This invention relates to the field of pipe jacking engineering technology, and in particular to a method for calculating the jacking force of long-distance rock pipe jacking in stable rock masses. Background Technology

[0002] The calculation model for the jacking force of pipe jacking in general soil layers is relatively mature and has been effectively verified in many practical projects. However, when pipe jacking technology is applied to rock strata, the calculation of the jacking force mostly borrows from the calculation method for general soil layers, which produces large errors and cannot assess the actual situation on site. Therefore, the problem of calculating the jacking force of pipe jacking in rock strata urgently needs to be solved.

[0003] Patent application number CN202310391176.3 discloses a method for calculating the contact pressure of pipe jacking in strongly weathered rock masses. The method includes: selecting a target rock jacking region; performing a stress analysis on the target region; further analyzing the lateral pressure coefficient within the target region; calculating the shear stress within the target region; and obtaining a soil arch model. This method effectively calculates the pipe jacking region in strongly weathered rock masses, accurately controlling the jacking region's condition. Based on stress deflection theory, it explains the stress state of pipe jacking in strongly weathered rock masses, provides the law governing the increase in jacking force, and calculates the contact pressure and friction of pipe jacking in any strongly weathered stratum.

[0004] Patent application number CN202210781022.0 discloses a method and apparatus for calculating vertical earth pressure on the top of a pipe in trenchless pipe jacking construction. The method includes: obtaining the macroscopic parameters of the soil in the trenchless pipe jacking construction area and the over-excavation amount of the pipe jacking machine; establishing a discrete element model based on the pipeline design parameters and the macroscopic parameters of the soil, and performing numerical simulation on the soil movement process caused by the over-excavation amount to determine the development height and average width of the shear band on the top of the pipe; and calculating the vertical earth pressure on the top of the pipe in trenchless pipe jacking construction based on the macroscopic parameters of the soil, the development height and average width of the shear band on the top of the pipe.

[0005] Existing theoretical calculation formulas do not comprehensively consider the grouting effect of bentonite. Bentonite grout has two mechanisms of action during pipe jacking: lubrication and filling / support. If the grouting is effective, under stable tunnel conditions, the pressure between the pipe section and the surrounding rock is the contact pressure, allowing the grout's buoyancy to be utilized. Ignoring the buoyancy of the pipe section during calculations will result in a significant discrepancy between the theoretically calculated contact pressure and the actual pressure. Furthermore, when the pipeline is jacked in rock formations, locally detached rocks and some rock debris in front of the cutterhead seep into the annular space and concentrate under their own weight on the lower side of the pipe, forming a sediment belt. This causes contact between the pipe wall and the sediment belt, also affecting the side friction resistance of the jacking pipe.

[0006] Therefore, we propose a method for calculating the jacking force of long-distance rock jacking pipes in stable rock masses to solve the problems existing in the above situation. Summary of the Invention

[0007] To address the aforementioned problems in existing technologies, this invention provides a method for calculating the jacking force of long-distance rock jacking pipes in stable rock masses.

[0008] The technical solution of the present invention is as follows:

[0009] A method for calculating the jacking force of long-distance rock jacking pipes in stable rock masses includes:

[0010] S110 analyzes the buoyancy of the mud per unit length of the pipe section;

[0011] S120 calculates the magnitude of the resultant pressure in the contact zone under the contact conditions of pipe rock and pipe slag;

[0012] S130 determines the side friction resistance per unit length of the pipe section under the pipe-rock contact state, and determines the side friction resistance per unit length of the pipe section when the pipe section is in contact with the sediment.

[0013] S140 obtains the magnitude of the jacking force of the pipe jacking.

[0014] In the aforementioned method for calculating the jacking force of long-distance rock jacking pipes in stable rock masses, in step S110, the buoyancy force of the mud per unit length of the pipe section is:

[0015]

[0016] Integral result:

[0017]

[0018] Where H is the distance between the free liquid surface and the top surface of the pipe section; R is the pipe radius; ω is the angle of the sediment at the bottom of the pipe; γ m The value is the specific weight of the liquid; the pipe length is taken as the unit length.

[0019] In the aforementioned method for calculating the jacking force of long-distance rock jacking pipes in stable rock masses, in step S120, the resultant pressure in the pipe-rock contact zone is:

[0020] P1 = F v -F up (0)

[0021] Among them, F v For the weight of the pipeline, F up (0) is the buoyancy value of the mud when ω=0.

[0022] In the aforementioned method for calculating the jacking force of long-distance rock jacking in stable rock masses, in step S120, the resultant pressure in the pipe-slag contact zone is:

[0023]

[0024] The general relationship for contact pressure is as follows:

[0025]

[0026] -ω / 2<θ<ω / 2

[0027] Where R is the tunnel radius; p(θ) is the contact zone pressure; ξ=tan(ω / 4) is an intermediate variable;

[0028] k = tan(θ / 2), which is an intermediate variable; ω is the contact area angle;

[0029] The integral is solved using the five-point Gauss-Legendre formula for numerical integration, and P(ω) is calculated.

[0030] In the aforementioned method for calculating the jacking force of long-distance rock jacking pipes in stable rock masses, in step S130, the side friction resistance per unit length of the pipe section under the pipe-rock contact state is:

[0031] f t =f r +f w =μ r P1+τ w (πD-b r )

[0032] τ w =μ w P w +C w

[0033] Among them, f t f is the frictional resistance per unit length of pipe wall. r f is the frictional resistance per unit length of the pipe against the rock. w τ is the frictional resistance per unit length of slurry pipe. w b is the shear force of the slurry. r The pipe-rock contact width is represented by D; the outer diameter of the pipe section is represented by μ. r μ is the friction coefficient of the pipe rock. w P is the friction coefficient between the pipe and the slurry; P1 is the contact pressure between the pipe and the rock; P w C is the grouting pressure; w This refers to the cohesive force of the slurry.

[0034] The resultant pressure in the contact zone between the tubular rock and the pipe is then incorporated.

[0035]

[0036] Further substituting F up (0)=γ m πR2 , can be obtained

[0037]

[0038] In the aforementioned method for calculating the jacking force of long-distance rock jacking in stable rock masses, in step S130, the side friction resistance per unit length of the pipe section under the contact state with the slag is:

[0039] f t2 =μ a P(ω)+(πD-ωR)τ w

[0040] Where, μ a This is the coefficient of friction between the pipeline and the slag.

[0041] In the aforementioned method for calculating the jacking force of long-distance rock jacking in stable rock masses, in step S140, the jacking force is:

[0042] F = xf t2 +(Lx)f t1 +F a

[0043] Among them, F a =P w A+F c ;

[0044] Among them, F a For head resistance; F c denoted as , where is the cutter penetration resistance; A is the cutter head area; L is the jacking length; and x is the length of the sediment belt.

[0045] The present invention has the following beneficial effects: The present invention provides a method for calculating the jacking force of long-distance rock jacking in stable rock masses, taking into account the buoyancy effect of mud, the contact pressure change caused by sediment at the bottom of the pipe section, and the distribution range of sediment along the pipeline, and deriving a formula for calculating the jacking force of long-distance rock jacking under stable surrounding rock conditions; The present invention can accurately calculate the magnitude of the jacking force of medium-to-long-distance rock jacking under stable surrounding rock conditions, improve the efficiency of pipe jacking equipment, reduce calculation errors, and achieve safe and economical production. Attached Figure Description

[0046] Figure 1 This is an overall flowchart of the calculation method of the present invention;

[0047] Figure 2 This is a schematic diagram of the contact between the pipe and the sediment according to the present invention.

[0048] The reference numerals in the figure are as follows:

[0049] 1. Tunnel; 2. Mud; 3. Pipe section; 4. Sediment. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] See Figure 1 It includes the following steps:

[0052] S110 analysis of the mud buoyancy force per unit length of pipe section 3;

[0053] S120 calculates the magnitude of the resultant pressure in the contact zone under the contact conditions of pipe rock and pipe slag;

[0054] S130 determines the side friction resistance per unit length of pipe section 3 under the pipe-rock contact state, and determines the side friction resistance per unit length of pipe section 3 when the pipe section is in contact with sediment 4.

[0055] S140 obtains the magnitude of the jacking force of the pipe jacking.

[0056] Specifically, the bentonite grout plays a role in filling and supporting the tunnel during the pipe jacking process. If the grouting effect is good and the tunnel 1 is stable, the pressure between the pipe section 3 and the surrounding rock is the contact pressure, and the buoyancy effect of the grout 2 will be brought into play. At the same time, when the pipe section 3 is jacked in the rock strata, the rocks that have been partially detached from the tunnel 1 and some rock debris in front of the cutterhead seep into the annular space and concentrate on the lower side of the pipe section 3 under its own weight, forming sediment 4. This causes the pipe wall to come into contact with the sediment 4, which will affect the side friction resistance of the pipe jacking. Considering the influence of the grout 2 and the sediment 4 at the bottom of the pipe section 3 on the friction resistance of the pipe section 3, the calculation results of the pipe jacking force are more accurate, and the design and construction of the pipe jacking are more reasonable, safe and economical.

[0057] Specifically, S110 analyzes the buoyancy of the mud 2 per unit length of pipe section 3. Considering the presence of mud 2 in the annular gap, the mud 2 will generate buoyancy on pipe section 3. In actual long-distance rock jacking projects, there is often sediment 4 at the bottom of pipe section 3, which prevents the bottom of pipe section 3 from experiencing buoyancy. Therefore, the buoyancy of pipe section 3 under different angles of sediment 4 is as follows:

[0058] Assume the distance from the liquid free surface to the top surface of pipe section 3 is H, the radius of pipe section 3 is R, the angle of the sediment at the bottom of the pipe is ω, the pipe length is taken as unit length, and the specific weight of the liquid is γ. m ;

[0059] The head height at the bottom of pipe section 3 where it contacts the liquid is H + R + Rcosδ, the surface area of ​​the infinitesimal segment of pipe section 3 is Rdδ, and the vertical force exerted by the liquid on this infinitesimal segment is:

[0060] ΔF up =γ m (H+R+Rcosδ)Rdδcosδ,

[0061] Integrating the vertical liquid force acting on pipe section 3 above ω, and considering symmetry, we get:

[0062]

[0063] Integral result:

[0064]

[0065] Specifically, S120 calculates the magnitude of the resultant pressure in the contact zone under the contact conditions of pipe rock and pipe slag. During long-distance jacking, there will be periodic over-excavation and under-excavation phenomena. In rock strata, the rock fragments and slag generated by the cutting tools in front of the excavation cannot completely enter the gaps on the cutterhead panel. Some rocks and debris seep into or are carried into the annular space between pipe section 3 and the hole, and most of them are deposited below the pipe under their own weight.

[0066] When the jacking pipe comes into contact with the rock strata, if the tunnel 1 remains stable after excavation, then the pipe section 3 will be in point or line contact with the rock under the action of its own weight and buoyancy in the vertical direction. Therefore, the resultant pressure in the pipe-rock contact zone is:

[0067] P1 = F v -F up (0)

[0068] like Figure 2 Due to the rough surface of sediment 4, the contact between sediment 4 and pipe section 3 mainly involves localized point contact between irregular stones and the pipe wall. The pressure within the contact area is complex. To simplify the calculation, a macroscopic contact calculation model is adopted, and the contact pressure is calculated with reference to the Persson contact model. The calculation formula is as follows:

[0069]

[0070] -ω / 2<θ<ω / 2

[0071] Where R is the tunnel radius; p(θ) is the contact zone pressure; ξ=tan(ω / 4), is an intermediate variable; k=tan(θ / 2), is an intermediate variable; ω is the contact zone angle;

[0072] Integrating, the resultant pressure in the contact zone of the slag pipe is:

[0073]

[0074] The integral is solved using the five-point Gauss-Legendre formula for numerical integration, and P(ω) is calculated.

[0075] Specifically, S130 determines the side friction resistance per unit length of pipe section 3 under the pipe-rock contact state, and determines the side friction resistance per unit length of pipe section 3 when pipe section 3 is in contact with sediment 4.

[0076] Ignoring the deformation of the surrounding rock itself, when the pipe is jacked in the rock strata, the side friction resistance per unit length of pipe wall consists of the rock friction resistance per unit length of pipe and the grout friction resistance per unit length of pipe. The calculation formula is as follows:

[0077] f t =f r +f w =μ r P1+τ w (πD-b r )

[0078] τ w =μ w P w +C w

[0079] Among them, f t f is the frictional resistance per unit length of pipe wall. r f is the frictional resistance per unit length of the pipe against the rock. w τ is the frictional resistance per unit length of slurry pipe. w b is the shear force of the slurry. r The pipe-rock contact width is represented by D; the outer diameter of the pipe section is represented by μ. r μ is the friction coefficient of the pipe rock. w P is the friction coefficient between the pipe and the slurry; P1 is the contact pressure between the pipe and the rock; P w C is the grouting pressure; w This refers to the cohesive force of the slurry.

[0080] Incorporating the resultant pressure in the pipe-rock contact zone, the side friction resistance per unit length of pipe section 3 under pipe-rock contact conditions is as follows:

[0081] f t1 =μ r (F v -F up (0))+2πRτ w

[0082] Further substituting F up (0)=γ m πR 2 , can be obtained

[0083] f t1 =μ r(F v -γ m πR 2 )+2πRτ w

[0084] Incorporating the combined pressure in the contact zone of pipe slag 4, the side friction resistance per unit length of pipe section 3 under the contact state of pipe slag 4 is:

[0085] f t2 =μ a P(ω)+(πD-ωR)τ w

[0086] Where, μ a The friction coefficient between pipe section 3 and the slag is given.

[0087] Specifically, S140 obtains the jacking force. Assuming the jacking length is L and the length of the sediment belt is x, the corresponding jacking force calculation formula is:

[0088] F = xf t2 +(Lx)f t1 +F a

[0089] Among them, F a =P w A+F c ;

[0090] Among them, F a For head resistance; F c A represents the tool penetration resistance; A is the area of ​​the tool disc.

[0091] In this invention, by simultaneously considering the influence of mud and sediment on the side friction resistance of the jacking pipe, the invention can more accurately calculate the jacking force of long-distance rock jacking under stable surrounding rock conditions, thereby improving the efficiency of the jacking equipment and achieving safe and economical production.

[0092] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for calculating the jacking force of long-distance rock jacking pipes in stable rock masses, characterized in that: Includes the following steps: S110. Analyze the buoyancy of the mud per unit length of the pipe section; S120. Calculate the magnitude of the resultant pressure in the contact zone under the contact conditions of pipe rock and pipe slag. S130. Determine the side friction resistance per unit length of the pipe section under the pipe-rock contact state, and determine the side friction resistance per unit length of the pipe section when the pipe section is in contact with the sediment. S140, Obtain the magnitude of the jacking force of the pipe jacking; In step S110, the buoyancy of the mud is: Integral result: Where H is the distance between the free liquid surface and the top surface of the pipe section; R is the pipe radius; The angle of the sediment at the bottom of the pipe; The specific gravity of the liquid is taken as the unit length; the pipe length is taken as the unit length. In step S120, the resultant pressure in the pipe-rock contact zone is: in, Due to the weight of the pipeline, for The mud buoyancy value when =0; In step S120, the resultant pressure in the slag contact zone is: The general relationship for contact pressure is as follows: in, The radius of the tunnel; For the contact area pressure; , which is an intermediate variable; , which is an intermediate variable; For the contact area angle; In step S130, the calculation steps for the side friction resistance per unit length of the pipe section under the pipe-rock contact state are as follows: in, The side friction resistance per unit length of pipe wall. The frictional resistance per unit length of the pipe against the rock. The frictional resistance per unit length of slurry pipe. For the shear force of the slurry, The contact width between the pipe and the rock is [missing information]. The outer diameter of the pipe section. For the friction coefficient of the pipe rock, The coefficient of friction between the pipe and the slurry. For the contact pressure between the tubular rock and the pipe, For grouting pressure, For the cohesive force of the slurry; The resultant pressure in the contact zone between the tubular rock and the pipe is then incorporated. Further substitution = , can be obtained ； In step S130, the calculation steps for the side friction resistance per unit length of the pipe section under the pipe slag contact state are as follows: in, This is the coefficient of friction between the pipeline and the slag. In step S140, the jacking force of the pipe is: in, For head-on resistance, For tool penetration resistance The area of ​​the cutter head, The jacking length is... This represents the length of the sediment belt.

2. The method for calculating the jacking force of long-distance rock jacking pipes in stable rock masses according to claim 1, characterized in that: The The integral solution is obtained by using the five-point Gauss-Legendre formula for numerical integration.

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