A vertical lifting displacement calculation method for lifting a roadbed by a bag pipe method

Abstract

This invention belongs to the field of roadbed uneven settlement treatment technology, and discloses a method for calculating the vertical lift displacement of roadbed using the bladder-tube grouting method, including: calculating the vertical lift displacement at a depth directly below the roadbed settlement section. H Horizontal layout n Root capsule; Determine the radius of the plastic zone of the soil surrounding the capsule after grouting. R p By utilizing the continuity condition of stress and displacement at the boundary of the elastoplastic region, the radial stress σ at the boundary of the elastoplastic region is determined. Rp In the elastic region, the problem of bladder expansion in a semi-infinite space is equivalent to the problem of pore expansion in an infinite elastic body. The displacement superposition method is used to calculate the soil displacement field caused by grouting of a single bladder. Based on the superposition principle of elasticity, the following calculations are performed. n Vertical displacement distribution on the roadbed surface under the combined action of root-capsule tubes. The advantages of this invention are: it accurately considers both the plastic zone of the soil induced by grouting and the free boundary conditions of the semi-infinite body, providing a more accurate and reliable theoretical basis for engineering design.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of subgrade uneven settlement treatment, and in particular to a vertical lifting displacement calculation method for subgrade lifting by capsule pipe grouting. BACKGROUND

[0002] Subgrade uneven settlement is a common disease in transportation infrastructure, which seriously affects driving safety and comfort. In dealing with such diseases, the capsule pipe grouting technology can be used to solve the problem. This technology has the advantages of strong engineering adaptability, high adjustment precision and high construction efficiency. By horizontally burying a capsule pipe in the soil under the settlement subgrade and injecting grout, pressure is exerted on the surrounding soil by the expansion of the capsule pipe, thereby generating lifting force to correct the subgrade settlement.

[0003] However, the core difficulty of this technology is how to accurately calculate the displacement caused by grouting lifting in advance, so as to design the grouting pressure and capsule pipe arrangement in detail. At present, in the theoretical research and engineering practice in this field, the displacement prediction mainly faces the following two key problems:

[0004] First, the calculation of the plastic zone of the soil during grouting. The grouting pressure of the capsule pipe is usually enough to make the surrounding soil enter the yield state and form a plastic zone. Many existing calculation methods often assume that the soil is a purely elastic material or are derived only in the framework of elastic theory in order to simplify. This method seriously ignores the influence of plastic deformation, resulting in a significant deviation between the theoretically predicted displacement and the actual lifting amount when the grouting pressure is high, which cannot accurately guide the construction.

[0005] Second, improper handling of the boundary conditions in the semi-infinite space. In actual engineering, the capsule pipe has a limited depth, and the surface of the soil is a free boundary. Some theoretical models simplify the problem as a hole expansion problem in an "infinite body" for mathematical convenience, which completely ignores the boundary effect brought by the existence of the free surface. When the range of the plastic zone generated by the expansion of the capsule pipe is close to the depth of the capsule pipe, this simplification will introduce a large error. Although some studies have tried to directly solve the problem in the semi-infinite space, the control equation is complex, and it is difficult to obtain an analytical solution that is convenient for engineering application, especially when analyzing the stress superposition effect of multiple capsule pipes acting together.

[0006] In summary, the existing technology lacks a capsule pipe grouting displacement calculation method that can simultaneously consider the elastic-plastic deformation of the soil and the free boundary of the semi-infinite space. This theoretical deficiency makes engineers often rely on experience or rough estimates when designing, resulting in inaccurate lifting control, either insufficient lifting requiring multiple grouting or excessive lifting causing new road damage, increasing engineering costs and risks. SUMMARY

[0007] The purpose of this invention is to provide a method for calculating the vertical lifting displacement of roadbeds using the grouting method in order to address the shortcomings of the prior art. This method accurately considers both the plastic zone of the soil and the free boundary conditions of the semi-infinite body induced by grouting, providing a more accurate and reliable theoretical basis for engineering design.

[0008] The objective of this invention is achieved through the following technical solutions:

[0009] A method for calculating the vertical displacement of roadbed raised by grouting using the tube method includes the following steps:

[0010] S1: Depth directly below the roadbed settlement section H Horizontal layout n Root capsule canal;

[0011] S2: Based on the designed expansion radius of the cyst tube R Grouting pressure p In addition to soil parameters, the radius of the plastic zone of the soil around the grouting tube after grouting is determined. R p The soil parameters include the soil elastic modulus. E Poisson's ratio of soil μ Soil cohesion c、 soil internal friction angle ϕ ;

[0012] S3: Radius of the plastic zone of the soil surrounding the grouting tube after injection R p By utilizing the continuity condition of stress and displacement at the boundary of the elastoplastic region, the radial stress at the boundary of the elastoplastic region can be determined. ;

[0013] S4: In the elastic zone, the problem of tube expansion in a semi-infinite space is equivalent to the problem of pore expansion in an infinite elastic body. The displacement field caused by grouting of a single tube is calculated by the displacement superposition method. The displacement superposition method includes: decomposing the original displacement field into a first displacement field of the pore under internal pressure in the infinite elastic body and a second displacement field used to satisfy the boundary conditions of the free surface, and superimposing the two.

[0014] S5: Based on the soil displacement field caused by single-cell grouting obtained in step S4, calculate the displacement field using the superposition principle of elasticity. n Vertical displacement distribution on the roadbed surface under the combined action of root sacs and tubes.

[0015] In step S2, the radius of the plastic zone of the soil surrounding the grouting tube after grouting. R p Calculated using the following formula:

[0016] ;

[0017] ;

[0018] wherein:

[0019] R p is in meters;

[0020] R is in meters;

[0021] p is in pascal;

[0022] c is in pascal;

[0023] ϕ is in degree;

[0024] I r is a stiffness index, dimensionless;

[0025] E is in pascal;

[0026] μ dimensionless.

[0027] In step S3, the radial stress at the elastic-plastic boundary is calculated by the following equation:

[0028] ;

[0029] wherein: is in pascal.

[0030] In step S4, the vertical displacement of an arbitrary point on the subgrade surface under the action of a single capsule tube (x,0) is calculated by the following equation:

[0031] ;

[0032] wherein:

[0033] is in meters;

[0034] is the analytical solution of the vertical displacement of the first displacement field, in meters; is the analytical solution of the vertical displacement of the second displacement field, in meters; the analytical solution of the vertical displacement of the first displacement field and the analytical solution of the vertical displacement of the second displacement field are both taken as absolute values;

[0035] x, H are all in meters.

[0036] In step S5, the vertical displacement of an arbitrary point on the subgrade surface under the action of a plurality of capsule tubes nUnder the action of root canals, any point on the roadbed surface (x,0) The total vertical displacement is calculated using the following formula:

[0037] ;

[0038] In the formula:

[0039] For each cyst tube at any point on the roadbed surface (x,0) The vector sum of the resulting displacements;

[0040] u z (x,0) , The units are all meters;

[0041] x m For the first m The horizontal coordinates of the root sac canal, in meters.

[0042] The advantages of this invention are:

[0043] 1. High calculation accuracy: The displacement calculation systematically considers both the elastoplastic behavior of the soil and the free boundary effect of the semi-infinite space, which fundamentally overcomes the huge errors brought about by traditional elastic theory or infinite body assumption, making the displacement prediction results more in line with engineering practice.

[0044] 2. Solid theoretical basis: It provides a complete analytical derivation process from single-bladder to multi-bladder and from soil interior to site displacement. The logic is rigorous, providing a solid theoretical foundation for bladder grouting and lifting technology.

[0045] 3. Strong guidance: The analytical solutions provided are concise and easy to apply in engineering. They can be directly used to guide engineering design, such as optimizing the spacing and burial depth of the bladder tubes and predicting the uplift under different grouting pressures, thereby achieving precise and controllable subgrade settlement control.

[0046] 4. Broad application prospects: This calculation method is not only applicable to roadbed uplift, but its core theory can also be extended to other geotechnical engineering problems involving the expansion or contraction of underground cavities. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the steps for calculating the vertical lifting displacement of the roadbed using the grouting method of the bladder tube method of the present invention;

[0048] Figure 2 This is a schematic diagram of the cross section of the roadbed raised by grouting with multiple tubes according to the present invention;

[0049] Figure 3 This is a diagram showing the placement of the capsule tube in this invention;

[0050] Figure 4 This is a longitudinal cross-sectional view of the expansive soil under stress in the capsule tube of the present invention;

[0051] Figure 5 This is a schematic diagram of the elastoplastic region transformation of the present invention;

[0052] Figure 6 This is a diagram illustrating the free boundary of the present invention.

[0053] Figure 7 This is a coordinate system diagram for solving the stress field and displacement field of field B in this invention;

[0054] Figure 8 This is a coordinate system diagram for solving the stress field and displacement field of the present invention.

[0055] like Figures 1-8 As shown in the figure, the labels represent:

[0056] 1. Tube; 2. Subgrade; 3. Plastic zone; 4. Elastic zone. Detailed Implementation

[0057] The features and other related features of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments, so as to facilitate understanding by those skilled in the art:

[0058] Example: Figure 1 As shown, this embodiment relates to a method for calculating the vertical displacement of a roadbed raised by grouting using the tube method. This calculation method mainly includes the following steps:

[0059] S1: As Figures 2-4 As shown, the depth directly below the settlement section of roadbed 2 is... H Horizontal layout n Root capsule 1.

[0060] In this embodiment, the length of the bladder tube is L The initial radius is r The design expansion radius is R , L ≫ R By sending n Grouting is performed simultaneously with the borehole tube. The expansion of the tube applies uniform pressure to the soil inside the borehole, thereby raising the roadbed.

[0061] S2: As Figure 2 and Figure 5 As shown, based on the design expansion radius of the cyst tube... R Grouting pressure p In addition to soil parameters, the radius of the plastic zone of the soil around the grouting tube after grouting is determined. R p Among them, soil parameters include the soil elastic modulus. E Poisson's ratio of soilμ cohesion of soil c、 internal friction angle of soil ϕ .

[0062] In this embodiment, considering that the soil around the capsule tube will enter the yield state and form a plastic zone during the grouting process, according to the continuity condition of stress and displacement at the boundary of the elastic-plastic zone, the problem of a semi-infinite body cylindrical hole under uniform internal pressure containing plastic zone 3 and elastic zone 4 is converted into an equivalent boundary value problem containing only elastic zone. Among them, the stress balance of the soil producing plastic deformation can be obtained according to the Mohr-Coulomb criterion:

[0063] ;

[0064] ;

[0065] In the formula, the maximum principal stress σ 1 is in units of pascal (Pa); the minimum principal stress σ 3 is in units of pascal (Pa); the cohesion of soil c is in units of pascal (Pa); the internal friction angle of soil ϕ is in units of degree (°).

[0066] In the hole expansion problem, the stress state is:

[0067] σ 1= σ θ ;

[0068] σ 3= σ ρ ;

[0069] σ θ -σ ρ= σ θ +σ ρ sinϕ + 2c*cosϕ ;

[0070] In the formula:

[0071] The unit of hoop tensile stress σ θ is pascal (Pa);

[0072] The unit of hoop angle θ is degree (°);

[0073] The unit of radial compressive stress σ is pascal (Pa).​ρ The unit is Pascal (Pa);

[0074] The radial distance ρ is measured in meters (m).

[0075] The yield condition is: ;

[0076] The equilibrium equation is: .

[0077] When the radius of the cystic duct expands to R hour, σ R= p Radial stress at the outer wall of the cyst duct σ R Grouting pressure p The units are all Pascals (Pa); at the elastoplastic boundary, both the plastic yield condition and the elastic stress relationship must be satisfied. σ θ =-σ ρ Based on the above conditions, the expression for the radius of the plastic zone during the plastic deformation stage is derived as follows:

[0078] ;

[0079] In the formula:

[0080] radius of the plastic zone during plastic deformation stage The unit is meter (m);

[0081] Design expansion radius of the cyst tube R The unit is meter (m).

[0082] Considering that the soil will not immediately yield under grouting pressure, but will first undergo elastic deformation to store some energy, and as the soil gradually yields, the release of elastic energy will indirectly increase the range of plastic deformation, the above plastic deformation formula is rigidly modified. The final formula for calculating the radius of the plastic zone is:

[0083] ;

[0084] ;

[0085] In the formula, the radius of the plastic zone R p The unit is meter (m);

[0086] Stiffness index I r Dimensionless;

[0087] Soil elastic modulus E The unit is Pascal (Pa);

[0088] Poisson's ratio of soil μ Non-dimensional.

[0089] S3: As Figure 2 and Figure 5 shown, based on the plastic zone radius of the soil around the capsule tube after grouting R p , the radial stress at the elastic-plastic boundary is determined by using the continuity condition of stress and displacement at the elastic-plastic boundary .

[0090] In this embodiment, the radial stress at the elastic-plastic boundary The calculation formula is:

[0091] ;

[0092] In the formula, the radial stress at the elastic-plastic boundary The unit is Pascal (Pa).

[0093] S4: As Figures 6-8 shown, in the elastic zone, the capsule tube inflation problem in the semi-infinite space is equivalent to the hole inflation problem in the infinite elastic body (assuming M point ( x , z ) is the point to be solved in the soil around the capsule tube), and the displacement superposition method is used to calculate the soil displacement field caused by single capsule tube grouting; wherein the displacement superposition method includes: decomposing the original displacement field (field A) into the first displacement field (field B) of the hole in the infinite elastic body under internal pressure and the second displacement field (field C) for meeting the free surface boundary condition, and superimposing the two.

[0094] In this embodiment, in view of the problem that the free boundary in the semi-infinite space leads to mathematical solving difficulty, the stress and displacement superposition method is used to decompose the original problem (cylindrical hole problem in the semi-infinite space) into two sub-problems which are easy to solve:

[0095] The solving process of field B is:

[0096] Solve the uniform internal pressure of the infinite body circular hole by using polar coordinates P According to the Lamé solution, the stress components (with compressive stress as positive) in the polar coordinate system are:

[0097] The radial stress of field B: ;

[0098] The hoop stress of field B: ;

[0099] The shear stress of field B: ;

[0100] wherein the radial stress of the field B , the hoop stress of the field B , the shear stress of the field B have the unit of pascal (Pa).

[0101] Since the length of the borehole is much larger than the size of the orifice, it can be considered as a plane strain problem, according to the physical equation and geometric equation of the polar coordinate plane strain problem, the analytical solution of the radial displacement of the field B is obtained as follows:

[0102] ;

[0103] wherein the analytical solution of the radial displacement of the field B has the unit of meter (m).

[0104] In the rectangular coordinate xoz , specifically, taking the top plane of the subgrade settlement section as the reference surface, the intersection point of the reference surface and the vertical line passing through the center of the first capsule tube is set as the origin o , x the axis extends in the transverse direction of the reference surface, z the vertical direction is positive, and the relationship between the displacement components and the polar coordinate components is as follows:

[0105] u z u ρ sinθ + u θ cosθ ;

[0106] wherein:

[0107] the vertical displacement u z , the radial displacement u ρ , the hoop displacement u θ u θ have the unit of meter (m);

[0108] , the vertical value z , the transverse value x , the capsule tube arrangement depth H have the unit of meter (m), and the analytical solution of the vertical displacement of the field B of a single capsule tube (taking the absolute value) is obtained as follows:

[0109] ;

[0110] wherein the analytical solution of the vertical displacement of the field B of a single capsule tube has the unit of meter (m).

[0111] ​​The solution process of field C is as follows:

[0112] A stress field is used to offset the additional stress introduced by field B at the free boundary, and a surface force opposite to field B is applied at a point on the free surface z =0 x = ξ (x ξ ,0) of the reference surface.

[0113] In rectangular coordinates, the relationship between stress components and polar coordinate components is as follows:

[0114] ;

[0115] In the formula, the vertical stress of field B is in units of pascal (Pa).

[0116] The unit concentrated force at the free surface position of field C (i.e., the vertical stress of field C) is:

[0117] ;

[0118] In the formula, the unit concentrated force at the free surface position of field C q(ξ) , and the vertical stress of field C are both in units of pascal (Pa).

[0119] At the free surface of field C, for a unit vertical point load P z =1 acting on point ξ (x ξ, 0 ,0), the displacement influence function at point (x

[0120] ) is:

[0121] Then the displacement component generated by the vertically distributed stress is:

[0122] ;

[0123] Therefore, the displacement generated at the free surface (x,0) is:

[0124] ;

[0125] Through integration, we get:

[0126] ;

[0127] Finally, the analytical solution of the vertical displacement of a single cystic duct in field C (taking the absolute value) is obtained:

[0128] ;

[0129] Analytical solution of vertical displacement of field C of single capsule tube The unit is meter (m).

[0130] The real solution of field A can be obtained by adding the analytical solution of vertical displacement of field C to the analytical solution of vertical displacement of field B. Based on this, the calculation formula of vertical displacement of subgrade surface under the action of single capsule tube is derived:

[0131]

[0132] The unit of vertical displacement of subgrade surface under single capsule tube is meter (m).

[0133] S5: Based on the superposition principle of elastic mechanics, the vertical displacement distribution of the subgrade surface under the joint action of multiple capsule tubes is calculated according to the soil displacement field caused by single capsule grouting obtained in step S4.

[0134] In this embodiment, based on the displacement solution of single capsule tube, the total vertical displacement of the subgrade surface at any target point under the joint action of multiple capsule tubes is calculated according to the superposition principle of elastic mechanics. The displacement is the vector sum of the displacements generated by each capsule tube at the point, and the calculation formula is: n

[0135]

[0136] The unit of total vertical displacement of subgrade surface at any target point is meter (m). u z (x,0) The unit of vector sum of displacements generated by each capsule tube at any target point of subgrade surface is meter (m). x m The horizontal position (x-axis) coordinate of the first capsule tube is meter (m). m x , m ∈1, 2, 3,... n , x 1 =0、x 2 =L 1 、x 3 =L 1 +L 2 、...、x n =L 1 +L 2 +...+L ​​​​​​n-1 。

[0137] The beneficial technical effects of the present embodiment are:

[0138] 1. High calculation accuracy: The elastic-plastic behavior of the soil and the free boundary effect of the semi-infinite space are considered simultaneously in displacement calculation, which fundamentally overcomes the huge error caused by traditional elastic theory or infinite body assumption, making the displacement prediction result more in line with the engineering practice;

[0139] 2. Solid theoretical basis: The complete analytical derivation process from single capsule tube to multiple capsule tubes, from the interior of the soil to the site displacement is provided, which is logically rigorous and provides a solid theoretical basis for the capsule grouting uplift technology;

[0140] 3. Strong guidance: The analytical solution is simple and easy to apply in engineering, which can be directly used to guide engineering design, such as optimizing the arrangement spacing and burial depth of the capsule tube, predicting the uplift amount under different grouting pressures, and thus realizing precise and controllable roadbed settlement control;

[0141] 4. Wide application prospect: The calculation method is not only suitable for roadbed uplift, but also the core theory can be extended to other geotechnical engineering problems involving underground hole expansion or contraction.

Claims

1. A method for calculating the vertical lift displacement of a roadbed raised by grouting using the tube method, characterized in that... The calculation method includes the following steps: S1: Depth directly below the roadbed settlement section H Horizontal layout n Root capsule canal; S2: Based on the designed expansion radius of the cyst tube R Grouting pressure p In addition to soil parameters, the radius of the plastic zone of the soil around the grouting tube after grouting is determined. R p The soil parameters include the soil elastic modulus. E Poisson's ratio of soil μ Soil cohesion c、 soil internal friction angle ϕ ; S3: Radius of the plastic zone of the soil surrounding the grouting tube after injection R p By utilizing the continuity condition of stress and displacement at the boundary of the elastoplastic region, the radial stress at the boundary of the elastoplastic region can be determined. ; S4: In the elastic zone, the problem of tube expansion in a semi-infinite space is equivalent to the problem of pore expansion in an infinite elastic body. The displacement field caused by grouting of a single tube is calculated by the displacement superposition method. The displacement superposition method includes: decomposing the original displacement field into a first displacement field of the pore under internal pressure in the infinite elastic body and a second displacement field used to satisfy the boundary conditions of the free surface, and superimposing the two. S5: Based on the soil displacement field caused by single-cell grouting obtained in step S4, calculate the displacement field using the superposition principle of elasticity. n Vertical displacement distribution on the roadbed surface under the combined action of root sacs and canals; In step S4, under the action of a single tube, any point on the roadbed surface... (x,0) The vertical displacement is calculated using the following formula: ； In the formula: The unit is meters; The vertical displacement is the analytical solution for the first displacement field, in meters. The vertical displacement of the second displacement field is the analytical solution, in meters; the vertical displacement of the first and second displacement fields are both taken as absolute values. x、H The units are all meters; In step S5, n Under the action of root canals, any point on the roadbed surface (x,0) The total vertical displacement is calculated using the following formula: ； In the formula: For each cyst tube at any point on the roadbed surface (x,0) The vector sum of the resulting displacements; u z (x,0) , The units are all meters; x m For the first m The horizontal coordinates of the root sac canal, in meters.

2. The method for calculating the vertical lift displacement of a roadbed raised by grouting using the tube method as described in claim 1, characterized in that... In step S2, the radius of the plastic zone of the soil surrounding the grouting tube after grouting. R p Calculated using the following formula: ； ； In the formula: R p The unit is meters; R The unit is meters; p The unit is Pascal; c The unit is Pascal; ϕ The unit is degrees; I r The stiffness exponent is dimensionless. E The unit is Pascal; μ Dimensionless.

3. The method for calculating the vertical lift displacement of a roadbed raised by grouting using the tube method as described in claim 2, characterized in that... In step S3, the radial stress at the boundary of the elastic-plastic region Calculated using the following formula: ； In the formula: The unit is Pascal.

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