Method for calculating uplift displacement of underlying tunnel caused by excavation of layered foundation pit

Abstract

The calculation method of the uplift displacement of a lower tunnel caused by a layered foundation pit excavation comprises the following steps: (1) according to the relative position relationship between the foundation pit and the lower tunnel, relevant parameters are determined, and a calculation analysis model is established; (2) according to the load acting on the inside of the soil, a stress-strain solution below the load acting surface is derived, the tunnel and the foundation are respectively equivalent to an Euler-Bernoulli long beam and a Lifshin foundation model, the change of the additional stress of the soil caused by the unloading of the foundation pit excavation is calculated by using the Mindlin solution of the elastic layered foundation, and thus a corresponding mechanical model is obtained, and a longitudinal deformation control differential equation of the tunnel under the unloading of the foundation pit excavation is derived; and (3) finally, the finite difference method is used to calculate the uplift deformation of the lower existing tunnel caused by the foundation pit excavation. The calculation method can more reasonably simulate the mechanical model of the layered foundation tunnel, and makes the calculation of the uplift amount of the lower tunnel caused by the foundation pit excavation more accurate and reliable.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of underground engineering, and particularly relates to a calculation method for uplift displacement of a lower tunnel caused by excavation of a layered foundation pit. BACKGROUND

[0002] With the rapid development of economy, underground rail transit systems have gradually developed. Excavation of a foundation pit near an existing tunnel will cause redistribution of stratum stress, thereby causing deformation of the existing tunnel. When the tunnel deforms too much, cracks will occur in the segments, thereby causing groundwater leakage in the tunnel and leading to longitudinal uneven deformation of the tunnel. Therefore, it is necessary to analyze and study the influence of the foundation pit excavation on the existing tunnel. At present, many scholars have carried out a series of researches in this regard by using methods such as field monitoring, model centrifuge test, numerical simulation and two-stage analysis method.

[0003] Among these methods, field monitoring and model test often have the shortcomings of long cycle and large cost; numerical calculation can simulate the complex tunnel-foundation soil interaction, but has large workload and complex modeling.

[0004] The two-stage analysis method has the characteristics of simplicity and convenience for evaluating the influence degree of the foundation pit excavation on the tunnel. The method has clear ideas and simple mechanical principles, and has been applied in engineering to a certain extent. Most scholars currently use the Mindlin solution to calculate the additional stress of the soil at the tunnel axis caused by the foundation pit excavation in the first stage of the two-stage method under the assumption that the tunnel does not exist. However, this method does not consider the stratification of the soil, so it has shortcomings. Existing research scholars consider the influence of soil heterogeneity, but the theoretical solution derived only considers the load acting on the surface of the layered foundation, without considering the load acting on the inside of the multi-layer system. The models used in the second stage of the two-stage method, from the Winker model to the Pasternak model and then to the Kerr model, are more and more close to the actual situation, but also bring the problems of more complex mathematical forms and inconvenience of engineering application. The Winkler model has a simple mathematical form, but this model ignores the continuity of the soil, so it cannot well simulate the influence degree of the foundation pit excavation on the tunnel. Compared with the Winkler model, the Pasternak model considers the continuity of the soil, but has a complex mathematical form and is inconvenient for engineering application. The Kerr model also considers the continuity of the soil like the Pasternak model, but has a more complex mathematical form. SUMMARY

[0005] The technical problem solved by the present application is to provide a calculation method for uplift displacement of a tunnel caused by excavation of a foundation pit in a layered ground, which can more reasonably simulate a mechanical model of a tunnel in a layered ground and make the calculation of uplift of a tunnel caused by excavation of a foundation pit more accurate and reliable, in view of the above-mentioned deficiencies in the existing research method for the influence of excavation of a foundation pit on deformation of a tunnel.

[0006] The technical scheme adopted by the present application to solve the above technical problem is:

[0007] The calculation method for uplift displacement of a tunnel caused by excavation of a foundation pit in a layered ground comprises the following steps:

[0008] (1) According to the relative position relationship between the foundation pit and the underlying tunnel, the relevant parameters are determined, and a calculation and analysis model is established;

[0009] (2) According to the condition that the load acts on the inside of the soil, the stress and strain solution below the load acting surface is derived, the tunnel and the ground are respectively equivalent to an Euler-Bernoulli long beam and a Lifshitz foundation model, the change of additional stress of the soil caused by unloading of the foundation pit excavation is calculated by using the Mindlin solution of the elastic layered ground, and thus the corresponding mechanical model is obtained, and the longitudinal deformation control differential equation of the tunnel under unloading of the foundation pit excavation is derived;

[0010] (3) Finally, the uplift deformation of the underlying existing tunnel caused by the excavation of the foundation pit is calculated by using the finite difference method.

[0011] In the step (1), the calculation and analysis model construction process comprises: taking the center o of the foundation pit as a global coordinate origin, establishing an xoy global coordinate system with the length direction of the foundation pit as the y axis and the width direction of the foundation pit as the x axis; drawing a perpendicular line of the tunnel from the center o of the foundation pit, and then taking the foot o' as a local coordinate origin, establishing an x'o'y' local coordinate system with the longitudinal direction of the tunnel as the y' axis and the transverse direction of the tunnel as the x' axis; the included angle between the tunnel axis and the short side of the foundation pit excavation is α, and the conversion relationship between the xoy and x'o'y' coordinates is as follows:

[0012] x=x'cosα+y'sinα+Rcosα

[0013] y=x'sinα+y'cosα+Rsinα

[0014] In the formula, R is the distance from the global coordinate origin o to the local coordinate origin o'.

[0015] In the step (2), the expression of the tunnel longitudinal deformation control differential equation is:

[0016]

[0017] Wherein, ω(t) is the longitudinal deformation curve of the tunnel; D is the diameter of the tunnel; σ z (t) is the additional stress change value of the tunnel axis caused by the foundation pit unloading load (t represents the coordinate of the node along the longitudinal direction of the tunnel in the (x0, y0, z) coordinate, and the other two coordinates are exact numbers in the rectangular coordinate system in actual engineering); k is the foundation bed coefficient; (EI) eq is the equivalent bending stiffness of the tunnel; α and β are both dimensionless parameters related to the properties of the foundation soil, and T is the half length of the tunnel length to be calculated.

[0018] According to the above scheme, the foundation bed coefficient k is calculated by the following formula:

[0019]

[0020] Wherein,

[0021]

[0022] E s and v are the elastic modulus and Poisson's ratio of the soil respectively, and Z0 is the buried depth of the existing tunnel.

[0023] According to the above scheme, the equivalent bending stiffness (EI) eq of the tunnel is calculated by the following formula:

[0024]

[0025] Wherein, E c is the elastic modulus of the segment concrete (kPa), and n is the number of longitudinal bolts; D t is the ring width of the segment ring; K b is the average linear stiffness of the joint bolt; A s is the cross-sectional area of the tunnel; when the horizontal diameter and the vertical diameter of the tunnel change, λ1 = gD (A1 + A2 - A3 - A4 - A5); λ2 = gD (A1 + A2 - A3 - A4 - A5); A1 = πD 2 / 16; Wherein is the position parameter of the center axis of the segment ring, and the value is determined according to the engineering measurement; g is the thickness of the segment.

[0026] According to the above scheme, the additional stress change value σ(x0, y0, z) of the foundation pit unloading load acting on the tunnel (i.e. σ z (t) in the foregoing) is calculated by the layered foundation Mindlin solution:

[0027]

[0028] σ z(t) = σ(x0, y0, z), where: S 34 , S 44 , a 43 , a 44 , f 33 , f 34 , f 43 , f 44 are the corresponding elements in the matrices S, a, f; p is the equivalent load of foundation pit excavation considering the influence of residual stress, J0is the zero-order Bessel function of the first kind; ξ is the integral variable, Ω is the area of the rectangular uniform vertical load, (x0, y0, z) is the coordinate of the calculation point;

[0029] The matrices S, a, f are defined as:

[0030]

[0031] where: z is the depth of the calculation point; H j is the distance from the bottom of the jth layer of soil to the ground surface; ΔH k (k = 1, 2, …, j, … n) is the thickness of each layer of soil, ΔH m1 is the distance from the foundation pit excavation to the ith layer of soil, and the distance from the bottom of the foundation pit to the top of the ith layer of soil, and w represents the elements in the matrix (H j -z), ΔH k , and ΔH m1 (replace w with (H j -z), ΔH k , and ΔH m1 , that is), then Φ(ξ, w) is called a transfer matrix, which is defined as:

[0032]

[0033] Expression of each element of the transfer matrix Φ(ξ, w):

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] In the formula: λ and G are Lamé constants, M = λ + 2G, E and μ are the elastic modulus and Poisson's ratio of each soil layer in the layered system;

[0052] The equivalent load for foundation pit excavation, taking into account the influence of residual stress, is calculated using the following formula:

[0053] p=(1-α0)γ i H i

[0054] In the formula, p represents the equivalent unloading during foundation pit excavation, in kN / m. 2 γ i The unit weight of the i-th soil layer is kN / m³. 3 H i The thickness (m) of the i-th soil layer to be excavated is given by α0, which is the residual stress coefficient (α0 = 0.3 in this invention).

[0055] According to the above scheme, α = 10 (as suggested by Jae Kim-min), and the values ​​of β are shown in Table 1:

[0056] Table 1 Recommended values ​​for parameter β (upper limit / lower limit)

[0057]

[0058] According to the above scheme, step (3) specifically involves dividing the tunnel longitudinally into nodes -2, -1, 0, 1, 2...n-1, n, n+1, n+2 (where -2, -1, n+1, n+2 are fictitious nodes for solving equations and do not exist in actual engineering), with the length between nodes being l, and the additional stress on each node i being σ. i The vertical displacement is ω iFor i = 0, 1, 2, ..., n, the finite difference method is used to calculate the uplift deformation [ω] of the underlying existing tunnel caused by the excavation of the foundation pit as follows:

[0059]

[0060] In the formula, [ω]=[ω0,ω1,ω2,…,ω n Assuming the tunnel is free at both ends, then the shear force Q and bending moment M at both ends of the tunnel are 0, which leads to the conclusion that... The values ​​are as follows:

[0061]

[0062]

[0063] f0, f1, ..., f n yes t = t i The value of t (i = 0, 1, 2, ..., n) i To divide the coordinate values ​​of the nodes along the longitudinal direction of the tunnel, Substituting into the above formula, we can obtain the longitudinal node displacement ω of the underlying existing tunnel caused by the excavation of the foundation pit. i .

[0064] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0065] 1. The calculation method of this invention considers the load acting inside the layered foundation and derives the stress-strain solution of the axisymmetric load acting inside the multi-layered soil. Based on the two-stage method, it considers both the fact that the foundation is actually layered and the case of the foundation pit excavation acting as an external load inside the multi-layered soil. It uses the Mindlin solution of elastic layered foundation to calculate the change of additional stress in the soil caused by the foundation pit excavation, so that the first stage of the two-stage method to solve the change of additional stress in the soil caused by the foundation pit excavation is closer to reality.

[0066] 2. The Liffkin foundation model is a type of three-parameter model. It retains the advantage of the Winkler model in its simple mathematical form. Compared with the Pasternak foundation and Kerr model, it is simpler in mathematical form. It can also consider the continuity of soil like the Pasternak model. In the second stage of this invention, the tunnel is simplified into an Euler-Bernoulli long beam placed in the Liffkin foundation model. The differential equation controlling the longitudinal deformation of the tunnel under the unloading of the foundation pit is derived. The differential equation is transformed into matrix form by using the finite difference method.

[0067] 3. This analytical calculation method is fast, simple, reliable, and has low calculation cost. It can more reasonably simulate the mechanical model of layered foundation tunnels, making the calculation of the uplift of the underlying tunnel caused by the excavation of the foundation pit more accurate and reliable. Attached Figure Description

[0068] Figure 1 This is a top view showing the relative positions of the foundation pit and the tunnel in this invention;

[0069] Figure 2 This is a discrete analysis diagram of the tunnel longitudinal section in this invention;

[0070] Figure 3 This is a cross-sectional view showing the relative positions of the foundation pit and the tunnel in this invention;

[0071] Figure 4 This is a comparison diagram of the calculation method of Example 1 of the present invention and the Boussinesq solution of the elastic layered theory to calculate the additional stress at the tunnel axis caused by the excavation of the foundation pit;

[0072] Figure 5 This is a comparison chart of the calculated tunnel heave value and the measured value in Example 1 of the present invention;

[0073] Figure 6 This is a comparison chart of the calculated tunnel heave value and the measured value in Example 2 of the present invention;

[0074] Figure 7 This is a comparison chart of the calculated tunnel heave value and the measured value in Example 3 of the present invention;

[0075] In the diagram, 1-excavation pit, 2-tunnel, 3-soil. Detailed Implementation

[0076] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0077] The method for calculating the uplift displacement of the underlying tunnel caused by the excavation of the layered foundation pit described in this invention considers the load acting inside the layered foundation and derives the stress-strain solution for the axisymmetric load acting inside the multi-layered soil. In the second stage, the tunnel is simplified as an Euler-Bernoulli long beam placed in the Lifkin foundation model, and the differential equation controlling the longitudinal deformation of the tunnel under the unloading of the pit excavation is derived. The differential equation is then transformed into matrix form using the finite difference method.

[0078] The specific calculation steps are as follows:

[0079] (1) Based on the relative positional relationship between the foundation pit and the underlying tunnel, clarify the relevant parameters and establish a calculation and analysis model, such as... Figure 1 , Figure 3As shown, the length, width, and depth of the foundation pit are L, B, and h, respectively, in meters; the diameter and center depth of the tunnel are D and Z0, respectively, in meters. A global coordinate system xoy is established with the center o of the foundation pit as the origin, the length direction as the y-axis, and the width direction as the x-axis. A perpendicular line o′ is drawn from the center o of the foundation pit to the tunnel axis, and a local coordinate system x′o′y′ is established with the foot of the perpendicular o′ as the origin, the longitudinal direction of the tunnel as the y′ axis, and the transverse direction as the x′ axis. The angle between the tunnel axis and the short side of the foundation pit excavation is α. The transformation relationship between xoy and x′o′y′ coordinates is shown below:

[0080] x=x′cosα+y′sinα+Rcosα

[0081] y=x′sinα+y′cosα+Rsinα

[0082] In the formula, R represents the distance from the global coordinate origin o to the local coordinate origin o. ′ The distance.

[0083] Calculation assumptions: The time and space factors of the foundation pit excavation are not considered; the impact of precipitation is not considered.

[0084] (2) Based on the load acting on the soil, the stress-strain solution below the load surface is derived. The tunnel and foundation are respectively equivalent to the Euler-Bernoulli long beam and the Liffkin foundation model. The change in additional soil stress caused by excavation and unloading is calculated using the Mindlin solution for elastic layered foundations. Thus, the corresponding mechanical model is obtained, and the expression of the differential equation controlling the longitudinal deformation of the tunnel under excavation and unloading is derived as follows:

[0085]

[0086] (3) Figure 2 As shown, the tunnel is divided into nodes -2, -1, 0, 1, 2...n-1, n, n+1, n+2 along its longitudinal direction. Nodes -2, -1, n+1, and n+2 are fictitious nodes used to solve the equations and do not exist in the actual engineering. The length between nodes is l, and the additional stress on each node i is σ. i The vertical displacement is ω i For i = 0, 1, 2, ..., n, the finite difference method is used to calculate the uplift deformation [ω] of the underlying existing tunnel caused by the excavation of the foundation pit as follows:

[0087]

[0088] Example 1: A case study of an engineering project in Shanghai's Bund involves the construction of an underground tunnel using the cut-and-cover method. The southern section of the tunnel forms angles of 90° and 75° with the existing southern and northern tunnels of Yan'an East Road at the intersection with Yan'an East Road. The excavation depth is approximately 11m, using bored piles as the retaining structure. Supports are installed within the pit. The pit length L, width B, and excavation depth h are 50m, 10m, and 11m respectively. The tunnel diameter D is 11m, the segment thickness g = 55cm, and the distance between the pit bottom and the tunnel arch is 5.5m. The burial depth Z0 of the existing tunnel is calculated to be 22m. To simplify the analysis, only the southern tunnel is calculated and analyzed. The equivalent bending stiffness (EI) of the tunnel is calculated. eq =9.52×10 8 kN·m 2 The parameters of each soil layer are shown in Table 2.

[0089] Considering the impact of soil reinforcement at the bottom of the pit, the elastic modulus E of the soil layer where the tunnel is located is theoretically calculated. s With a pressure of 19 MPa and a dimensionless parameter β = 1.5, this invention is applicable to the calculation of this case because the foundation is a layered soil.

[0090] When calculating the uplift deformation of the underlying tunnel caused by the excavation of this foundation pit using the method of this invention, the equivalent unloading p of the foundation pit excavation considering residual stress is first calculated. Then, the tunnel is divided into n+4 units with a unit length of l and a total of n+5 nodes. Based on the soil parameters, the additional stress at each node at the tunnel axis is solved using the Mindlin solution formula of the layered theory mentioned above. The subgrade coefficient k is then solved using the above formula.

[0091] Table 2 Relevant Mechanical Parameters of Soil Layers

[0092]

[0093] To reflect the difference between the method of this invention and the method of solving for additional soil stress by only considering the load acting on the surface of the layered foundation, the calculation results are as follows: Figure 4 As shown, both methods reach the maximum additional stress at the center of the foundation pit. Figure 4 It is evident that considering only the load acting on the layered foundation, the additional stress in the soil is greater than considering the load acting within the multi-layered system. This aligns with the rules of Boussinesq and Mindlin solutions in soil mechanics. However, for excavation work, the Mindlin solution with the load acting within the soil is widely accepted by researchers. Therefore, the method of this invention is closer to reality. In the second stage, the tunnel is simplified as an Euler-Bernoulli beam, and the foundation model uses the Liffkin model. The deformation of the underlying tunnel caused by excavation calculated by these two methods is as follows: Figure 5 .

[0094] Depend on Figure 5It can be seen that the maximum value calculated by the model of this invention is close to the actual engineering measurement, thus verifying the applicability and accuracy of the calculation method of this invention in predicting tunnel deformation caused by adjacent foundation pit excavation. In the second stage, when all parameters are the same, the calculation results of tunnel heave values ​​are all too large due to the consideration of the additional stress of the soil on the layered foundation surface under load, and the tunnel is simplified to an Euler-Bernoulli beam model. Therefore, this invention considers the case of load acting on the soil interior to study the impact of foundation pit excavation disturbance, simplifies the tunnel to an Euler-Bernoulli beam in the Liffkin foundation, and the proposed model has certain applicability and accuracy.

[0095] Example 2: The Shanghai Pudong Dongfang Road Interchange project is located directly above Metro Line 2. The angle α between the tunnel axis and the short side of the excavation pit is 45°. The pit dimensions are 26m × 18m (length L × width B), the excavation depth h is 6.5m, and the distance from the top of the tunnel to the bottom of the pit is 2.76m. Therefore, the calculated burial depth of the existing tunnel is Z0 = 12.36m. The tunnel diameter D is 6.2m, the segment thickness g = 35cm, and the dimensionless parameter β = 1.5. Soil parameters are shown in Table 3. The equivalent bending stiffness of the tunnel is (EI). eq =1.087×10 8 kN·m 2 A 1.88m thick concrete slab was poured at the bottom of the excavation pit. Taking this factor into account during calculations, the elastic modulus E of the soil layer at the tunnel axis was... s Take 6.8 MPa.

[0096] Table 3 Relevant mechanical parameters of each soil layer

[0097]

[0098] When calculating the heave deformation of the underlying tunnel caused by the excavation of this foundation pit using the method of this invention, the tunnel is divided into n+4 elements, each with a length of l, and a total of n+5 nodes. Considering the layered foundation load acting on the interior of multiple soil layers, the additional stress at the tunnel axis is calculated using the Mindlin solution for layered foundations based on the soil's compression modulus and Poisson's ratio. Then, the Livkin model is used to simulate the continuity of the soil, treating the tunnel as an Euler-Bernoulli beam, and the heave value of the tunnel is calculated according to the formula. The tunnel heave deformation calculated by the method of this invention is compared with the measured data from the engineering site, and the results are as follows: Figure 6 .Depend on Figure 6It can be seen that the calculation results of the method of the present invention are basically consistent with the field measured data, indicating that the theoretical calculation method proposed in this invention has a certain degree of reliability and practicality. The figure also shows that the Boussinesq solution, which only considers the load on the layered foundation surface, seriously overestimates the change in additional stress at the tunnel axis caused by the excavation of the foundation pit. This results in the calculated tunnel heave value exceeding the 20mm limit specified in the Shanghai Metro Tunnel Code, even when all other parameters are the same.

[0099] Example 3: The underground space engineering project of the Guangxi University Station – Xiuling Road Station section of Nanning Metro Line 5, located beneath the road from Guangxi University to the School of Finance and Economics on Mingxiu West Road, was constructed using the open-cut method. A section was selected to verify the method of this invention. The excavation dimensions were 38m × 30m (length L × width B), with an excavation depth h of 8m. The horizontal distance from the right tunnel axis to the center of the excavation pit was 5.8m. The entire tunnel axis was parallel to the bottom of the excavation pit. The tunnel diameter D was 6m, the segment thickness g = 0.35m, and the distance from the top of the tunnel to the bottom of the excavation pit was 6.2m. Therefore, the calculated burial depth Z0 of the existing tunnel was 17.2m. The equivalent bending stiffness of the tunnel is (EI). eq =1.76×10 8 kN·m 2 Considering that the concrete pad has already been poured, the elastic modulus E at the tunnel axis is taken. s Take 28 MPa, dimensionless parameter β = 1. Soil layer parameters are shown in Table 4.

[0100] from Figure 7 It can be seen that the maximum tunnel uplift value calculated by the method of the present invention is close to the actual measurement, and the uplift trend is basically consistent. The influence range of the excavation of the foundation pit on the underlying tunnel calculated by the method of the present invention is about 80m. The maximum tunnel uplift value calculated by the method of the present invention is close to the actual maximum tunnel uplift value. The actual maximum value is slightly smaller than the value calculated by the method of the present invention. The reason is that the actual project involves segmented excavation and retaining piles around the foundation pit, thus verifying the rationality of the method of the present invention.

[0101] Table 4 Soil parameters for the Guangcai Intersection Underground Space Project

[0102]

[0103] This invention is not limited to the applications listed in the specification and embodiments. For those skilled in the art, various corresponding modifications and variations can be made according to this invention, and all such modifications and variations fall within the protection scope of the claims of this invention.

Claims

1. A method for calculating the uplift displacement of an underlying tunnel caused by excavation of a layered foundation pit, characterized in that, Includes the following steps: (1) Based on the relative positional relationship between the foundation pit and the underlying tunnel, clarify the relevant parameters and establish a calculation and analysis model; (2) Based on the load acting on the soil, the stress and strain solution below the load surface is derived. The tunnel and the foundation are equivalent to the Euler-Bernoulli long beam and the Lifkin foundation model, respectively. The change of additional stress in the soil caused by the excavation and unloading of the foundation pit is calculated using the Mindlin solution of the elastic layered foundation. The corresponding mechanical model is obtained, and the differential equation controlling the longitudinal deformation of the tunnel under the excavation and unloading of the foundation pit is derived. (3) Finally, the finite difference method was used to calculate the uplift deformation of the underlying existing tunnel caused by the excavation of the foundation pit; In step (1), the calculation and analysis model construction process includes: establishing a global coordinate system with the center o of the foundation pit as the origin, the length direction of the foundation pit as the y-axis, and the width direction of the foundation pit as the x-axis. Global coordinate system; a perpendicular line from the center of the excavation pit (o) to the tunnel, and then the perpendicular foot... The local coordinate origin is defined by the longitudinal direction of the tunnel. The axis and the tunnel are transverse. Axis establishment Local coordinate system; the angle between the tunnel axis and the short side of the excavation pit is... , and The transformation relationships between coordinates are shown below: ； ； In the formula, R represents the coordinate system originating from the global coordinate system origin. To the local coordinate origin The distance; In step (2), the differential equation for controlling the longitudinal deformation of the tunnel is expressed as follows: ； In the formula, denoted as the longitudinal deformation curve of the tunnel; D is the tunnel diameter. The value of the additional stress change at the tunnel axis caused by the unloading load during the excavation of the foundation pit; The bed mass coefficient; The equivalent bending stiffness of the tunnel; All of these are dimensionless parameters related to the properties of the foundation soil. To calculate half the length of the tunnel; The bed coefficient The following formula is used for calculation: ； In the formula, ； and These are the elastic modulus and Poisson's ratio of soil, respectively. This refers to the burial depth of existing tunnels.

2. The method for calculating the uplift displacement of the underlying tunnel caused by excavation of a layered foundation pit according to claim 1, characterized in that, The equivalent bending stiffness of the tunnel The calculation formula is: ； In the formula, Let n be the elastic modulus of the segment concrete (kPa), and n be the number of longitudinal bolts. This refers to the ring width of the segment ring; The average linear stiffness of the joint bolts; This represents the cross-sectional area of ​​the tunnel; without considering changes in the tunnel's horizontal and vertical diameters, ; ; ; ; ; ; ;in is the position parameter of the central axis of the segment ring, and the value is determined based on actual engineering measurements; g is the thickness of the segment.

3. The method for calculating the uplift displacement of the underlying tunnel caused by the excavation of a layered foundation pit according to claim 1, characterized in that, Additional stress variation value of excavation unloading load at the tunnel location The results were obtained using the Mindlin solution for layered foundations: ； In the formula: , , , , , , , For matrix The corresponding elements in; To account for the equivalent load of foundation pit excavation considering the influence of residual stress, It is a zero-order Bessel function of the first kind; For integration parameters, Let be the area of ​​a rectangular, uniformly distributed vertical load. To calculate the coordinates of the point; matrix Defined as: ； In the formula: To calculate the depth of the point; Let be the distance from the bottom of the j-th soil layer to the ground surface; (k=1, 2, ..., j, ..., n) represents the thickness of each soil layer. Let be the distance from the bottom of the excavation pit to the top of the i-th soil layer. In the matrix , and Elements, This is called the transfer matrix, and is defined as follows: ； Transfer matrix Expressions for each element: ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ， ； In the formula: and It is the Lame constant. , and This corresponds to the elastic modulus and Poisson's ratio of each soil layer in the layered system; The equivalent load for foundation pit excavation, taking into account the influence of residual stress, is calculated using the following formula: ； In the formula, Equivalent unloading during foundation pit excavation, unit: kN / m 2 , For the first The unit weight of the soil layer, in kN / m 3 , For the excavation of the first The thickness of the soil layer (m), This represents the residual stress coefficient.

4. The method for calculating the uplift displacement of the underlying tunnel caused by excavation of a layered foundation pit according to claim 1, characterized in that, Step (3) specifically involves dividing the tunnel longitudinally into nodes -2, -1, 0, 1, 2...n-1, n, n+1, n+2, with the length of each node being... The additional stress on each node i is The vertical displacement is For i=0,1,2,…,n, the finite difference method is used to calculate the uplift deformation of the underlying existing tunnel caused by the excavation of the foundation pit. as follows: ； In the formula, Assuming the tunnel is free at both ends, then the shear force Q and bending moment M at both ends of the tunnel are 0, which leads to the conclusion that... The values ​​are as follows: ； ； yes middle The value of (i=0,1,2,…,n), To divide the coordinate values ​​of the nodes along the longitudinal direction of the tunnel, Substituting into the above formula, we can obtain the longitudinal node displacement of the underlying existing tunnel caused by the excavation of the foundation pit. .

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