CN111428304A - Displacement deformation prediction method for shield tunnel with anti-floating anchor rod under excavation of foundation pit - Google Patents

Abstract

The invention discloses a displacement and deformation prediction method for a shield tunnel with anti-floating anchor rods under foundation pit excavation, and belongs to the technical field of underground engineering. The specific prediction method is as follows: establish the positional relationship between the shield tunnel with anti-floating anchor and the ground foundation pit, calculate the additional load of the shield tunnel with anti-floating anchor caused by the excavation of the foundation pit, and consider the rotation and staggered platform. The joint deformation model of the segment ring is used to calculate the total deformation potential energy E _pm of the shield tunnel under the action of the anti-floating anchor. The amount of stagger δ _m2 between the slices and the shear force Qm between adjacent shield segments. The prediction method has the characteristics of considering the number of segments acting on the anti-floating bolt, the deformation of the shield tunnel and the real situation, and has the characteristics of high accuracy.

Description

Displacement and deformation prediction method of shield tunnel with anti-floating anchor under foundation pit excavation

technical field

The invention belongs to the technical field of underground engineering, in particular to a method for predicting displacement and deformation of shield tunnels with anti-floating anchors under excavation of foundation pits, which is suitable for shield tunnels with anti-floating anchors under the influence of excavation of upper foundation pits The resulting displacement and deformation values are predicted.

Background technique

In recent years, with the development of underground engineering construction, the urban shallow ground space has become more and more crowded, and the situation of construction projects adjacent to existing shield tunnels has become more and more frequent. Among them, the excavation of the foundation pit adjacent to the existing tunnel will have an unloading effect on the soil above the existing tunnel, resulting in the floating deformation of the existing tunnel, which may cause the deformation and damage of the shield tunnel structure and seriously threaten the safety of the tunnel. .

At present, the measures to control the floating of the tunnel include stacking back pressure in the tunnel cavity, setting up isolation piles on the side of the tunnel, and setting up anti-floating anchor rods. Among them, the anti-floating bolt uses the shear force of the anchor body composed of bolt and mortar and the rock and soil layer to resist the buoyancy of the underground structure. At present, it is mainly used in basements, shallow tunnels, pools and other structures. There are still few upwards, and the effect of controlling the floating of shield tunnels needs to be further studied. The main method of existing research is finite element simulation, the results of which are closely related to the reduction degree of modeling to real working conditions, and the accuracy of the results cannot be guaranteed. Related research on displacement and deformation of existing tunnels with anti-floating anchors.

To sum up, most of the research on the displacement and deformation of shield tunnels with anti-floating bolts under excavation of foundation pits is focused on finite element numerical simulation, which is difficult to ensure accuracy, and there is no derivation method for theoretical solutions. Related research.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the above deficiencies, and propose a displacement and deformation prediction method for shield tunnels with anti-floating anchor rods under excavation of foundation pits.

The purpose of the present invention is to be achieved through the following technical solutions: a method for predicting displacement and deformation of shield tunnels with anti-floating anchor rods under excavation of foundation pits, comprising the following steps:

(1) Establish a coordinate system with the center of the foundation pit on the ground as the coordinate origin, measure the excavation dimension L of the foundation pit parallel to the axis direction of the tunnel, the excavation dimension B of the foundation pit perpendicular to the axis direction of the tunnel, the excavation depth d of the foundation pit, and the depth of the foundation pit. The insertion depth d ₀ of the enclosure structure below the bottom of the pit, the outer diameter of the shield tunnel D, the distance s from the top of the shield tunnel to the bottom of the foundation pit, the horizontal distance a between the tunnel axis and the center of the foundation pit, and the total height of the foundation pit enclosure structure is calculated H=d+d0, the buried depth of the tunnel axis h=s+D/2+d, obtain the calculation ring number 2N of the tunnel lining affected by the excavation of the foundation pit; obtain the calculation ring of the tunnel lining affected by the anti-floating bolt according to the working conditions Count 2N ₁ to establish the positional relationship between the shield tunnel with anti-floating bolt and the foundation pit on the ground.

(2) Calculate the additional load of the shield tunnel with anti-floating anchors caused by the excavation of the foundation pit, specifically:

According to the Mindlin solution, it is deduced that a certain point (ξ, η, d) at the bottom of the foundation pit is under the unloading action of p=-(1-α ₀ )γd, causing a certain point (a, l, h) on the shield tunnel axis ) of the vertical additional load p(l):

Among them, γ is the soil gravity, and α ₀ is the residual stress coefficient.

(3) Predict the displacement and deformation of shield tunnels with anti-floating anchors under foundation pit excavation, which specifically includes the following sub-steps:

(3.1) Considering the rotating and staggered segment ring synergistic deformation model, calculate the total potential energy E _pm of shield tunnel deformation under the action of anti-floating anchors:

E _pm =W _L +W _Rm +W _S +W _T (2)

Among them, W _L is the work done by the additional load of the shield tunnel, W _Rm is the work done by overcoming the formation resistance under the action of the anti-floating bolt, W _S is the work done by overcoming the shear force between rings, and _WT is the work done by overcoming the tension force between the rings.

w(l) is the longitudinal displacement deformation function of the shield tunnel, km is the resistance coefficient of the anti-floating anchor soil body, _k is the foundation bed coefficient of the soil, and D _t is the ring width of each shield tunnel.

(3.2) The longitudinal displacement deformation function of the shield tunnel is symmetrical about the middle point of the excavation of the foundation pit, and it is obtained by the Fourier series expansion:

in:

A=(a ₁ a ₂ a ₃ L a _n ) ^T ;

n is the expansion series of Fourier;

(3.3) The longitudinal displacement function w(l), the displacement δ _m2 between adjacent shield segments and the shear force Q _m between adjacent shield segments are obtained by the variational control equation:

Based on the principle of minimum potential energy, the total potential energy E _pm in step (3.1) is taken as the extreme value for each undetermined coefficient, namely:

In the formula: a _i is the i-th element in matrix A, that is, the coefficient of the polynomial of the longitudinal displacement deformation function of the tunnel;

In matrix form:

([K _r ]+[K _sm ]) AT=[P] ^T (7)

In the formula: [K _r ] ^AT is the interaction effect between the tunnel rings:

[K _sm ]A ^T is the effect of soil resistance under the action of anti-floating anchors:

Where: [P] ^T represents the effect of additional load on the tunnel lining:

The undetermined coefficient matrix AT is obtained by calculating [P] ^T , [K _r ] and [K _sm ] obtained by the above steps:

A ^T =([K _r ]+[K _sm ]) ^-1 [P] ^T (11)

The longitudinal displacement deformation function w(l) of the tunnel is obtained:

w(l)=T _n (l) A ^T (12)

The stagger amount δ _m2 between adjacent shield segments is:

δ _m2 =(1-j){w[(m+1)D _t ]-w(mD _t )} (13)

The shear force Q _m between adjacent shield segments is:

Q _m =(1-j){w[(m+1)D _t ]-w(mD _t )}×k _t (14)

Further, the process of obtaining the calculation loop number 2N of the tunnel lining affected by the excavation of the foundation pit in step 1 is as follows: when 2N is a different value, the corresponding maximum uplift value forms a change curve, and the change curve eventually tends to be stable, and 2N is taken such that The change curve tends to a stable minimum value.

Further, 2N is 50 or more rings.

Further, [K _t ] and [K _sm ] described in step 3 are 10th order matrices.

Compared with the prior art, the beneficial effects of the present invention are:

1. Introduced the "Segment Ring Synergistic Deformation Model Considering Rotation and Displacement", which comprehensively considers the shear deformation and dislocation deformation between the tunnel ring and the ring, which is more in line with the actual stress and deformation of the tunnel structure, and improves the performance of the tunnel. The accuracy of the prediction method.

2. The shield tunnel is combined with the downward elastic force of the upper soil and the anti-buoyancy force generated by the anti-floating anchor rod into a larger vertical downward elastic force, which makes the calculation model more concise and easy to understand.

3. Introduce a new anti-floating anchor soil resistance coefficient _km , and use 2N ₁ to represent the number of shield tunnel segments affected by the anti-floating anchor. The deformation of shield tunnels with anti-floating anchors under various working conditions can be reflected by changing the values of km and _{N 1} during programming calculation. When one of km and _{N 1} is set to 0, it is Calculation method of shield tunnel deformation caused by excavation of foundation pit without anti-floating anchors. After the calculation and comparison of examples, the empirical value of the resistance coefficient km of the anti-floating anchor soil body under different working conditions can be obtained to guide the design of the actual engineering scheme. By changing the value of N1 during prediction, it is possible to optimize the application scheme of anti-floating anchors in shield tunnels.

4. The present invention proposes a displacement and deformation prediction method for shield tunnels with anti-floating anchor rods under foundation pit excavation, which can be used for the prediction of actual foundation pit excavation projects, and can also be used as the selection of anti-floating anchor rods as shield tunnels Reference for anti-floating measures.

Description of drawings

Figure 1 is a model diagram of a circular shield tunnel with anti-floating anchor rods;

Figure 2 is a mechanical model diagram of a circular shield tunnel with anti-floating anchor rods;

Fig. 3 is a schematic diagram of the influence of foundation pit excavation on a subterranean shield tunnel with anti-floating anchors;

Figure 4 is a diagram showing the positional relationship between the foundation pit and the shield tunnel;

Figure 5 is a ring number diagram for tunnel lining calculation;

FIG. 6 is a reliability verification diagram of the prediction method of the present invention.

Detailed ways

The present invention will be further described below with reference to the embodiments and accompanying drawings. The descriptions of the following embodiments are used to help understand the present invention and to verify the reliability of the prediction method proposed by the present invention. It should be pointed out that for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can also be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Example

Based on the paper "Yang Shidong, Tang Yanli, Liu Qingfang, et al. Research on the protection technology of ultra-short-distance submerged existing shield tunnels during foundation pit excavation construction [J]. Tunnel Construction (Chinese and English), 2017, 37 (Add 2) :35-46." Using the finite difference software FLAC3D for numerical calculation results as a case to carry out predictive analysis, the specific steps are as follows:

Step 1: Build a shield tunnel model with anti-floating anchors

As shown in Figure 1, the anti-floating bolt is reserved on the lower segment of the shield tunnel in the tunnel section where the surrounding rock is weak and broken, and the self-stability is poor. The soft rock is used as early support; it is combined with bolts, steel mesh, and shotcrete to form a joint support, and the vacancy is connected to the shield tunnel. When the surrounding environment of the shield tunnel with anti-floating anchors does not change, the anti-floating anchors do not work; when there is foundation pit excavation above the shield tunnel with anti-floating anchors, the unloading effect of the excavation surface It will be transmitted to the shield tunnel below through the soil, causing additional load on the tunnel structure, destroying the force balance of the segment structure, resulting in deformation. At this time, the anti-floating anchor will give the shield tunnel a Downward buoyancy. As shown in Figure 2, the present invention simplifies each segment ring of the shield tunnel as a short beam of elastic foundation. At this time, the shield tunnel can be regarded as being subjected to the downward elastic force of the upper soil and the anti-buoyancy force generated by the anti-floating anchor rod. , which can be combined into a larger vertical downward elastic force.

As shown in Figure 3-5, a coordinate system is established with the center of the ground foundation pit as the coordinate origin, and the excavation dimension L parallel to the tunnel axis direction, the foundation pit excavation dimension B perpendicular to the tunnel axis direction, and the excavation depth of the foundation pit are measured. d. The insertion depth d ₀ of the enclosure structure below the bottom of the foundation pit, the outer diameter of the shield tunnel D, the distance s from the top of the shield tunnel to the bottom of the foundation pit, the horizontal distance a between the tunnel axis and the center of the foundation pit, and calculate the foundation pit enclosure The total height of the structure is H=d+d0, and the buried depth of the tunnel axis is h=s+D/2+d. Obtain the calculated ring number of the tunnel lining affected by the excavation of the foundation pit 2N; obtain the tunnel affected by the anti-floating anchor according to the working conditions. The number of rings for lining calculation is 2N ₁ , and the positional relationship between the shield tunnel with anti-floating bolt and the ground foundation pit is established.

The process of obtaining the calculation ring number 2N of the tunnel lining affected by the excavation of the foundation pit is specifically as follows: when 2N is a different value, the corresponding maximum uplift value forms a change curve, and the change curve eventually tends to be stable, and 2N is taken so that the change curve tends to be stable minimum value. 2N is more than 50 rings.

Step 2: Calculate the additional loads of shield tunnels with anti-floating anchors caused by excavation of foundation pits

According to the Mindlin solution, it is deduced that a certain point (ξ, η, d) at the bottom of the foundation pit is under the unloading action of p=-(1-α ₀ )γd, causing a certain point (a, l, h) on the shield tunnel axis ) of the vertical additional load p(l):

Among them, γ is the soil gravity, and α ₀ is the residual stress coefficient.

Step 3: Calculate the displacement and deformation of the shield tunnel with anti-floating bolts under the excavation of the foundation pit

In order to make the calculated results of tunnel settlement and deformation closer to the real results, the present invention uses a segment-ring cooperative deformation model considering rotation and staggered platforms. By changing the formula for overcoming the stratum resistance, the work to overcome the stratum resistance under the action of the anti-floating bolt is obtained, so as to calculate the total deformation potential energy of the shield tunnel under the action of the anti-floating bolt, and then through the Fourier expansion and transformation of the longitudinal displacement function of the shield tunnel. The calculation method of displacement and deformation of shield tunnel with anti-floating anchor rod under foundation pit excavation is obtained by solving the sub-governing equations. Specifically, it includes the following sub-steps:

(3.1) Considering the rotating and staggered segment ring synergistic deformation model, calculate the total potential energy E _pm of shield tunnel deformation under the action of anti-floating anchors:

Set the relative vertical displacement of the adjacent lining rings numbered m and m+1 as δ _m , we get:

δ _m =w[(m+1)D _t ]-w(mD _t ) (15)

In the formula: m and m+1 are the serial numbers of the two adjacent segment rings; D _t is the ring width of the segment ring, and the unit symbol is m;

When the rotation angle θ _m between the lining rings is small:

The inter-ring shear force F _sm is:

F _sm =(1-j)k _s δ _m (17)

The maximum tension F _tm between the rings is:

F _tm = k _t θ _m D (18)

The formation resistance F _k is:

F _k = kDw(l) (19)

μ为土的泊松比，E₀为地基土的变形模量，

E_s为土的压缩模量，E_tI_t为隧道的等效抗弯刚度，b为地基梁宽度。Where: k _s is the inter-ring shear stiffness of the tunnel, k _t is the inter-ring tensile stiffness of the tunnel, j is the proportional coefficient of the rigid body rotation effect of the segment ring, k is the soil foundation bed coefficient, which is calculated by the Vesic formula,

μ is the Poisson’s ratio of soil, E ₀ is the deformation modulus of foundation soil,

Es is the compressive modulus of soil, E _t It _is the equivalent bending stiffness of the tunnel _, and b is the width of the foundation beam.

The total potential energy of the deformation of the shield tunnel can be divided into four parts. In the method of the present invention, a new anti-floating anchor soil resistance coefficient k _m is introduced in the work part to overcome the stratum resistance, which can be used to express the effect of the anti-floating anchor. Overcome the resistance of the stratum and do work, so as to obtain the total potential energy of the shield tunnel deformation under the action of the anti-floating bolt, as follows:

Additional load work caused by foundation pit excavation:

Under the action of the anti-floating anchor rod, work is done to overcome the formation resistance:

Since the soil resistance effect will change under the action of the anti-floating anchor, the present invention introduces the anti-floating anchor soil resistance coefficient k _m to obtain the calculation of the soil resistance effect under the action of the anti-floating anchor method:

In the formula: km is the resistance _coefficient of the soil mass against the floating anchor.

Work to overcome the shear force between rings:

Overcome the tension between the rings to do work:

The total potential energy E _pm of the deformation of the lower shield tunnel under the action of the anti-floating bolt:

E _pm =W _L +W _Rm +W _S +W _T (2)

(3.2) The longitudinal displacement deformation function of the shield tunnel is symmetrical about the middle point of the excavation of the foundation pit, and it is obtained by the Fourier series expansion:

in:

A=(a ₁ a ₂ a ₃ L a _n ) ^T ;

n is the expansion series of Fourier;

(3.3) The longitudinal displacement function w(l), the displacement δ _m2 between adjacent shield segments and the shear force Q _m between adjacent shield segments are obtained by the variational control equation:

Based on the principle of minimum potential energy, the total potential energy E _pm in step (3.1) is taken as the extreme value for each undetermined coefficient, namely:

In the formula: a _i is the i-th element in matrix A, that is, the coefficient of the polynomial of the longitudinal displacement deformation function of the tunnel;

In matrix form:

([K _r ]+[K _sm ])A ^T =[P] ^T (7)

In the formula: [K _r ] ^AT is the interaction effect between the tunnel rings:

[K _sm ]A ^T is the effect of soil resistance under the action of anti-floating anchors:

Where: [P] ^T represents the effect of additional load on the tunnel lining:

The undetermined coefficient matrix A ^T is obtained by calculating [P] ^T , [K _r ] and [K _sm ] obtained in the above steps:

A ^T =([K _r ]+[K _sm ]) ^-1 [P] ^T (11)

The longitudinal displacement deformation function w(l) of the tunnel is obtained:

w(l)=T _n (l) A ^T (12)

The stagger amount δ _m2 between adjacent shield segments is:

δ _m2 =(1-j){w[(m+1)D _t ]-w(mD _t )} (13)

The shear force Q _m between adjacent shield segments is:

Q _m =(1-j){w[(m+1)D _t ]-w(mD _t )}×k _t (14)

The above prediction method can be programmed and calculated by Matlab software, wherein the matrices [K _t ] and [K _sm ] use 10th-order calculation matrices to ensure accuracy.

The specific parameter values in the Matlab software of this embodiment are as follows:

When there is no anti-floating anchor rod:

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× ¹⁰³ kPa, _Dt =1.2m, D= ^6m , N=61, ks=1.94×106 kN/m, _kt =7.45× _{105 kN/m, EtIt} ⁼ 1.1× ₁₀₈ ^kN · ^m2 , b=0.22m, j=0.3, a=7.5m, h= _15.9m , N1 ₌ 0, km=0.

When there is an anti-floating anchor rod:

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× ¹⁰³ kPa, _Dt =1.2m, D= ^6m , N=61, ks=1.94×106 kN/m, _kt =7.45× _{105 kN/m, EtIt} ⁼ 1.1× ₁₀₈ ^kN · ^m2 , b=0.22m, j=0.3, a=7.5m, h= _15.9m , N1 ₌ 40, km=1.4.

Among the above parameters, the dimensions L and B of the foundation pit have been appropriately adjusted on the basis of the original text because the finite element model is not a standard foundation pit excavation condition.

The calculated and simulated results of the displacement and deformation of the existing subterranean tunnel with anti-floating anchors caused by the excavation of the foundation pit obtained at this time are shown in Figure 6. It can be seen from Fig. 6 that the vertical displacement value predicted by the method of the present invention is in good agreement with the simulated value. The maximum value of the vertical displacement calculated when the tunnel has no bolt is 23.4mm, and the simulated value in the original text is 23mm. The maximum value of the vertical displacement calculation is 18.6mm, and the simulated value in the original text is 18.9mm, and the calculation results meet the accuracy requirements. It shows that the prediction method of the present invention can better reflect the displacement and deformation of the existing subterranean tunnel with anti-floating anchors caused by the excavation of the foundation pit.

Claims (4)

1. a method for predicting displacement and deformation with anti-floating bolt shield tunnel under excavation of foundation pit, is characterized in that, comprises the steps: (1) Establish a coordinate system with the center of the foundation pit on the ground as the coordinate origin, measure the excavation dimension L of the foundation pit parallel to the axis direction of the tunnel, the excavation dimension B of the foundation pit perpendicular to the axis direction of the tunnel, the excavation depth d of the foundation pit, and the depth of the foundation pit. The insertion depth d ₀ of the enclosure structure below the bottom of the pit, the outer diameter of the shield tunnel D, the distance s from the top of the shield tunnel to the bottom of the foundation pit, the horizontal distance a between the tunnel axis and the center of the foundation pit, and the total height of the foundation pit enclosure structure is calculated H=d+d0, the buried depth of the tunnel axis h=s+D/2+d, obtain the calculation ring number 2N of the tunnel lining affected by the excavation of the foundation pit; obtain the calculation ring of the tunnel lining affected by the anti-floating bolt according to the working conditions Count 2N ₁ to establish the positional relationship between the shield tunnel with anti-floating bolt and the foundation pit on the ground. (2) Calculate the additional load of the shield tunnel with anti-floating anchors caused by the excavation of the foundation pit, specifically: According to the Mindlin solution, it is deduced that a certain point (ξ, η, d) at the bottom of the foundation pit is under the unloading action of p=-(1-α ₀ )γd, causing a certain point (a, l, h) on the shield tunnel axis ) of the vertical additional load p(l):

Among them, γ is the soil gravity, and α ₀ is the residual stress coefficient. (3) Predict the displacement and deformation of shield tunnels with anti-floating anchors under foundation pit excavation, which specifically includes the following sub-steps: (3.1) Considering the rotating and staggered segment ring synergistic deformation model, calculate the total potential energy E _pm of shield tunnel deformation under the action of anti-floating anchors: E _pm =W _L +W _Rm +W _S +W _T (2) Among them, W _L is the work done by the additional load of the shield tunnel, W _Rm is the work done by overcoming the formation resistance under the action of the anti-floating bolt, W _S is the work done by overcoming the shear force between rings, and _WT is the work done by overcoming the tension force between the rings.

w(l) is the longitudinal displacement deformation function of the shield tunnel, km is the resistance coefficient of the anti-floating anchor soil body, _k is the foundation coefficient of the soil, and D _t is the ring width of each shield tunnel. (3.2) The longitudinal displacement deformation function of the shield tunnel is symmetrical about the middle point of the excavation of the foundation pit, and it is obtained by the Fourier series expansion:

in:

A=(a ₁ a ₂ a ₃ L a _n ) ^T ; n is the expansion series of Fourier; (3.3) The longitudinal displacement function w(l), the displacement δ _m2 between adjacent shield segments and the shear force Q _m between adjacent shield segments are obtained by the variational control equation: Based on the principle of minimum potential energy, the total potential energy E _pm in step (3.1) is taken as the extreme value for each undetermined coefficient, namely:

In the formula: a _i is the i-th element in matrix A, that is, the coefficient of the polynomial of the longitudinal displacement deformation function of the tunnel; In matrix form: ([K _r ]+[K _sm ])A ^T =[P] ^T (7) In the formula: [K _r ] ^AT is the interaction effect between the tunnel rings:

[K _sm ]A ^T is the effect of soil resistance under the action of anti-floating anchors:

Where: [P] ^T represents the effect of additional load on the tunnel lining:

The undetermined coefficient matrix A ^T is obtained by calculating [P] ^T , [K _r ] and [K _sm ] obtained by the above steps: A ^T =([K _r ]+[K _sm ]) ^-1 [P] ^T (11) The longitudinal displacement deformation function w(l) of the tunnel is obtained: w(l)=T _n (l) A ^T (12) The stagger amount δ _m2 between adjacent shield segments is: δ _m2 =(1-j){w[(m+1)D _t ]-w(mD _t )} (13) The shear force Q _m between adjacent shield segments is: Q _m =(1-j){w[(m+1)D _t ]-w(mD _t )}×k _t (14) 2. The prediction method according to claim 1 is characterized in that, in step 1, the process of obtaining the tunnel lining calculation ring number 2N affected by foundation pit excavation is specifically: when 2N is a different value, the corresponding maximum uplift value forms a change curve, the change curve eventually tends to be stable, and 2N takes the minimum value that makes the change curve tend to be stable. 3 . The prediction method according to claim 2 , wherein 2N is more than 50 rings. 4 . 4 . The prediction method according to claim 1 , wherein [K _t ] and [K _sm ] in step 3 are 10th-order matrices. 5 .

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