Structure node angle variable-based tunnel under-crossing building damage prediction and reinforcement method

Abstract

The invention relates to the technical field of tunnel construction ground building risk assessment, in particular to a tunnel under-crossing building damage prediction and reinforcement method based on structural node angle variables. Comprising the following steps that S1, a free ground settlement curve is obtained according to soil layer data, and a building settlement curve is obtained after correction; s2, calculating the gradient of the settlement curve of the building, and judging whether the building is damaged or not according to the gradient value; s3, calculating a node angle variable of the building structure: calculating a node angle variable of a first layer of the building structure by using a difference value between a rotation angle and a rigid body rotation amount, and calculating node angle variables of the building structure and each layer by using a matrix displacement method layer by layer; and S4, the damage grades of the building structure are divided based on the node angle variables, and the building is reinforced according to the different damage grades. According to the method, possible damage to the building when the tunnel passes through the building can be predicted more accurately, targeted reinforcement measures are provided, and the safety of the ground building is protected.

Description

Technical Field

[0001] The invention relates to the technical field of risk assessment of ground buildings during tunnel construction, and in particular to a method for predicting and reinforcing a tunnel-underpassing building damage based on structural node angle variables. Background Art

[0002] At present, the scale of subways in large and medium-sized cities in my country is getting larger and larger, and there are dense buildings above the subways. The subway tunnel will inevitably have an impact on the surrounding buildings. If the subway tunnel has a destructive impact on the surrounding buildings, it will not only cause significant economic losses, but also bring about social instability. The noise loss is irreparable. For this reason, the impact of existing buildings above the tunnel construction team has attracted more and more attention from engineers, experts and scholars in related professions.

[0003] At present, most of the methods used at home and abroad are tests or simulations to calculate the degree of damage to buildings caused by tunnels. The time and cost of the test or simulation process are relatively high, and errors are difficult to avoid. The accumulation of errors and uncertainties in numerical methods will reduce the accuracy of the test or simulation results, and thus the degree of damage to buildings caused by tunnels cannot be accurately obtained. Summary of the invention

[0004] The purpose of the present invention is to overcome the above-mentioned defects of the prior art and propose a method for predicting and reinforcing the damage of a tunnel under a building based on structural node angle variables. The method can more accurately predict the damage that a tunnel may cause to a building when passing through the building, and proposes targeted reinforcement measures to protect the safety of ground buildings.

[0005] The technical solution of the present invention is: a method for predicting and reinforcing the damage of a tunnel under a building based on structural node angle variables, which includes the following steps:

[0006] S1. Obtain the free ground settlement curve based on the soil layer data, and obtain the building settlement curve after correction;

[0007] S2. Calculate the slope of the building settlement curve and determine whether the building is damaged based on the slope value;

[0008] S3. Calculate the angle variables of the building structure nodes: calculate the angle variables of the nodes of the building structure on one layer by using the difference between the rotation angle and the rigid body rotation, and calculate the angle variables of the nodes of the building structure on each layer layer by layer by using the matrix displacement method;

[0009] S4. The damage levels of building structures are divided based on node angle variables, and buildings are reinforced according to different damage levels.

[0010] In step S1 of the present invention, geological exploration is performed to determine soil layer data to obtain a free ground settlement curve.

[0011]

[0012] Where A is the tunnel excavation area; V l is the bottom loss rate; K is the width parameter of the sedimentation tank; z o is the tunnel depth; x is the horizontal distance from the tunnel centerline to the calculation point;

[0013] Introducing the correction factor λ n , n = 1, 2, 3..., the width parameter K of the sedimentation trough is corrected to obtain the building settlement curve, and the correction coefficient λ n Including but not limited to: the correction coefficient λ1 of the door and window opening ratio to the width of the settlement tank, the correction coefficient λ2 of the building depreciation rate to the width of the settlement tank, and the correction coefficient λ3 of the building's own weight to the width of the settlement tank.

[0014]

[0015] Among them, K b =λ1λ2λ3…λ n K.

[0016] In step S2, the slope is the first-order derivative of the building settlement curve.

[0017]

[0018] The corresponding slope is:

[0019]

[0020] Among them, s max is the ground settlement of the tunnel centerline; t is the distance from the lowest point of the building settlement curve to the inflection point of the curve;

[0021] When the calculated slope ω exceeds 1 / 500, it indicates that the building is damaged. At this time, through steps S3 and S4, the damage degree of the building is specifically judged, and corresponding reinforcement measures are taken according to the damage degree of the building.

[0022] In step S3, the calculation formula of the node angle variable β of the first floor of the building structure is:

[0023]

[0024] Among them, β ij is the node angle variable, that is, the rotation angle θ and the rigid body rotation The difference between i and j is the node position; θ ij is the turning angle of the slope of the settlement curve, Δi, Δj are the relative settlement values ​​of the nodes; L ijis the distance between node i and node j.

[0025] In step S3, when calculating the node angle variables of the second floor and above of the building structure, the beams of each floor are simplified, and the simplified beam model includes the beams A1D1 of the building that are not damaged before the tunnel passes under the building, the beams A2B2C2D2 that are damaged after the tunnel passes under the building, and the intersection points B2 and C2 of the beams and columns;

[0026] The matrix displacement method is used to establish the overall stiffness matrix K.

[0027]

[0028] Where E is the elastic modulus of the beam, in N / m 2 ; I is the cross-sectional inertia moment of the beam, in m 4 ; L is the distance between adjacent nodes, in meters.

[0029] According to the equation KΔ=P, the node displacement Δ can be calculated, where P is the equivalent node load and Δ is the node displacement.

[0030] P=(-F1,0,-F2,0) T ,

[0031] Among them, F1 and F2 are the deadweight of the upper building and the live load transferred down, so,

[0032] Right now Through the above matrix equation, we can get:

[0033]

[0034] The x1 and x2 obtained by solving the above formula are the relative displacements of the upper beams caused by the tunnel passing through the building, and β1 and β2 are the node angle variables caused by the tunnel passing through the building;

[0035] According to the forces F1 and F2 of each floor of the building, the node angle variable β of each floor of the building can be calculated layer by layer.

[0036] In step S4, the damage level of the building structure is divided according to the node angle variable calculated in step S3:

[0037] When the node angle variable β is greater than or equal to 1 / 750, the operation of settlement-sensitive machines may become difficult;

[0038] When the node angle variable β is greater than or equal to 1 / 600, the frame structure with diagonal braces may be dangerous:

[0039] When the node angle variable β is greater than or equal to 1 / 500, it may be detrimental to the safety of buildings that do not allow cracks to occur:

[0040] When the node angle variable β is greater than or equal to 1 / 400, cracks may begin to appear in the partition wall;

[0041] When the node angle variable β is greater than or equal to 1 / 300, crane operation may become difficult;

[0042] When the node angle variable β is greater than or equal to 1 / 250, the rigid high-rise building may have obvious tilt;

[0043] When the node angle variable β is greater than or equal to 1 / 150, the number of cracks may increase and the building may suffer structural damage.

[0044] When the node angle variable β of a certain layer of the building structure is calculated to be greater than or equal to 1 / 750 and less than 1 / 600, the carbon fiber reinforcement method can be used around the node to reinforce the building structure of this layer;

[0045] When the node angle variable β of a certain layer of the building structure is calculated to be ≥ 1 / 600, the external steel reinforcement method can be used in advance to reinforce the building structure of this layer;

[0046] When the node angle variable β of a certain layer of the building structure is calculated to be ≥ 1 / 400, the building structure of this layer can be reinforced by adding support points;

[0047] When the calculated node angle variable β of the building structure is ≥ 1 / 300, the building structure can be reinforced by using the stress relief method, tracking grouting method, or pile foundation underpinning;

[0048] When the node angle variable β of the building structure is calculated to be ≥ 1 / 250, the partition method can be used to reinforce the building structure in advance.

[0049] The beneficial effects of the present invention are:

[0050] (1) In this application, the width of the settlement trough in the building settlement curve is corrected by introducing building-related parameters to obtain a settlement curve that better fits the building;

[0051] (2) Assessing the degree of building damage by calculating the node angle variables of the building structure: Since the first floor of the building and the ground deform in coordination, the node angle variables of the first floor of the building structure in this application are calculated using the difference between the rotation angle and the rigid body rotation; Since the angle variables of the second floor and above are generated due to the relative displacement deformation of the columns and the difference in the self-weight and live load of the upper building, the node angle variables of the remaining floors of the building structure in this application are calculated by the matrix displacement method;

[0052] (3) At the same time, this application divides the building damage level into seven damage levels according to the node angle variables, and proposes reinforcement measures based on the node angle variables. Compared with the existing test prediction or simulation prediction methods, this application can save a lot of construction time and construction costs when predicting the damage to buildings caused by tunnel underpasses. Through the calculation of node angle variables, it can achieve accurate prediction of building damage, and carry out targeted reinforcement measures for buildings based on the predicted building damage, avoiding over-reinforcement or under-reinforcement, and protecting ground buildings more safely and effectively. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a schematic diagram of the process of the method of the present invention;

[0054] Figure 2 is a cross-sectional view of a building and a stratum in an embodiment of the present invention;

[0055] Figure 3 is a schematic diagram of defining deformation variables of a building in an embodiment of the present invention;

[0056] Figure 4 It is a simplified model diagram of a building beam in an embodiment of the present invention. DETAILED DESCRIPTION

[0057] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0058] In the following description, specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in a variety of other ways than those described herein, and those skilled in the art can make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0059] This application proposes a method for predicting and reinforcing the damage of tunnels under buildings based on structural node angle variables. This application can evaluate and predict in advance the damage that may be caused to adjacent buildings during tunnel excavation to ensure construction safety and protect the safety and stability of existing building structures. At the same time, reinforcement measures based on angle variables are proposed. Figure 1 , the steps included in the method described in this application are specifically introduced.

[0060] The first step is to conduct geological survey to determine the soil layer data and obtain the free ground settlement curve.

[0061]

[0062] Where A is the tunnel excavation area; V l is the formation loss rate; K is the width parameter of the sedimentation trough; zo is the tunnel burial depth; x is the horizontal distance from the tunnel centerline to the calculation point.

[0063] By changing the settlement trough width parameter K in the free ground settlement curve, the building-related correction factor λ is introduced n , n = 1, 2, 3..., the width parameter K of the sedimentation tank is corrected to improve the calculation accuracy of the angle variable.

[0064] Correction coefficient λ n Including but not limited to: the correction coefficient λ1 of the door and window opening rate to the width of the settlement tank; the correction coefficient λ2 of the building depreciation rate to the width of the settlement tank; the correction coefficient λ3 of the building's deadweight to the width of the settlement tank. Thus, the building settlement curve is obtained.

[0065]

[0066] Where K b =λ1λ2λ3…λ n K.

[0067] The building settlement curve obtained by the above equation is as follows Figure 2 As shown in the figure. After tunnel excavation, the settlement caused by the building is significantly different from the settlement caused by the natural ground. Due to the existence of building stiffness, the actual settlement deformation curve of the building is much gentler than the settlement deformation curve of the natural ground, but the impact range is larger. It can be seen that the stiffness of the building has a significant restraining effect on the surface settlement, so the restraining effect of the building stiffness cannot be ignored in the research on surface settlement prediction.

[0068] The frame structure is relatively simple and can be regarded as a building with uniform stiffness distribution. Therefore, the deformation curve of the frame structure caused by surface settlement should also be a continuous curve, and the position of the maximum settlement point remains unchanged.

[0069] The second step is to calculate the slope of the building settlement curve. When the slope exceeds a certain critical value, the building will be damaged.

[0070] The slope is the first derivative of the building settlement curve.

[0071]

[0072] The corresponding slope is:

[0073]

[0074] In the formula, s max is the surface settlement of the tunnel centerline; t is the distance from the lowest point of the building settlement curve to the inflection point of the curve.

[0075] For slopes less than 1 / 500 and settlement points less than 10mm, the estimated loss can be ignored. When the slope is greater than 1 / 500, the building will be damaged. The maximum slope of surface settlement occurs at the inflection point of the settlement curve, so it is only necessary to calculate the slope at the inflection point of the settlement curve to determine whether it exceeds the critical value of 1 / 500.

[0076] When the calculated slope ω exceeds 1 / 500, it means that the building is damaged. At this time, it is necessary to make a specific judgment on the degree of damage to the building through the following steps, and take corresponding reinforcement measures according to the degree of damage to the building.

[0077] The third step is to calculate the node angle variables of the building structure. In this application, the node angle variables of one layer of the building structure are calculated using the difference between the rotation angle and the rigid body rotation, and the node angle variables of the remaining layers of the building structure are calculated layer by layer using the matrix displacement method.

[0078] The reason why different methods are used to calculate the node angle variables for the first floor and the upper floors of the building structure is that the first floor deforms in coordination with the free ground, and the settlement curve of the building can be obtained by correcting the settlement trough width coefficient of the free ground; while the upper floors are not in direct contact with the ground, and the change in their node angle variables is mainly due to the relative vertical displacement of the columns after the deformation of the first floor, as well as the deadweight and live load of the upper building.

[0079] The calculation formula of the node angle variable β of the first floor of the building structure is as follows:

[0080]

[0081] Among them, β ij is the node angle variable, that is, the rotation angle θ and the rigid body rotation The difference between i and j is the node position; θ ij is the turning angle of the slope of the settlement curve, Δi, Δj are the relative settlement values ​​of the nodes; L ij is the distance between node i and node j. Figure 3 Define schematic diagrams for building deformation variables.

[0082] The angle variable β of the nodes on the second floor and above is calculated as follows. For the beam-column nodes on the second floor and above, the rotation angle of each beam-column node is calculated using the matrix displacement method, considering the deadweight of the building above each floor and the different live loads.

[0083] Simplify the beams of each layer. The simplified beam model is as follows Figure 4As shown. Among them, beam A1D1 is a simplified diagram of the beam before the tunnel passes through and the building is not damaged; A2B2C2D2 is a simplified diagram of the beam after the tunnel passes through and is damaged, where B2 and C2 are the intersection points of the beam and column. x1 and x2 are the relative displacements of nodes B2 and C2 relative to beam A2D2. The overall stiffness matrix K is established using the matrix displacement method.

[0084]

[0085] Where E is the elastic modulus of the beam, in N / m 2 ; I is the cross-sectional inertia moment of the beam, in m 4 ; L is the distance between adjacent nodes, in meters.

[0086] Solving the equation KΔ=P, we can find the node displacement Δ. Where P is the equivalent node load and Δ is the node displacement.

[0087] P = (-F1, 0, -F2, 0) T ,

[0088] therefore,

[0089] Among them, F1 and F2 are the deadweight of the upper building and the live load transferred down. Through the above matrix equation, we can get:

[0090]

[0091]

[0092] The x1 and x2 obtained by solving the above formula are the relative displacements of the upper beams caused by the tunnel passing through the building, and β1 and β2 are the node angle variables caused by the tunnel passing through the building.

[0093] By analogy, the node angle variables of the second floor of the building can be calculated based on the forces F1 and F2 of the second floor of the building; the node angle variables of the third floor of the building can be calculated based on the forces F1 and F2 of the third floor of the building. The node angle variables β of each layer of the frame structure are calculated layer by layer, and the degree of damage is determined based on each node angle variable β, so as to take reasonable reinforcement measures.

[0094] The fourth step is to divide the building structure into damage levels based on the node angle variables and reinforce the building.

[0095] The building structure is divided into seven levels of damage based on the node angle variable, as shown in Table 1.

[0096] Table 1 Building structure damage levels based on node angle variable β

[0097] Risk Level Node angle variable β Degree of damage to buildings 1 1 / 750 Difficulty in operating settlement-sensitive machines 2 1 / 600 Danger in frame structures with diagonal braces 3 1 / 500 It is not good for the safety of buildings where cracks cannot be allowed to occur. 4 1 / 400 Cracks began to appear in the partition wall 5 1 / 300 Crane operation difficulties 6 1 / 250 Rigid high-rise buildings have obvious tilt 7 1 / 150 The number of cracks increases, causing structural damage to the building

[0098] By predicting the level of building damage caused by tunnelling, the following reinforcement measures can be taken before, during and after construction.

[0099] When the node variable β of a certain layer of the building structure is calculated to be 1 / 750≤β<1 / 600, the carbon fiber reinforcement method can be used around the node.

[0100] The specific method of carbon fiber reinforcement is: by pasting epoxy resin on the surface of the structure, the pre-impregnated epoxy resin ensures good bonding between the carbon fiber and the original concrete structure, thereby achieving the synergy of the two and significantly improving the structure's crack resistance, rigidity and ductility. The carbon fiber reinforcement method is convenient to construct, light in material, saves time and cost, and its application effect is particularly significant in places where space is limited.

[0101] When the calculated node variable β of a certain layer of the building structure is ≥1 / 600, the external steel reinforcement method can be used in advance to reinforce the building structure of this layer.

[0102] The specific method of external steel reinforcement is: by using angle steel, channel steel or steel plate to cover the original components, and injecting high-strength cement mortar or epoxy resin slurry into the gap between the external steel and the original components, and after curing, use connecting parts such as tie plates or hoops to tightly combine them.

[0103] When the calculated node variable β of a certain layer of the building structure is ≥1 / 400, the method of adding support points can be used to strengthen the building structure of that layer.

[0104] The specific practice of the reinforcement method of adding fulcrums is: before the shield passes through, additional fulcrums can be added to shorten the calculated span of the component, thereby effectively reducing the stress inside the component and thus reducing the angle variable. This reinforcement method will take up more space and may affect the use function of the original building. Therefore, careful consideration and planning are required in actual construction to ensure that the reinforcement effect is coordinated with the use requirements of the building.

[0105] When the calculated node variable β of a certain layer of the building structure is ≥1 / 300, the stress relief method, tracking grouting method, or pile foundation underpinning method can be used to reinforce the building structure. Before the shield tunneling, the stress relief method can be used; during the shield tunneling construction, the tracking grouting method can be used; when the foundation is a pile foundation, the pile foundation underpinning method can be used.

[0106] The specific approach of the stress relief method is: if the node angle variation is not less than 1 / 300, the overall angle variation of the building is too large, and the building will tilt beyond expectations. After the shield tunneling, if the overall tilt of the building is serious, a relief hole can be set on the side with smaller settlement to promote stress redistribution of the foundation soil, thereby causing an increase in local settlement to regulate and balance the overall settlement of the building. This method helps to reduce the uneven settlement of the entire building by increasing the settlement of a specific area in a controlled manner, thereby protecting the structural integrity and safety of the building.

[0107] The specific practice of the tracking grouting method is: during the construction process, the bottom foundation is grouted at the bottom foundation where the predicted node angle variable is large to enhance the bearing capacity and stability of the foundation. The grouting operation needs to be carried out under a certain pressure control to ensure that the slurry can fully penetrate into the voids of the soil, thereby effectively filling and reinforcing the soil layer. During the grouting process, attention should be paid to layering. Through multiple grouting, the reinforcement materials can be distributed more evenly and the reinforcement effect can be improved. At the same time, maintaining a faster grouting speed is also key, which helps to adjust the settlement of the building in time and reduce the settlement differences between different parts.

[0108] According to the actual working conditions, it is decided to choose the stress relief method or the tracking grouting method. The stress relief method is suitable for thick soft soil foundations, while the tracking grouting method is suitable for stable strata. The stress relief method is a reinforcement measure applied after the shield tunneling construction, while the tracking grouting method is a reinforcement measure applied during the shield tunneling process.

[0109] The specific practice of pile foundation underpinning is as follows: For buildings with pile foundations, pile foundation underpinning can be used when the angular variation exceeds 1 / 300. During the construction process, the existing foundation is reinforced and replaced in stages to prevent excessive fluctuations in the stress of the original building structure. When the foundation conditions are poor, the differential settlement is obvious, and the building angular variation is large, pile foundation underpinning can be used to ensure the overall safety of the building.

[0110] When the calculated node angle variable β of the building structure is ≥ 1 / 250, the partition method can be used to strengthen the building structure.

[0111] The specific approach of the partition method is: when the distance between the tunnel and the existing building is closer, the building angle variation is larger, and the angle variation is greater than 1 / 250, the partition method can be used in advance to reduce the angle variation after construction. Usually, a series of standard partition measures can be adopted, including steel sheet piles, underground continuous walls, deep mixing piles, tree root piles and bored piles. These partition structures can effectively isolate the tunnel construction area from the building, and the partition wall can bear the lateral pressure of the soil and reduce the negative friction between the soil and the foundation. In this way, the angle variation of the frame structure caused by the tunnel underpass can be effectively reduced to ensure the safety and stability of the building.

[0112] The above is a detailed introduction to the damage prediction and reinforcement method for tunnels underpass buildings based on structural node angle variables provided by the present invention. This article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method and core ideas of the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention. The above description of the disclosed embodiments enables professionals and technicians in this field to implement or use the present invention. Various modifications to these embodiments will be obvious to professionals and technicians in this field, and the general principles defined in this article can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown in this article, but will conform to the widest scope consistent with the principles and novel features disclosed in this article.

Claims

1. A method for predicting and reinforcing the damage of a tunnel under a building based on structural node angle variables, characterized in that: The following steps are involved: S1. Obtain the free ground settlement curve based on the soil layer data, and obtain the building settlement curve after correction; S2. Calculate the slope of the building settlement curve and determine whether the building is damaged based on the slope value; S3. Calculate the angle variables of the building structure nodes: calculate the angle variables of the nodes of the building structure on one layer by using the difference between the rotation angle and the rigid body rotation, and calculate the angle variables of the nodes of the building structure on each layer layer by layer by using the matrix displacement method; S4. The damage levels of building structures are divided based on node angle variables, and buildings are reinforced according to different damage levels.

2. The method for predicting and reinforcing the damage of a tunnel under a building based on structural node angle variables according to claim 1 is characterized in that: In step S1, geological exploration is performed to determine soil layer data to obtain a free ground settlement curve. Where A is the tunnel excavation area; V l is the bottom loss rate; K is the width parameter of the sedimentation tank; z o is the tunnel depth; x is the horizontal distance from the tunnel centerline to the calculation point; Introducing the correction factor λ n , n = 1, 2, 3..., the width parameter K of the sedimentation trough is corrected to obtain the building settlement curve, and the correction coefficient λ n Including but not limited to: the correction coefficient λ1 of the door and window opening ratio to the width of the settlement tank, the correction coefficient λ2 of the building depreciation rate to the width of the settlement tank, and the correction coefficient λ3 of the building's own weight to the width of the settlement tank. Among them, K b =λ1λ2λ3…λ n K.

3. The method for predicting and reinforcing the damage of a tunnel under a building based on structural node angle variables according to claim 1 is characterized in that: In step S2, the slope is the first-order derivative of the building settlement curve. The corresponding slope is: Among them, s max is the ground settlement of the tunnel centerline; t is the distance from the lowest point of the building settlement curve to the inflection point of the curve; When the calculated slope ω exceeds 1 / 500, it indicates that the building is damaged. At this time, through steps S3 and S4, the damage degree of the building is specifically judged, and corresponding reinforcement measures are taken according to the damage degree of the building.

4. The method for predicting and reinforcing the damage of a tunnel under a building based on structural node angle variables according to claim 1 is characterized in that: In step S3, the calculation formula of the node angle variable β of the first floor of the building structure is: Among them, β ij is the node angle variable, that is, the rotation angle θ and the rigid body rotation The difference between i and j is the node position; θ ij is the turning angle of the slope of the settlement curve, Δi, Δj are the relative settlement values ​​of the nodes; L ij is the distance between node i and node j.

5. The method for predicting and reinforcing the damage of a tunnel under a building based on structural node angle variables according to claim 1 is characterized in that: In step S3, when calculating the node angle variables of the second floor and above of the building structure, the beams of each floor are simplified, and the simplified beam model includes the beams A1D1 of the building that are not damaged before the tunnel passes under the building, the beams A2B2C2D2 that are damaged after the tunnel passes under the building, and the intersection points B2 and C2 of the beams and columns; The matrix displacement method is used to establish the overall stiffness matrix K. Where E is the elastic modulus of the beam, in N / m 2 ; I is the cross-sectional inertia moment of the beam, in m 4 ; L is the distance between adjacent nodes, in meters; According to the equation KΔ=P, the node displacement Δ can be calculated, where P is the equivalent node load and Δ is the node displacement. P=(-F1,0,-F2,0) T , Among them, F1 and F2 are the deadweight of the upper building and the live load transferred down, so, Right now Through the above matrix equation, we can get: The x1 and x2 obtained by solving the above formula are the relative displacements of the upper beams caused by the tunnel passing through the building, and β1 and β2 are the node angle variables caused by the tunnel passing through the building; According to the forces F1 and F2 of each floor of the building, the node angle variable β of each floor of the building can be calculated layer by layer.

6. The method for predicting and reinforcing the damage of a tunnel under a building based on structural node angle variables according to claim 1 is characterized in that: In step S4, the damage level of the building structure is divided according to the node angle variable calculated in step S3: When the node angle variable β is greater than or equal to 1 / 750, the operation of settlement-sensitive machines may become difficult; When the node angle variable β is greater than or equal to 1 / 600, the frame structure with diagonal braces may be dangerous; When the node angle variable β is greater than or equal to 1 / 500, it may be detrimental to the safety of the building where cracks are not allowed to occur; When the node angle variable β is greater than or equal to 1 / 400, cracks may begin to appear in the partition wall; When the node angle variable β is greater than or equal to 1 / 300, crane operation may become difficult; When the node angle variable β is greater than or equal to 1 / 250, the rigid high-rise building may have obvious tilt; When the node angle variable β is greater than or equal to 1 / 150, the number of cracks may increase and the building may suffer structural damage.

7. The method for predicting and reinforcing the damage of a tunnel under a building based on structural node angle variables according to claim 6 is characterized in that: When the node angle variable β of a certain layer of the building structure is calculated to be greater than or equal to 1 / 750 and less than 1 / 600, the carbon fiber reinforcement method can be used around the node to reinforce the building structure of this layer; When the node angle variable β of a certain layer of the building structure is calculated to be ≥ 1 / 600, the external steel reinforcement method can be used in advance to reinforce the building structure of this layer; When the node angle variable β of a certain layer of the building structure is calculated to be ≥ 1 / 400, the building structure of this layer can be reinforced by adding support points; When the calculated node angle variable β of the building structure is ≥ 1 / 300, the building structure can be reinforced by using the stress relief method, tracking grouting method, or pile foundation underpinning; When the node angle variable β of the building structure is calculated to be ≥ 1 / 250, the partition method can be used to reinforce the building structure in advance.

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