Method for predicting formation and tunnel deformations caused by foundation pit excavation based on two-stage surrogate model

Abstract

The present invention provides a method for predicting the deformation of strata and tunnels caused by foundation pit excavation based on a two-stage surrogate model, which mainly includes: 1) selecting the input parameters and output parameters of the model and establishing a parametric finite element model; 2) obtaining training data by combining experimental design and the parametric finite element model; 3) constructing a two-stage surrogate model with the training data and verifying the prediction accuracy; 4) extracting the relevant parameters of the actual project as the input of the model to predict and fit the deformation of the strata and tunnels. The present invention takes into account the mechanical mechanism of tunnel deformation, and changes the prediction mode of tunnel deformation from the original {foundation pit excavation → tunnel deformation mode} to {foundation pit excavation → strata deformation → tunnel deformation mode}, improving the prediction accuracy without changing the number of training samples and the number of input parameters of the surrogate model.

Description

Technical Field

[0001] The present invention relates to the field of tunnel engineering, and particularly relates to a method for predicting the deformation of stratum and tunnel caused by foundation pit excavation based on a two-stage surrogate model. Background Art

[0002] In recent years, with the continuous growth of urban population and the rapid development of urban construction, the urban underground rail transit network has become increasingly dense, and some foundation pit projects on the ground will inevitably be adjacent to existing subway tunnels. This poses a great threat to the structural safety of the tunnels and the operation safety of the subway. Therefore, how to predict the response of existing tunnels caused by foundation pit excavation in order to discover and rectify it in advance has become the research focus in the field. The traditional research methods mainly include the measured data analysis method, the analytical method and the finite element numerical simulation method. However, it is difficult to meet the requirements of both rapidity and accuracy by using these methods to predict the tunnel structural response. With the progress of digital technology, digital twin has become a promising tool for the operation and maintenance risk management of urban infrastructure. Digital twin is a bridge connecting theory and visual information, and its key problem lies in realizing rapid simulation and prediction under various risk scenarios. Therefore, it is urgent to introduce the surrogate model method to solve this problem.

[0003] At present, there are few studies on using surrogate models to predict the deformation of stratum and tunnel. Some existing surrogate prediction models only predict the tunnel deformation under specific working conditions and are difficult to be extended to other practical problems. Moreover, the training of surrogate models requires a lot of time to obtain a large number of sample point data, and the mechanical mechanism of tunnel deformation is not considered in the establishment process of surrogate models, resulting in low modeling efficiency and poor prediction effect. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting the deformation of stratum and tunnel caused by foundation pit excavation based on a two-stage surrogate model to overcome the defects of the above-mentioned existing technologies.

[0005] To solve the above technical problems, a method for predicting the deformation of stratum and tunnel caused by foundation pit excavation based on a two-stage surrogate model provided by the present invention mainly includes the following steps:

[0006] 1) Select the input and output parameters of the model and establish a parametric finite element model;

[0007] 2) Obtain training data by combining experimental design and parametric finite element model;

[0008] 3) Construct a two-stage surrogate model with the training data and verify the prediction accuracy;

[0009] 4) Extract the relevant parameters of the actual project as the input of the model, and predict and fit the deformation of the stratum and tunnel.

[0010] The method for predicting the deformation of the stratum and tunnel caused by foundation pit excavation based on a two-stage surrogate model, wherein the process of establishing the parametric finite element model in step 1) includes:

[0011] 1.1) Select the input parameters and output parameters of the finite element model according to the sensitivity analysis results;

[0012] 1.2) Based on reasonable assumptions and simplifications, realize the parametric modeling that can automatically generate a new model only by modifying the values of the input parameters in the finite element model through the parametric design language in the finite element modeling software and the script program interface of the software.

[0013] The method for predicting the deformation of the stratum and tunnel caused by foundation pit excavation based on a two-stage surrogate model, wherein: in step 1.1), select the parameters with the greatest influence on the output as the input parameters to reduce the number of input parameters;

[0014] The output parameters of the finite element model in step 1.1) include stratum deformation and tunnel deformation;

[0015] The input parameters of the finite element model in step 1.1) include soil layer thickness, water head, unit weight, soil compression modulus, effective cohesion, Poisson's ratio, effective internal friction angle, tunnel outer diameter, tunnel lining stiffness, tunnel burial depth, distance between the tunnel and the foundation pit, foundation pit length, foundation pit width, foundation pit depth, retaining structure stiffness, support stiffness, and support spacing;

[0016] The sensitivity analysis in step 1.1) is to combine the results of global sensitivity analysis and local sensitivity analysis, and combine the top 50% of the sensitive parameters calculated by the two and eliminate the repeated parameters as the input parameters of the parametric finite element model.

[0017] The method for predicting the deformation of the stratum and tunnel caused by foundation pit excavation based on a two-stage surrogate model, wherein the specific process of obtaining the training data of the surrogate model in step 2) includes:

[0018] 2.1) Obtain the value ranges of the selected input parameters from the geological exploration reports of multiple other engineering projects in the project area;

[0019] 2.2) Use the Latin hypercube experimental design method to sample within the value ranges of each parameter and perform random combinations. The combined sample data point set is denoted as S;

[0020] 2.3) Substitute the sample point data into the parametric finite element model to calculate the corresponding stratum and tunnel deformations as the output response set Y;

[0021] 2.4) Normalize the sample point data set S and the corresponding output response set Y and use them as the training data set of the surrogate model.

[0022] The method for predicting the deformation of the stratum and tunnel caused by foundation pit excavation based on a two-stage surrogate model, wherein the normalization process in step 2.4) is to transform the values of each design variable of the sample points to a unified interval [0, 1] to improve the accuracy and robustness of the surrogate model. The normalization process is specifically calculated as follows:

[0023]

[0024] In the above formula (14), i = 1, 2,..., n; k = 1, 2,..., m; is the minimum value of all sample points on the k-th dimensional design variable; is the maximum distance between sample points on the k-th dimensional design variable.

[0025] The method for predicting the deformation of the stratum and tunnel caused by foundation pit excavation based on a two-stage surrogate model, wherein the surrogate model adopts a Kriging surrogate model, and its form is as follows:

[0026] y(x) = F(β, x) + Z(x) = f T (x)β + Z(x) (15);

[0027] In the above formula (15), f T (x) is a known regression model, which serves to provide a global approximation of the simulation. β is an undetermined regression coefficient; Z(x) is a stochastic process with a mean of 0 and a variance of The covariance is expressed as follows:

[0028]

[0029] In the above formula (16), x i and x j are any two different points in the design space. R(x i , x j , θ) is a correlation function that only depends on the spatial positions of the two points, and its function expansion is:

[0030]

[0031] In the above formula (17), θ = [θ 1 θ 2 ··· θ m T is an undetermined model parameter, and R k is any one of a linear function, an exponential function, a Gaussian function, a spherical function, and a cubic spline function;

[0032] Based on the above assumptions, if the given training sample set S = [x (1) ​, x (2) , ···, x m ] T and its response set Y = [y (1) , y (2) , ···, y m ] T After that, for any new point x to be measured new the predicted response value can be estimated by linearly combining the response values Y of the known sample points:

[0033]

[0034] In the above formula (18), c(x) T is the weight coefficient vector of the response value to be solved, and the prediction error is expressed as:

[0035] MSE = E(c T Y - y(x new ) 2 (19);

[0036] For the above assumptions, the surrogate model will find the optimal weight coefficient vector c(x) T to minimize the error of the prediction result.

[0037] The method for predicting the deformation of the stratum and tunnel caused by foundation pit excavation based on the two - stage surrogate model, wherein the construction and verification of the two - stage surrogate model in step 3) mainly include the following steps:

[0038] 3.1) Divide the normalized data into two groups: a training set and a verification set. Divide the surrogate model prediction process into two stages. The first - stage surrogate model is used to predict stratum deformation, and the second - stage surrogate model is used to predict tunnel deformation. First, train the first - stage surrogate model with the normalized training set, and predict the stratum deformation through the first - stage surrogate model. The first - stage surrogate model is a surrogate model established through the mapping relationship between the foundation pit excavation parameters S and the stratum deformation parameters Y;

[0039] 3.2) Update the input parameters of the finite - element model determined according to the sensitivity analysis result in step 1.1) to the stratum deformation parameters predicted by the first - stage surrogate model plus four tunnel - stratum related parameters, and use this as the input parameters of the second - stage surrogate model. The tunnel deformation parameters are used as the output parameters of the second - stage surrogate model. The stratum deformation parameters in the input parameters of the second - stage surrogate model are the directly predicted results in the first - stage surrogate model, without additional sampling and calculation. The tunnel - stratum related parameters are defined as the ratios of the following four tunnel parameters to the stratum structure parameters:

[0040] ① R h, the ratio of the horizontal distance between the tunnel center and the retaining wall to the foundation pit depth, and the calculation formula is:

[0041] R h =(D h -0.5L) / H;

[0042] Among them, D h is the distance between the tunnel center and the foundation pit center, L is the excavation length of the foundation pit, and H is the excavation depth of the foundation pit;

[0043] ②R d , the ratio of the buried depth of the tunnel center to the foundation pit depth, and the calculation formula is:

[0044] R d =D v / H;

[0045] Among them, D v is the buried depth of the tunnel center;

[0046] ③R s , the ratio of the tunnel lining stiffness to the soil compression modulus, and the calculation formula is:

[0047] R s =E l / E s ;

[0048] Among them, E l is the tunnel lining stiffness, and E s is the soil compression modulus;

[0049] ④R w , the ratio of the tunnel lining stiffness to the retaining wall stiffness, and the calculation formula is:

[0050] R w =E l / EA;

[0051] Among them, EA is the retaining wall stiffness;

[0052] The above four tunnel parameters R h 、R d 、R s 、R w can all be directly calculated from the input parameters in the first-stage surrogate model, so no additional sampling and calculation are required;

[0053] 3.3) Normalize the input parameters and output parameters of the updated second-stage surrogate model and use them to train the second-stage surrogate model, and then use the second-stage surrogate model to predict the tunnel deformation;

[0054] 3.4) Combine the first-stage surrogate model and the second-stage surrogate model to obtain a two-stage surrogate model; substitute the input parameters of the validation set into the two-stage surrogate model formed by combining the established first-stage surrogate model and the second-stage surrogate model for prediction, and compare the predicted results with the original parametric finite element calculation results to verify the prediction accuracy of the surrogate model.

[0055] The method for predicting the deformation of the stratum and tunnel caused by foundation pit excavation based on a two-stage surrogate model, wherein the steps of actual engineering deformation prediction in step 4) specifically include:

[0056] 4.1) Extract the parameters required for the surrogate model as the input of the model according to the complete geological exploration report and engineering overview of the project;

[0057] 4.2) After normalizing the input parameters, substitute them into the two-stage surrogate model formed by combining the first-stage surrogate model and the second-stage surrogate model for prediction;

[0058] 4.3) Compare the predicted results with the actual engineering measurement results to verify the prediction accuracy of the two-stage surrogate model formed by combining the first-stage surrogate model and the second-stage surrogate model for the actual project;

[0059] 4.4) According to the characteristic values of the predicted stratum deformation and tunnel deformation, fit the actual deformation curves of the stratum and the tunnel.

[0060] The method for predicting the deformation of the stratum and tunnel caused by foundation pit excavation based on a two-stage surrogate model, wherein: the method for simulating the actual deformation curves of the stratum and the tunnel in step 4.4) is as follows:

[0061] The stratum deformation includes the deformation of the retaining structure and the ground surface settlement. The deformation of the retaining structure and the ground surface settlement are respectively simulated by a composite deformation curve and a combined settlement curve;

[0062] For the deformation curve of the retaining structure, when the maximum horizontal displacement of the retaining structure and the position where the maximum horizontal displacement occurs are known, the expression of the composite deformation curve of the retaining structure is:

[0063]

[0064] In the above formula (24), δ max is the maximum horizontal displacement of the retaining structure (mm), z is the distance from the deformation point to the top of the retaining structure to be calculated (m), z m is the distance between the position where the maximum horizontal displacement of the retaining structure occurs and the top of the retaining structure;

[0065] For the ground surface settlement curve, a ground surface settlement calculation model is established by means of the concept of ground loss. The calculation model assumes that the ground surface settlement curve outside the pit is in the form of a skewed distribution curve, and the function expression is:

[0066]

[0067] In the above formula (25), δ ν is the ground settlement at any point outside the pit, x is the distance from the settlement point to be determined to the edge of the pit, and x m is the distance from the maximum settlement point to the edge of the pit, S v·w is the area of the settlement curve envelope, and w is an empirical coefficient; for complex strata, the empirical coefficient w can be directly solved according to the above formula (25) when the position x m of the maximum settlement is known; the calculation formula for the area S v·w of the settlement curve envelope is:

[0068] S v·w = 2.95·δ v·max ·x m (26);

[0069] In the above formula (26), δ v·max is the maximum ground settlement outside the pit;

[0070] For the tunnel deformation curve, after the horizontal and vertical displacements of the top P0, left waist P1, bottom P2, and right waist P3 on the tunnel are known, its deformation curve can be fitted by a cubic B-spline curve:

[0071] The B-spline curve is a piecewise curve, and its mathematical expression is:

[0072]

[0073] In the above formula (27), P k is the characteristic point that controls the curve; F k,n (t) is the nth-order B-spline basis function, and the expression is:

[0074]

[0075] When n = 3, the cubic B-spline curve equation is obtained:

[0076] P(t) = P 0 F 0,3 (t) + P 1 F 1,3 (t) + P 2 F 2,3 (t) + P 3 F 3,3 (t) (29);

[0077] The top P0, left waist P1, bottom P2, and right waist P3 on the tunnel can define a cubic B-spline curve, and the cubic B-spline curve basis function in the above formula (29) can be expressed as:

[0078]

[0079] In the above formula (30), 0 ≤ t ≤ 1 is the normalized time from the initial state to the target state;

[0080] Substitute the four characteristic points P0, P1, P2, and P3 after the tunnel deformation into the above formula (29), and a cubic B-spline curve approximately fitted by these four characteristic points P0, P1, P2, and P3 can be obtained to represent the deformation curve of the tunnel;

[0081] After obtaining the deformation curve of the formation-tunnel fitting, the deformation magnitudes of each point on the ground surface, retaining wall, and tunnel can be estimated through these three deformation curves.

[0082] Adopting the above technical solution, the present invention has the following beneficial effects:

[0083] The method for predicting the deformation of the formation and tunnel caused by foundation pit excavation based on the two-stage surrogate model of the present invention has a reasonable concept, obtains sample data based on the parametric finite element model, and greatly reduces the time cost of modeling and calculation.

[0084] Different from directly predicting using a single surrogate model, the present invention considers the mechanical mechanism of the tunnel deformation process, changes the prediction mode of the tunnel deformation from the original {foundation pit excavation → tunnel deformation mode} to {foundation pit excavation → formation deformation → tunnel deformation mode}, and improves the prediction accuracy without changing the number of training samples and input parameters of the surrogate model. Users do not need to measure the formation deformation parameters that are difficult to measure anymore. Instead, they can directly predict the tunnel structure deformation caused by foundation pit excavation based on the known or easily measurable foundation pit, soil body, and tunnel parameters.

[0085] Based on the two-stage surrogate model, the present invention can realize the rapid and accurate prediction of the deformation of the formation and tunnel caused by foundation pit excavation under various working conditions, and can meet the requirements of real-time simulation of the digital twin platform. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0087] Figure 1 It is a flow chart of the method for predicting the deformation of the formation and tunnel caused by foundation pit excavation based on the two-stage surrogate model of the present invention;

[0088] Figure 2 Schematic diagram of the parametric finite element model established in the method for predicting stratum and tunnel deformations caused by foundation pit excavation based on the two-stage surrogate model of the present invention;

[0089] Figure 3 Principle block diagram of the two-stage surrogate model method involved in the method for predicting stratum and tunnel deformations caused by foundation pit excavation based on the two-stage surrogate model of the present invention;

[0090] Figure 4 Comparison diagram of the predicted values and finite element calculated values of the two-stage surrogate model in the method for predicting stratum and tunnel deformations caused by foundation pit excavation based on the two-stage surrogate model of the present invention.

[0091] Figure 5 Deformation curve diagram fitted according to the characteristic values of stratum and tunnel deformations predicted by the two-stage surrogate model in the method for predicting stratum and tunnel deformations caused by foundation pit excavation based on the two-stage surrogate model of the present invention. Detailed implementation manners

[0092] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention belong to the scope of protection of the present invention.

[0093] The present invention will be further explained and described below in conjunction with specific implementation manners.

[0094] As Figure 1 shown, the method for predicting stratum and tunnel deformations caused by foundation pit excavation based on the two-stage surrogate model provided in this embodiment mainly includes the following steps:

[0095] 1) Select the input and output parameters of the model and establish a parametric finite element model;

[0096] 2) Obtain training data by combining experimental design and the parametric finite element model;

[0097] 3) Construct a two-stage surrogate model with the training data and verify the prediction accuracy;

[0098] 4) Extract the relevant parameters of the actual engineering case as the input of the model, and predict and fit the stratum and tunnel deformations.

[0099] The establishment process of the parametric finite element model in the above step 1) includes:

[0100] 1.1) Select the input parameters of the model according to the sensitivity analysis results: In this embodiment, the output parameters of the finite element model are determined to be 4 formation deformation characteristic values (the maximum surface settlement value Sg, the position Pg where the maximum surface settlement occurs, the maximum horizontal deformation value Sd of the retaining wall, and the position Pd where the maximum horizontal deformation of the retaining wall occurs) and 8 tunnel deformation characteristic values (the horizontal and vertical displacements u x , u y ) at the top, bottom, left waist, and right waist of the tunnel. There are many input parameters that affect formation deformation and tunnel deformation, including soil layer thickness, water head, unit weight, soil compression modulus, effective cohesion, Poisson's ratio, effective internal friction angle, tunnel outer diameter, tunnel lining stiffness, tunnel burial depth, distance between the tunnel and the foundation pit, foundation pit length, foundation pit width, foundation pit depth, retaining structure stiffness, support stiffness, support spacing, etc.;

[0101] The number of training set data required to establish a proxy model with good accuracy increases exponentially with the increase of input parameters. Therefore, on the premise of meeting the reliability of the model, parameters with the greatest impact on the output should be selected as input parameters as much as possible to reduce the number of input parameters.

[0102] The sensitivity analysis in step 1.1) above combines local sensitivity analysis and global sensitivity analysis. In this specific embodiment, based on the results of global sensitivity analysis and local sensitivity analysis, 8 parameters with greater sensitivity are obtained as the input parameters of the parametric finite element model, which are the soil compression modulus E s , effective cohesion c′, effective internal friction angle tunnel center burial depth D v , the ratio T of the distance between the tunnel center and the foundation pit center to the foundation pit width r , foundation pit length L, foundation pit depth H, and retaining structure stiffness EA.

[0103] Global sensitivity refers to exploring the sensitivity of parameters within the entire experimental space, which can well reflect the global characteristics of parameters and the interaction between parameters. Global sensitivity analysis uses the Sobol method. The Sobol method is a global sensitivity analysis method based on variance, which can be applied to various non-linear and non-monotonic objective functions. The Monte Carlo method is often used for random sampling. By calculating the first-order sensitivity, high-order sensitivity, and total sensitivity of parameters, the influence of a single parameter on the objective function and the interaction between multiple parameters can be analyzed.

[0104] The core idea of the Sobol method is variance decomposition. Assume that the objective function is f(x) = f(x 1 , x 2 , …, x k ), which can be decomposed into:

[0105]

[0106] The influence of all parameters on the objective function is represented by the total variance V, and the influence of a single parameter x i on the objective function is represented by the partial variance V i . The influence of the interaction of multiple parameters on the objective function is represented by the partial variance . Their calculation formulas are as follows:

[0107]

[0108]

[0109]

[0110] The sensitivity coefficient can be expressed as:

[0111]

[0112] where S i , S ij , are the first-order sensitivity, second-order sensitivity, and s-order sensitivity respectively. The sum of the sensitivities of each order containing is the total sensitivity of the parameter and can be expressed as:

[0113]

[0114] Use the Monte Carlo method to independently extract two samples x = (x 1 , x 2 , …, x k ), x' = (x' 1 , x' 2 , …, x' k ). The number of samples each time is N. Then, the first-order sensitivity S i of the parameter x i and the total sensitivity

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] First-order sensitivity S i Represents the parameter x i The influence of the individual change on the objective function, total sensitivity Represents the parameter x i The total influence on the objective function caused by the interaction with other parameters.

[0122] Local sensitivity analysis refers to calculating the influence of the individual change of a certain parameter on the objective function by selecting the point of interest and slightly changing the value of a certain parameter. Its analysis only represents the sensitivity of a single parameter near the point of interest. The calculation formula is as follows:

[0123]

[0124] Wherein, Is the local sensitivity index of parameter i at the point of interest x = x i0 At the point, Δx i Is the change amount of parameter i near the point of interest, x i0 Is the value of parameter i at the point of interest, f(x i0 +Δx i ) - f(x i0 ) Is the change amount of the objective function value caused by the change of parameter i, f(x i0 ) Is the objective function value at the point of interest.

[0125] Combining the results of global sensitivity analysis and local sensitivity analysis, the parameters with the top 50% sensitivity calculated by the two are combined and duplicate parameters are removed as the input parameters of the parametric finite element model.

[0126] 1.2) Simplify the entire foundation pit excavation process into a unified step: First, generate the existing tunnel and reset the displacement to 0; then build the retaining wall; then carry out foundation pit dewatering and excavation; and set the excavation method such as excavating 1.5m for the first time and then 3m for each subsequent excavation; finally, repeat the excavation steps until the excavation is completed. Assume that the buried depth of the retaining wall is twice the foundation pit excavation depth, the length of the model is 4 times the foundation pit excavation length L plus the diameter D of the tunnel, and the width is 80m. Then, based on the Python script interface in the PLAXIS finite element modeling software, implement the parametric modeling of the foundation pit excavation finite element model adjacent to the tunnel. The schematic diagram of the model established by parametric modeling is shown in Figure 2 .

[0127] The specific process of obtaining the training data of the surrogate model in step 2) above includes:

[0128] 2.1) Obtain the value range of the selected input parameters from the geological exploration reports of multiple other previous engineering projects in the project area, as shown in Table 1 for example:

[0129] Table 1 Value range of input parameters

[0130]

[0131] 2.2) Sampling is carried out within the value range of each parameter by using the Latin hypercube experimental design method and randomly combined, and the combined set of sample data points is denoted as S.

[0132] 2.3) Substitute the sample point data into the parametric finite element model to calculate the corresponding formation and tunnel deformations as the output response set Y.

[0133] 2.4) The sample point data set S and the corresponding output response set Y are normalized and used as the training data set of the surrogate model. The so-called normalization is to transform the values of each design variable of the sample points into a unified interval [0,1], in order to improve the accuracy and robustness of the surrogate model. The specific calculation method of the normalization step is as follows:

[0134]

[0135] In formula (14): i = 1, 2,..., n; k = 1, 2,..., m; is the minimum value of all sample points on the k-th dimensional design variable; is the maximum distance between sample points on the k-th dimensional design variable. For example, in the form shown in Table 2:

[0136] Table 2 Example of normalization calculation

[0137]

[0138] In this specific embodiment of the present invention, the Kriging surrogate model is selected for the surrogate model. The Kriging surrogate model can not only predict the function value at any position in the design space of an unknown function, but also give the prediction error analysis based on the prediction result.

[0139] As a semi-parametric interpolation model, the form of the Kriging surrogate model can be described as follows:

[0140] y(x) = F(β, x) + Z(x) = f T (x)β + Z(x) (15);

[0141] In the above formula (15), f T (x) is a known regression model, whose role is to provide a global approximation of the simulation, β is the undetermined regression coefficient; Z(x) is a random process, whose mean is 0 and variance is The covariance is expressed as follows:

[0142]

[0143] In the above formula (16), x i and x j are any two different points in the design space, and R(x i , x j , θ) is a correlation function that only depends on the spatial positions of the two points. Its function expansion is as follows:

[0144]

[0145] In the above formula (17), θ = [θ 1 θ 2 ··· θ m T is the model parameter to be determined, and R k is any one of a linear function, an exponential function, a Gaussian function, a spherical function, and a cubic spline function; the hyperparameters in the Kriging surrogate model are optimized according to the predicted residuals, and the optimal surrogate model can be obtained by training the model parameters.

[0146] Based on the above assumptions, if a training sample set S = [x (1) , x (2) , ···, x m T and its response set Y = [y (1) , y (2) , ···, y m T are given, the predicted response value of any new point x new to be measured can be estimated by linearly combining the response values Y of the known sample points:

[0147]

[0148] In the above formula (18), c(x) T is the weight coefficient vector of the response value to be solved, and the prediction error is expressed as:

[0149] MSE = E(c T Y - y(x new ) 2 (19);

[0150] For the above assumptions, the Kriging surrogate model will find the optimal weight coefficient vector c(x) T to minimize the error of the prediction result.

[0151] The Kriging surrogate model is established using the DACE toolbox in MATALB. In the DACE toolbox, the hyperparameters that affect the Kriging surrogate model include the initial value θ 0 ​​​, the upper bound upb of the θ value, the lower bound lob of the θ value, the regression model form regr, and the correlation function form corr. Different values of these parameters will greatly affect the prediction effect of the Kriging surrogate model. Therefore, before using the DACE toolbox to establish the Kriging surrogate model, it is necessary to first determine the optimal combination of the values of each hyperparameter in the model. The method of constructing the Kriging surrogate model using this toolbox is as follows:

[0152] The Kriging surrogate model in the DACE toolbox specifically includes the following functions and parameters:

[0153] ① Dacefit function

[0154] Its function is to construct a surrogate model in the given sample data set, regression model, and correlation function.

[0155] The representation is [dmodel, perf] = dacefit(S, Y, regr, corr, theta0) or [dmodel, perf] = dacefit(S, Y, regr, corr, theta0, lob, upb)

[0156] Among them, S is the input sample set, Y is the corresponding response set, regr is the regression model form, corr is the correlation function form, theta0 is the initial value of θ in the correlation function, upb and lob are the upper and lower limits of the θ value respectively, dmodel represents the generated surrogate model, and perf is the model optimization information.

[0157] ② Predictor function

[0158] Its function is to use the surrogate model constructed by the dacefit function to predict the response value of the point to be measured. The representation method is y = predictor(x, dmodel), where x is the sample data of the point to be measured, y is the predicted response value, and dmodel represents the established Kriging surrogate model.

[0159] ③ Regression model

[0160] regploy0 zero-order regression model;

[0161] regploy1 first-order regression model;

[0162] regploy2 second-order regression model;

[0163] ④ Correlation function

[0164] correxp the correlation function is an exponential function;

[0165] correxpg the correlation function is a generalized exponential function;

[0166] The corrGauss correlation function is a Gaussian function;

[0167] The corrLin correlation function is a linear function;

[0168] The corrSpherical correlation function is a spherical function;

[0169] The corrSpline correlation function is a cubic spline function;

[0170] From the above Dacefit function, it can be seen that the hyperparameters that have an impact on the Kriging surrogate model are the initial value θ of θ 0 , the upper bound upb of θ value, the lower bound lob of θ value, the regression model form regr, and the correlation function form corr. Different values of these parameters will greatly affect the prediction effect of the Kriging surrogate model. Therefore, before using the DACE toolbox to establish the Kriging surrogate model, it is necessary to first determine the optimal combination of the values of each hyperparameter in the model.

[0171] The hyperparameter optimization method for the Kriging surrogate model is the particle swarm optimization method, and its principle can be described as follows:

[0172] The particle swarm optimization algorithm originated from the study of the foraging behavior of bird flocks. The basic idea of the particle swarm optimization algorithm is that each particle in the group will benefit from the experience discovered and accumulated by all members in this process, and the optimal solution is found through the cooperation and information sharing among the particles in the group. In the particle swarm optimization algorithm, a certain number of particles are randomly generated as effective solutions in the problem search space, the fitness value of the particles is determined through the fitness function corresponding to the problem, and then iterative search is carried out, continuously updating the velocity and position of the particles, and finally the optimization result is obtained.

[0173] v id (k + 1) = v id (k) + c 1 r 1 [p id (k) - x id (k)] + c 2 r 2 [p gd (k) - x id (k)] (20);

[0174] In the above formula (20), v id (k + 1), v id (k) are the velocities of the d-th dimension of the i-th particle at the (k + 1)-th iteration and the k-th iteration respectively, c 1 , c 2 are learning factors; r 1 , r 2 are random numbers between [0, 1];

[0175] x id (k + 1) = x id (k) + v id (k + 1)(21);

[0176] In the above formula (21), x id (k + 1), x id (k) are the velocities of the d - th dimension of the i - th particle at the (k + 1)-th iteration and the k - th iteration respectively;

[0177]

[0178] In the above formula (22), p id (k) is the individual optimal position of the d - th dimension of the i - th particle in a total of k iterations;

[0179] p gd (k) = min{p 1d (k),..., p id (k)}, i ∈ N (23);

[0180] In the above formula (23), p gd (k) is the global optimal position of the d - th dimension of the entire population in a total of k iterations;

[0181] Formula (20) represents the velocity update formula of the particle swarm optimization algorithm; Formula (21) updates the position of the particle according to the velocity updated by the velocity update formula; Formulas (22) and (23) are the update formulas for the individual optimal position p id (k) and the global optimal position p gd (k), where f is the fitness function and N is the population size.

[0182] The hyperparameter combination of the Kriging surrogate model obtained by optimizing through the particle swarm optimization method is regarded as the optimal hyperparameter combination, and inputting it into the DACE toolbox can establish the optimal Kriging surrogate model.

[0183] Using the particle swarm optimization method to optimize the hyperparameters in the surrogate model, the specific process is as follows

[0184] ① Initialize the particle swarm

[0185] Randomly generate a certain number of particles in the feasible space, and assign the position and velocity of each particle as well as initialize parameters such as the learning factor and inertia weight;

[0186] ② Evaluate the fitness of each particle in the particle swarm

[0187] Substitute the position of each particle into the objective function to calculate the fitness, which is used to measure the quality of the current particle position and serves as an important basis for the iterative update of the algorithm;

[0188] ③ Update the individual optimal position according to formula (22).

[0189] Record the best position of each particle in history for use when updating the velocity and position.

[0190] ④ Update the global optimal position according to formula (23).

[0191] Update the global optimal position of the current entire population according to the individual optimal positions of the updated particles.

[0192] ⑤ Update the velocity and position of the particles according to formulas (20) and (21).

[0193] Calculate the new velocity and new position of the particle based on the individual optimal position of the current particle and the global optimal position of the entire particle population, combined with parameters such as the learning factor.

[0194] ⑥ Constraint handling

[0195] According to the constraint conditions of the position and velocity of the particles, handle the particles that exceed the bounds according to the constraint handling method.

[0196] ⑦ Check the termination condition

[0197] When the predetermined maximum number of iterations is reached or a specific convergence condition is satisfied, end the iteration and output the optimal solution.

[0198] Repeat steps ② to ⑦ above until the termination condition is met; during the operation of the algorithm, the particles will gradually tend to the global optimal solution through continuous search and iteration.

[0199] The hyperparameter combination of the Kriging surrogate model obtained by optimizing through the particle swarm optimization method is regarded as the optimal hyperparameter combination.

[0200] The construction of the two-stage surrogate model in step 3) above includes the following steps:

[0201] 3.1) Divide the normalized data into two groups: a training set and a validation set. In this specific embodiment of the present invention, a total of 200 groups of training set data and 40 groups of validation set data are extracted, and the ratio of the training set to the validation set is 5:1. Divide the prediction process of the surrogate model into two stages (representing two different surrogate models). The first-stage surrogate model is used to predict the formation deformation, and the second-stage surrogate model is used to predict the tunnel deformation. Use the 200 groups of training set after normalization to train the first-stage surrogate model and predict the formation deformation characteristic values (the maximum surface settlement S g 、the location P where the maximum surface settlement occurs g 、the maximum horizontal deformation value S of the retaining wall d 、the location P where the maximum horizontal deformation of the retaining wall occursd )。

[0202] 3.2) Update the 8 input parameters of the finite element model determined according to the sensitivity analysis results in step 1.1) to the formation deformation parameters predicted by the first-stage surrogate model plus 4 tunnel-soil related parameters, and use these as the input parameters of the second-stage surrogate model. The 8 tunnel deformation characteristic values (the horizontal and vertical displacements u x , u y ) of the four points at the top, bottom, left waist, and right waist of the tunnel are used as the output parameters of the second-stage surrogate model.

[0203] The tunnel-soil related parameters are defined as the ratios of the following 4 tunnel parameters to the soil structure parameters:

[0204] ① R h , the ratio of the horizontal distance from the tunnel center to the retaining wall to the foundation pit depth, and the calculation formula is R h = (D h - 0.5L) / H, where D h is the distance between the tunnel center and the foundation pit center, L is the excavation length of the foundation pit, and H is the excavation depth of the foundation pit;

[0205] ② R d , the ratio of the buried depth of the tunnel center to the foundation pit depth, and the calculation formula is R d = D v / H; where D v is the buried depth of the tunnel center;

[0206] ③ R s , the ratio of the tunnel lining stiffness to the soil compression modulus, and the calculation formula is R s = E l / E s , where E l is the tunnel lining stiffness and E s is the soil compression modulus;

[0207] ④ R w , the ratio of the tunnel lining stiffness to the retaining wall stiffness, and the calculation formula is R w = E l / EA, where EA is the retaining wall stiffness;

[0208] It should be noted that the formation deformation parameters in the new input parameters are the prediction results in the first-stage surrogate model, and the tunnel-soil related parameters can be directly calculated from the input parameters in the first-stage surrogate model without additional sampling and calculation.

[0209] 3.3) Normalize the input and output data of the updated second-stage surrogate model and use them to train the second-stage surrogate model, and then use the second-stage surrogate model to predict the tunnel deformation.

[0210] 3.4) Finally, the first-stage surrogate model and the second-stage surrogate model are combined to obtain the two-stage surrogate model. The principle of the entire two-stage surrogate model is as Figure 3 shown. Substitute the verification set data into the established two-stage surrogate model for prediction, and compare the predicted results with the original parametric finite element calculation results to verify the prediction accuracy of the surrogate model. Use the percentage of absolute error P ae to represent the model prediction error situation:

[0211]

[0212] In the formula, y is the predicted value of the surrogate model, is the actual finite element calculation value. Here, we consider that when |P ae | is less than or equal to 15%, the predicted result of this time is considered accurate. The finite element verification results of the two-stage surrogate model in this specific embodiment are as Figure 4 shown. The overall prediction accuracy of the surrogate model is represented by ACC, and its definition is the ratio of the number of accurate predictions to the total number of predictions. The calculation formula is as follows:

[0213]

[0214] Among them, in the formula, N is the total amount of prediction data, and I(·) is the indicator function, which is equal to 1 when the condition in the parentheses is satisfied and 0 otherwise.

[0215] In this specific embodiment, the prediction accuracy of stratum deformation ACC = 93.13%, and the prediction accuracy of tunnel deformation ACC = 92.81%, which can meet the prediction accuracy requirements (ACC≥90%). If the final prediction accuracy is less than 90%, then the parameters of the surrogate model need to be adjusted, the structure of the surrogate model needs to be optimized, and a new surrogate model needs to be reconstructed.

[0216] The actual engineering deformation prediction in the above step 4) includes the following steps:

[0217] 4.1) Extract the parameters required for the surrogate model as the input of the model according to the complete geological exploration report and engineering overview of the project: In this specific embodiment, a foundation pit project in Shanghai is selected. The floor area of this foundation pit is 4400m 2 , and it is only 3.8m away from the outer line of the adjacent subway. The excavation depth of the foundation pit is 11m, the retaining structure is a diaphragm wall with a thickness of 0.8m, the buried depth of the retaining wall is 20m, the buried depth of the tunnel is 13m, and the outer diameter is 6.2m. This foundation pit can be approximated as a rectangular foundation pit with a length of 70m and a width of 63m. The distance between the center of the foundation pit and the center of the tunnel is about 41.9m. The soil properties are determined according to the local geological exploration report. The values of the input parameters of the surrogate model for this foundation pit project are shown in Table 3:

[0218] Input parameter values of the surrogate model for the actual case in Table 3

[0219]

[0220] 4.2) Substitute the normalized input parameters into the two - stage surrogate model for prediction: After normalizing the above 8 input parameters, establish the first - stage surrogate model. Use the first - stage surrogate model to predict the ground deformation caused by foundation pit excavation, and update the input parameters according to the two - stage surrogate model method to establish the second - stage surrogate model. Use the second - stage surrogate model to predict the tunnel deformation caused by foundation pit excavation.

[0221] 4.3) Compare the predicted results with the actual engineering measurement results to verify the prediction accuracy of the two - stage surrogate model for actual engineering: Compare the results predicted by the surrogate model with the on - site measured data. The comparison results are shown in Table 4. It can be seen that the two - stage surrogate model established in this embodiment can basically meet the accuracy requirements for the prediction of actual engineering cases and has engineering application value.

[0222] Table 4 Errors of the surrogate model in predicting actual cases

[0223]

[0224] 4.4) Fit the actual deformation curves of the ground and the tunnel according to the predicted characteristic values of ground and tunnel deformation: After obtaining the characteristic values of ground and tunnel deformation caused by foundation pit excavation through the two - stage surrogate model prediction, the actual deformation curves of the overall ground and tunnel can be fitted through relevant deformation curve equations.

[0225] The method for simulating the actual deformation curves of the ground and the tunnel in step 4.4) above is as follows:

[0226] Ground deformation includes the deformation of the retaining structure and ground settlement. The deformation patterns of the retaining structure and ground settlement caused by foundation pit excavation are diverse. Under different deformation patterns of the retaining structure, even if the maximum horizontal displacement value of the retaining structure is the same, there can be significant differences in the influence range of excavation on the soil outside the pit. The deformation patterns of the retaining structure can be classified into 4 types: cantilever, toe - kick, inward - bulge, and composite. The ground settlement deformation patterns can be divided into triangular settlement, groove - shaped settlement, and combined settlement. In actual engineering, the most common deformation pattern of the retaining structure is the composite deformation, and the most common deformation pattern of ground settlement is the combined settlement, and the two deformation patterns usually occur simultaneously. Therefore, in the present invention, the composite deformation curve and the combined settlement curve are used to simulate the deformation of the retaining structure and ground settlement respectively.

[0227] For the deformation curve of the retaining wall, when the maximum horizontal displacement of the retaining structure and the position where the maximum horizontal displacement occurs are known, the fitting curve expression of the composite deformation of the retaining structure is:

[0228]

[0229] In Equation (24), δ max is the maximum horizontal displacement of the retaining structure (mm), z is the distance from the deformation point to be determined to the top of the retaining structure (m), and z m is the distance between the position where the maximum horizontal displacement of the retaining structure occurs and the top of the retaining structure.

[0230] For the ground settlement curve, when the maximum ground settlement and the position where the maximum settlement occurs are known, a ground settlement calculation model is established by means of the concept of ground loss. The calculation model assumes that the ground settlement curve outside the excavation is in the shape of a skewed distribution curve, and its functional expression is:

[0231]

[0232] S v·w = 2.95·δ v·max ·x m (26);

[0233] In Equations (25)-(26), δ v (x) is the ground settlement amount at any point outside the excavation (mm); x is the distance from the settlement point to be determined to the edge of the excavation (m); x m is the distance from the maximum settlement point to the edge of the excavation (m); S v·w is the area of the settlement curve envelope (m·mm); w is an empirical coefficient. For complex strata, the empirical coefficient can be directly solved according to the above formula when the position x m where the maximum settlement is known; δ v·max is the maximum ground settlement outside the excavation.

[0234] For the tunnel deformation curve, after the horizontal and vertical displacements of 4 characteristic points on the tunnel are known, its deformation curve can be fitted by a cubic B-spline curve:

[0235] The B-spline curve is a piecewise curve, and its mathematical expression is:

[0236]

[0237] In Equation (27), P k is the characteristic point controlling the curve; F k,n (t) is the nth-order B-spline basis function, and its expression is:

[0238]

[0239] When n = 3, the cubic B-spline curve equation is obtained:

[0240] P(t) = P 0 F 0,3(t) + P 1 F 1,3 (t) + P 2 F 2,3 (t) + P 3 F 3,3 (t) (29);

[0241] Four adjacent vertices can define a cubic B-spline curve. The cubic B-spline curve basis function in the above formula (29) can be expressed as:

[0242]

[0243] In the above formula (30), 0 ≤ t ≤ 1 is the normalized time from the initial state to the target state.

[0244] Substitute the four characteristic points P0, P1, P2, and P3 after the tunnel deformation into the above formula (29), and a cubic B-spline curve approximately fitted by these four vertices can be obtained to represent the deformation curve of the tunnel;

[0245] After obtaining the deformation curves of the formation and the tunnel fitting, the user can quickly and accurately estimate the deformation magnitudes of each point on the ground surface, retaining wall, and tunnel through these 3 deformation curves.

[0246] Figure 5 Schematic diagram of the deformation curves of the formation and the tunnel fitted in this specific embodiment. The user can quickly and accurately estimate the deformation magnitudes of each point on the ground surface, retaining wall, and tunnel through these 3 deformation curves.

[0247] The present invention takes into account the mechanical mechanism of tunnel deformation and changes the prediction mode of tunnel deformation from the original {foundation pit excavation → tunnel deformation mode} to {foundation pit excavation → formation deformation → tunnel deformation mode}, improving the prediction accuracy without changing the number of training samples and input parameters of the surrogate model.

[0248] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting ground and tunnel deformation caused by foundation pit excavation based on a two-stage proxy model, characterized in that: The main steps include: 1) Select the input parameters and output parameters of the model and establish a parametric finite element model; 2) Combine experimental design with parametric finite element model to obtain training data; 3) Construct a two-stage proxy model through training data and verify the prediction accuracy; 4) Extract relevant parameters of actual engineering as input of the model to predict and fit the deformation of strata and tunnels; Step 1) includes: 1.1) Select the input parameters and output parameters of the finite element model based on the sensitivity analysis results; 1.2) Based on reasonable assumptions and simplifications, parametric modeling can be achieved by automatically generating new models by simply modifying the input parameter values ​​in the model based on the parametric design language in the finite element modeling software and the scripting interface of the software; The proxy model adopts a Kriging proxy model; The construction and verification of the two-stage proxy model in step 3) mainly includes the following steps: 3.1) The normalized data is divided into two groups: a training set and a validation set. The proxy model prediction process is divided into two stages. The first stage proxy model is used to predict stratum deformation, and the second stage proxy model is used to predict tunnel deformation. First, the first stage proxy model is trained with the normalized training set, and the stratum deformation is predicted by the first stage proxy model. The first stage proxy model is a proxy model established by mapping the excavation parameters of the foundation pit with the stratum deformation parameters. 3.2) The input parameters of the finite element model determined in step 1.1) according to the sensitivity analysis results are updated to the stratum deformation parameters predicted by the first-stage proxy model plus four tunnel-stratum related parameters, which are used as the input parameters of the second-stage proxy model, and the tunnel deformation parameters are used as the output parameters of the second-stage proxy model; the stratum deformation parameters in the input parameters of the second-stage proxy model are the results directly predicted by the first-stage proxy model, and no additional sampling and calculation are required; the tunnel-stratum related parameters are defined as the ratios of the following four tunnel parameters to the stratum structure parameters: ①R h , the ratio of the horizontal distance from the tunnel center to the retaining wall to the foundation pit depth, calculated as: R h =(D h -0.5L) / H; Among them, D h is the distance between the center of the tunnel and the center of the foundation pit, L is the length of the foundation pit excavation, and H is the depth of the foundation pit excavation; ②R d , the ratio of the tunnel center burial depth to the foundation pit depth, calculated as: R d =D v / H; Among them, D v The burial depth of the tunnel center; ③R s , the ratio of tunnel lining stiffness to soil compression modulus, calculated as: R s =And l / AND s ; Among them, E l is the tunnel lining stiffness, E s is the soil compression modulus; ④R w , the ratio of tunnel lining stiffness to retaining wall stiffness is calculated as: R w =Yes l / EA; Among them, EA is the stiffness of the retaining wall; The above four tunnel parameters R h , R d , R s , R w They are all directly calculated from the input parameters in the first-stage proxy model, so no additional sampling and calculation are required; 3.3) normalizing the input parameters and output parameters of the updated second-stage proxy model to train the second-stage proxy model, and then using the second-stage proxy model to predict tunnel deformation; 3.4) The first-stage proxy model and the second-stage proxy model are combined to obtain a two-stage proxy model; the validation set input parameters are substituted into the two-stage proxy model that combines the first-stage proxy model and the second-stage proxy model to perform predictions, and the predicted results are compared with the original parameterized finite element calculation results to verify the prediction accuracy of the proxy model.

2. The method for predicting ground and tunnel deformation caused by foundation pit excavation based on a two-stage proxy model as claimed in claim 1, characterized in that: The step 1.1) is to select the parameter with the greatest impact on the output as the input parameter to reduce the number of input parameters; The output parameters of the finite element model in step 1.1) include stratum deformation and tunnel deformation; The input parameters of the finite element model in step 1.1) include soil layer thickness, water head, gravity, soil compression modulus, effective cohesion, Poisson's ratio, effective internal friction angle, tunnel outer diameter, tunnel lining stiffness, tunnel burial depth, distance between tunnel and foundation pit, foundation pit length, foundation pit width, foundation pit depth, retaining structure stiffness, support stiffness and support spacing; The sensitivity analysis in step 1.1) is performed by combining the results of the global sensitivity analysis and the local sensitivity analysis, combining the top 50% of the sensitivity parameters calculated by the two and eliminating the duplicate parameters as the input parameters of the parametric finite element model.

3. The method for predicting ground and tunnel deformation caused by foundation pit excavation based on a two-stage proxy model as claimed in claim 1, characterized in that: The specific process of obtaining training data in step 2) includes: 2.1) Obtain the selected input parameter value range from geological survey reports of multiple other engineering projects in the project area; 2.2) The Latin hypercube experimental design method is used to sample and randomly combine within the range of each parameter. The combined sample point data set is denoted as S; 2.3) Substitute the sample point data into the parameterized finite element model to calculate the corresponding stratum and tunnel deformation as the output response set Y; 2.4) Normalize the sample point data set S and the corresponding output response set Y.

4. The method for predicting ground and tunnel deformation caused by foundation pit excavation based on a two-stage proxy model as claimed in claim 3, characterized in that: The normalization process in step 2.4) is to transform the values ​​of each design variable of the sample point into a uniform interval [0,1] to improve the accuracy and robustness of the proxy model. The normalization process is specifically calculated in the following way: In the above formula (14), i = 1, 2, ..., n; k = 1, 2, ..., m; It is the minimum value of all sample points on the k-th dimension design variable; is the maximum distance between sample points on the k-th dimension design variable.

5. The method for predicting ground and tunnel deformation caused by foundation pit excavation based on a two-stage proxy model as claimed in claim 1, characterized in that: The actual engineering deformation prediction steps in step 4) specifically include: 4.1) Extract the parameters required by the proxy model based on the complete geological survey report and engineering overview of the project as the input of the model; 4.2) After the input parameters are normalized, they are fed into a two-stage proxy model that combines the first-stage proxy model and the second-stage proxy model for prediction; 4.3) Compare the predicted results with the actual engineering measurement results to verify the prediction accuracy of the two-stage proxy model, which combines the first-stage proxy model with the second-stage proxy model, for the actual project; 4.4) According to the predicted characteristic values ​​of stratum deformation and tunnel deformation, the actual deformation curves of stratum and tunnel are fitted.

6. The method for predicting ground and tunnel deformation caused by foundation pit excavation based on a two-stage proxy model as claimed in claim 5, characterized in that: The method for fitting the actual deformation curve of the stratum and the tunnel in step 4.4) is as follows: The stratum deformation includes deformation of the retaining structure and ground settlement, and the deformation of the retaining structure and ground settlement are simulated respectively by a composite deformation curve and a combined settlement curve; For the deformation curve of the enclosure structure, when the maximum horizontal displacement of the enclosure structure and the location where the maximum horizontal displacement occurs are known, the composite deformation curve expression of the enclosure structure is: In the above formula (24), δ max is the maximum horizontal displacement of the enclosure structure, z is the distance between the deformation point to be determined and the top of the enclosure structure, m The distance between the location where the maximum horizontal displacement of the enclosure structure occurs and the top of the enclosure structure; For the surface settlement curve, the surface settlement calculation model is established with the help of the concept of stratum loss. The calculation model assumes that the surface settlement curve outside the pit is in the form of a skewed distribution curve, and the function expression is: In the above formula (25), δ ν is the surface settlement of any point outside the pit, x is the distance from the settlement point to be calculated to the pit edge, and x m is the distance from the maximum settlement point to the pit edge, S v·w is the area of ​​the settlement curve envelope, and w is the empirical coefficient; for complex formations, the empirical coefficient w is at the maximum settlement position x m If it is known, it can be directly solved according to the above formula (25); the area of ​​the settlement curve envelope S v·w The calculation formula is: S v·w =2.95·d v·max ·x m (26); In the above formula (26), δ v·max is the maximum surface settlement outside the pit; For the tunnel deformation curve, after the horizontal and vertical displacements of the top P0, left waist P1, bottom P2, and right waist P3 of the tunnel are known, the deformation curve is fitted using a cubic B-spline curve: The B-spline curve is a piecewise curve, and its mathematical expression is: In the above formula (27), P k is the characteristic point of the control curve; F k,n (t) is the n-order B-spline basis function, expressed as: When n=3, the cubic B-spline curve equation is obtained: P(t)=P0F 0,3 (t)+P1F 1,3 (t)+P2F 2,3 (t)+P3F 3,3 (t) (29); The top P0, left waist P1, bottom P2, and right waist P3 of the tunnel define a cubic B-spline curve. The cubic B-spline curve basis function in equation (29) is expressed as: In the above formula (30), 0≤t≤1 is the normalized time from the initial state to the target state; Substituting the four characteristic points P0, P1, P2, and P3 of the tunnel after deformation into the above formula (29), a cubic B-spline curve approximately fitted by the four characteristic points P0, P1, P2, and P3 is obtained to represent the deformation curve of the tunnel; After obtaining the deformation curves of the stratum and the tunnel fitting, the deformation sizes of various points on the surface, retaining wall and tunnel are estimated through the deformation curves.

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