A method for calculating additional stress of roadbed soil body by using bag pipe method for grouting lifting

Abstract

The present application relates to geotechnical engineering and road engineering technical field, especially a kind of additional stress calculation method suitable for capsule pipe method grouting lifting roadbed soil body, based on the superposition principle in elasticity, the soil stress field caused by capsule pipe grouting is decomposed into the classic Lame solution (field B) of the borehole under internal pressure in infinite body and the correction stress field (field C) introduced to eliminate the stress of free surface;By establishing rectangular coordinate system, the stress component under polar coordinates is converted into rectangular coordinate form, and the stress field caused by vertical and shear distribution load is calculated respectively by using Flamant solution and horizontal point load influence function under plane strain condition;Finally, the additional stress distribution caused by capsule pipe grouting in semi-infinite soil body is obtained by superimposing the stress solution of field B and field C.The present application has the advantages that the coupling effect of borehole boundary and free surface is considered, it is suitable for stress prediction and control in roadbed lifting engineering, and it has the advantages of rigorous theory and high calculation precision.

Description

Technical Field

[0001] This invention relates to the fields of geotechnical engineering and road engineering, and in particular to a method for calculating the additional stress of roadbed soil raised by grouting using the tube method. Background Technology

[0002] Tube grouting is a highly efficient technology for roadbed lifting and settlement repair. This method involves drilling horizontal holes in the roadbed soil and inserting tubes, then injecting grout into the tubes under pressure, utilizing the expansion effect of the tubes to lift the upper roadbed.

[0003] Currently, stress analysis and prediction for the uplift process in the grouting method using the tube method largely rely on empirical formulas or simplified numerical models, lacking rigorous theoretical solutions. Existing methods often struggle to accurately account for the simultaneous influence of two key boundary conditions: the borehole free boundary and the surface free boundary. However, neglecting the coupling effect of these boundary conditions can lead to deviations in the calculation of additional stress in the soil, thereby affecting the accuracy of assessments of uplift amount, affected area, and potential damage risk.

[0004] Therefore, there is an urgent need for a theoretically rigorous and computationally accurate method that can accurately predict the additional stress field induced by grouting in semi-infinite subgrade soil. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by providing a method for calculating the additional stress on subgrade soil raised by grouting using the bladder method. This method decomposes the stress field caused by grouting into a stress field of uniformly distributed internal pressure on the borehole wall in an infinite elastic body and a corrected stress field. The final solution is obtained based on the superposition principle of elasticity, and the solution is accurate while considering the stress distribution influenced by the borehole boundary and the free boundary of the ground surface.

[0006] The objective of this invention is achieved through the following technical solutions:

[0007] A method for calculating the additional stress on subgrade soil raised by grouting using a bladder tube method, comprising subgrade soil and a bladder tube embedded therein through a borehole, wherein the bladder tube expands by grouting to raise the subgrade soil, characterized in that the calculation method includes the following steps:

[0008] S1. Establish the roadbed soil as a uniform, isotropic linear elastic semi-infinite body model. Compared with the borehole radius, the borehole length located in the linear elastic semi-infinite body model is regarded as infinitely long and treated as a plane strain problem.

[0009] S2. The total additional stress field A caused by the grouting expansion of the tube in the subgrade soil is divided into the stress field B of the borehole inner wall subjected to uniform internal pressure P in the linear elastic semi-infinite body model, and the corrected stress field C to eliminate the stress caused by field B on the free surface.

[0010] S3. Solve for the stress field B and the corrected stress field C separately. Based on the superposition principle of elasticity, superimpose the stress field B and the corrected stress field C to obtain the total additional stress field A caused by the grouting expansion of the bladder tube in the subgrade soil.

[0011] The corrected stress field C is achieved by applying a surface force on the free surface that is equal in magnitude and opposite in direction to the stress field B.

[0012] The stress field B is calculated using the Lamé solution.

[0013] Convert the stress components of the stress field B in the polar coordinate system to the stress components in the rectangular coordinate system; calculate the stress components caused by the stress field B on the free surface.

[0014] Based on the stress of the stress field B on the free surface, a distributed load function for the corrected stress field C is constructed. Using the Flamant solution and the horizontal point load influence function, the stress fields caused by the vertical distributed load and the shear distributed load in the corrected stress field C are calculated respectively.

[0015] The expression for the total additional stress field A is:

[0016] ;

[0017] ;

[0018] ;

[0019] In the formula:

[0020] Let A be the x-axis stress component of the total additional stress field A in a rectangular coordinate system, in Pascals.

[0021] Let be the stress component along the x-axis of stress field B in a rectangular coordinate system, in Pascals.

[0022] In a rectangular coordinate system, the stress component along the x-axis of the corrected stress field C is given, in Pascals.

[0023] Let A be the stress component along the z-axis of the total additional stress field A in a rectangular coordinate system, in Pascals.

[0024] Let be the stress component along the z-axis of stress field B in a rectangular coordinate system, in Pascals.

[0025] For the z-axis stress component of the corrected stress field C in a rectangular coordinate system, the unit is Pascal;

[0026] Let be the shear stress along the z-axis on the plane perpendicular to the x-axis of the total additional stress field A in a rectangular coordinate system, in Pascals.

[0027] Let be the shear stress along the z-axis on the plane perpendicular to the x-axis of field B in a rectangular coordinate system, in Pascals.

[0028] Let be the shear stress along the z-axis on the plane perpendicular to the x-axis of field C in a rectangular coordinate system, in Pascals.

[0029] The grouting pressure is expressed in Pascals.

[0030] The radius of the borehole is in meters.

[0031] The lateral distance from the point in question to the center of the borehole is in meters.

[0032] The vertical depth from the point in question to the roadbed surface is expressed in meters.

[0033] The depth of the borehole is expressed in meters.

[0034] It is the abscissa value of a point on the roadbed surface, which serves as the reference plane.

[0035] The advantages of this invention are:

[0036] 1) Rigorous Theory: Based on the superposition principle of elasticity and classical solutions, the derivation process is scientific and rigorous, avoiding the arbitrariness of empirical formulas.

[0037] 2) High accuracy: The coupling effect between the borehole boundary and the free boundary of the surface is fully considered, the calculation results are closer to the real situation, and the final solution obtained has high accuracy.

[0038] 3) High practicality: It provides a complete calculation framework that can be used for quantitative analysis, and is suitable for the design, optimization and safety assessment of grouting-lifted roadbeds using the tube method, which is convenient for practical application in various projects. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the steps of the present invention;

[0040] Figure 2 This is a schematic diagram illustrating the calculation of additional stress on the overlying soil of the A-tube in the midfield of this invention.

[0041] Figure 3 This is a schematic diagram illustrating the superposition of additional stress calculations for soil A in the midfield of this invention;

[0042] Figure 4 This is a schematic diagram of the decomposition calculation of the additional stress in soil C in the midfield of this invention;

[0043] Figure 5 This is a schematic diagram illustrating the calculation of soil stress under vertically distributed load C in the midfield according to the present invention.

[0044] Figure 6 This is a schematic diagram illustrating the calculation of soil stress under mid-field C shear distribution load according to the present invention. Detailed Implementation

[0045] 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:

[0046] Example: Figures 1 to 6 As shown in the figure, the calculation method for the additional stress of roadbed soil raised by grouting using the bladder tube method in this embodiment is used to calculate the stress on the roadbed soil when a horizontal hole is drilled in the roadbed soil and a bladder tube is inserted. The expansion effect of the bladder tube after grouting is used to accurately assess the amount of uplift, the range of influence and the potential risk of damage.

[0047] In this embodiment, the complex real-world physical problem (field A, i.e., the problem of drilling a hole with internal pressure in a semi-infinite body) is decomposed into two solvable subproblems, and the final solution is obtained through the superposition principle. The specific steps are as follows:

[0048] S1: Establish a model of the soil as a uniform, isotropic linear elastic semi-infinite body. Compared to the borehole radius, the borehole length can be regarded as infinitely long and treated as a plane strain problem.

[0049] like Figure 2 As shown, in this linear elastic semi-infinite body model, the burial depth is... The borehole inner wall is subjected to uniformly distributed internal pressure The stress field. Among them, These are the stress components in the polar coordinate system, representing radial stress, circumferential stress, and stress perpendicular to the polar coordinate system. θ tangential stress in the axial direction, perpendicular to ρ Tangential stress of the shaft; The stress components in the rectangular coordinate system represent the stress components perpendicular to the x-axis. axial surface along Forces acting in the axial direction are perpendicular to axial surface along Forces acting in the axial direction are perpendicular to axial surface along Forces acting in the axial direction are perpendicular to axial surface along Forces acting in the axial direction; M and N represent forces extracted from the soil containing... noodle, Face to face A tiny triangular plate with a thickness of 1.

[0050] S2: Decompose the total additional stress field A caused by grouting in the subgrade soil into two subproblems (assuming the point to be solved is M). () represents the point to be solved within the subgrade soil surrounding the cyst tube.

[0051] Field B: In a linear elastic semi-infinite body model, the borehole inner wall is subjected to uniformly distributed internal pressure. P The stress field was calculated using the Lamé solution.

[0052] Field C: A corrective stress field introduced to eliminate the stress caused by field B on the free surface, which is achieved by applying a surface force on the free surface that is equal in magnitude and opposite in direction to the stress of field B.

[0053] The stress solution for field B (the infinite body problem) is the classic Lamé solution. In polar coordinates, the stress components (with compressive stress as positive) are:

[0054] Radial stress of field B: ;

[0055] Circumferential stress in field B: ;

[0056] Tangential stress in field B: ;

[0057] In the formula:

[0058] Radial stress of field B Circumferential stress of field B Tangential stress of field B The units are all Pascals;

[0059] The grouting pressure is expressed in Pascals.

[0060] It is the radial distance from the point M to the center of the borehole, i.e. , The lateral distance from the point in question to the center of the borehole is in meters. The vertical depth from the point in question to the roadbed surface is expressed in meters. The depth of the borehole is expressed in meters.

[0061] The radius of the borehole is in meters.

[0062] S3: Convert the stress components of field B in polar coordinates to stress components in rectangular coordinates using a coordinate transformation formula. In rectangular coordinates... Specifically, the top plane of the roadbed soil is used as the reference plane, and the intersection of the reference plane and the plumb line passing through the center of the borehole is set as the origin. o , The shaft extends laterally along the reference plane. The axis pointing vertically downwards is considered positive.

[0063] The relationship between the stress components of field B in polar coordinates and their components in rectangular coordinates is as follows:

[0064] ;

[0065] ;

[0066] ;

[0067] In the formula:

[0068] In a rectangular coordinate system, field B Axial stress components, in Pascals;

[0069] In a rectangular coordinate system, field B Axial stress components, in Pascals;

[0070] In a rectangular coordinate system, the perpendicular axis of field B Along the direction plane Axial shear stress, in Pascals;

[0071] Let be the radial stress of field B in polar coordinates, expressed in Pascals.

[0072] Let be the circumferential stress of field B in polar coordinates, expressed in Pascals.

[0073] Let be the tangential stress of field B in polar coordinates, expressed in Pascals.

[0074] , ;

[0075] The required vertical depth from point M to the roadbed surface The required lateral distance from point M to the borehole center , borehole burial depth The radial distance from the point to the borehole center The unit for all values ​​is meters.

[0076] Polar stress components are converted to stress components in Cartesian coordinates using coordinate transformation formulas:

[0077] Normal stress components: ;

[0078] Shear stress components: .

[0079] S4: Calculate the stress components induced by field B on the free surface (z=0).

[0080] The stress components induced at the location of the free surface (z=0) of field B are:

[0081] ;

[0082] ;

[0083] In the formula, the normal stress component induced by field B on the free surface (z=0) is... The shear stress components induced by field B at the free surface (z=0) All units are Pascals.

[0084] S5: Based on the stress of field B on the free surface, construct the distributed load function of the corrected stress field C.

[0085] Construct the distributed load function of field C, i.e., at a point on the free surface (z=0). = ( At a point on the roadbed surface (which serves as the reference surface), a set of surface forces, equal in magnitude but opposite in direction to the stress generated by field B, are applied.

[0086] Vertical distributed load: ;

[0087] Shear distributed load: ;

[0088] In the formula:

[0089] Vertical distributed load at the free surface location of field C Shear distributed load The units are all Pascals;

[0090] The grouting pressure is expressed in Pascals.

[0091] The radius of the borehole is in meters.

[0092] The lateral distance from the point in question to the center of the borehole is in meters.

[0093] The vertical depth from the point in question to the roadbed surface is expressed in meters.

[0094] The depth of the borehole is expressed in meters.

[0095] This is the x-coordinate value of a point on the roadbed surface, which serves as the reference plane.

[0096] S6: Using the Flamant solution and the influence function of the horizontal point load, calculate the stress field caused by the vertically distributed load and the shear distributed load in field C, respectively.

[0097] The Flamant solution and the influence function of the horizontal point load are determined by the following equation:

[0098] For a unit vertical point load Acting on a point ( ,0), at the desired point M The resulting stress influence function:

[0099] ;

[0100] ;

[0101] .

[0102] For a unit horizontal point load Acting on a point ( ,0), at the desired point M The resulting stress influence function:

[0103] ;

[0104] ;

[0105] .

[0106] Then the point M is required The stress field caused by the perpendicularly distributed load at point C is:

[0107] ;

[0108] ;

[0109] ;

[0110] In the formula:

[0111] In a rectangular coordinate system, the load caused by the perpendicular distribution of field C Axial stress components, in Pascals;

[0112] In a rectangular coordinate system, the load caused by the perpendicular distribution of field C Axial stress components, in Pascals;

[0113] In a rectangular coordinate system, the vertical load caused by the vertical distribution of field C. Along the axial plane Axial shear stress, in Pascals; K This is the corresponding stress influence function.

[0114] Then the point M is required The stress field caused by the shear load at point C is:

[0115] ;

[0116] ;

[0117] ;

[0118] In the formula:

[0119] In a rectangular coordinate system, the field C is caused by a shear load distribution. Axial stress components, in Pascals;

[0120] In a rectangular coordinate system, the field C is caused by a shear load distribution. Axial stress components, in Pascals;

[0121] In a rectangular coordinate system, the vertical force caused by the shear load C is... Along the axial plane Axial shear stress, in Pascals;

[0122] K This is the corresponding stress influence function.

[0123] Combining the stress field caused by the vertically distributed load C and the stress field caused by the shear distributed load, the required point M... The expression for the additional stress field at point C is:

[0124] ;

[0125] ;

[0126] ;

[0127] In the formula:

[0128] In a rectangular coordinate system, the field C Axial stress components, in Pascals;

[0129] In a rectangular coordinate system, the field C Axial stress components, in Pascals;

[0130] In a rectangular coordinate system, the perpendicularity of field C Along the axial plane Axial shear stress, in Pascals;

[0131] K This is the corresponding stress influence function.

[0132] S7: By superimposing the stress fields of field B and field C, the total additional stress field A caused by grouting in semi-infinite soil is obtained as follows:

[0133] ;

[0134] ;

[0135] .

[0136] This embodiment is based on the superposition principle of elasticity, which can accurately solve the stress distribution that simultaneously considers the influence of borehole boundary and surface free boundary, and finally obtain the total additional stress field caused in semi-infinite soil. Then, based on the total additional stress field, the uplift of the subgrade soil, the range of influence and the potential damage risk can be accurately assessed.

[0137] Although the above embodiments have described the concept and embodiments of the present invention in detail with reference to the accompanying drawings, those skilled in the art will recognize that various improvements and modifications can still be made to the present invention without departing from the scope of the claims, and therefore will not be elaborated here.

Claims

1. A method for calculating the additional stress of subgrade soil raised by grouting using a bladder tube method, comprising subgrade soil and a bladder tube embedded therein through a borehole, wherein the bladder tube raises the subgrade soil through grouting expansion, characterized in that: The calculation method includes the following steps: S1. Establish the roadbed soil as a uniform, isotropic linear elastic semi-infinite body model. Compared with the borehole radius, the borehole length located in the linear elastic semi-infinite body model is regarded as infinitely long and treated as a plane strain problem. S2. The total additional stress field A caused by the grouting expansion of the tube in the subgrade soil is divided into the stress field B of the borehole inner wall subjected to uniform internal pressure P in the linear elastic semi-infinite body model, and the corrected stress field C to eliminate the stress caused by field B on the free surface. S3. Solve for the stress field B and the corrected stress field C respectively. Based on the superposition principle of elasticity, superimpose the stress field B and the corrected stress field C to obtain the total additional stress field A caused by the grouting expansion of the bladder tube in the subgrade soil. The stress field B is calculated using the Lamé solution; Based on the stress of the stress field B on the free surface, a distributed load function of the corrected stress field C is constructed. Using the Flamant solution and the horizontal point load influence function, the stress fields caused by the vertical distributed load and the shear distributed load in the corrected stress field C are calculated respectively. The expression for the total additional stress field A is: ； ； ； In the formula: Let A be the x-axis stress component of the total additional stress field A in a rectangular coordinate system, in Pascals. Let be the stress component along the x-axis of stress field B in a rectangular coordinate system, in Pascals. In a rectangular coordinate system, the stress component along the x-axis of the corrected stress field C is given, in Pascals. Let A be the stress component along the z-axis of the total additional stress field A in a rectangular coordinate system, in Pascals. Let be the stress component along the z-axis of stress field B in a rectangular coordinate system, in Pascals. For the z-axis stress component of the corrected stress field C in a rectangular coordinate system, the unit is Pascal; Let be the shear stress along the z-axis on the plane perpendicular to the x-axis of the total additional stress field A in a rectangular coordinate system, in Pascals. Let be the shear stress along the z-axis on the plane perpendicular to the x-axis of field B in a rectangular coordinate system, in Pascals. Let be the shear stress along the z-axis on the plane perpendicular to the x-axis of field C in a rectangular coordinate system, in Pascals. The grouting pressure is expressed in Pascals. The radius of the borehole is in meters. The lateral distance from the point in question to the center of the borehole is in meters. The vertical depth from the point in question to the roadbed surface is expressed in meters. The depth of the borehole is expressed in meters. This is the x-coordinate value of a point on the roadbed surface, which serves as the reference plane.

2. The method for calculating the additional stress of subgrade soil raised by grouting using the tube method according to claim 1, characterized in that: The corrected stress field C is achieved by applying a surface force on the free surface that is equal in magnitude and opposite in direction to the stress field B.

3. The method for calculating the additional stress of subgrade soil raised by grouting using the tube method according to claim 1, characterized in that: The stress components of the stress field B in the polar coordinate system are converted into stress components in the rectangular coordinate system. Calculate the stress components induced by stress field B on the free surface.

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