CN111428304A - Displacement deformation prediction method for shield tunnel with anti-floating anchor rod under excavation of foundation pit - Google Patents
Displacement deformation prediction method for shield tunnel with anti-floating anchor rod under excavation of foundation pit Download PDFInfo
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Abstract
The invention discloses a displacement deformation prediction method for a shield tunnel with an anti-floating anchor rod under excavation of a foundation pit, and belongs to the technical field of underground engineering. The prediction method specifically comprises the following steps: establishing the position relation between the shield tunnel with the anti-floating anchor rods and the ground foundation pit, calculating the additional load of the shield tunnel with the anti-floating anchor rods caused by foundation pit excavation, considering the rotation and staggered segment ring cooperative deformation model, and calculating the total deformation potential energy E of the shield tunnel under the action of the anti-floating anchor rodspmObtaining a longitudinal displacement function w (l) and the quantity of staggered platforms between adjacent shield segments through Fourier expansion and a variation control equationm2And shear forces Qm between adjacent shield segments. The prediction method has the characteristics of considering the number of the anti-floating anchor rod acting pipe pieces, approaching the deformation condition of the shield tunnel to the real condition and having high accuracy.
Description
Technical Field
The invention belongs to the technical field of underground engineering, and particularly relates to a displacement deformation prediction method for a shield tunnel with an anti-floating anchor rod under foundation pit excavation, which is suitable for predicting displacement and deformation values of the shield tunnel with the anti-floating anchor rod under the influence of the upper foundation pit excavation.
Background
In recent years, with the development of underground engineering construction, urban shallow stratum spaces become more and more crowded, and the situation that construction engineering is adjacent to an existing shield tunnel occurs more and more frequently. The adjacent existing tunnel is subjected to foundation pit excavation engineering, so that an unloading effect is generated on soil above the existing tunnel, floating deformation of the existing tunnel is caused, deformation and damage of a shield tunnel structure can be caused, and the safety of the tunnel is seriously threatened.
At present, measures for controlling the floating of the tunnel include carrying out pile loading back pressure in the tunnel, arranging an isolation pile at the side of the tunnel, arranging an anti-floating anchor rod and the like. The anti-floating anchor rod utilizes an anchoring body consisting of the anchor rod and mortar and shearing force of a rock-soil layer to resist buoyancy borne by an underground structure, is mainly applied to structures such as basements, shallow tunnels, pools and the like at present, is less in application of shield tunnels, and has yet to be continuously researched for controlling the floating effect of the shield tunnels. The existing research method is mainly finite element simulation, the result of the finite element simulation has a large relation with the reduction degree of the modeling on the real working condition, the accuracy of the result cannot be ensured, and the existing research of displacement deformation of the downward lying tunnel with the anti-floating anchor rod caused by excavation of the foundation pit is not solved by a useful theory at present.
In summary, most researches on displacement deformation of shield tunnels with anti-floating anchor rods under foundation pit excavation are focused on finite element numerical simulation, accuracy is difficult to ensure, and a derivation method without theoretical solution is urgent to carry out relevant researches.
Disclosure of Invention
The invention aims to overcome the defects and provides a displacement deformation prediction method for a shield tunnel with an anti-floating anchor rod under foundation pit excavation.
The purpose of the invention is realized by the following technical scheme: a displacement deformation prediction method for a shield tunnel with an anti-floating anchor rod under foundation pit excavation comprises the following steps:
(1) establishing a coordinate system by taking the center of the ground foundation pit as a coordinate origin, measuring the excavation size L of the foundation pit parallel to the axial direction of the tunnel, the excavation size B of the foundation pit vertical to the axial direction of the tunnel, the excavation depth d of the foundation pit, and the insertion depth d of the enclosure structure below the bottom of the foundation pit0The method comprises the following steps of calculating the total height H of a foundation pit enclosure structure as D + D0, the buried depth H of the tunnel axis as s + D/2+ D, and obtaining the number of calculation rings of the tunnel lining influenced by foundation pit excavation as 2N; obtaining the number of the calculation rings 2N of the tunnel lining influenced by the anti-floating anchor rod according to the working condition1And establishing the position relation between the shield tunnel with the anti-floating anchor rod and the ground foundation pit.
(2) Calculating the additional load of the shield tunnel with the anti-floating anchor rod caused by excavation of the foundation pit, and specifically comprising the following steps:
deducing that a certain point (ξ, d) at the bottom of the foundation pit is positioned at the size p- (1- α) according to the Mindlin solution0) And gamma d is unloaded to cause vertical additional load p (l) of a certain point (a, l, h) on the axis of the shield tunnel:
wherein gamma is the gravity of the soil, α0Is the residual stress factor.
(3) Predicting the displacement deformation of the shield tunnel with the anti-floating anchor rod under excavation of the foundation pit, and specifically comprising the following substeps:
(3.1) calculating the total deformation potential energy E of the shield tunnel under the action of the anti-floating anchor rod by considering the rotation and staggered segment ring collaborative deformation modelpm：
Epm＝WL+WRm+WS+WT(2)
Wherein, WLActing on additional load of shield tunnel, WRmFor overcoming the resistance of the formation to work under the action of the anti-floating anchor rod, WSTo overcome the inter-ring shear force, WTWork is done to overcome the tension between the rings.
w (l) is a deformation function of the longitudinal displacement of the shield tunnel, kmIs the resistance coefficient of the soil body of the anti-floating anchor rod, k is the foundation bed coefficient of the soil, DtThe width of each shield tunnel is the ring width.
(3.2) the shield tunnel longitudinal displacement deformation function is symmetrical about the excavation midpoint of the foundation pit and is obtained by Fourier series expansion:
wherein:
A＝(a1a2a3L an)T；
n is the expansion series of Fourier;
(3.3) obtaining a longitudinal displacement function w (l) and the quantity of staggered platforms between adjacent shield segments through a variational control equationm2And the shearing force Q between adjacent shield segmentsm：
Based on the principle of minimum potential energy, the total potential energy E of the step (3.1) is calculatedpmAnd (3) taking an extreme value for each undetermined coefficient, namely:
in the formula: a isiThe coefficient of the ith element in the matrix A, namely the polynomial of the longitudinal displacement deformation function of the tunnel;
expressed in matrix form:
([Kr]+[Ksm])AT＝[P]T(7)
in the formula: [ K ]r]ATFor the interaction effect between the tunnel rings:
[Ksm]ATthe soil resistance effect under the action of the anti-floating anchor rod is as follows:
wherein: [ P ]]TRepresents the effect of the additional load on the tunnel lining:
[ P ] obtained by the above procedure]T、[Kr]And [ K ]sm]Calculating to obtain an undetermined coefficient matrix AT:
AT＝([Kr]+[Ksm])-1[P]T(11)
obtaining a longitudinal displacement deformation function w (l) of the tunnel:
w(l)＝Tn(l)AT(12)
staggering quantity between adjacent shield segmentsm2Then it is:
m2＝(1-j){w[(m+1)Dt]-w(mDt)} (13)
shearing force Q between adjacent shield segmentsmComprises the following steps:
Qm＝(1-j){w[(m+1)Dt]-w(mDt)}×kt(14)
further, the process of acquiring the number 2N of the calculation loops of the tunnel lining affected by the excavation of the foundation pit in the step 1 specifically comprises the following steps: and when the 2N is different, the corresponding maximum bump value forms a change curve, the change curve finally tends to be stable, and the 2N is the minimum value which enables the change curve to tend to be stable.
Further, 2N is 50 rings or more.
Further, step 3 is described as [ K ]t]And [ K ]sm]Is a 10 th order matrix.
Compared with the prior art, the invention has the beneficial effects that:
1. a segment ring cooperative deformation model considering rotation and slab staggering is introduced, shearing deformation and slab staggering deformation between tunnel rings are comprehensively considered, the stress deformation condition of a real tunnel structure is better met, and the accuracy of the prediction method is improved.
2. The downward elastic force of the upper soil body and the anti-floating force generated by the anti-floating anchor rod on the shield tunnel are combined and simplified into a larger vertical downward elastic force, so that the calculation model is simpler and more understandable.
3. Introducing a new soil resistance coefficient k of the anti-floating anchor rodmAnd using 2N in combination1And the number of the shield tunnel segments influenced by the anti-floating anchor rods is shown. Can be calculated by changing k during programmingmAnd N1The numerical value of the k is used for reflecting the deformation of the shield tunnel with the anti-floating anchor rod under various working conditions, and when the k ismAnd N1And when one item is 0, the calculation method is the shield tunnel deformation caused by the excavation of the foundation pit without the anti-floating anchor rod. After example calculation and comparison, the empirical values of the resistance coefficient km of the anti-floating anchor rod soil body under different working conditions can be obtained so as to guide the design of an actual engineering scheme. By changing the value of N1 in prediction, the application scheme of the anti-floating anchor rod in the shield tunnel can be optimized.
4. The invention provides a method for predicting displacement deformation of a shield tunnel with an anti-floating anchor rod under foundation pit excavation, which can be used for predicting actual foundation pit excavation engineering and can also be used as a reference for selecting the anti-floating anchor rod as a shield tunnel anti-floating measure.
Drawings
FIG. 1 is a model diagram of a circular shield tunnel with anti-floating anchor rods;
FIG. 2 is a mechanical model diagram of a circular shield tunnel with anti-floating anchor rods;
FIG. 3 is a schematic diagram illustrating the influence of excavation of a foundation pit on a lower horizontal shield tunnel with anti-floating anchors;
FIG. 4 is a diagram showing a relationship between the positions of a foundation pit and a shield tunnel;
FIG. 5 is a graph of a tunnel lining calculation loop number;
FIG. 6 is a reliability verification diagram of the prediction method of the present invention.
Detailed Description
The invention is further described with reference to the following examples and the accompanying drawings. The following examples are presented to aid in understanding the present invention and to verify the reliability of the prediction method proposed by the present 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.
Examples
The method is characterized in that a paper of Yangshitong, Tang gorgeous, Liu Qing, and the like is used for carrying out prediction analysis on a protection technology research [ J ] of an existing shield tunnel lying in an ultra-short distance in foundation pit excavation construction, tunnel construction (Chinese and English), 2017,37 (increase 2): 35-46', and a result obtained by numerical calculation through finite difference software F L AC3D is used as a case, and the specific steps are as follows:
step 1: establishing shield tunnel model with anti-floating anchor rod
As shown in fig. 1, the anti-floating anchor rod is reserved on a segment at the lower part of the shield tunnel to serve as an early support in a tunnel section with weak surrounding rocks, severe breakage and poor self-stability, and soft rocks in V-level surrounding rocks, VI-level surrounding rocks and IV-level surrounding rocks; the combined support is combined with an anchor rod, a reinforcing mesh and sprayed concrete to form a combined support, and the vacancy is connected with the shield tunnel. When the surrounding environment of the shield tunnel with the anti-floating anchor rod is unchanged, the anti-floating anchor rod does not work; when a foundation pit is excavated above the shield tunnel with the anti-floating anchor rod, the unloading function of the excavation surface can be transmitted to the shield tunnel below through a soil body, an additional load is caused on the tunnel structure, the stress balance of the segment structure is damaged, and deformation is generated, and the anti-floating anchor rod gives a downward anti-floating force to the shield tunnel through the friction function with the soil body. As shown in fig. 2, each segment ring of the shield tunnel is simplified into an elastic foundation short beam, and at the moment, the shield tunnel can be regarded as being subjected to downward elastic force of an upper soil body and anti-floating force generated by an anti-floating anchor rod, and can be combined and simplified into a larger vertical downward elastic force.
Referring to fig. 3-5, a coordinate system is established with the ground foundation pit center as the origin of coordinates, and the excavation size L of the foundation pit parallel to the axial direction of the tunnel, the excavation size B of the foundation pit perpendicular to the axial direction of the tunnel, the excavation depth d of the foundation pit, and the insertion depth d of the enclosure structure below the bottom of the foundation pit are measured0The method comprises the following steps of calculating the total height H of a foundation pit enclosure structure as D + D0, the buried depth H of the tunnel axis as s + D/2+ D, and obtaining the number of calculation rings of the tunnel lining influenced by foundation pit excavation as 2N; obtaining the number of the calculation rings 2N of the tunnel lining influenced by the anti-floating anchor rod according to the working condition1And establishing the position relation between the shield tunnel with the anti-floating anchor rod and the ground foundation pit.
The process of acquiring the number 2N of the calculated rings of the tunnel lining affected by the excavation of the foundation pit specifically comprises the following steps: and when the 2N is different, the corresponding maximum bump value forms a change curve, the change curve finally tends to be stable, and the 2N is the minimum value which enables the change curve to tend to be stable. 2N is more than 50 rings.
Step 2: calculating additional load of shield tunnel with anti-floating anchor rod caused by foundation pit excavation
Deducing that a certain point (ξ, d) at the bottom of the foundation pit is positioned at the size p- (1- α) according to the Mindlin solution0) And gamma d is unloaded to cause vertical additional load p (l) of a certain point (a, l, h) on the axis of the shield tunnel:
wherein gamma is the gravity of the soil, α0Is the residual stress factor.
And step 3: calculating displacement deformation of shield tunnel with anti-floating anchor rod under excavation of foundation pit
In order to enable the result of calculating the settlement and deformation of the tunnel to be closer to the real result, the invention uses a segment ring cooperative deformation model considering rotation and dislocation. The displacement deformation calculation method of the shield tunnel with the anti-floating anchor rods under the excavation of the foundation pit is obtained by changing a formula for overcoming the stratum resistance to obtain acting for overcoming the stratum resistance under the action of the anti-floating anchor rods, so that the total deformation potential energy of the shield tunnel under the action of the anti-floating anchor rods is calculated, and then the displacement deformation calculation method of the shield tunnel with the anti-floating anchor rods under the excavation of the foundation pit is obtained through Fourier expansion of a longitudinal displacement function of the shield. The method specifically comprises the following substeps:
(3.1) calculating the total deformation potential energy E of the shield tunnel under the action of the anti-floating anchor rod by considering the rotation and staggered segment ring collaborative deformation modelpm：
Let the relative vertical displacement of adjacent lining rings numbered m and m +1 bemObtaining:
m＝w[(m+1)Dt]-w(mDt) (15)
in the formula: the serial numbers of two adjacent ring pipe sheet rings of m and m + 1; dtThe ring width of the pipe sheet ring is shown, and the unit symbol is m;
when the lining rings rotate by an angle thetamWhen the ratio is small:
shear force F between ringssmComprises the following steps:
Fsm＝(1-j)ks m(17)
maximum tension F between ringstmComprises the following steps:
Ftm＝ktθmD (18)
formation resistance FkComprises the following steps:
Fk＝kDw(l) (19)
wherein: k is a radical ofsFor the inter-annular shear stiffness, k, of the tunneltThe inter-ring tensile stiffness of the tunnel, j is the segment ring rigid body rotation effect proportionThe coefficient k is the foundation bed coefficient of the soil, the Vesic formula is adopted for calculation,
mu is the Poisson's ratio of the soil, E0Is the deformation modulus of the foundation soil,
Esis the compressive modulus of soil, EtItIs the equivalent flexural rigidity of the tunnel, and b is the width of the foundation beam.
The total potential energy of the shield tunnel deformation can be divided into four parts, and a new anti-floating anchor rod soil resistance coefficient k is introduced into the stratum resistance acting part in the method of the inventionmThe method can be used for indicating that the stratum resistance is overcome to do work under the action of the anti-floating anchor rod, so that the total deformation potential energy of the shield tunnel under the action of the anti-floating anchor rod is obtained, and the method specifically comprises the following steps:
performing work on additional load caused by excavation of the foundation pit:
overcoming the resistance of the stratum to do work under the action of the anti-floating anchor rod:
because the soil resistance effect can be changed under the action of the anti-floating anchor rod, the invention introduces the soil resistance coefficient k of the anti-floating anchor rodmAnd obtaining a calculation method for the soil resistance effect when the anti-floating anchor rod acts:
in the formula: k is a radical ofmIs the resistance coefficient of the soil body of the anti-floating anchor rod.
Overcoming the inter-ring shearing force to do work:
overcoming tension between rings to do work:
total potential energy E of horizontal shield tunnel deformation under action of anti-floating anchor rodpm：
Epm＝WL+WRm+WS+WT(2)
(3.2) the shield tunnel longitudinal displacement deformation function is symmetrical about the excavation midpoint of the foundation pit and is obtained by Fourier series expansion:
wherein:
A＝(a1a2a3L an)T；
n is the expansion series of Fourier;
(3.3) obtaining a longitudinal displacement function w (l) and the quantity of staggered platforms between adjacent shield segments through a variational control equationm2And the shearing force Q between adjacent shield segmentsm：
Based on the principle of minimum potential energy, the total potential energy E of the step (3.1) is calculatedpmAnd (3) taking an extreme value for each undetermined coefficient, namely:
in the formula: a isiThe coefficient of the ith element in the matrix A, namely the polynomial of the longitudinal displacement deformation function of the tunnel;
expressed in matrix form:
([Kr]+[Ksm])AT＝[P]T(7)
in the formula: [ K ]r]ATFor the interaction effect between the tunnel rings:
[Ksm]ATthe soil resistance effect under the action of the anti-floating anchor rod is as follows:
wherein: [ P ]]TRepresents the effect of the additional load on the tunnel lining:
[ P ] obtained by the above procedure]T、[Kr]And [ K ]sm]Calculating to obtain a matrix A of undetermined coefficientsT：
AT＝([Kr]+[Ksm])-1[P]T(11)
Obtaining a longitudinal displacement deformation function w (l) of the tunnel:
w(l)＝Tn(l)AT(12)
staggering quantity between adjacent shield segmentsm2Then it is:
m2＝(1-j){w[(m+1)Dt]-w(mDt)} (13)
shearing force Q between adjacent shield segmentsmComprises the following steps:
Qm＝(1-j){w[(m+1)Dt]-w(mDt)}×kt(14)
the prediction method can be programmed and calculated by Matlab software, wherein the matrix [ K [ ]t]And [ K ]sm]A calculation matrix of order 10 is used to ensure accuracy.
In this embodiment, specific parameters in Matlab software are taken as follows:
when no anti-floating anchor rod acts:
L＝90m，B＝70m，H＝18.9m，d＝11.2m，d0＝7.7m，α0＝0，μ＝0.35，γ＝19kN/m3，c＝30kPa，Es＝8×103kPa，Dt＝1.2m，D＝6m，N＝61，ks＝1.94×106kN/m，kt＝7.45×105kN/m，EtIt＝1.1×108kN·m2,b＝0.22m，j＝0.3，a＝7.5m，h＝15.9m，N1＝0，km＝0。
when the anti-floating anchor rod acts:
L＝90m，B＝70m，H＝18.9m，d＝11.2m，d0＝7.7m，α0＝0，μ＝0.35，γ＝19kN/m3，c＝30kPa，Es＝8×103kPa，Dt＝1.2m，D＝6m，N＝61，ks＝1.94×106kN/m，kt＝7.45×105kN/m，EtIt＝1.1×108kN·m2,b＝0.22m，j＝0.3，a＝7.5m，h＝15.9m，N1＝40，km＝1.4。
among the above parameters, the values of the foundation pit size L and B are properly adjusted on the basis of the original text because the finite element model is not the standard foundation pit excavation condition.
The calculated value and the simulated value of the displacement deformation of the lower horizontal existing tunnel with the anti-floating anchor rod caused by the excavation of the foundation pit are shown in fig. 6. As can be seen from fig. 6, the vertical displacement value predicted by the method of the present invention is relatively consistent with the analog value, wherein the maximum value of the calculated vertical displacement value when no anchor rod exists in the tunnel is 23.4mm, the analog value in the original text is 23mm, the maximum value of the calculated vertical displacement value when an anchor rod exists in the tunnel is 18.6mm, the analog value in the original text is 18.9mm, and the calculation result meets the accuracy requirement. The prediction method provided by the invention can better reflect the displacement deformation of the existing tunnel with the anti-floating anchor rod in the horizontal direction caused by the excavation of the foundation pit.
Claims (4)
1. A displacement deformation prediction method for a shield tunnel with an anti-floating anchor rod under foundation pit excavation is characterized by comprising the following steps:
(1) establishing a coordinate system by taking the center of the ground foundation pit as a coordinate origin, and measuring L the excavation size of the foundation pit parallel to the axial direction of the tunnel, B the excavation size of the foundation pit vertical to the axial direction of the tunnel, d the excavation depth of the foundation pit, and an enclosure structure below the bottom of the foundation pitDepth of insertion d0The method comprises the following steps of calculating the total height H of a foundation pit enclosure structure as D + D0, the buried depth H of the tunnel axis as s + D/2+ D, and obtaining the number of calculation rings of the tunnel lining influenced by foundation pit excavation as 2N; obtaining the number of the calculation rings 2N of the tunnel lining influenced by the anti-floating anchor rod according to the working condition1And establishing the position relation between the shield tunnel with the anti-floating anchor rod and the ground foundation pit.
(2) Calculating the additional load of the shield tunnel with the anti-floating anchor rod caused by excavation of the foundation pit, and specifically comprising the following steps:
deducing that a certain point (ξ, d) at the bottom of the foundation pit is positioned at the size p- (1- α) according to the Mindlin solution0) And gamma d is unloaded to cause vertical additional load p (l) of a certain point (a, l, h) on the axis of the shield tunnel:
wherein gamma is the gravity of the soil, α0Is the residual stress factor.
(3) Predicting the displacement deformation of the shield tunnel with the anti-floating anchor rod under excavation of the foundation pit, and specifically comprising the following substeps:
(3.1) calculating the total deformation potential energy E of the shield tunnel under the action of the anti-floating anchor rod by considering the rotation and staggered segment ring collaborative deformation modelpm：
Epm＝WL+WRm+WS+WT(2)
Wherein, WLActing on additional load of shield tunnel, WRmFor overcoming the resistance of the formation to work under the action of the anti-floating anchor rod, WSTo overcome the inter-ring shear force, WTWork is done to overcome the tension between the rings.
w (l) is a deformation function of the longitudinal displacement of the shield tunnel, kmIs the resistance coefficient of the soil body of the anti-floating anchor rod, k is the foundation bed coefficient of the soil, DtThe width of each shield tunnel is the ring width.
(3.2) the shield tunnel longitudinal displacement deformation function is symmetrical about the excavation midpoint of the foundation pit and is obtained by Fourier series expansion:
wherein:
A＝(a1a2a3L an)T；
n is the expansion series of Fourier;
(3.3) obtaining a longitudinal displacement function w (l) and the quantity of staggered platforms between adjacent shield segments through a variational control equationm2And the shearing force Q between adjacent shield segmentsm：
Based on the principle of minimum potential energy, the total potential energy E of the step (3.1) is calculatedpmAnd (3) taking an extreme value for each undetermined coefficient, namely:
in the formula: a isiThe coefficient of the ith element in the matrix A, namely the polynomial of the longitudinal displacement deformation function of the tunnel;
expressed in matrix form:
([Kr]+[Ksm])AT＝[P]T(7)
in the formula: [ K ]r]ATFor the interaction effect between the tunnel rings:
[Ksm]ATthe soil resistance effect under the action of the anti-floating anchor rod is as follows:
wherein: [ P ]]TRepresents the effect of the additional load on the tunnel lining:
[ P ] obtained by the above procedure]T、[Kr]And [ K ]sm]Calculating to obtain a matrix A of undetermined coefficientsT：
AT＝([Kr]+[Ksm])-1[P]T(11)
Obtaining a longitudinal displacement deformation function w (l) of the tunnel:
w(l)＝Tn(l)AT(12)
staggering quantity between adjacent shield segmentsm2Then it is:
m2＝(1-j){w[(m+1)Dt]-w(mDt)} (13)
shearing force Q between adjacent shield segmentsmComprises the following steps:
Qm＝(1-j){w[(m+1)Dt]-w(mDt)}×kt(14)
2. the prediction method according to claim 1, wherein the step 1 of obtaining the number 2N of the calculation loops of the tunnel lining affected by excavation of the foundation pit specifically comprises the following steps: and when the 2N is different, the corresponding maximum bump value forms a change curve, the change curve finally tends to be stable, and the 2N is the minimum value which enables the change curve to tend to be stable.
3. The prediction method according to claim 2, wherein 2N is 50 rings or more.
4. The prediction method of claim 1, wherein [ K ] is defined in step 3t]And [ K ]sm]Is a 10 th order matrix.
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| CN112597674A (en) * | 2020-12-05 | 2021-04-02 | 福建工程学院 | Method for determining lateral pipeline transverse additional internal force caused by foundation pit excavation |
| CN115146420A (en) * | 2022-09-05 | 2022-10-04 | 中南大学 | Method for establishing railway tunnel anchor rod refined model |
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