CN112464485A - Evaluation method for grouting deviation rectifying effect aiming at horizontal deformation of shield tunnel - Google Patents
Evaluation method for grouting deviation rectifying effect aiming at horizontal deformation of shield tunnel Download PDFInfo
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Abstract
The invention discloses a method for evaluating grouting deviation rectifying effect aiming at horizontal deformation of a shield tunnel, which comprises the following steps: establishing a grouting volume expansion mechanical calculation model, and deducing a calculation formula of simplified horizontal additional stress at any point in a soil layer caused by grouting based on a mirror image method; adopting a uniform expansion model of a grouting area, obtaining the volume of a soil body after grouting expansion according to the amount of slurry injected by the sleeve valve pipe and the volume expansion rate of the grouting ring, and substituting the volume into the calculation formula to obtain the horizontal additional stress at the tunnel to be rectified; the horizontal additional stress at the position of the tunnel to be corrected is brought into a tunnel horizontal displacement formula through a tunnel shearing dislocation and rigid body rotation cooperative deformation calculation model, so that the tunnel horizontal displacement correction quantity of any point in a calculation range can be obtained; and evaluating according to the horizontal displacement correction amount of the tunnel, and referring to the I-level control standard in the urban rail transit structure safety protection technical regulation, if the offset axis center of the tunnel is less than 5mm, the tunnel is reasonable, otherwise, the tunnel is unreasonable.
Description
Technical Field
The invention belongs to the technical field of underground engineering, and particularly relates to an evaluation method for a grouting deviation rectifying effect aiming at horizontal deformation of a shield tunnel, which is suitable for soil layer grouting deviation rectifying engineering by adopting sleeve valve pipes and is used for evaluating the working condition of compensating grouting on the horizontal displacement deviation rectifying control effect of an existing tunnel.
Background
Along with the development of subway cities, the safety requirement of subway tunnels is higher and higher, and the horizontal displacement is easily caused by the influence of excavation of side foundation pits, and sleeve valve pipe grouting technology is often adopted in engineering to carry out micro-disturbance grouting deviation correction. The compensation grouting method is a mature deviation rectifying technology, is commonly used for settlement control of tunnels and lifting of existing buildings, and has more and more projects for rectifying the horizontal displacement of the existing tunnels by adopting compensation grouting in recent years. Therefore, the research on the compensation grouting has important significance on the horizontal displacement deviation rectifying effect and the influence rule of the existing tunnel.
Aiming at the estimation of the deviation rectifying effect of compensation grouting on the existing tunnel, scholars at home and abroad mainly develop related researches by a numerical simulation method, an actual measurement data analysis method and a model test method at present. The precision of the numerical simulation method depends on the selection of modeling level, boundary conditions and parameters to a great extent, the precision cannot be effectively guaranteed, and the compensation grouting involves permeation, compaction and splitting of slurry, so that the action mechanism is relatively complex, and direct research and analysis are difficult to realize. The field measured data analysis needs more control factors and more complex relationships. The reduced size model test can not avoid the influence of the reduced size effect, is sensitive to disturbance of external factors, and can not effectively guarantee the accuracy. At present, random medium theory is mostly used for researching soil displacement and additional stress, but the random medium theory is generally used for researching the soil displacement condition of slurry bubble expansion on an upper soil layer and a ground surface, the random medium theory can only calculate the soil displacement and the additional stress on an upper part of a contraction point or an expansion point, and a calculation point at the same depth or a lower position cannot obtain a result, so that a calculation method based on the random medium theory cannot analyze the grouting level deviation rectifying effect. Therefore, at present, no study on the calculation of the tunnel horizontal deviation correction caused by sleeve valve tube grouting is seen.
In summary, there is no calculation method for the deviation correction amount of the horizontal displacement of the existing tunnel caused by compensation grouting, so that a research method is necessary.
Disclosure of Invention
The invention aims to provide an evaluation method for the grouting deviation rectifying effect of horizontal deformation of a shield tunnel, and aims to solve the problems of the existing numerical simulation method, the actual measurement data analysis method and the reduced size model experiment method in the evaluation for the grouting deviation rectifying effect of the horizontal deformation of the shield tunnel.
In order to achieve the above purpose, the technical solution adopted by the embodiment of the present invention is as follows: a method for evaluating grouting deviation rectifying effect aiming at horizontal deformation of a shield tunnel comprises the following steps:
according to the principle of the horizontal deviation rectifying effect of compensation grouting, a sleeve valve pipe grouting volume expansion mechanical calculation model is established, and a calculation formula of simplified horizontal additional stress at any point in a soil layer caused by grouting is deduced based on the mirror image method principle;
adopting a uniform expansion model of a grouting area, obtaining the volume of a soil body after grouting expansion according to the amount of slurry injected by the sleeve valve pipe and the volume expansion rate of the grouting ring, and substituting the volume into the calculation formula to obtain the horizontal additional stress at the tunnel to be rectified;
deducing a tunnel horizontal displacement formula caused by grouting through a tunnel shearing dislocation and rigid body rotation cooperative deformation calculation model, substituting the horizontal additional stress at the tunnel to be corrected into the tunnel horizontal displacement formula, thus obtaining a final calculation formula of the tunnel horizontal displacement to be corrected, and substituting the final calculation formula into any point in a calculation range to obtain the horizontal displacement correction amount of the tunnel;
and evaluating according to the horizontal displacement correction amount of the tunnel, and referring to the I-level control standard in the urban rail transit structure safety protection technical regulation, if the offset axis center of the tunnel is less than 5mm, the tunnel is reasonable, otherwise, the tunnel is unreasonable.
Further, the formula for calculating the simplified horizontal additional stress at any point in the soil layer caused by grouting based on the mirror image method principle specifically includes:
step 1) neglecting the existence of the ground, converting the problem of a semi-infinite body in the actual engineering into the problem of the infinite body, and generating the normal stress-sigma at the original ground position by the existing volume expansion point0And shear stress tau0；
Step 2) with the ground as a boundary, a void point with the same size is supposed at the position of the mirror image of the original expansion point in an infinite body, and the void point generates positive stress sigma at the position of the original ground0And shear stress tau0；
Step 3) the normal stresses generated in the original place by the two steps are mutually offset, and the shear stress is 2 tau0In order to meet the actual free boundary condition, the generated additional shear stress is reversely applied to the surface of the semi-infinite body;
the sum of the stresses generated in the three steps is the solution of the additional stress caused by the volume expansion point;
based on the concept of the mirror image method, point (x)0,y0,z0) A spherical expansion region with a radius a will produce a displacement component S at point (x, y, z)i1：
In the formula:
a is the spherical expansion zone radius;
in its mirror position (x)0,y0,z0) The displacement component generated at the point (x, y, z) at the gap point with equal size is Si2：
In the formula:
according to the basic equation of elasticity mechanics, the calculation formulas of the strain and the stress generated in the soil body in the three steps are as follows:
in the formula: epsiloni，γxz，γyzStrain, σ, for the soil massiThe stress generated by the soil body, E is the elastic modulus of the soil body, mu is the Poisson ratio, and G is the shear modulus of the soil body;
substituting the formula (1) to the formula (5) into the formula (6) to obtain the calculation formula of the horizontal additional stress generated in the steps 1) and 2) as follows:
step 1) and step 2) the shear stress generated at the earth surface satisfies tauxz＝GγxzAnd τyz＝GγyzAnd reversely acting the shear stress on the earth surface, and integrating through Cerrtuti solution to obtain the stress calculation formula of the step 3) as follows:
additional stress sigmax3Compare sigmax1-2Neglected and long calculation time, the additional stress sigma in the horizontal x direction caused by partial volume expansionx' is:
the influence of grouting on surrounding soil is simulated through the volume expansion of the soil in a grouting area, and the original volume of a to-be-grouted area is assumed to be V1Volume increase after grouting is V2Then, the calculation formula of the horizontal additional stress at any point in the soil layer caused by grouting is as follows:
further, the method comprises the following steps of obtaining the volume of a soil body after grouting expansion according to the amount of slurry injected into the sleeve valve pipe and the volume expansion rate of the grouting ring by adopting a uniform expansion model of the grouting area, and substituting the volume into the calculation formula to obtain the horizontal additional stress at the tunnel to be rectified as follows:
taking the radius of a region to be grouted as R1The radius of the reinforced area of the cylinder after grouting is R2Assuming that the height in the depth direction is constant, the depth of the upper top surface of the grouting cylindrical region is h1Depth of bottom surface is h2The corresponding plane coordinate of the sleeve valve tube is (x)1,y1) The radius of the tunnel to be rectified is RsThe buried depth of the axis is H, and the axis of the tunnel is positioned on the yoz plane and is parallel to the y axis;
when a grouting area uniform expansion model is adopted, the horizontal additional stress of any point at the position of the tunnel to be rectified is obtained and expressed as:
in the formula: a. b is the integral upper and lower limits of a variable xi (along an x axis), c and d are the integral upper and lower limits of a variable zeta (along a y axis), e and f are the integral upper and lower limits of a variable eta (along a z axis), 1 in a subscript represents a pre-grouting state, and 2 represents a post-grouting volume expansion state; the calculation formula of the upper and lower limits of each integral is as follows: a is1＝x1-R1,b1＝x1+R1,
e1＝h1,f1＝h2,a2＝x1-R2,b2＝x1+R2,
e2＝h1,f2＝h2。
Further, the volume process of the soil body after grouting expansion obtained according to the amount of the slurry injected by the sleeve valve pipe and the volume expansion rate of the grouting ring is as follows:
the volume expansion rate Q of the soil before and after grouting is defined as:
in the formula R1Radius of the area to be grouted, R2Radius of the reinforced area of the cylinder after grouting, h1For the depth of the upper top surface of the grouting cylinder area, h2The depth of the lower bottom surface;
volume expansion rate Q and grouting amount V of grouting ringinjAnd grouting efficiency xiinjAbout, expressed as:
further conversion can be:
further, a tunnel horizontal displacement formula caused by grouting is deduced through a tunnel shearing dislocation and rigid body rotation cooperative deformation calculation model, and the horizontal additional stress at the tunnel to be corrected is introduced into the tunnel horizontal displacement formula, so that a final calculation formula of the tunnel horizontal displacement to be corrected can be obtained, and the method specifically comprises the following steps:
from the analysis of the longitudinal deformation work doing and energy conversion angles of the tunnel, the additional stress caused by grouting can be used for overcoming the stratum resistance, the shearing force between the segment rings and the tension between the rings to do work respectively, namely the requirements are met:
Wσ＝WR+WS+WT (15)
in the formula: wσAdding total work amount for grouting stress; wRActing to overcome the resistance of the stratum; wSActing to overcome the inter-ring shear force; wTActing to overcome tension between rings;
by integrating the additional stress, the formation resistance, the shearing force and the tension force in the longitudinal direction of the tunnel, the respective work amount W can be obtainedσ、WR、WS、WTThe respective calculation formula:
in the formula: n is the number of the pipe piece rings on one side of the central point of the tunnel affected by the additional stress; k is a radical ofsThe tunnel inter-ring shear stiffness; k is a radical oftThe tensile rigidity between the tunnel rings; m and m +1 are serial numbers of adjacent two ring pipe sheet rings; d is the diameter of the tunnel; dtThe width of the ring of the pipe sheet is wide; j is the segment ring rigid body rotation effect proportional coefficient; w (y) is the tunnel horizontal displacement;
according to the energy variation method, a horizontal displacement function of the shield tunnel is assumed:
in the formula:
a is a matrix of undetermined coefficients in the displacement function, and A is { a ═ a0,a1…an}T(ii) a n is the expansion order of Fourier series;
the two sides of the equal sign of the formula (16) are respectively subjected to derivation to obtain the coefficient to be determined
In the formula: a isiJ is the jth element in the matrix a, j is 1,2,3, …, n;
the equations (17) to (20) are further solved in place of the equation (22), so that a control equation of the tunnel horizontal displacement can be obtained:
equation (23) is simplified to a matrix form:
([Kr]+[Ks])AT＝{σx}T (23)
in the formula: [ K ]r]ATFor the interaction effect between the ring segments, [ K ]r]Is an inter-ring stiffness matrix; [ K ]s]ATIs the effect of soil resistance action, wherein [ Ks]A soil stiffness matrix; { sigma. }x}TThe effect of horizontal additional stress caused by grouting on the tunnel is achieved;
from equation (24), the undetermined coefficient matrix A can be obtainedT：
AT＝([Kr]+[Ks])-1{σx}T (24)
A is to beTThe final calculation formula of the transverse horizontal displacement of the tunnel to be rectified can be obtained by substituting the formula (21):
ω(y)＝{Tn(y)}AT (25)。
it should be noted that the above correlation calculation may be programmed and calculated by Matlab, or may be written by other voices, and when the expansion coefficient n is 10, the calculation accuracy requirement may be met.
According to the technical scheme, the embodiment of the invention has the beneficial effects that:
1. according to the embodiment of the invention, a calculation formula of the horizontal additional stress of the surrounding soil body caused by grouting of the sleeve valve pipe is deduced, and the horizontal deviation correction value of the tunnel is calculated.
2. The shearing dislocation and rigid body rotation cooperative deformation model provided by the embodiment of the invention is more consistent with the actual stress deformation mode of the tunnel structure, so that the calculation result is more accurate.
3. The invention takes actual engineering as a case to calculate, compares and analyzes a theoretical calculation value with actually measured data, and researches the influence of a uniform expansion model and a non-uniform expansion model on a theoretical calculation result.
4. The modeling of the embodiment of the invention is simple and clear, the calculation process can be realized by Matalb programming, and the calculation and analysis processes are more convenient.
5. The calculation method provided by the embodiment of the invention has a wide application range, can be used for independently calculating the horizontal displacement value of the existing tunnel caused by compensation grouting, can also be used for researching the influence rule of different grouting amounts, grouting distances and grouting depths on the grouting deviation correction amount, and has a certain reference value for the design of a compensation grouting scheme in practical engineering.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a flow chart of a computing method provided by an embodiment of the invention;
FIG. 2 is a flow chart of an evaluation method provided in the practice of the present invention;
FIG. 3 is a schematic diagram illustrating a horizontal deviation correction effect of the grouting provided by the present invention;
FIG. 4 is a diagram of a model for mechanical computation provided in the practice of the present invention;
FIG. 5 is a graph of the uniform expansion of the grouting area in accordance with the practice of the present invention;
FIG. 6 is a layout diagram of a sleeve valve tube deviation rectifying project according to an embodiment of the present invention;
fig. 7 is a graph comparing the horizontal displacement of the tunnel caused by grouting with the measured data according to the embodiment of the present invention;
FIG. 8 is a comparison graph of the tunnel horizontal displacement obtained by the original calculation method and the simplified method;
FIG. 9 is a graph comparing the horizontal displacement of the tunnel obtained by the two models provided by the embodiment of the present invention;
FIG. 10 is a graph comparing the effect of different grouting amounts on the horizontal displacement of the tunnel in the embodiment;
FIG. 11 is a graph comparing the effect of different grouting distances on the horizontal displacement of the tunnel in the embodiment;
FIG. 12 is a graph comparing the effect of different grouting depths on the horizontal displacement of a tunnel in the embodiment;
description of reference numerals: a tunnel 1 to be rectified; soil body lateral displacement 2; a grouting area 3; soil body expansion caused by grouting 4; a sleeve valve tube 5.
Detailed Description
The present invention will be further described with reference to the following examples. The following examples are set forth merely to aid in the understanding of the invention. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.
FIG. 1 is a flow chart of a computing method provided by an embodiment of the invention; the method for evaluating the grouting deviation rectifying effect aiming at the horizontal deformation of the shield tunnel provided by the embodiment of the invention comprises the following steps:
s101, according to the principle of the horizontal deviation rectifying effect of compensation grouting, the soil body lateral displacement 2 caused by grouting can be generated, a grouting soil body volume expansion model is established, and the horizontal additional stress sigma of any point in the soil layer caused by grouting is deduced based on the mirror image methodxThe calculation formula of (2).
Step S102, forming a grouting reinforcement area similar to a cylinder by adopting a uniform expansion model of the grouting area 3, and obtaining the volume V of a soil body after expansion 4 caused by grouting according to the amount of slurry injected by the sleeve valve pipe 5 and the volume expansion rate of the grouting area 32Substituting the calculation formula to obtain the horizontal additional stress sigma at the position of the tunnel 1 to be rectifiedx；
Step S103, deducing a tunnel horizontal displacement formula caused by grouting through a shearing dislocation and rigid body rotation cooperative deformation calculation model of the tunnel 1 to be corrected, substituting horizontal additional stress into the formula to obtain a final calculation formula of the horizontal displacement of the tunnel 1 to be corrected, and substituting the final calculation formula into any point in a calculation range to obtain a horizontal displacement correction amount omega of the tunnel 1 to be corrected;
and S104, evaluating according to the horizontal displacement deviation correction amount of the tunnel, and referring to the I-level control standard in urban rail transit structure safety protection technical regulation, if the center of the offset axis of the tunnel is less than 5mm, the tunnel is reasonable, otherwise, the tunnel is unreasonable, so that theoretical calculation guarantee is provided for actual grouting construction in engineering.
Prior to the study, the following assumptions were first made: (1) the foundation soil is assumed to be an isotropic, homogeneous, continuous, semi-infinite elastomer, and to extend indefinitely in both the depth and horizontal directions; (2) after grouting, the grout can form a uniform cylindrical reinforcing area by taking the sleeve valve pipe 5 as an axis.
Specifically, the step S101 specifically includes:
firstly, converting a semi-infinite body into an infinite body, then, assuming a volume expansion with the same size as the original gap mirror image position in the infinite body by taking the ground as a boundary, and solving the normal stress and the shear stress caused by a gap point and an expansion point to deduce the displacement value and the stress value of any point in the original semi-infinite body. Based on the same idea, the additional stress value of any point in the soil layer caused by soil body grouting expansion can be solved only by exchanging the positions of the void point and the expansion point in the traditional mirror image method. The specific analysis steps are as follows:
1) neglecting the existence of the ground, the problem of a semi-infinite body in the practical engineering is converted into the problem of the infinite body, and the existing volume expansion point will generate normal stress-sigma at the original ground position0And shear stress tau0。
2) Using the ground as a boundary, and assuming a void point with the same size at the mirror image position of the original expansion point in an infinite body, the void point will generate a positive stress sigma at the original ground position0And shear stress tau0。
3) The normal stress generated in the original plane by the two steps is mutually counteracted, and the shear stress is 2 tau0In order to meet the actual free boundary conditions, the additional shear stress generated is applied in reverse to the semi-infinite surface.
The sum of the stresses generated in the above steps is the solution of the additional stress caused by the volume expansion point.
Based on the concept of the mirror image method, point (x)0,y0,z0) A spherical expansion region with a radius a will produce a displacement component S at point (x, y, z)i1：
In its mirror position (x)0,y0,z0) The displacement component generated at the point (x, y, z) at the gap point with equal size is Si2：
In the formula:
according to the basic equation of elasticity mechanics, the calculation formula of the strain and the stress generated in the soil body in the process is as follows:
in the formula: e is the soil elasticity modulus, mu is the Poisson's ratio, and G is the soil shear modulus.
Substituting the formula (1) to the formula (5) into the formula (6) to obtain the calculation formula of the horizontal additional stress generated in the steps 1) and 2) as follows:
step 1) and step 2) the shear stress generated at the earth surface satisfies tauxz＝GγxzAnd τyz＝GγyzThe shear stress is reversely acted on the earth surfaceIntegrating through Cerrtuti solution to obtain the stress calculation formula of the step 3) as follows:
additional stress sigmax3Compare sigmax1-2Neglected and long calculation time, part of the additional stress sigma 'in the horizontal x direction caused by the expansion of unit volume'xComprises the following steps:
the influence of grouting on the surrounding soil is simulated through the volume expansion of the soil in the grouting area 3, and the original volume of the area to be grouted is assumed to be V1Volume increase after grouting is V2And then any point horizontal additional stress in the soil layer caused by grouting is as follows:
specifically, step S102 specifically includes the following steps:
in the horizontal deviation rectifying process, the sleeve valve pipe 5 is generally vertically driven into a soil layer, and slurry outlet holes are formed in the sleeve valve pipe 5 at intervals, so that the soil layer within a certain depth range can be grouted. Assuming that the grout spreads evenly along the radial direction of the grout outlet, the grouting will be followed by forming a grouting reinforcement area which is approximately cylindrical by taking the sleeve valve pipe 5 as an axis. Assuming that the direction along the axis of the tunnel is a y-axis, the direction vertical to the axis of the tunnel is an x-axis, a z-axis is vertically established downwards, and the radius of a region to be grouted is R1The radius of the reinforced area of the cylinder after grouting is R2. Assuming that the height in the depth direction is constant, the depth of the upper top surface of the grouting cylindrical area is h1Depth of bottom surface is h2The corresponding plane coordinate of the sleeve valve tube 5 is (x)1,y1). The radius of the tunnel 1 to be rectified is RsThe buried depth of the axis is H, and the axis of the tunnel is located on the yoz plane and is parallel to the y axis.
The above parameters are further explained as follows:
the x axis is along the direction vertical to the axis of the tunnel, the x coordinate is the distance from the axis of the tunnel, and the unit symbol is m;
the y axis is along the direction of the axis of the tunnel, the y coordinate is the distance along the tunnel, and the unit symbol is m;
the z axis is along the vertical direction, the z coordinate is the calculated depth, and the unit symbol is m;
R1the radius of the area to be grouted is shown, and the unit symbol is m;
R2the radius of a reinforced area of the cylinder after grouting is represented by a unit symbol m;
h1the depth of the upper top surface of the grouting cylindrical area is m;
h2the depth of the lower bottom surface is m;
Rsthe unit symbol is m, which is the radius of the tunnel 1 to be rectified;
h is the axis burial depth, and the unit symbol is m;
when a uniform expansion model of the grouting area 3 is used, equation (10) can be expressed as:
in the formula: a. b is the integral upper and lower limits of a variable xi (along an x axis), c and d are the integral upper and lower limits of a variable zeta (along a y axis), e and f are the integral upper and lower limits of a variable eta (along a z axis), 1 in a subscript represents a pre-grouting state, and 2 represents a post-grouting volume expansion state; the calculation formula of the upper and lower limits of each integral is as follows: a is1＝x1-R1,b1＝x1+R1,
e1＝h1,f1＝h2,a2＝x1-R2,b2＝x1+R2,
e2＝h1,f2＝h2。
The volume expansion rate Q of the soil before and after grouting is defined as:
volume expansion rate Q and grouting amount V of grouting ringinjAnd grouting efficiency xiinjIn this regard, it can be expressed as:
further conversion can be:
in addition, let epsilon be the radial expansion amount of the grouting area, namely, the following conditions are satisfied:
ε＝R2-R1 (15)
specifically, step S103 specifically includes:
the adjacent pipe sheets of the existing tunnel can generate relative rotation angle and staggered deformation under the influence of additional stress, the relative rotation angle and the staggered deformation jointly cause the total deformation of the tunnel in the longitudinal direction, and the inter-ring tension and the inter-ring shearing force can be generated between the adjacent pipe sheet rings of each pipe sheet to resist the deformation. From the analysis of the longitudinal deformation work doing and energy conversion angles of the tunnel, the additional stress caused by grouting can be used for overcoming the stratum resistance, the shearing force between the segment rings and the tension between the rings to do work respectively, namely the requirements are met:
Wσ＝WR+WS+WT (16)
in the formula: wσAdding total work amount for grouting stress; wRActing to overcome the resistance of the stratum; wSActing to overcome the inter-ring shear force; wTWork is done to overcome the tension between the rings.
The respective work amount can be obtained by integrating the additional stress, the formation resistance, the inter-ring shearing force and the inter-ring pulling force respectively along the longitudinal direction of the tunnel. Wσ、WR、WS、WTThe respective calculation formula:
in the formula: n is the number of the pipe piece rings on one side of the central point of the tunnel affected by the additional stress; k is a radical ofsThe tunnel inter-ring shear stiffness; k is a radical oftThe tensile rigidity between the tunnel rings; m and m +1 are serial numbers of adjacent two ring pipe sheet rings; d is the diameter of the tunnel; dtThe width of the ring of the pipe sheet is wide; j is the segment ring rigid body rotation effect proportional coefficient; w (y) is the tunnel horizontal displacement.
According to the energy variation method, a horizontal displacement function of the shield tunnel is assumed:
in the formula:
a is a matrix of undetermined coefficients in the displacement function, and A is { a ═ a0,a1…an}T(ii) a n is the expansion order of the Fourier series.
The two sides of the equal sign of the formula (16) are respectively subjected to derivation to obtain the coefficient to be determined
In the formula: a isiJ is the jth element in the matrix a, j is 1,2,3, …, n;
the equations (17) to (20) are further solved in place of the equation (22), so that a control equation of the tunnel horizontal displacement can be obtained:
equation (23) is simplified to a matrix form:
([Kr]+[Ks])AT＝{σx}T (24)
in the formula: [ K ]r]ATFor the interaction effect between the ring segments, [ K ]r]Is an inter-ring stiffness matrix; [ K ]s]ATIs the effect of soil resistance action, wherein [ Ks]A soil stiffness matrix; { sigma. }x}TThe horizontal additional stress caused by grouting has a tunneling effect.
From equation (24), the undetermined coefficient matrix A can be obtainedT：
AT＝([Kr]+[Ks])-1{σx}T (25)
A is to beTThe calculation function of the transverse horizontal displacement of the tunnel can be obtained in the formula (21):
ω(y)＝{Tn(y)}AT (26)
the main parameters needing to be input in the Matlab program calculation process comprise soil body parameters, deviation correcting tunnel and grouting related parameters and two blocks.
1. Soil body parameters:
poisson ratio mu of soil; compression modulus E of foundation soilsSymbol unit is kPa;
2. the tunnel 1 to be rectified and the relevant parameters of the grouting body are as follows:
the buried depth of the existing tunnel axis is H, and the symbol unit is m; radius of existing tunnel is RsThe unit symbol is m; the radius of the area to be grouted is R1The unit symbol is m; the radius of the reinforced area of the cylinder after grouting is R2The symbol unit is m; the depth of the upper top surface of the grouting cylindrical area is h1The unit symbol is m; depth of bottom surface is h2The unit symbol is m.
The following detailed description of the embodiments of the present invention is made with reference to the accompanying drawings.
Referring to a flow chart of an evaluation method shown in fig. 2, the evaluation method for compensating the deviation rectifying effect of the shield tunnel caused by grouting provided by the invention comprises the following steps of firstly determining an evaluation project, then collecting a tunnel 1 to be rectified and related data of grouting related to the project, substituting calculation software according to construction conditions and equipment, calculating by a Matlab program, referring to a level I control standard in urban rail transit structure safety protection technical regulation, if the center of an offset axis of the tunnel is less than 5mm, judging that the construction is reasonable, guiding construction by the sampling grouting amount, grouting distance and grouting depth, and if the center of the offset axis of the tunnel is not reasonable, adjusting related parameters to substitute the calculation again until the calculation is met.
As shown in fig. 3, a schematic diagram of the horizontal deviation rectifying effect of grouting according to the present invention is shown, and compensation grouting is mainly applied to the lifting engineering of surface buildings or tunnels, and most of the current research focuses on analyzing the lifting effect in the vertical direction caused by grouting, and the research on the control effect in the horizontal direction caused by grouting is less. In recent years, more and more existing tunnel projects generate horizontal deformation due to the unloading effect of peripheral projects, and the sleeve valve pipe 5 grouting technology is adopted for multiple times in actual projects to carry out deviation rectification control on the horizontal displacement of the existing tunnel.
FIGS. 4 and 5 are the model of mechanics calculationThe model and the uniform expansion model can be used for grouting soil layers within a certain depth range due to the fact that the sleeve valve pipe 5 is generally vertically driven into the soil layer in the horizontal deviation rectifying process, and the sleeve valve pipe 5 is provided with the slurry outlet holes at intervals. Assuming that the grout spreads evenly along the radial direction of the grout outlet, the grouting will be followed by forming a grouting reinforcement area which is approximately cylindrical by taking the sleeve valve pipe 5 as an axis. Assuming that the radius of the region to be grouted is R1The radius of the reinforced area of the cylinder after grouting is R2. Assuming that the height in the depth direction is constant, the depth of the upper top surface of the grouting cylindrical area is h1Depth of bottom surface is h2The corresponding plane coordinate of the sleeve valve tube 5 is (x)1,y1). The existing tunnel has a radius of RsThe buried depth of the axis is H, and the axis of the tunnel is located on the yoz plane and is parallel to the y axis.
Fig. 6 and 7 are layout diagrams of deviation rectification engineering of the sleeve valve pipe 5 under the working condition of the example. The tunnel deviation correcting site is located on the adjacent side of the diaphragm wall of a certain foundation pit project. Due to the unloading effect influence of the early foundation pit excavation, the existing tunnel has a certain horizontal deformation. To correct this horizontal displacement, two sleeve valve tubes 5 are provided at a distance of 10.3m from the tunnel side wall. The diameter of the sleeve valve pipe 5 is 30mm, the distance between the two sleeve valve pipes 5 is 4m, the two sleeve valve pipes 5 work simultaneously in the grouting process, and the grouting amount of a single sleeve valve pipe 5 is 4m3The depth range of grouting is 15 m-20 m, and the selected grouting reinforcement area is a cylinder with the height of 5m and the radius of 0.8 m. The outer diameter of the tunnel 1 to be rectified is 6.2m, and the tunnel lining is a C50 strength concrete prefabricated pipe piece.
FIG. 8 is a comparison between the correction amount of horizontal displacement of the tunnel caused by grouting and the measured data. As can be seen from the figure: (1) the tunnel horizontal displacement curve obtained by the calculation method of the embodiment of the invention is in normal distribution, the distribution of the actually measured data also has the characteristics of large middle and small two ends, and the distribution rules of the two are similar; (2) the maximum horizontal displacement value of the center obtained by the calculation method of the embodiment of the invention is 3.22mm, while the horizontal displacement value near the center obtained by actual measurement is 3.01mm, which is slightly smaller than the theoretical calculation value, but the difference value is smaller, thus meeting the accuracy requirement; (3) the influence range of the tunnel horizontal deviation correction obtained by the calculation method of the embodiment of the invention is approximately the same as the influence range reflected by the measured data, and the influence ranges are all from-30 m to 30 m. In summary, the results obtained by the calculation method of the embodiment of the present invention are relatively consistent with the measured data, which proves the reliability of the method of the embodiment of the present invention. The embodiment of the invention has certain accuracy in calculating the horizontal deviation correction quantity of the existing tunnel caused by grouting. In order to accurately correct the horizontal deformation of the tunnel, parameters such as grouting position, grouting depth and grouting amount need to be designed and controlled in advance in engineering. Parameters can be adjusted through repeated substitution and calculation, and the method helps to guide actual engineering design.
Fig. 9 shows a comparison of the tunnel horizontal displacement (correction amount) obtained by the original calculation method and the simplified method. As can be seen from the figure: (1) the change rule of the horizontal displacement curve of the tunnel obtained by the simplified method is the same as that of the curve obtained by the original method, the horizontal displacement curve and the curve are normally distributed, and the influence ranges are basically the same; (2) the whole tunnel horizontal displacement curve obtained by the simplified method is smaller than that obtained by the original method, the maximum displacement difference between the two is generated at the position where y is 0, the maximum central horizontal displacement value obtained by the original method is 3.22mm, the maximum central horizontal displacement value obtained by the simplified method is 2.65mm, and the maximum central horizontal displacement value accounts for 82.3% of the displacement value obtained by the original method; (3) comparing the interval from-10 m to 10m, the simplified horizontal displacement value is 79.8% -82.3% of the original method, i.e. the horizontal displacement value obtained by the simplified method is about 80% of the displacement value obtained by the original method in the main influence interval of the horizontal displacement.
In summary, the value obtained by the simplified method is smaller than that obtained by the original method, and in order to improve the accuracy of the simplified method, in the embodiment of the present invention, the result of the simplified method after the correction is obtained by multiplying the result of the simplified method by the correction coefficient q, and for the value of the correction coefficient q, the embodiment of the present invention provides a reference value where q is 1.25 according to the above research. As shown in fig. 9, the horizontal displacement curve obtained by the simplified method after correction is substantially identical to the curve obtained by the original calculation method, the central maximum values of the horizontal displacement curve and the curve are respectively 3.31mm and 3.22mm, the difference is only 0.09mm, and the accuracy requirement is met. Therefore, the corrected calculation method can simultaneously take account of the calculation efficiency and the accuracy of the result, and is more suitable for popularization and application. In the subsequent research, the embodiment of the invention uniformly adopts a simplified method after correction to calculate and analyze for the convenience of calculation.
The original parameters related to the standard case in the calculation process are specifically as follows:
(1) soil body parameters: poisson ratio mu of soil20.3; the elastic modulus E of the foundation soil is 25 MPa; compression modulus Es of soil body
＝9.32Mpa
(2) Grouting related parameters: the diameter of the sleeve valve pipe 5 is 30mm, the distance between the two sleeve valve pipes 5 is 4m, the two sleeve valve pipes 5 work simultaneously in the grouting process, and the grouting amount of a single sleeve valve pipe 5 is 4m3The depth range of grouting is 15 m-20 m, and the selected grouting reinforcement area is a cylinder with the height of 5m and the radius of 0.8 m.
(3) And (3) tunnel parameters: the outer diameter of the tunnel 1 to be rectified is 6.2m, and the tunnel lining is a C50 strength concrete prefabricated pipe piece. Segment ring rigid body rotation effect proportionality coefficient j is 0.3, and tunnel inter-ring shear rigidity ks＝7.45×105kN/m, tensile stiffness k between tunnel ringst＝1.94×106kN/m，EI＝1.1×108kN/m2Number of ring segments N is 175, tunnel diameter Dt＝1.5m。
Fig. 10 is a comparison of the effect of different grouting amounts on the horizontal displacement (deviation correction amount) of the tunnel, as shown in the figure: (1) the horizontal displacement value curves of the tunnel under different grouting amount working conditions are in normal distribution; (2) along with the increase of the grouting amount, the horizontal displacement value of the tunnel is gradually increased, and when the grouting amount is respectively 2m3、4m3、6m3、8m3、10m3When in use, the maximum horizontal displacement value of the center of the tunnel is 1.80mm, 3.31mm, 4.71mm, 6.16mm and 7.51mm in sequence; (3) with the increase of the grouting amount, the affected range of the tunnel is basically kept unchanged, and the occurrence area of the horizontal displacement is mainly concentrated between-25 m and 25 m.
Fig. 11 is a graph comparing the effect of different grouting distances on the horizontal displacement (correction amount) of the tunnel. As can be seen in the figure: (1) the change of the grouting distance has great influence on the horizontal displacement of the tunnel, but the horizontal displacement value curves of the tunnel are in normal distribution; (2) the horizontal displacement of the tunnel is gradually reduced along with the increase of the grouting distance, and when the grouting distance is respectively 5m, 10m, 15m and 20m, the maximum horizontal displacement value of the center of the tunnel is sequentially 17.8mm, 5.75mm, 2.6mm and 1.4 mm. This shows that in the actual engineering, when the slip casting point is nearer to the tunnel, the slight change of slip casting distance all can produce great influence to the volume of rectifying, needs to carry out strict control.
Fig. 12 shows a comparison of the effect of different grouting depths on the horizontal displacement (correction) of the tunnel. As can be seen from the figure: (1) the change of the grouting depth has an influence on the horizontal displacement of the tunnel, wherein the maximum horizontal displacement values of the centers of the tunnel of the control group and the experimental groups 1-5 are 3.31mm, 3.08mm, 3.01mm, 3.28mm, 2.98mm and 2.13mm in sequence; (2) the grouting deviation rectifying effect of the control group is superior to that of each experimental group, namely, a grouting depth scheme adopted in the 3.1-section engineering case is an optimal method, and the buried depth of a grouting section of the control group is 15-20 m, namely, the equal depth of the lower end face of the grouting section and the lower end point of the tunnel. In the actual engineering, under the condition of determining that the grouting length is not changed, when the burial depth h of the lower end surface of the grouting section is equal to the preset value2When the deviation of the grouting deviation is equal to the lower end point of the tunnel, the deviation rectifying effect of the grouting is the largest, and the grouting deviation rectifying efficiency can be improved by adopting the scheme in the construction.
Fig. 9, 10, 11 and 12 are obtained by selecting and substituting parameters and calculating the Matlab program under the standard working condition of the case, and finally drawing.
The invention relates to partial parameters and cited shearing staggered platform and rigid body rotation deformation models, which are derived from the thesis of ' Wei class, Shu Ye, Yanbo ', the calculation of shearing staggered platform deformation of the existing tunnel under a newly built shield tunnel [ J ]. the university report of Hunan (natural science edition), 2018,45(9) ' 103 plus 112 ' and ' Wei class, Zhang Xinhai ', the excavation of a foundation pit causes the rotation of a lower horizontal shield tunnel and the calculation of staggered platform deformation [ J ]. the university report of Zhongnan: the natural science edition, 2019,50(9):2273 plus 2284 ' the calculation of soil displacement caused by tunnel construction refers to ' Jianliang ' the report of Xinjiang Zhao, Shi Min, and the mirror image method in the calculation of the soil displacement of tunnel construction [ J ]. the university of Harbin industry, 2005(06):801 plus 803 ], and the rest of partial parameters are reasonably determined according to the practical experience of the engineering.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (5)
1. A method for evaluating grouting deviation rectifying effect aiming at horizontal deformation of a shield tunnel is characterized by comprising the following steps:
according to the principle of the horizontal deviation rectifying effect of compensation grouting, a sleeve valve pipe grouting volume expansion mechanical calculation model is established, and a calculation formula of simplified horizontal additional stress at any point in a soil layer caused by grouting is deduced based on the mirror image method principle;
adopting a uniform expansion model of a grouting area, obtaining the volume of a soil body after grouting expansion according to the amount of slurry injected by the sleeve valve pipe and the volume expansion rate of the grouting ring, and substituting the volume into the calculation formula to obtain the horizontal additional stress at the tunnel to be rectified;
deducing a tunnel horizontal displacement formula caused by grouting through a tunnel shearing dislocation and rigid body rotation cooperative deformation calculation model, substituting the horizontal additional stress at the tunnel to be corrected into the tunnel horizontal displacement formula, thus obtaining a final calculation formula of the tunnel horizontal displacement to be corrected, and substituting the final calculation formula into any point in a calculation range to obtain the horizontal displacement correction amount of the tunnel;
and evaluating according to the horizontal displacement correction amount of the tunnel, and referring to the I-level control standard in the urban rail transit structure safety protection technical regulation, if the offset axis center of the tunnel is less than 5mm, the tunnel is reasonable, otherwise, the tunnel is unreasonable.
2. The method for evaluating the effect of correcting the horizontal displacement of the shield tunnel caused by the compensation grouting according to claim 1, wherein the formula for calculating the simplified horizontal additional stress at any point in the soil layer caused by the grouting based on the mirror image method principle comprises:
step 1) neglecting the existence of the ground, converting the semi-infinite body problem in the actual engineering into the problem in the infinite body, wherein the existing bodyThe volume expansion point will generate normal stress-sigma at the original ground position0And shear stress tau0；
Step 2) with the ground as a boundary, a void point with the same size is supposed at the position of the mirror image of the original expansion point in an infinite body, and the void point generates positive stress sigma at the position of the original ground0And shear stress tau0；
Step 3) the normal stresses generated in the original place by the two steps are mutually offset, and the shear stress is 2 tau0In order to meet the actual free boundary condition, the generated additional shear stress is reversely applied to the surface of the semi-infinite body;
the sum of the stresses generated in the three steps is the solution of the additional stress caused by the volume expansion point;
based on the concept of the mirror image method, point (x)0,y0,z0) A spherical expansion region with a radius a will produce a displacement component S at point (x, y, z)i1：
In the formula:
a is the spherical expansion zone radius;
in its mirror position (x)0,y0,z0) The displacement component generated at the point (x, y, z) at the gap point with equal size is Si2：
In the formula:
according to the basic equation of elasticity mechanics, the calculation formulas of the strain and the stress generated in the soil body in the three steps are as follows:
in the formula: epsiloni，γxz，γyzStrain, σ, for the soil massiThe stress generated by the soil body, E is the elastic modulus of the soil body, mu is the Poisson ratio, and G is the shear modulus of the soil body;
substituting the formula (1) to the formula (5) into the formula (6) to obtain the calculation formula of the horizontal additional stress generated in the steps 1) and 2) as follows:
step 1) and step 2) the shear stress generated at the earth surface satisfies tauxz＝GγxzAnd τyz＝GγyzAnd reversely acting the shear stress on the earth surface, and integrating through Cerrtuti solution to obtain the stress calculation formula of the step 3) as follows:
additional stress sigmax3Compare sigmax1-2Neglected and long calculation time, part of the additional stress sigma 'in the horizontal x direction caused by the expansion of unit volume'xComprises the following steps:
the influence of grouting on surrounding soil is simulated through the volume expansion of the soil in a grouting area, and the original volume of a to-be-grouted area is assumed to be V1Volume increase after grouting is V2Then, the calculation formula of the horizontal additional stress at any point in the soil layer caused by grouting is as follows:
3. the method for evaluating the grouting deviation rectifying effect for the horizontal deformation of the shield tunnel according to claim 1, wherein a uniform expansion model of a grouting area is adopted, the volume of a soil body after grouting is obtained according to the amount of slurry injected by a sleeve valve pipe and the volume expansion rate of a grouting ring, and the calculation formula is substituted to obtain the horizontal additional stress at the tunnel to be rectified as follows:
taking the radius of a region to be grouted as R1The radius of the reinforced area of the cylinder after grouting is R2Assuming that the height in the depth direction is constant, the depth of the upper top surface of the grouting cylindrical region is h1Depth of bottom surface is h2The corresponding plane coordinate of the sleeve valve tube is (x)1,y1) The radius of the tunnel to be rectified is RsThe buried depth of the axis is H, and the axis of the tunnel is positioned on the yoz plane and is parallel to the y axis;
when a grouting area uniform expansion model is adopted, the horizontal additional stress of any point at the position of the tunnel to be rectified is obtained and expressed as:
in the formula: a. b is the upper and lower integral limits of the variable xi (along the x-axis), c, d are the variable zeta (along the y-axis)Axis), e, f are the integral upper and lower limits of the variable η (along the z-axis), 1 in the subscript represents the pre-grouting state, 2 represents the post-grouting volume expansion state; the calculation formula of the upper and lower limits of each integral is as follows: a is1＝x1-R,b1＝x1+R1,
e1＝h1,f1＝h2,a2＝x1-R2,b2＝x1+R2,
e2＝h1,f2＝h2。
4. The method for evaluating the grouting deviation rectifying effect for the horizontal deformation of the shield tunnel according to claim 1, wherein the volume process of the soil body after grouting expansion obtained according to the amount of the grout injected from the sleeve valve pipe and the volume expansion rate of the grouting ring is as follows:
the volume expansion rate Q of the soil before and after grouting is defined as:
in the formula R1Radius of the area to be grouted, R2Radius of the reinforced area of the cylinder after grouting, h1For the depth of the upper top surface of the grouting cylinder area, h2The depth of the lower bottom surface;
volume expansion rate Q and grouting amount V of grouting ringinjAnd grouting efficiency xiinjAbout, expressed as:
further conversion can be:
5. the method for evaluating the grouting rectification effect for the horizontal deformation of the shield tunnel according to claim 1, wherein a tunnel horizontal displacement formula caused by grouting is derived through a tunnel shearing slab staggering and rigid body rotation cooperative deformation calculation model, and the horizontal additional stress at the tunnel to be rectified is brought into the tunnel horizontal displacement formula, so that a final calculation formula of the tunnel horizontal displacement to be rectified can be obtained, which is specifically as follows:
from the analysis of the longitudinal deformation work doing and energy conversion angles of the tunnel, the additional stress caused by grouting can be used for overcoming the stratum resistance, the shearing force between the segment rings and the tension between the rings to do work respectively, namely the requirements are met:
Wσ＝WR+WS+WT (15)
in the formula: wσAdding total work amount for grouting stress; wRActing to overcome the resistance of the stratum; wSActing to overcome the inter-ring shear force; wTActing to overcome tension between rings;
by integrating the additional stress, the formation resistance, the shearing force and the tension force in the longitudinal direction of the tunnel, the respective work amount W can be obtainedσ、WR、WS、WTThe respective calculation formula:
in the formula: n is the number of the pipe piece rings on one side of the central point of the tunnel affected by the additional stress; k is a radical ofsThe tunnel inter-ring shear stiffness; k is a radical oftThe tensile rigidity between the tunnel rings; m and m +1 are serial numbers of adjacent two ring pipe sheet rings; d is the diameter of the tunnel; dtThe width of the ring of the pipe sheet is wide; j is the segment ring rigid body rotation effect proportional coefficient; w (y) is the tunnel horizontal displacement;
according to the energy variation method, a horizontal displacement function of the shield tunnel is assumed:
in the formula:
a is a matrix of undetermined coefficients in the displacement function, and A is { a ═ a0,a1…an}T(ii) a n is the expansion order of Fourier series;
the two sides of the equal sign of the formula (16) are respectively subjected to derivation to obtain the coefficient to be determined
In the formula: a isiJ is the jth element in the matrix a, j is 1,2,3, …, n;
the equations (17) to (20) are further solved in place of the equation (22), so that a control equation of the tunnel horizontal displacement can be obtained:
equation (23) is simplified to a matrix form:
([Kr]+[Ks])AT＝{σx}T (23)
in the formula: [ K ]r]ATFor the interaction effect between the ring segments, [ K ]r]Is an inter-ring stiffness matrix; [ K ]s]ATIs the effect of soil resistance action, wherein [ Ks]A soil stiffness matrix; { sigma. }x}TThe effect of horizontal additional stress caused by grouting on the tunnel is achieved;
from equation (24), the undetermined coefficient matrix A can be obtainedT：
AT＝([Kr]+[Ks])-1{σx}T (24)
A is to beTThe final calculation formula of the transverse horizontal displacement of the tunnel to be rectified can be obtained by substituting the formula (21):
ω(y)＝{Tn(y)}AT (25)。
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| CN113791174A (en) * | 2021-07-09 | 2021-12-14 | 上海市隧道工程轨道交通设计研究院 | Tunnel bottom grouting jacking model test device and test method |
| CN115404846A (en) * | 2022-09-23 | 2022-11-29 | 中国建筑第五工程局有限公司 | Deviation rectifying device and method for tunnel deformation |
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| CN113791174A (en) * | 2021-07-09 | 2021-12-14 | 上海市隧道工程轨道交通设计研究院 | Tunnel bottom grouting jacking model test device and test method |
| CN115404846A (en) * | 2022-09-23 | 2022-11-29 | 中国建筑第五工程局有限公司 | Deviation rectifying device and method for tunnel deformation |
| CN115404846B (en) * | 2022-09-23 | 2024-01-26 | 中国建筑第五工程局有限公司 | Deviation correcting device and method for tunnel deformation |
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