Accurate prediction method for adjacent tunnel upheaval deformation caused by foundation pit excavation based on system energy method

Abstract

The invention discloses an accurate prediction method for adjacent tunnel upheaval deformation caused by foundation pit excavation based on a system energy method, and the method comprises the steps: determining a stress mode and a model sketch of a tunnel, superposing the dynamic load influence of an operating subway train, determining the size of the additional stress of the tunnel, and predicting the upheaval deformation of the adjacent tunnel. Establishing a total energy formula of a tunnel upheaval deformation system based on a Kerr foundation model; then, based on the energy variation principle, obtaining Kerr foundation lower layer spring matrix analysis, obtaining tunnel upheaval displacement analysis according to a relational expression of tunnel upheaval displacement and lower layer springs, and obtaining a bending moment and shearing force expression of the tunnel according to the Euler-Bernoulli beam theory. The three-parameter Kerr foundation model adopted by the method can overcome the problem that a Winkler foundation cannot fully consider the continuity of a soil body, the influence of the load of an operating subway train on tunnel deformation is considered, matrix analysis is simple and practical, and the method has guiding significance on prediction of upheaval deformation of the underlying tunnel caused by excavation of a foundation pit.

Description

Technical Field

[0001] The present invention relates to the field of underground engineering technology, and in particular to a method for accurately predicting the uplift deformation of an adjacent tunnel caused by foundation pit excavation based on a system energy method. Background Art

[0002] With the socioeconomic development of cities, the expansion of underground space has greatly optimized limited urban land resources, but its safety is also receiving increasing attention. Foundation pit excavation inevitably has significant adverse effects on nearby existing tunnels or pipelines, potentially even causing serious safety issues such as cracking, water seepage, and joint rupture in tunnel or pipeline segments. Evaluating the impact of foundation pit excavation on adjacent tunnels has become a major research topic in the field of underground engineering.

[0003] Excavation can have several detrimental effects on adjacent tunnels. On the one hand, significant tunnel deformation can be detrimental to the tunnel itself. On the other hand, tunnel deformation can generate bending moments, leading to the opening of tunnel joints, increased leakage, and even mud seepage. This can pose significant long-term risks to the tunnel. Therefore, accurately predicting the uplift, deformation, and bending moments of the underlying tunnel during excavation is crucial.

[0004] Regarding the study of uplift of adjacent tunnels caused by foundation pit excavation, existing technologies have simplified the existing tunnel into an Euler-Bernoulli beam placed on a Winkler foundation model, and established the tunnel mechanical equilibrium control equation based on the stress state. However, this method ignores the system energy changes during the tunnel deformation process and does not consider the impact of the dynamic load of operating subway trains. In addition, the matrix analysis of the method of the present invention is simple and practical. The three-parameter Kerr foundation model adopted by the method of the present invention can overcome the problem that the Winkler foundation cannot fully consider the continuity of the soil. Summary of the Invention

[0005] The purpose of the present invention is to address the problems existing in the prior art and provide an accurate method for estimating the uplift deformation of an underlying tunnel caused by foundation pit excavation based on the energy variation principle, so as to make a more accurate prediction of the vertical displacement of an adjacent tunnel caused by actual foundation pit excavation through a simple and practical method.

[0006] The object of the present invention is achieved through the following technical solution: a method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method, comprising the following steps:

[0007] (1) Determine the profile parameters of the foundation pit and the underlying tunnel as well as the physical and mechanical parameters of the soil;

[0008] (2) Determine the tunnel's stress pattern and model diagram;

[0009] (3) Determine the magnitude of the additional stress in the tunnel and further obtain the total energy formula of the tunnel uplift deformation system based on the Kerr foundation model;

[0010] (4) Obtain the analytical w2 matrix of the Kerr foundation lower spring based on the energy variation principle;

[0011] (5) The analytical expression of w is obtained based on the relationship between the tunnel uplift displacement w and the lower layer spring w2, and the expressions of the tunnel bending moment and shear force are obtained based on the Euler-Bernoulli beam theory.

[0012] Furthermore, the expression for the additional stress at the tunnel axis caused by the foundation pit excavation is as follows:

[0013]

[0014] in, p = γH, γ is the soil weight, H is the excavation depth of the foundation pit, L and B are the length and width of the foundation pit, υ is the Poisson's ratio of the soil, and z0 is the buried depth of the tunnel axis.

[0015] Furthermore, considering that the tunnel axis is not parallel to the long side of the foundation pit, the coordinate system on the tunnel axis needs to be incorporated into the global coordinate system of the foundation pit. The plane relationship between the two coordinate systems is as follows:

[0016]

[0017] Among them, λ and η are the coordinate values ​​of a point on the bottom of the foundation pit in the λOη coordinate system, α is the angle between the long side of the foundation pit and the tunnel axis, and S0 is the shortest distance from the center point of the foundation pit to the tunnel axis.

[0018] The load impact of the operating subway trains can be further assumed to be a statically determinate load placed on the existing tunnel, and satisfying the following conditions:

[0019]

[0020] Among them, G1 and G2 represent the weight of the subway train and the passengers in the train respectively. It is expressed as the train dynamic load factor, which is generally taken as 1.2. q2 is the magnitude of the additional stress caused by the train dynamic load on the tunnel axis.

[0021] The total additional stress at the tunnel axis is:

[0022] q=q1+q2

[0023] The lower spring displacement w2 of the Kerr foundation model satisfies:

[0024]

[0025] Where: w2 represents the spring displacement of the lower layer of the Kerr foundation model; L1 is half the tunnel length; A i is an undetermined coefficient; x is the coordinate value along the longitudinal direction of the tunnel; i = 0, 1, 2, ..., n-1, n; n represents that the tunnel is divided into n micro units, and the matrix can be expressed as:

[0026]

[0027] Furthermore, considering that the total energy T of the tunnel deformation system can be divided into the sum of the bending deformation energy T1, the foundation reaction work T2 in the Kerr model, and the additional load work T3, that is,

[0028]

[0029] Where EI is the tunnel bending stiffness; D is the tunnel diameter; q is the additional stress on the tunnel; k is the foundation elastic stiffness; G is the foundation shear layer stiffness; and w1 is the displacement of the upper spring in the Kerr foundation model. c, k, and G can be calculated using the following method:

[0030] c=7k,k=4E s / 3z0,G=2E s z0 / 9(1+ν)

[0031] Where, E s is the soil modulus; υ is the soil Poisson's ratio; z0 is the depth of the tunnel axis

[0032] Based on the energy variation method, we know that:

[0033] δT=δT1+δT2+δT3=0

[0034] Right now

[0035]

[0036] At this time,

[0037] (K1-K2+K3-K4)·A=-qD

[0038] Where: K1 is the tunnel bending stiffness matrix, K2 is the stiffness matrix related to soil elasticity c; K3 is the soil shear stiffness matrix; K4 is the stiffness matrix related to soil elasticity k; q is the additional stress vector. The expressions of K1, K2, K3 and K4 are:

[0039]

[0040]

[0041] Furthermore, the tunnel uplift deformation expression is:

[0042]

[0043] The bending moment and shear force expressions of the pipeline are:

[0044]

[0045] Furthermore, the specific implementation steps are as follows:

[0046] S1: Determine the profile parameters of the foundation pit and the existing tunnel, including the tunnel diameter, burial depth, length, width and depth of the foundation pit, and the shortest distance from the midpoint of the foundation pit to the tunnel; the tunnel stiffness is the tunnel bending stiffness; the angle is the angle between the long side of the foundation pit and the tunnel axis; the soil physical and mechanical parameters include the soil elastic modulus E s and Poisson's ratio υ

[0047] S2: Simplify the existing tunnel into an Euler-Bernoulli beam placed on the Kerr foundation model;

[0048] S3: The additional stress imposed by excavation on the underlying tunnel is calculated using the Mindlin formula. Combined with the dynamic load effect of operating subway trains, the total additional stress on the tunnel is determined. Based on the Kerr foundation model, a formula for the total energy of the tunnel uplift deformation system is established.

[0049] S4: Obtain the w2 matrix of the lower spring of Kerr foundation analytically based on the energy variation principle;

[0050] S5: The analysis of the tunnel uplift deformation w is obtained based on the relationship between the tunnel uplift displacement w and the lower layer spring w2, and the expressions of the tunnel bending moment and shear force are obtained based on the Euler-Bernoulli beam theory.

[0051] Furthermore, the model diagram simplifies the tunnel into an infinitely long Euler-Bernoulli beam.

[0052] Furthermore, the additional stress generated by the excavation of the foundation pit on the tunnel at different angles can be changed by changing the angle between the foundation pit and the tunnel axis.

[0053] The model diagram places the tunnel on the three-parameter Kerr foundation model, overcoming the problem that the Winkler foundation model cannot fully consider the continuous deformation of the soil.

[0054] The precise calculation method is to change the angle between the foundation pit and the tunnel axis to realize the additional stress generated by the foundation pit excavation on the tunnel at different angles; compared with the traditional mechanical equilibrium theory, this method obtains the tunnel uplift deformation w matrix analysis based on the energy variation principle.

[0055] The precise calculation method is to further obtain the total additional stress magnitude at the tunnel axis by considering the influence of the dynamic load of the subway train; compared with the additional stress magnitude close to the tunnel axis caused by traditional foundation pit excavation, the tunnel working condition calculated by this method is more in line with the actual situation.

[0056] The beneficial effect of the present invention lies in that, by adopting the accurate method provided by the present invention for predicting the uplift deformation of the underlying tunnel caused by foundation pit excavation, the Winkler foundation model cannot fully consider the continuous deformation of the soil, and the influence of the dynamic load of the operating subway train is considered. In addition, the present invention obtains the tunnel uplift deformation w matrix analysis based on the energy variation principle, which overcomes the traditional theory that studies the interaction between the tunnel and the soil from the perspective of mechanical equilibrium. In addition, the matrix analysis is simple and practical, and has great promotion and application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0058] Figure 1 Schematic diagram of a method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method.

[0059] Figure 2 It is a schematic diagram of the interaction between the foundation pit and the existing tunnel of the present invention.

[0060] Figure 3 It is a top view of the relative positions of the foundation pit and the tunnel of the present invention.

[0061] Figure 4 This is a diagram of the tunnel-soil interaction model under the Kerr foundation of the present invention.

[0062] Figure 5 A comparison chart of the calculation results provided by this implementation case and the on-site monitoring data.

[0063] In the figure: 1 is the tunnel; 2 is the foundation pit; 3 is the ground surface; 4 is the additional load q; 5 is the elastic stiffness k of the soil; 6 is the shear stiffness G of the soil; 7 is the elastic stiffness c of the soil. DETAILED DESCRIPTION

[0064] In order to facilitate understanding of the present invention, the present invention is further described below with reference to the accompanying drawings and engineering examples.

[0065] according to Figure 1As shown, the present invention provides a method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method. The specific steps are as follows:

[0066] S1: Determine the profile parameters of the foundation pit and the existing tunnel, including tunnel diameter, burial depth, length, width and depth of the foundation pit, and the shortest distance from the midpoint of the foundation pit to the tunnel; determine the tunnel stiffness as the tunnel bending stiffness; determine the angle between the long side of the foundation pit and the tunnel axis; determine the physical and mechanical parameters of the soil, including the elastic modulus E of the soil s and Poisson's ratio υ:

[0067] The tunnel diameter is 11m, the axis depth is 22m, the excavation depth of the foundation pit is 11m, and the length, width and depth of the foundation pit are 100m, 10m and 11m respectively; the shortest distance from the midpoint of the foundation pit to the tunnel is 0, and the bending stiffness of the tunnel is 3.99×10 5 MN·m 2 The angle between the long side of the foundation pit and the tunnel axis is 75°; the elastic modulus and Poisson's ratio of the soil are 30.8 MPa and 0.2 respectively.

[0068] S2: Determine the tunnel's stress pattern and model diagram;

[0069] Determine the maximum allowable value w of tunnel uplift deformation displacement according to the tunnel level max The tunnel uplift deformation mode is a process where the maximum displacement gradually decreases towards the two ends of the tunnel until the displacement at both ends of the tunnel is close to 0. The displacement deformation diagram is shown in Figure 2 As shown, the relative position of the foundation pit and the tunnel is shown in the top view. Figure 3 shown.

[0070] S3: The weight of each subway car in operation is about 400 kN, and the weight of passengers is about 0 to 200 kN. The average weight of passengers is taken as 100 kN to determine the magnitude of the additional stress in the tunnel. The total energy formula of the tunnel uplift deformation system based on the Kerr foundation model is established:

[0071] S31: The additional stress at the tunnel axis caused by foundation pit excavation is calculated as follows:

[0072]

[0073] in, p = γH, γ is the soil density, H is the excavation depth of the foundation pit, v is the Poisson's ratio of the soil, z0 is the buried depth of the tunnel axis, and B and L represent the width and length of the foundation pit.

[0074] S32: Considering that the tunnel axis and the pit wall are not parallel, the coordinate system on the tunnel axis needs to be incorporated into the global coordinate system of the foundation pit. The plane relationship between the two coordinate systems is as follows:

[0075]

[0076] Among them, λ and η are the coordinate values ​​of a point at the bottom of the foundation pit in the λOη coordinate system, α is the angle between the long side of the foundation pit and the tunnel axis, and S0 is the shortest distance from the center point of the foundation pit to the tunnel axis.

[0077] The load impact of the operating subway trains can be further assumed to be a statically determinate load placed on the existing tunnel, and satisfying the following conditions:

[0078]

[0079] Among them, G1 and G2 represent the weight of the subway train and the passengers in the train respectively. It is expressed as the train dynamic load factor, which is generally taken as 1.2. q2 is the magnitude of the additional stress caused by the train dynamic load on the tunnel axis.

[0080] The total additional stress at the tunnel axis is:

[0081] q=q1+q2

[0082] S33: Obtain the total energy formula of the tunnel uplift deformation system based on the Kerr foundation model:

[0083] The lower spring displacement w2 of the Kerr foundation model satisfies:

[0084]

[0085] Where: w2 represents the spring displacement of the lower layer of the Kerr foundation model; L1 is half the tunnel length; A i is an undetermined coefficient; x is the coordinate value along the longitudinal direction of the tunnel; i = 0, 1, 2, ..., n-1, n; n represents that the tunnel is divided into n micro units, and the matrix can be expressed as:

[0086]

[0087] The Kerr foundation tunnel-soil interaction model is shown in the figure Figure 4 As shown in Figure 2, considering that the total energy T of the tunnel deformation system can be divided into the sum of the bending deformation energy T1, the foundation reaction work T2 in the Kerr model, and the additional load work T3, that is,

[0088]

[0089] Where EI is the tunnel bending stiffness; D is the tunnel diameter; q is the additional stress on the tunnel; k is the foundation elastic stiffness; G is the foundation shear layer stiffness; and w1 is the displacement of the upper spring in the Kerr foundation model. c, k, and G can be calculated using the following method:

[0090] c=7k,k=4E s / 3z0,G=2Es z0 / 9(1+ν)

[0091] Where, E s is the soil modulus; υ is the Poisson's ratio of the soil; z0 is the buried depth of the tunnel axis.

[0092] Based on the energy variation method, we know that:

[0093] δT=δT1+δT2+δT3=0

[0094] where represents the symbol of variation.

[0095] Right now

[0096]

[0097] At this time,

[0098] (K1-K2+K3-K4)·A=-qD

[0099] Where: K1 is the tunnel bending stiffness matrix, K2 is the stiffness matrix related to soil elasticity c; K3 is the soil shear stiffness matrix; K4 is the stiffness matrix related to soil elasticity k; q is the additional stress vector. The expressions of K1, K2, K3 and K4 are:

[0100]

[0101]

[0102] S5: Based on the relationship between the tunnel uplift displacement w and the lower spring w2, the w equation is obtained. Based on the Euler-Bernoulli beam theory, the tunnel bending moment and shear force expressions are obtained.

[0103] The tunnel uplift deformation expression is:

[0104]

[0105] The bending moment and shear force expressions of the pipeline are:

[0106]

[0107] The calculation method of this embodiment is used to calculate the tunnel project of an underground passage foundation pit passing through an existing tunnel. The calculation results are compared with the on-site monitoring data. Figure 5 As shown by Figure 5As can be seen, the tunnel uplift deformation calculated using this implementation method is highly consistent with the trends in the on-site monitoring data, with the peak values ​​being essentially identical. This demonstrates that this implementation method can be used to calculate and predict the uplift deformation of underlying tunnels caused by excavation in soft soil areas. The method is relatively simple and practical, and is of great significance for estimating the impact of excavation on adjacent tunnels.

[0108] The above embodiments are used to illustrate the present invention rather than to limit the present invention. Any modifications and changes made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method, characterized in that: The following steps are involved: (1) Determine the profile parameters of the foundation pit and the underlying tunnel as well as the physical and mechanical parameters of the soil; (2) Determine the tunnel's stress pattern and model diagram; (3) Combined with the influence of the dynamic load of the operating subway train, the magnitude of the additional stress in the tunnel is determined, and the total energy formula of the tunnel uplift deformation system based on the Kerr foundation model is further obtained; (4) Obtain the analytical w2 matrix of the Kerr foundation lower spring based on the energy variation principle; (5) The analytical expression of w is obtained based on the relationship between the tunnel uplift displacement w and the lower layer spring w2, and the expressions of the tunnel bending moment and shear force are obtained based on the Euler-Bernoulli beam theory.

2. The method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method according to claim 1 is characterized in that: The expression for the additional stress at the tunnel axis caused by the foundation pit excavation is as follows: in, p = γH, γ is the soil weight, H is the excavation depth of the foundation pit, L and B are the length and width of the foundation pit, υ is the Poisson's ratio of the soil, and z0 is the buried depth of the tunnel axis.

3. The method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method according to claim 2 is characterized in that: Considering that the tunnel axis is not parallel to the long side of the foundation pit, the coordinate system on the tunnel axis needs to be incorporated into the global coordinate system of the foundation pit. The plane relationship between the two coordinate systems is as follows: Among them, λ and η are the coordinate values ​​of a point at the bottom of the foundation pit in the λOη coordinate system, α is the angle between the long side of the foundation pit and the tunnel axis, and S0 is the shortest distance from the center point of the foundation pit to the tunnel axis; The load impact of the operating subway trains can be further assumed to be a statically determinate load placed on the existing tunnel, and satisfying the following conditions: Among them, G1 and G2 represent the weight of the subway train and the passengers in the train respectively. It is expressed as the train dynamic load factor, which is generally taken as 1.

2. q2 is the magnitude of the additional stress on the tunnel axis caused by the train dynamic load; The total additional stress at the tunnel axis is: q=q1+q2 The lower spring displacement w2 of the Kerr foundation model satisfies: Where: w2 represents the spring displacement of the lower layer of the Kerr foundation model; L1 is half the tunnel length; A i is an undetermined coefficient; x is the coordinate value along the longitudinal direction of the tunnel; i = 0, 1, 2, ..., n-1, n; n represents that the tunnel is divided into n micro units, and the matrix can be expressed as:

4. The method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method according to claim 1 is characterized in that: Considering that the total energy T of the tunnel deformation system can be divided into the sum of bending deformation energy T1, foundation reaction work T2 in the Kerr model, and additional load work T3, that is, Where EI is the tunnel bending stiffness; D is the tunnel diameter; q is the additional stress on the tunnel; k is the foundation elastic stiffness, G is the foundation shear layer stiffness, and w1 is the displacement of the upper spring in the Kerr foundation model. c, k, and G can be calculated using the following method: c=7k,k=4E s / 3z0,G=2E s z0 / 9(1+ν) Where, E s is the soil modulus; υ is the soil Poisson's ratio; z0 is the depth of the tunnel axis Based on the energy variation method, we know that: δT=δT1+δT2+δT3=0 Right now At this time, (K1-K2+K3-K4)·A=-qD Where: K1 is the tunnel bending stiffness matrix, K2 is the stiffness matrix with respect to soil elasticity c; K3 is the soil shear stiffness matrix; K4 is the stiffness matrix with respect to soil elasticity k; q is the additional stress vector; the expressions of K1, K2, K3 and K4 are:

5. The method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method according to claim 1 is characterized in that: The tunnel uplift deformation expression is: The bending moment and shear force expressions of the pipeline are:

6. The method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method according to claim 1 is characterized in that: The specific implementation steps are as follows: S1: Determine the profile parameters of the foundation pit and the existing tunnel, including the tunnel diameter, burial depth, length, width and depth of the foundation pit, and the shortest distance from the midpoint of the foundation pit to the tunnel; the tunnel stiffness is the tunnel bending stiffness; the angle is the angle between the long side of the foundation pit and the tunnel axis; the soil physical and mechanical parameters include the soil elastic modulus E s and Poisson's ratio υ S2: Simplify the existing tunnel into an Euler-Bernoulli beam placed on the Kerr foundation model; S3: The additional stress imposed by excavation on the underlying tunnel is calculated using the Mindlin formula. Combined with the dynamic load of operating subway trains, the total additional stress on the tunnel is determined. A formula for the total energy of the tunnel uplift deformation system is established based on the Kerr foundation model. S4: Obtain the w2 matrix of the lower spring of Kerr foundation analytically based on the energy variation principle; S5: The analysis of the tunnel uplift deformation w is obtained based on the relationship between the tunnel uplift displacement w and the lower layer spring w2, and the expressions of the tunnel bending moment and shear force are obtained based on the Euler-Bernoulli beam theory.

7. The method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method as claimed in claim 6, characterized in that: In the model diagram, the tunnel is simplified into an infinitely long Euler-Bernoulli beam.

8. The method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method as claimed in claim 6, characterized in that: By changing the angle between the foundation pit and the tunnel axis, the additional stress generated by the foundation pit excavation on the tunnel at different angles can be changed.

9. The method for accurately predicting the uplift deformation of adjacent tunnels caused by foundation pit excavation based on the system energy method as claimed in claim 6, characterized in that: By considering the influence of the dynamic load of the subway train, the total additional stress at the tunnel axis caused by foundation pit excavation under real working conditions is further obtained.

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