Method for predicting settlement of large-diameter shield tunnel underpassing building
By establishing a settlement prediction regression model through numerical simulation and response surface methodology, the problems of long prediction time and high cost of settlement of shield tunnels passing under buildings in existing technologies are solved, and rapid and accurate settlement prediction is achieved, thereby improving construction safety and efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- OCEAN UNIV OF CHINA
- Filing Date
- 2026-03-13
- Publication Date
- 2026-06-16
AI Technical Summary
Existing technologies for predicting settlement of buildings under shield tunnels suffer from problems such as long time, high cost, and high hardware requirements, making it difficult to predict settlement quickly and accurately.
Numerical simulation system was used to analyze factors such as horizontal distance, vertical distance, stratum parameters and reinforcement range. The response surface method was used to design the experiment and establish a settlement prediction regression model. The analysis conditions were derived using the minimization maximum deviation method. The parameters of the response surface formula were solved using Python to establish a settlement prediction formula.
It enables more accurate prediction of building settlement caused by shield tunneling, effectively reducing the time and cost of repeated on-site tests and numerical modeling, and improving construction safety and efficiency.
Smart Images
Figure CN121859286B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for predicting building settlement caused by construction, and in particular, a method for predicting building settlement caused by a large-diameter shield tunnel passing under a building. Background Technology
[0002] With the continuous acceleration of urban underground space development, shield tunneling technology has been widely used in infrastructure construction such as subways and integrated utility tunnels. During the shield tunneling process, it is often unavoidable to pass under various existing buildings. Due to soil disturbance and ground stress release caused by tunneling, shield construction often leads to varying degrees of surface settlement, which can pose a serious threat to project and operational safety. Therefore, accurately predicting the settlement impact on buildings before construction is particularly important.
[0003] Existing methods for predicting shield tunnels passing under buildings mainly include: computational methods, numerical simulation methods, and machine learning prediction methods.
[0004] Patent application CN202411375469.3 discloses a method for predicting and reinforcing damage to structures passing under tunnels. First, a settlement curve for the structure is obtained using soil data and a correction coefficient, and damage is assessed based on the curve's slope. Then, the angular variables at the structural nodes are calculated (the first floor is calculated using interpolation, and the upper floors use a matrix displacement method). Based on these angular variables, damage is categorized into seven levels, and corresponding targeted measures such as carbon fiber reinforcement and pile foundation replacement are proposed. This method accurately quantifies damage through angular variables, achieving precise prediction of damage risk and graded reinforcement, thus improving the protection effect and engineering safety of existing structures.
[0005] Patent CN202411531652.8 discloses a method for predicting deformation during shield tunneling through buildings. This method first acquires building settlement, tilt, shield parameters, and geological data through a monitoring system, and calculates the distance between the construction face and the building. Subsequently, a multi-factor matrix is constructed based on multi-time data, and a smart model integrating CNN and LSTM is used for spatiotemporal feature extraction and time-series prediction. Dynamic adjustments are achieved through parameter optimization. This method, combining multi-source data and intelligent algorithms, enables dynamic and refined prediction of building deformation, significantly improving construction safety control capabilities and the level of intelligence.
[0006] Although traditional methods consider many factors and can accurately predict settlement through finite element numerical simulation, theoretical formula derivation, and artificial intelligence prediction, these methods have high technical barriers, require a long time, and have high hardware requirements, making it difficult to quickly estimate the settlement of buildings in a short period of time. Therefore, there is an urgent need to propose a fast and efficient prediction method. Summary of the Invention
[0007] The purpose of this invention is to overcome the above-mentioned defects in the existing technology and to propose a method for predicting the settlement of buildings under large-diameter shield tunnels. This method can more accurately predict the settlement of buildings caused by shield tunneling and provides a reference and basis for the efficient and accurate prediction of the settlement of buildings under shield tunnels.
[0008] The technical solution of this invention is: a method for predicting settlement of a large-diameter shield tunnel passing under a building, comprising the following steps:
[0009] S1. Factors affecting the settlement of buildings under a shield tunnel include horizontal distance (A), vertical distance (B), geological parameters (C), and reinforcement range (D).
[0010] S2. Response surface methodology tests were conducted on the horizontal distance A, vertical distance B, geological parameters C, and reinforcement range D through numerical simulation; a settlement prediction regression model was established, and the settlement prediction function was fitted by minimizing the maximum deviation method.
[0011] In this invention, in step S1, the horizontal distance is set to 0-2d; the vertical distance is set to 0-2d; the geological parameters are selected as 10 MPa-50 MPa; and the reinforcement range is selected as 0-0.2d.
[0012] The specific implementation process of step S2 is as follows:
[0013] S2.1 Using four influencing factors, including horizontal distance A, vertical distance B, stratum parameters C, and reinforcement range D, as independent variables, the settlement of the building is obtained through numerical simulation as the dependent variable response value. A four-factor, three-level response surface analysis test is designed, and the BBD design is used to select test points. The settlement of each representative point is calculated through numerical simulation.
[0014] S2.2 Based on the response surface function values obtained in step S2.1, a settlement prediction regression model is established. The analysis conditions are derived by minimizing the maximum deviation method, and the parameters of the response surface formula are solved using Python.
[0015] The specific implementation process of step S2.2 is as follows:
[0016] Let the settlement prediction function be:
[0017] , (1)
[0018] Where, x i The expression is:
[0019] , (2)
[0020] in, This represents the response surface function value corresponding to the sample point; x (j) β represents the vector of the j-th sample point, with a total of m sample points; i represents the coefficients to be determined; k represents the number of coefficients to be determined;
[0021] Based on minimizing the maximum deviation of the response surface function from the sample values, a mathematical model is established:
[0022] , (3)
[0023] Where, y(x (j) The ) represents the sample value corresponding to the sample point, which will be used as y in the following formulas. (j) Replace; E k Let represent a real vector of k elements; δ represents the absolute value of the error.
[0024] Solving the above equation, its equivalent form can be written as:
[0025] , (4)
[0026] Will Substitute into the above formula:
[0027] , (5)
[0028] Where, x (j) The i-th variable represents the j-th y-value;
[0029] To ensure that the effective parameters are non-negative, the following formula is introduced:
[0030] , (6)
[0031] Where, α i Indicates the first auxiliary parameter introduced; γ i This indicates the introduction of a second auxiliary parameter;
[0032] Substituting equation (6) into equation (5), we get:
[0033] , (7)
[0034] Expand the two constraints in equation (7) and write them as matrices:
[0035] (8)
[0036] make:
[0037] , (9)
[0038] , (10)
[0039] , (11)
[0040] , (12)
[0041] , (13)
[0042] The settlement prediction regression model then transforms into the following form:
[0043] , (14)
[0044] Using the established settlement prediction regression model, Python was used to perform a maximum error minimization analysis on the data obtained in step S3.1, and regression fitting was performed on the experimental data to obtain the settlement prediction formula for the shield tunnel passing under the building with respect to horizontal distance A, vertical distance B, stratum parameter C, and reinforcement range D:
[0045] (15).
[0046] The beneficial effects of this invention are:
[0047] This application uses a numerical simulation system to analyze the coupling relationship of multiple factors such as horizontal distance, vertical distance, geological parameters, and reinforcement range, and establishes a settlement prediction regression model. Based on the BBD design in the response surface methodology, representative points are selected, and then the analysis conditions are derived using the minimization of maximum deviation method. The parameters of the response surface formula are solved using the settlement prediction regression model. Through the method proposed in this application,
[0048] (1) It can more accurately predict building settlement caused by shield tunneling;
[0049] (2) This method can effectively avoid the construction quality problems caused by excessive local errors in the least squares method, and provides a scientific basis for the optimization of tunneling parameters and settlement control when large-diameter shield tunnels pass under sensitive buildings. It can effectively reduce the time and cost of repeated on-site tests and numerical modeling, and improve construction safety and efficiency. Attached Figure Description
[0050] Figure 1 This is a flowchart of the method described in this invention;
[0051] Figure 2 This is a numerical simulation diagram showing the response value of a building with its settlement as the dependent variable. Detailed Implementation
[0052] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0053] Specific details are set forth in the following description to provide a full understanding of the invention. However, the invention can be practiced in many ways other than those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.
[0054] The settlement prediction method for large-diameter shield tunnels passing under buildings according to the present invention includes the following steps, and the flowchart of the method is as follows: Figure 1 As shown.
[0055] The first step, based on construction experience, is that the main factors affecting the settlement of buildings affected by underpasses include the shortest horizontal distance between the tunnel and the edge of the building foundation, the shortest vertical distance between the tunnel and the edge of the building foundation, the characteristics of the strata, i.e. the bearing capacity of the foundation, and the soil reinforcement status, i.e. the range of grouting reinforcement above the tunnel in any way. Therefore, the response surface influencing factors selected in this application are horizontal distance, vertical distance, strata parameters, and reinforcement range.
[0056] In engineering construction, the Peck formula is widely used to predict soil settlement caused by shield tunneling. The formula is as follows:
[0057] ,
[0058] in, This represents the settlement value at any point on the ground. The maximum value of ground settlement is located at the center of symmetry of the settlement curve; This is the distance from the center of the settlement curve to the point being calculated. The distance from the center of symmetry of the settlement curve to the inflection point of the curve is generally called the width of the settlement trough.
[0059] Based on O'Reilly and New's experience in the London area and tunnel depth The following simple linear relationship exists between them:
[0060] ,
[0061] in, This is the settlement trough width coefficient, which mainly depends on the soil properties.
[0062] From the above formulas, we can summarize several commonly used calculation parameters: horizontal distance, soil layer parameters, and tunnel depth. Furthermore, during tunnel boring, grouting reinforcement has been proven to be a major parameter affecting ground settlement. Therefore, this application selects four parameters—horizontal distance, vertical distance, soil layer parameters, and reinforcement range—as the main controlling factors affecting the tunnel's passage under structures.
[0063] The horizontal distance chosen in this application is 0-2d, where d is the tunnel diameter. This is because classical theories such as Peck's formula suggest that the width of the main settlement trough is approximately 2.5. ,in The width of the settlement trough is approximately 1-2d. When the horizontal distance exceeds 2d, the building is usually located outside the edge of the settlement trough, and the risk of differential settlement and tilting is significantly reduced.
[0064] The vertical distance selected in this application is 0-2d. The reason is that when the vertical distance exceeds twice the tunnel diameter, the impact of tunnel excavation on surface buildings is significantly reduced, and the settlement is usually within a controllable range.
[0065] The geological parameters used in this application are selected from 10 MPa to 50 MPa, which are commonly encountered in actual construction. This is because this range basically covers the common geological formations in shield tunnels, making the study widely applicable.
[0066] The reinforcement range selected in this application is 0-0.2d. The reason is that engineering experience shows that forming a reinforcement layer with a thickness of 0.1d-0.2d around the tunnel can effectively control the formation loss rate; beyond 0.2d, the effect is not significantly improved, but the cost increases significantly.
[0067] The second step involves designing a four-factor, three-level experiment using horizontal distance A, vertical distance B, geological parameters C, and reinforcement range D as experimental factors, as shown in Table 1. The relationship between the four factors and the settlement amount is calculated using the settlement amount as the response value.
[0068] Table 1. Factors and levels of a four-factor, three-level experimental design
[0069]
[0070] The third step is to establish a settlement prediction regression model and fit the settlement prediction function by minimizing the maximum deviation method.
[0071] First, using four influencing factors—horizontal distance A, vertical distance B, geological parameters C, and reinforcement range D—as independent variables, the settlement of the building was obtained through numerical simulation as the dependent variable response value. A schematic diagram of the numerical simulation is shown below. Figure 2 As shown, a four-factor, three-level response surface methodology experiment was designed, and the experimental points were selected using a BBD design.
[0072] In this embodiment, BBD design points were selected, and the settlement of each representative point was calculated using numerical simulation, as shown in Table 2.
[0073] Table 2 Response Surface Experimental Design and Data Results
[0074]
[0075] Second, a settlement prediction regression model is established, the analysis conditions are derived by minimizing the maximum deviation method, and finally the parameters of the response surface formula are solved using Python.
[0076] Let the settlement prediction function be:
[0077] , (1)
[0078] Where, x i The expression is:
[0079] , (2)
[0080] in, This represents the response surface function value corresponding to the sample point; x (j) β represents the vector of the j-th sample point, with a total of m sample points; i represents the coefficients to be determined; k represents the number of coefficients to be determined.
[0081] Based on minimizing the maximum deviation of the response surface function from the sample values, a mathematical model is established:
[0082] , (3)
[0083] Where y(x) (j) ) represents the sample value corresponding to the sample point, and y is used in subsequent formulas. (j) Replace; E k δ represents a real vector of k elements; δ represents the absolute value of the error.
[0084] Solving the above equation, its equivalent form can be written as:
[0085] , (4)
[0086] Will Substitute into the above formula:
[0087] , (5)
[0088] Where, x i (j) Let i represent the i-th variable that represents the j-th y-value.
[0089] To ensure that the effective parameters are non-negative, the following formula is introduced:
[0090] , (6)
[0091] Where, α i Indicates the first auxiliary parameter introduced; γ iThis indicates the introduction of a second auxiliary parameter. These two parameters are used to ensure that the value of β is not negative.
[0092] Substituting equation (6) into equation (5), we get:
[0093] , (7)
[0094] Expand the two constraints in equation (7) and write them as matrices:
[0095] , (8)
[0096] make:
[0097] , (9)
[0098] , (10)
[0099] , (11)
[0100] , (12)
[0101] , (13)
[0102] The settlement prediction regression model then transforms into the following form:
[0103] , (14)
[0104] Using the established settlement prediction regression model, Python was used to perform maximum error minimization analysis on the data in Table 2. Regression fitting was then performed on the experimental data to obtain the following formula for predicting settlement y of the shield tunnel passing under a building, considering horizontal distance A, vertical distance B, ground parameters C, and reinforcement range D:
[0105] (15),
[0106] The maximum deviation method proposed in this application is compared with the least squares method. The maximum absolute error, sum of squared residuals, and mean absolute error of the two methods are shown in Table 3.
[0107] Table 3 Comparison between the Minimum Error Method and the Least Squares Method
[0108] Fitting method Maximum absolute error Sum of Squares of Residuals Mean Absolute Error Minimize maximum deviation method 0.105105 0.213305 0.087997 Least squares method 0.150880 0.133254 0.060628
[0109] As shown in Table 3, the maximum absolute error of the method of minimizing the maximum deviation is smaller. This indicates that within the predictable range, the method proposed in this application can constrain the maximum error, minimizing the difference between the predicted difference and the actual value across the entire range, thus improving its reliability.
[0110] Example 1
[0111] Taking the Suzhou East Tunnel shield tunnel passing under the Tingyuan residential area as an example, the settlement was measured, and the settlement prediction formula for shield tunnels passing under buildings proposed in this application was used for prediction.
[0112] The numerical simulation parameters are set as follows: horizontal distance is 1 d; vertical distance is 1 d; formation parameter is 10 MPa; reinforcement range is 0.1 d.
[0113] The actual measurement showed that the settlement of the building was 4.82 mm; the same parameters were then substituted into the settlement prediction formula for shield tunnels passing under buildings proposed in this application for calculation.
[0114] The calculation using the formula shows that the settlement in this scenario is 4.95 mm, with a relative error of 2.63% compared to the actual situation. This indicates that, under numerical simulation conditions, the formula can reasonably reflect the settlement of the shield tunnel passing under the building.
[0115] Example 2
[0116] Taking the tunnel shield tunnel passing under the Moujia residential area in Nanchang as an example, the settlement was measured, and the settlement prediction formula for shield tunnels passing under buildings proposed in this application was used for prediction.
[0117] Numerical simulation parameter settings: Horizontal distance is set to 1.5d; vertical distance is set to 2d; formation parameter is set to 15 MPa; reinforcement range is set to 0.2d.
[0118] Actual measurements showed that the building's settlement was 2.01 mm; the same parameters were then substituted into the settlement prediction formula for shield tunnels passing under buildings proposed in this application for calculation.
[0119] The calculation using the formula shows that the settlement in this scenario is 1.93 mm, with a relative error of 3.98% compared to the actual situation. This indicates that, under numerical simulation conditions, the formula can reasonably reflect the settlement of the shield tunnel passing under the building.
[0120] The effectiveness of the proposed method for predicting settlement of large-diameter shield tunnels passing under buildings was verified through implementation of Example 1 and Example 2, demonstrating its promising application prospects and promotional value.
[0121] The settlement prediction method for large-diameter shield tunnels passing under buildings provided by this invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. It should be noted that for those skilled in the art, several improvements and modifications can be made to this invention without departing from the principles of this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention. The above description of the disclosed embodiments enables those skilled in the art to implement or use this invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of this invention. Therefore, this invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for predicting settlement of a large diameter shield tunnel underpassing a building, characterized by, Includes the following steps: S1. Factors affecting the settlement of buildings under a shield tunnel include horizontal distance (A), vertical distance (B), geological parameters (C), and reinforcement range (D). S2. Response surface methodology tests were conducted using numerical simulations to evaluate horizontal distance A, vertical distance B, geological parameters C, and reinforcement range D. A settlement prediction regression model was established, and the settlement prediction function was fitted using the minimization of maximum deviation method. The specific implementation process of step S2 is as follows: S2.1 Using four influencing factors, including horizontal distance A, vertical distance B, stratum parameters C, and reinforcement range D, as independent variables, the settlement of the building is obtained through numerical simulation as the dependent variable response value. A four-factor, three-level response surface analysis test is designed, and the BBD design is used to select test points. The settlement of each representative point is calculated through numerical simulation. S2.2 Based on the response surface function values obtained in step S2.1, a settlement prediction regression model is established. The analysis conditions are derived by minimizing the maximum deviation method, and the parameters of the response surface formula are solved using Python. The specific implementation process of step S2.2 is as follows: Let the settlement prediction function be: ， （1） wherein x i The expression is: ， （2） wherein, represents the response surface function value corresponding to the sample point; x (j) represents the jth sample point vector, and there are m sample points; β i represents the undetermined coefficient; k represents the number of undetermined coefficients; Based on minimizing the maximum deviation of the response surface function from the sample values, a mathematical model is established: ， （3） where y(x (j) ) represents the sample value corresponding to the sample point, which is replaced by y (j) later; E k represents a real vector composed of k elements; and δ represents the absolute value of the error. Solving the above equation, its equivalent form can be written as: ， （4） Substituting into the above equation: Substituting into the above equation: Substituting into the ， （5） wherein x i (j) represents the ith variable for the jth y value; To ensure that the effective parameters are non-negative, the following formula is introduced: ， （6） wherein a i represents the first introduced auxiliary parameter; γ i represents the second introduced auxiliary parameter; Substituting equation (6) into equation (5), we get: ， （7） Expand the two constraints in equation (7) and write them as matrices: ， （8） make: ， （9） ， （10） ， （11） ， （12） ， （13） The settlement prediction regression model then transforms into the following form: ， （14） Using the established settlement prediction regression model, Python was used to perform a maximum error minimization analysis on the data obtained in step S2.1, and regression fitting was performed on the experimental data to obtain the settlement prediction formula for the shield tunnel passing under the building with respect to horizontal distance A, vertical distance B, stratum parameter C, and reinforcement range D: 。 （15） 2. The method of claim 1, wherein, In step S1, the horizontal distance is set to 0-2d; the vertical distance is set to 0-2d; the geological parameters are selected as 10 MPa-50 MPa; the reinforcement range is selected as 0-0.2d; where d is the tunnel diameter.