A method for analyzing the longitudinal deformation of an existing shield tunnel when a new tunnel passes through it

Abstract

A method for analyzing the longitudinal deformation of an existing shield tunnel when a new tunnel passes through it includes the following steps: S1, simplifying the existing shield tunnel longitudinally into an elastic continuous beam placed on the foundation, and establishing an equivalent continuous beam model of the existing shield tunnel; S2, applying the mutual coupling between the soil and the tunnel to the equivalent continuous beam model, and obtaining the functional relationship between the vertical displacement of the tunnel node and the vertical free displacement of the soil; S3, obtaining the vertical free displacement of the layered foundation soil under the unloading action of the new tunnel excavation, and deriving the longitudinal displacement distribution of the existing shield tunnel. The present invention takes into account the natural stratification of the soil, reduces the corresponding foundation parameter selection and homogenization processing steps, and can more truly reflect the longitudinal deformation law of the existing shield tunnel under the unloading action of the new tunnel excavation; at the same time, the coupling method can better reflect the stress concentration or stress diffusion phenomenon caused by the change of the elastic modulus of the natural foundation.

Description

Technical Field

[0001] The invention belongs to the technical field of subway shield tunnels, and in particular relates to a method for analyzing the longitudinal deformation of an existing shield tunnel when a new tunnel passes through the tunnel. Background Art

[0002] With the continuous increase in subway mileage, the number of new tunnels passing through existing shield tunnels is also increasing. The unloading of new tunnel excavation will cause the stress release of the lower strata, which will cause the existing subway tunnel below to bulge and deform. If the deformation is too large, the existing shield tunnel structure will produce a series of defects such as cracking of the pipe segments, water seepage and leakage, bolt breakage, and longitudinal uneven settlement, which will seriously affect the normal service of the existing shield tunnel. Therefore, studying the impact of the construction of new tunnels passing through existing shield tunnels and exploring the longitudinal deformation mechanism of existing shield tunnels are of great practical significance for ensuring the normal service of existing subway lines.

[0003] At present, the main methods for solving the longitudinal deformation of existing shield tunnels when a new tunnel passes through are the two-stage analysis method and the residual stress method. However, these methods treat the natural strata as homogeneous strata when calculating the additional stress or vertical displacement of the soil caused by the unloading of the new tunnel excavation, without considering the stratification of the natural soil layer. When the physical properties of the soil layers are quite different, these methods will lead to a miscalculation of the longitudinal deformation of the existing shield tunnel. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for analyzing the longitudinal deformation of an existing shield tunnel when a new tunnel passes through the existing shield tunnel, in view of the above-mentioned shortcomings of the existing method for solving the longitudinal deformation of an existing shield tunnel when a new tunnel passes through the existing shield tunnel. The method takes into account the natural stratification of the soil, reduces the corresponding foundation parameter selection and homogenization treatment steps, and can more truly reflect the longitudinal deformation law of the existing shield tunnel under the unloading effect of the excavation of the new tunnel.

[0005] A method for analyzing the longitudinal deformation of an existing shield tunnel when a new tunnel passes through the tunnel comprises the following steps:

[0006] S1. Simplify the existing shield tunnel into an elastic continuous beam placed on the foundation along the longitudinal direction, and establish an equivalent continuous beam model of the existing shield tunnel;

[0007] S2, applying the mutual coupling effect between the soil and the tunnel to the equivalent continuous beam model to obtain the functional relationship between the vertical displacement of the tunnel node and the vertical free displacement of the soil;

[0008] S3. Obtain the vertical free displacement of the layered foundation soil under the unloading action of the new tunnel excavation, and derive the longitudinal displacement distribution of the existing shield tunnel.

[0009] According to the above scheme, in step S1, the existing shield tunnel is discretized into n beam units according to the finite element method, with a total of n+1 nodes; the influence of the axial deformation of the existing shield tunnel is not considered, the beginning and end of the tunnel are regarded as fixed constraints, and the remaining part is subjected to vertical additional stress.

[0010] According to the above scheme, in step S2, the functional relationship between the vertical displacement of the tunnel node and the vertical free displacement of the soil is derived as follows:

[0011] Step S21: Assuming that the existing shield tunnel does not exist, the excavation of the new tunnel will cause the vertical free displacement vector {w} of the soil at the node of the existing shield tunnel below, then {w} can be expressed as:

[0012] {w}={w(1),w(2),w(3),…,w(i),…,w(n),w(n+1)}

[0013] Where w(i) is the vertical free displacement of soil at the i-th node;

[0014] Step S22: Taking the existing shield tunnel as the analysis object, when the tunnel is coupled with the surrounding soil to a stable state, the tunnel is subjected to the non-uniformly distributed force f from the surrounding soil. g (y), by f g The corresponding vertical displacement caused by (y) is w g (y), w g (y) is converted into the vertical displacement vector of the tunnel node {w g}, then {w g} is represented as

[0015] {w g}={w g (1),w g (2),…,w g (i),…,w g (n),w g (n+1)}

[0016] In the formula, w g (i) is the non-uniformly distributed force f in the tunnel g (y) causes vertical displacement at the i-th tunnel node;

[0017] Step S23, ignoring the influence of the axial deformation of the existing shield tunnel, the tunnel non-uniform distribution force f acting on the tunnel g (y) is converted into tunnel node force vector {F g}, {F g} is represented as:

[0018] {F g}={F g (1),Fg (2),F g (3),…,F g (i),…,F g (n),F g (n+1)}

[0019] In the formula, F g (i) is the vertical force acting on the soil at the i-th tunnel node;

[0020] Step S24: according to the two vertical free stiffness matrices of the single beam unit node, boundary constraints are set to obtain the overall stiffness matrix [K] of the tunnel, which is expressed as:

[0021]

[0022] Where, EI is the equivalent longitudinal bending stiffness of the existing shield tunnel, l is the length of a single beam unit;

[0023] The tunnel node force vector {F g} and the vertical displacement vector of the tunnel node {w g The relationship between} is:

[0024] {F g}=[K]{w g}

[0025] Step S25: Taking the soil around the existing shield tunnel as the research object, when the tunnel and the surrounding soil are coupled to a stable state, the soil is subjected to a non-uniformly distributed force f from the tunnel in the stable state. s (y), f s (y) is transformed into soil node force vector {f s}, {f s} and the tunnel node force vector {F g}Equal in size and opposite in direction: {f s}=-{F g};

[0026] The relationship between the non-uniformly distributed force of the soil and the vertical displacement of the soil at the tunnel node is:

[0027] {w s}=[R]{f s}

[0028] In the formula, {w s} is {f s}; [R] is the soil flexibility matrix, which has symmetry and is expressed as:

[0029]

[0030] Step S26: Based on the assumption that the tunnel and the soil are not separated, the overall coupling equation between the tunnel and the surrounding soil is obtained as follows:

[0031] {w g}={w}+{w s}

[0032] Step S27, combined with steps S21 to S26, derive the functional relationship between the vertical displacement of the tunnel node of the existing shield tunnel caused by the excavation of the new tunnel and the vertical free displacement of the soil:

[0033] ([R][K]+[E]){w g}={w}

[0034] Where [E] is the unit matrix.

[0035] According to the above scheme, in step S3, the calculation method of the vertical free displacement of the layered foundation soil under the unloading action of the new tunnel excavation is:

[0036] Step S31: After the new tunnel is excavated, the surrounding soil will produce an unloading effect. The Mindlin solution of elastic mechanics is used to obtain the point (x r ,y r ,z r ) The jth soil point in the vertical direction (x r ,y r ,z rj ) vertical strain ε zj (z rj )for:

[0037]

[0038] In the formula, σ zj (z rj ) is the jth soil point (x r ,y r ,z rj ) vertical stress at σ xj (z rj ) is the jth soil point (x r ,y r ,z rj ) at the longitudinal stress; σ yj (z rj ) is the jth soil point (x r ,y r ,z rj ) at the transverse stress; v j is the Poisson's ratio of the j-th layer of soil; E rj is the unloading elastic modulus of the j-th layer of soil;

[0039] Step S32: vertical strain ε in step S31 zj (z rj ) is integrated to obtain the vertical displacement w of the j-th layer of soil j for:

[0040]

[0041] In the formula, h j is the thickness of the j-th soil layer;

[0042] Step S33: Considering the stratification of the natural foundation, the layered sum method is used to obtain the point (x r ,y r ,z r ) is:

[0043]

[0044] Where m is the number of soil layers within the influence range of tunnel excavation.

[0045] According to the above scheme, in step S33, according to the vertical additional stress σ of the mth layer of soil caused by excavation, zm Not greater than its effective deadweight stress σ szm The value of m is determined at 10% of zm ≤0.1σ szm The maximum value of .

[0046] According to the above scheme, in step S3, the derivation process of the longitudinal displacement distribution of the existing shield tunnel is specifically as follows: the soil vertical free displacement w obtained in step S33 is substituted into the functional relationship between the tunnel node vertical displacement and the soil vertical free displacement in step S27 in a vector manner, and the tunnel node vertical displacement vector {w g}, that is, the longitudinal displacement distribution of the existing shield tunnel is obtained.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] 1. The present invention proposes a calculation model that can take into account the natural stratification of soil. First, the overall coupled equilibrium equation of the existing shield tunnel and the surrounding soil is derived to obtain the displacement equation at the node of the existing shield tunnel. Then, the vertical load distribution at the position of the existing shield tunnel under the unloading action of the new tunnel excavation is calculated based on the classical solution of Mindlin elastic mechanics and the layered summation method, and it is brought into the coupled equilibrium equation to obtain the analytical solution of the longitudinal displacement of the existing shield tunnel. Compared with the traditional existing shield tunnel vertical deformation analysis method, the natural stratification of soil is more realistically considered, and the corresponding foundation parameter selection and homogenization treatment steps are reduced.

[0049] 2. When calculating heterogeneous natural foundations, by comparing with the two-stage method, it is found that the coupling method can better reflect the stress concentration or stress diffusion phenomenon caused by the change of elastic modulus in the natural foundation (heterogeneous foundation);

[0050] 3. Through comparative analysis with measured data, it is found that the theoretical calculation results are relatively consistent with the measured data, which can basically reflect the longitudinal deformation law of the existing shield tunnel under the unloading effect of new tunnel excavation, verifying the rationality of the theoretical method, thus providing a reference basis for the rapid and safe protection of the tunnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is a discrete schematic diagram of an existing shield tunnel in an embodiment of the present invention;

[0052] Figure 2 is a schematic diagram of an equivalent continuous beam model in an embodiment of the present invention;

[0053] Figure 3 is a schematic diagram of the "tunnel-soil" coupling effect in an embodiment of the present invention;

[0054] Figure 4 is a schematic diagram of the forces acting on an existing shield tunnel when it is stable in an embodiment of the present invention;

[0055] Figure 5 It is a calculation model diagram of the vertical displacement of soil at a node caused by tunnel excavation in an embodiment of the present invention;

[0056] Figure 6 The comparison chart of the calculated tunnel uplift value with the measured value and the calculation result of Timoshenko beam model;

[0057] Figure 7 This is a comparison chart between the calculated tunnel uplift value and the measured value and the calculation results of the Euler-Bernoulli beam model. DETAILED DESCRIPTION

[0058] The present invention will be further described below in conjunction with specific embodiments and accompanying drawings. These embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0059] The invention discloses a method for analyzing the longitudinal deformation of an existing shield tunnel when a new tunnel passes through the existing shield tunnel. The method takes into account the stratification of the foundation, including establishing an equivalent continuous beam model of the existing shield tunnel, performing an overall coupling analysis on the "tunnel-soil" deformation, and calculating the vertical free displacement of the soil caused by the excavation of the new tunnel in the layered foundation. The method specifically includes the following steps:

[0060] Step 1: Establish an equivalent continuous beam model of an existing shield tunnel

[0061] The existing shield tunnel is simplified into an elastic continuous beam placed on the foundation along the longitudinal direction, and the existing shield tunnel is discretized into n beam units, with a total of n+1 nodes, such as Figure 1 As shown in the figure, the influence of the axial deformation of the existing shield tunnel is not considered, the beginning and end of the tunnel are regarded as fixed constraints, and the rest of the tunnel is subjected to vertical additional stress; the non-uniformly distributed force f g (y) is converted into the equivalent nodal force F at the two end nodes of the corresponding beam element g (i) F g (i+1) and equivalent node bending moment M g (i) M g (i+1). When the length l of a single beam unit is small enough, the equivalent node bending moment can be approximately taken as 0. In this case, the continuous beam structure can be expressed as follows: Figure 2 shown.

[0062] Step 2: Overall coupling analysis of “tunnel-soil” deformation

[0063] Under the unloading effect of the new tunnel excavation, the existing shield tunnel at the bottom and the soil will interact with each other. On the one hand, since the existing shield tunnel is a rigid structure, it will hinder the upward displacement of the surrounding soil; on the other hand, the large-scale floating of the surrounding soil layer will inevitably cause the existing shield tunnel to produce longitudinal displacement; the two continue to couple to dissipate the additional stress in the stratum until the additional stress disappears, and the existing shield tunnel and the surrounding soil are coupled into a new stable state, such as Figure 3 shown.

[0064] 21) Assuming that the existing shield tunnel does not exist, the excavation of the new tunnel will cause the vertical free displacement vector {w} of the soil at the node of the existing shield tunnel below, then {w} can be expressed as:

[0065] {w}={w(1),w(2),w(3),…,w(i),…,w(n),w(n+1)} (1)

[0066] Where w(i) is the vertical free displacement of the soil at the i-th node;

[0067] 22) Taking the existing shield tunnel as the analysis object, when the tunnel and the surrounding soil are coupled to a stable state, the tunnel in the stable state is subjected to the non-uniformly distributed force f from the surrounding soil. g (y), by f g The corresponding vertical displacement caused by (y) is w g (y), w g (y) is converted into the vertical displacement vector {w g}, then {w g} can be expressed as

[0068] {wg}={w g (1),w g (2),…,w g (i),…,w g (n),w g (n+1)} (2)Where w g (i) is the non-uniformly distributed force f in the tunnel g (y) causes vertical displacement at the i-th tunnel node;

[0069] 23) Ignoring the influence of the axial deformation of the existing shield tunnel, the non-uniform distributed force acting on the tunnel can be g (y) is converted into tunnel node force vector {F g}, {F g} can be expressed as:

[0070] {F g}={F g (1),F g (2),F g (3),…,F g (i),…,F g (n),F g (n+1)} (3)

[0071] In the formula, F g (i) is the vertical force acting on the soil at the i-th tunnel node;

[0072] 24) According to the relevant knowledge of structural mechanics, the stiffness matrix of two vertical degrees of freedom of a single beam unit node [K] e for

[0073]

[0074] Where EI is the equivalent longitudinal bending stiffness of the existing shield tunnel, and l is the length of a single beam unit.

[0075] The EI value adopts the formula for estimating the equivalent longitudinal bending stiffness of the tunnel proposed by Japanese tunnel expert Yukio Shiba et al.:

[0076]

[0077] In the formula, is the position of the central axis of the tunnel structure, which is determined by the following formula:

[0078]

[0079] In the formula, E c is the elastic modulus of a single segment; I c is the longitudinal inertia moment of the tunnel; n is the number of bolts at the joint; k bis the average linear stiffness of the joint bolts, k b =E b A b / l b , E b is the elastic modulus of the bolt, A b is the cross-sectional area of ​​the bolt, l b is the bolt length; l is the ring width; A c is the cross-sectional area of ​​the tunnel segment.

[0080] The overall stiffness matrix [K] of the entire continuous beam can be obtained by the unit stiffness matrix [K] e Finite superposition is performed to obtain the boundary constraint conditions to limit the overall displacement of the tunnel. The distance along the longitudinal direction of the existing shield tunnel is 10 times the diameter or width of the new tunnel at the intersection of the old and new tunnel planes. t The existing shield tunnel is no longer affected by the excavation of the new tunnel, and the boundary conditions can be expressed as:

[0081]

[0082] Where: w g (-10L t ) and w g (-10L t ) are 10L on both sides of the central axis of the new tunnel t The node displacement of the existing shield tunnel; w g '(-10L t ) and w g '(-10L t ) are 10L on both sides of the central axis of the new tunnel t The node curvature of the existing shield tunnel;

[0083] According to the boundary condition (7), the overall stiffness matrix [K] of the tunnel can be expressed as:

[0084]

[0085] The tunnel node force vector {F g} and the vertical displacement vector of the tunnel node {w g The relationship between} is:

[0086] {F g}=[K]{w g} (9)

[0087] 25) The soil around the existing shield tunnel is taken as the research object. When the tunnel and the surrounding soil are coupled to a stable state, the soil in the stable state is subjected to the non-uniformly distributed force f from the tunnel. s (y), f s(y) is transformed into soil node force vector {f s}, {f s} and the tunnel node force vector {F g}Equal in size and opposite in direction:

[0088] {f s}=-{F g} (10)

[0089] The soil is subjected to the soil node force vector {f s The vertical displacement vector {w s} can be expressed as:

[0090] {w s}=[R]{f s} (11)

[0091] Where [R] is the soil flexibility matrix, which has symmetry and is expressed as:

[0092]

[0093] In the formula, the element R in [R] ij represents the vertical displacement at the i-th node caused by the unit force acting at the j-th node in the soil. According to Mindlin’s solution, R ij It can be expressed as:

[0094]

[0095] Where G is the shear modulus of soil (MPa); v is the Poisson's ratio of soil; y i and j The ordinates of point i and point j are respectively; |y i -y j | is the horizontal distance between two nodes; z0 is the vertical distance between the node and the ground.

[0096] 26) Based on the assumption that the tunnel and the soil are not separated, the overall coupling equation between the tunnel and the surrounding soil is obtained as follows:

[0097] {w g}={w}+{w s} (14)

[0098] 27) Combining equations (9) to (14), the functional relationship between the vertical displacement of the tunnel node of the existing shield tunnel caused by the excavation of the new tunnel and the vertical free displacement of the soil is obtained as follows:

[0099] ([R][K]+[E]){w g}={w} (15)

[0100] Where E is the unit matrix,

[0101] Step 3: Calculate the vertical free displacement of layered foundation soil caused by new tunnel excavation

[0102] 31) Establish the global coordinate system o-xyz and the local coordinate system o'-x'y'z'. The local coordinate system o'-x'y'z' is formed by rotating the global coordinate system o-xyz counterclockwise by an angle α with o as the base point xoy in the plane, and then offsetting the x-axis, y-axis, and z-axis by distances m, n, and 0 respectively. Figure 5 The relationship between the global coordinate system o-xyz and the local coordinate system o'-x'y'z' is:

[0103]

[0104] 32) Using the Mindlin stress solution of elastic mechanics, we can find the point (x) caused by tunnel excavation. r ,y r ,z r ) The jth soil point in the vertical direction (x r ,y r ,z rj ) vertical (z-axis direction) stress σ zj (z rj )for:

[0105]

[0106] Where p is the unloading load per meter along the transverse direction of the newly constructed tunnel excavation, that is, the difference between the weight of the soil removed by excavation and the weight of the segment (kPa), p = (γ s S s -γ t S t ) / L t , γ s , γ t are the weights of soil and segment respectively (kN / m 3 ), S s , S t are the excavation surface and segment area (m 2 ), L t is the horizontal length of the excavation face (m); L1 and L2 are the distances from the tail of the newly built tunnel to the origin along the x′ axis in the local coordinate system o′-x′y′z′ (m); is the weighted average Poisson's ratio of each soil layer; H is the vertical distance from the bottom of the tunnel to the ground (m); the values ​​of R1 and R2 are:

[0107] R1=((x r cosα+y r sinα-x)2 +(y r cosα-x r sinα-y) 2 +(z rj -H) 2 ) 1 / 2 (18)

[0108] R2=((x r cosα+y r sinα-x) 2 +(y r cosα-x r sinα-y) 2 +(z rj +H) 2 ) 1 / 2 (19)

[0109] New tunnel excavation caused point (x r ,y r ,z r ) The jth soil point in the vertical direction (x r ,y r ,z rj ) at the longitudinal (x-axis direction) stress σ xj (z rj )for:

[0110]

[0111] In the formula, x′=x r cosα+y r sinα-x

[0112] Replace x′ in equation (20) with y′=y r cosα-x r sinα-y can be obtained by excavating the new tunnel. r ,y r ,z r ) The jth soil point in the vertical direction (x r ,y r ,z rj ) transverse (y-axis direction) stress σ yj (z rj ).

[0113] 33) Combined with the unloading form of shield excavation and considering the three-dimensional strain of the soil, the j-th layer of soil point (x r ,y r ,z rj ) vertical strain ε zj (z rj )for:

[0114]

[0115] In the formula, E rj is the unloading elastic modulus of the jth layer of soil (MPa), obtained from field geotechnical tests. If there are no relevant parameters, the reference value of the rebound modulus for different foundation soils in the "Highway Asphalt Pavement Design Code" (JTG D50-2006) can be used.

[0116] 34) By integrating equation (21), we can obtain the vertical displacement w of the j-th layer of soil: j for:

[0117]

[0118] According to the layered summation method, the new tunnel bottom point (x r ,y r ,z r ) is the vertical free displacement w of the soil at

[0119]

[0120] Where m is the number of soil layers within the influence range of tunnel excavation, which can be calculated based on the vertical additional stress σ of the mth layer of soil caused by excavation. zm Not greater than its effective deadweight stress σ szm The value of m is determined at 10% of zm ≤0.1σ szm The maximum value of .

[0121] 35) Substituting equation (23) into equation (15) and solving it programmatically, we can obtain the vertical displacement vector {w g}, that is, the longitudinal displacement distribution of the existing shield tunnel is obtained.

[0122] Comparative Example

[0123] In order to verify the applicability and rationality of the method proposed in the present application in the longitudinal deformation analysis of a new tunnel passing through an existing shield tunnel in stratified soil, based on the field monitoring results in the article "Construction of a large-section long pedestrian underpass using pipe jacking in muddy silty clay: A case study" published by Zhang et al. in the journal "Tunneling and UndergroudSpace Technology" in 2016, the method of the present invention was compared with the calculation results of the Timoshenko continuous beam model and the Euler-Bernoulli beam model that do not consider the stratification of the stratum.

[0124] The basic working conditions of the project are as follows: the soil layer through which the pipe is pierced is a silty clay layer, covered with about 4m thick fill. The size of the pipe jacking machine is 7.02m×4.32m, and the buried depth is 8.63m; the pipe section is made of concrete, with a size of 7m×4.3m and a thickness of 0.5m, and a total of 63 sections are used; about 4m is advanced every day; the lower Line 2 subway tunnel is buried at a depth of 14.2m, mainly located in silty clay; the subway tunnel is a double-circle tunnel with an outer diameter of 6.2m. Its specific tunnel structure is detailed in Table 2. The new tunnel first passes through the Metro Line 2 up tunnel at α=90°, and then the down tunnel. The tunnel longitudinal equivalent bending stiffness EI is calculated by formulas (5) to (6) as 7.8×10 7 kN / m 2 ; Excavated soil weight γ s 17kN / m 2 ; Segment weight γ t 23kN / m 2 The soil parameters are detailed in Table 1. The field monitoring data of the newly built tunnel crossing the down line 20m and the up line 20m were used for analysis.

[0125] Table 1 Physical parameters of foundation soil layers

[0126]

[0127] Table 2 Structural parameters of subway tunnel

[0128]

[0129] Figure 6 and Figure 7This is a comparison of the measured results when the jacking pipe passes through the up and down lines of the double circle tunnel of Metro Line 2 for 20m and the calculation results of different methods. It can be seen that the size and trend of the longitudinal displacement of the tunnel calculated by the present invention are closest to the measured data. However, the calculation results of the Euler-bernoulli beam model and the Timoshenko beam model without considering the stratification of the stratum have a certain gap with the measured results, especially for the vertical displacement calculation on both sides of the axis of the newly built tunnel. Although the overall shape is also normally distributed, it does not show the displacement concentration characteristics of the measured data, and the width of the uplift area is relatively large. This is because the unloading elastic modulus of different strata in the example is quite different. The unloading elastic modulus of the silty fine sand layer located in the lower layer of the foundation is much larger than the upper clay layer. Stress concentration will occur in such a layered foundation, resulting in a narrow width of the tunnel uplift curve. The Euler-bernoulli beam model and the Timoshenko beam model without considering the stratification of the stratum are based on the solution of homogeneous soil, and the layered foundation parameters are approximated to the homogeneous foundation for solution. Therefore, the calculated results cannot reflect the stress concentration or stress diffusion phenomenon in the natural layered foundation, resulting in a certain error with the measured results. However, the coupling method in this paper takes into account the natural layering of the foundation soil, and the results obtained are highly consistent with the measured results.

[0130] The above shows that the method proposed in the present invention has better calculation accuracy than the traditional two-stage analysis method in the foundation with a large difference in the unloading elastic modulus of the soil.

[0131] The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A method for analyzing the longitudinal deformation of an existing shield tunnel when a new tunnel passes through it, characterized in that: The following steps are involved: S1. Simplify the existing shield tunnel into an elastic continuous beam placed on the foundation along the longitudinal direction, and establish an equivalent continuous beam model of the existing shield tunnel; S2. The mutual coupling between the soil and the tunnel is applied to the equivalent continuous beam model to obtain the functional relationship between the vertical displacement of the tunnel node and the vertical free displacement of the soil. The functional relationship between the vertical displacement of the tunnel node and the vertical free displacement of the soil is derived as follows: Step S21: Assuming that the existing shield tunnel does not exist, the excavation of the new tunnel will cause the vertical free displacement vector {w} of the soil at the node of the existing shield tunnel below, then {w} is expressed as: {w}={w(1),w(2),w(3),…,w(i),…,w(n),w(n+1)} Where w(i) is the vertical free displacement of soil at the i-th node; Step S22: Taking the existing shield tunnel as the analysis object, when the tunnel is coupled with the surrounding soil to a stable state, the tunnel is subjected to the non-uniformly distributed force f from the surrounding soil. g (y), by f g The corresponding vertical displacement caused by (y) is w g (y), w g (y) is converted into the vertical displacement vector of the tunnel node {w g }, then {w g } is represented by {w g }={w g (1),w g (2),…,w g (i),…,w g (n),w g (n+1)} In the formula, w g (i) is the non-uniformly distributed force f in the tunnel g (y) causes vertical displacement at the i-th tunnel node position; Step S23, ignoring the influence of the axial deformation of the existing shield tunnel, converting the non-uniform distributed tunnel force fg(y) acting on the tunnel into the tunnel node force vector {F g }, {F g } is represented as: {F g }={F g (1),F g (2),F g (3),…,F g (i),…,F g (n),F g (n+1)} In the formula, F g (i) is the vertical force acting on the soil at the i-th tunnel node; Step S24: according to the two vertical free stiffness matrices of the single beam unit node, boundary constraints are set to obtain the overall stiffness matrix [K] of the tunnel, which is expressed as: Where, EI is the equivalent longitudinal bending stiffness of the existing shield tunnel, l is the length of a single beam unit; The tunnel node force vector {F g } and the vertical displacement vector of the tunnel node {w g The relationship between} is: {F g }=[K]{w g } Step S25: Taking the soil around the existing shield tunnel as the research object, when the tunnel and the surrounding soil are coupled to a stable state, the soil is subjected to a non-uniformly distributed force f from the tunnel in the stable state. s (y), f s (y) is transformed into soil node force vector {f s }, {f s } and the tunnel node force vector {F g }Equal in size and opposite in direction: {f s }=-{F g }; The relationship between the non-uniformly distributed force of the soil and the vertical displacement of the soil at the tunnel node is: {w s }=[R]{f s } In the formula, {w s } is {f s }; [R] is the soil flexibility matrix, which has symmetry and is expressed as: Step S26: Based on the assumption that the tunnel and the soil are not separated, the overall coupling equation between the tunnel and the surrounding soil is obtained as follows: {In g }={in}+{in s } Step S27, combined with steps S21 to S26, derive the functional relationship between the vertical displacement of the tunnel node of the existing shield tunnel caused by the excavation of the new tunnel and the vertical free displacement of the soil: ([R][K]+[E]){w g }={w} Where [E] is the unit matrix; S3. Obtain the vertical free displacement of the layered foundation soil under the unloading action of the new tunnel excavation, and derive the longitudinal displacement distribution of the existing shield tunnel; the calculation method for the vertical free displacement of the layered foundation soil under the unloading action of the new tunnel excavation is: Step S31: After the new tunnel is excavated, the surrounding soil will produce an unloading effect. The Mindlin solution of elastic mechanics is used to obtain the point (x r ,y r ,z r ) The jth soil point in the vertical direction (x r ,y r ,z rj ) vertical strain ε zj (z rj )for: In the formula, σ zj (z rj ) is the jth soil point (x r ,y r ,z rj ) vertical stress at σ xj (z rj ) is the jth soil point (x r ,y r ,z rj ) at the longitudinal stress; σ yj (z rj ) is the jth soil point (x r ,y r ,z rj ) at the transverse stress; v j is the Poisson's ratio of the j-th layer of soil; E rj is the unloading elastic modulus of the j-th layer of soil; Step S32: vertical strain ε in step S31 zj (z rj ) is integrated to obtain the vertical displacement w of the j-th layer of soil j for: In the formula, h j is the thickness of the j-th soil layer; Step S33: Considering the stratification of the natural foundation, the layered sum method is used to obtain the point (x r ,y r ,z r ) is: Where m is the number of soil layers within the influence range of tunnel excavation.

2. The method for analyzing longitudinal deformation of an existing shield tunnel when a new tunnel passes through the tunnel according to claim 1 is characterized in that: In the step S1, the existing shield tunnel is discretized into n beam units according to the finite element method, with a total of n+1 nodes; The influence of the axial deformation of the existing shield tunnel is not considered, the beginning and end of the tunnel are regarded as fixed constraints, and the rest of the tunnel is subjected to vertical additional stress.

3. The method for analyzing longitudinal deformation of an existing shield tunnel when a new tunnel passes through the tunnel according to claim 1 is characterized in that: In step S33, according to the vertical additional stress σ of the m-th layer of soil caused by excavation zm Not greater than its effective deadweight stress σ szm The value of m is determined at 10% of zm ≤0.1σ szm The maximum value of .

4. The method for analyzing longitudinal deformation of an existing shield tunnel when a new tunnel passes through the tunnel according to claim 1 is characterized in that: In step S3, the derivation process of the longitudinal displacement distribution of the existing shield tunnel is specifically as follows: the soil vertical free displacement w obtained in step S33 is substituted into the functional relationship between the tunnel node vertical displacement and the soil vertical free displacement in step S27 in a vector manner, and the tunnel node vertical displacement vector {w g }, that is, the longitudinal displacement distribution of the existing shield tunnel is obtained.

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