Soft soil shield tunnel stratum displacement probability analysis method based on gap parameters

Abstract

The invention discloses a soft soil shield tunnel stratum displacement probability analysis method based on gap parameters. The method comprises the following steps: determining related size parameters of a soft soil shield tunnel to be analyzed; the method comprises the following steps: determining a probability distribution model, a mean value and a variable coefficient of parameters related to an equivalent three-dimensional gap, randomly sampling, substituting a theoretical solution and obtaining a sample, obtaining a tunneling parameter value of a lining cross section to be calculated, performing Bayesian updating on edge distribution, a mean value and a standard deviation of shield attitude related gaps based on a multivariate probability distribution model of tunneling parameters, and calculating the shield attitude related gaps. A probability distribution model of the grouting filling rate is determined; probability distribution of a physical gap is obtained by combining a shield tail gap; a sample of the physical gap is obtained by random sampling; samples of three important components of gap parameters are summarized and are input into a formation displacement calculation method based on the gap parameters, so that a formation displacement sample is obtained; and carrying out simplified probability analysis by adopting a Monte Carlo strategy. According to the method, the stratum displacement of the soft soil shield tunnel can be predicted from the perspective of probability, and the failure probability related to the stratum displacement of the soft soil shield tunnel is efficiently calculated.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel engineering, and in particular to a probability analysis method for stratum displacement in a soft soil shield tunnel based on gap parameters. Background Art

[0002] Once the shield tunnel or the surrounding environment is damaged during shield construction, the damage will develop rapidly and cover a large area. After the damage occurs, most or all of the engineering functions will be lost and difficult to repair. The serious social impact and huge economic and property losses caused cannot be ignored. Therefore, the problem of ground displacement caused by shield tunnel excavation has always been the focus of engineers. In order to effectively prevent the risk of excessive ground displacement caused by shield tunnels and ensure the safety of the surrounding environment, it is necessary to analyze the probability of ground deformation in shield tunnels.

[0003] The shield tunnel can be regarded as a highly nonlinear system, including several links and numerous parameters, any of which may affect the final stratum displacement. Affected by human and external factors, each link and parameter has strong uncertainty. Although many theoretical solutions or empirical solutions can efficiently calculate stratum displacement, they all need to fully simplify the mechanical model and make sufficient assumptions to ensure smooth solution. This makes it impossible to fully reflect the uncertainty in the shield tunneling process. In contrast, three-dimensional refined numerical simulation can more realistically reflect the shield tunneling process, but it is often accompanied by high costs. In addition, traditional displacement prediction methods cannot rely on field data to dynamically update displacement, resulting in a large amount of field data waste. In recent years, many scholars have applied machine learning methods to the prediction of stratum displacement, but this method cannot reflect the inherent mechanism of stratum deformation, and is limited by the uniqueness of stratum parameters, so the prediction effect may not be ideal. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a soft soil shield tunnel stratum displacement probability analysis method based on gap parameters.

[0005] The technical solution of the present invention to solve the above technical problem is as follows: A method for probabilistic analysis of stratum displacement in a soft soil shield tunnel based on gap parameters, comprising the following steps:

[0006] S1: Determine the relevant dimensional parameters of the soft soil shield tunnel to be analyzed;

[0007] S2: Determine the probability distribution model, mean and coefficient of variation of parameters related to the equivalent three-dimensional gap, and perform random sampling based on the statistical characteristics of the related parameters, input them into the theoretical formula of the equivalent three-dimensional gap, and obtain samples of a specific sample size;

[0008] S3: Obtain the excavation parameter values ​​at the cross section of the tunnel lining to be calculated, determine the shield attitude related gap, obtain the mean and standard deviation of the updated shield attitude related gap based on the multivariate probability distribution model of the shield attitude related gap and the Bayesian update process, update the edge distribution of the shield attitude related gap, and randomly sample the updated shield attitude related gap edge distribution to obtain samples of a specific sample size;

[0009] S4: determine the probability distribution model of the grouting filling rate, obtain the probability distribution of the physical gap in combination with the shield tail gap, perform random sampling on it, and obtain samples of a specific sample size;

[0010] S5: Summarize the three specific sample quantities of gap parameters obtained in S2-S4, obtain samples of gap parameters, input the samples into the formation displacement calculation method based on gap parameters or formation loss rate, obtain samples of formation displacement, and then use the Monte Carlo strategy to perform simplified probability analysis on the samples of formation displacement.

[0011] Furthermore, the relevant dimensional parameters in step S1 include the buried depth of the tunnel axis, the tunnel diameter, and the shield tail gap.

[0012] Furthermore, the relevant parameters in S2 include soil compartment pressure, soil weight, and undrained shear strength.

[0013] Furthermore, the tunneling parameter values ​​in step S3 include cylinder pressure, articulated extension, total thrust, cutterhead speed, soil compartment pressure, and soil weight.

[0014] Furthermore, when obtaining samples of shield attitude related gaps in step S3, the excavation parameter values ​​are first normalized, and the general spatial parameters are converted into standard normal distribution spatial parameters according to the multivariate normal distribution model parameters, and then the marginal distribution of the shield attitude related gaps after Bayesian update is calculated, and the marginal distribution is sampled to finally obtain samples of the shield attitude related gaps.

[0015] Furthermore, in step S4, the distribution of grouting thickness in the tunnel detection radar data is fitted to obtain a normal distribution model of the grouting filling rate, which is verified by the KS test, and then a physical gap sample is generated based on the shield tail gap value.

[0016] Furthermore, in step S5, the samples of three specific sample amounts of the gap parameters obtained in S2-S4 are summarized to obtain the samples of the gap parameters, which are input into the semi-empirical solution based on the gap parameters to obtain the displacement samples, and the function is set:

[0017] G=S max -s

[0018] s is the maximum allowable value of ground settlement or uplift. The failure probability P can be calculated from the performance function and displacement sample values.f , and thus conduct probability analysis.

[0019] Furthermore, the multivariate probability distribution model in step S3 is uniquely determined by the mean vector and the covariance matrix:

[0020]

[0021] Among them, the mean vector of the standard normal probability density function is 0.

[0022] Furthermore, in the Bayesian update process in step S3, the Bayesian update is first performed in the standard normal distribution space, and then the update in the general space is completed.

[0023] Furthermore, the specific implementation method of the semi-empirical solution is:

[0024] After tunnel excavation, the vertical displacement and horizontal displacement of any point in space are:

[0025]

[0026] Where: R is the radius of the tunnel; ν is the Poisson's ratio of the soil; z is the vertical distance from any point in space to the ground surface; x is the horizontal distance from any point in space to the tunnel axis; the equivalent formation loss parameter is g is the gap parameter value.

[0027] The present invention has the following beneficial effects: the present invention provides a method for analyzing the probability of ground displacement in a soft soil shield tunnel based on gap parameters.

[0028] (1) This method improves the traditional gap parameter method by combining a mechanically driven theoretical solution model with a data-driven probability distribution model, and implements probabilistic analysis under the gap parameter framework. The theoretical solution of the equivalent three-dimensional gap is combined with an empirical model of the three-dimensional deformation in front of the tunnel face that can reflect the unloading effect of soft soil and the cumulative deformation of gradual excavation, which can more accurately predict the equivalent three-dimensional gap parameters.

[0029] (2) The multivariate probability distribution model of shield attitude related gap adopted by this method solves the problem of relying on experience and wasting data when solving the existing shield attitude related gap. Compared with the machine learning method, this multivariate probability distribution model can explain the correlation structure between uncertainty parameters and is more suitable for probability analysis.

[0030] (3) The multivariate probability distribution model adopted by this method can use field data to timely update the shield posture-related gaps, comprehensively consider the uncertainty of multiple factors in the shield tunneling process, and explain the fundamental cause of soft soil deformation during shield tunneling from both data and mechanism aspects. It can efficiently predict the probability of stratum deformation and provide substantive suggestions for field parameter control. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0032] Figure 2 A schematic diagram of the gap parameter definition of the present invention;

[0033] Figure 3 is the sampling result of the equivalent three-dimensional gap of the present invention;

[0034] Figure 4 It is the edge distribution before and after the shield posture related gap update of the present invention, and the red arrow represents the measured data of the shield posture.

[0035] Figure 5 It is the sampling result of the gap related to the shield posture of the present invention.

[0036] Figure 6 A probability distribution model of grouting filling rate is obtained by fitting the grouting thickness data in the tunnel detection radar case of the present invention;

[0037] Figure 7 The sampling result of the physical gap of the present invention;

[0038] Figure 8 This is the sampling result of the maximum surface settlement of the present invention. DETAILED DESCRIPTION

[0039] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0040] like Figures 1 to 8 As shown, a method for probabilistic analysis of stratum displacement in a soft soil shield tunnel based on gap parameters comprises the following steps:

[0041] S1: Determine the relevant dimensional parameters of the soft soil shield tunnel to be analyzed; the relevant dimensional parameters include the tunnel axis burial depth, tunnel diameter, and shield tail gap.

[0042] S2: Determine the probability distribution model, mean and coefficient of variation of parameters related to the equivalent three-dimensional gap, and perform random sampling based on the statistical characteristics of the relevant parameters, input them into the theoretical formula of the equivalent three-dimensional gap, and obtain samples of a specific sample size. The relevant parameters include soil compartment pressure, soil weight, and undrained shear strength.

[0043] Specifically, according to the engineering background, the soil pressure at the section is 1.32 bar, and the average gravity and undrained shear strength at the axis are 16.56 kN·m 2The deterministic parameter value is taken as the mean value, and the coefficient of variation of soil tank pressure, gravity and undrained shear strength are taken as 0.1, 0.05 and 0.4 respectively. The probability distribution models of the three are all normal distribution. The soil tank pressure, gravity and undrained shear strength are sampled and input into the theoretical formula of equivalent three-dimensional gap to obtain 10,000 sets of samples of equivalent three-dimensional gap.

[0044] The theoretical formula for the equivalent three-dimensional gap is:

[0045]

[0046] δ y1 =δ y1 '+δ y2 '

[0047]

[0048] Where: y is the intrusion displacement on the tunnel face during tunnel excavation; δ y1 is the intrusion displacement on the section at a distance dL in front of the tunnel face during tunnel excavation, dL is = 0.5D; fitting parameter a = 0.152; fitting parameter b = -0.623; fitting parameter a1 is 0.00123; fitting parameter ω is 0.3; D is the tunnel diameter; H is the buried depth of the tunnel axis; γ is the soil weight; λ is the support pressure ratio; c u is the undrained shear strength;

[0049] S3: Obtain the excavation parameter values ​​at the cross-section of the tunnel lining to be calculated, determine the shield attitude related gaps, obtain the mean and standard deviation of the updated shield attitude related gaps based on the multivariate probability distribution model of the shield attitude related gaps and the Bayesian update process, update the marginal distribution of the shield attitude related gaps, and randomly sample the updated shield attitude related gap marginal distribution to obtain samples of a specific sample size; the excavation parameter values ​​include cylinder pressure, articulated elongation, total thrust, cutterhead speed, soil compartment pressure, and soil weight.

[0050] When obtaining samples of shield attitude related gaps in step S3, the excavation parameter values ​​are first normalized, and the general spatial parameters are converted into standard normal distribution spatial parameters according to the multivariate normal distribution model parameters. Then, the marginal distribution of the shield attitude related gaps after Bayesian update is calculated, and the marginal distribution is sampled to finally obtain samples of the shield attitude related gaps.

[0051] Specifically, according to engineering data, the pressure of the oil cylinder of group A at the dissection surface to be determined is 50 bar, the pressure of the oil cylinder of group C is 70 bar, the articulated extensions of groups D, C, A, and B are 69 mm, 102 mm, 63 mm, and 86 mm respectively, the total thrust is 6400 kN, the cutterhead speed is 1.2 r / min, the soil cabin pressure is 1.32 bar, and the average weight of the soil on the tunnel face is 18.5 kN·m -3 First, the data is normalized and solved, and the Y space parameters are converted to X space according to the multivariate normal distribution model parameters. The marginal distribution of the shield attitude related gap after Bayesian update is calculated, and the marginal distribution is sampled. The sampling size is still 10000, and the samples of the shield attitude related gap are obtained.

[0052] In addition, the multivariate probability distribution model in step S3 is uniquely determined by the mean vector and the covariance matrix:

[0053]

[0054] Among them, the mean vector of the standard normal probability density function is 0. According to the definition of the covariance matrix, the covariance matrix of a set of parameters that obey the standard normal distribution is consistent with the correlation coefficient matrix, and the correlation coefficient matrix is ​​as shown in the following table.

[0055] Table 1 Correlation coefficient matrix

[0056]

[0057] The multivariate probability distribution model is used to describe the data in the original sample library. One of the advantages of using the multivariate normal distribution model is that the calculation is very simple. The calculation process is as follows: Let U be a 11×1 vector including 11 independent standard normal variables. Let L be the lower triangular matrix after Cholesky decomposition, and satisfy the condition C=LL T , where C is the 11×11 correlation coefficient matrix given in Table 1. The corresponding standard normal distribution variable is X=LU, where X is the random variable vector (X1, X2,…, X 13 ) T The transformed simulation samples are calculated as follows:

[0058] For SU distribution:

[0059] Y i =b yi +a yi sinh(X ni )

[0060] For SB distribution:

[0061]

[0062] For SL distribution:

[0063]

[0064] Where X ni =(Xb xi ) / a xi .

[0065] The parameters of the Johnson distribution family are shown in Table 2.

[0066] Table 2 Parameters of the Johnson distribution family

[0067]

[0068] In the Bayesian update process in step S3, the Bayesian update is first performed in the standard normal distribution space, and then the update in the general space is completed.

[0069] Specifically, the main steps of Bayesian updating can be divided into: updating in X space and updating in Y space. Here, X and Y space refer to the standard normal distribution space (X space) and general space (Y space) in the Johnson distribution family respectively.

[0070] First, perform a Bayesian update in the X space. Before the update, X i (i.e. any parameter in the X space, i = 1 to 11) obeys the standard normal distribution, and the corresponding mean μ and standard deviation σ are 0 and 1 respectively. j ,X k ,…) after updating, X i Still a normal distribution, but with a mean of μ i ' and standard deviation σ i 'Changed, its value is:

[0071]

[0072] To simplify the above two equations, the covariance matrix C (correlation coefficient matrix) and the updated data set X are introduced:

[0073]

[0074] Mean μ i ' and standard deviation σ i ' can be written as:

[0075] μ i '=C (12) C (22) -1 X (2)

[0076]

[0077] If the parameters to be updated are a group of parameters, then the result of the above formula is the covariance matrix of this group of parameters. The standard deviation of the updated parameters can also be calculated based on this matrix.

[0078] Next, complete the update in the Y space. i ' and standard deviation σ i Substitute the following transformation formula, and we have:

[0079]

[0080] Where Z is a standard normal variable. Obviously, the updated probability distribution model and the prior distribution are both Johnson distribution family and the same distribution type. The updated distribution parameters are:

[0081] a' X,i =a X,i / σ' i

[0082] b' X,i =(b X,i -μ' i ) / σ' i

[0083] b' Y,i =b Y,i

[0084] a' X,i =a X,i

[0085] S4: determine the probability distribution model of the grouting filling rate, obtain the probability distribution of the physical gap in combination with the shield tail gap, perform random sampling on it, and obtain samples of a specific sample size;

[0086] The distribution of grouting thickness in tunnel detection radar data is fitted to obtain the normal distribution model of grouting filling rate, which is verified by KS test and then physical gap samples are generated based on the shield tail gap value.

[0087] Specifically, the probability distribution model of the grouting filling rate is obtained by fitting the data of the grouting thickness in the tunnel detection radar case, and the normal distribution parameters are μ = 0.811 and σ = 0.064. The KS test of goodness of fit is performed, h is 0, and p is greater than 0.05, indicating that the original hypothesis that the sample conforms to the distribution can be accepted at the 5% significance level. Based on the value of the shield tail gap, 10,000 sets of physical gap samples are generated.

[0088] S5: Summarize the three specific sample quantities of gap parameters obtained in S2-S4, obtain samples of gap parameters, input the samples into the formation displacement calculation method based on gap parameters or formation loss rate, obtain samples of formation displacement, and then use the Monte Carlo strategy to perform simplified probability analysis on the samples of formation displacement.

[0089] In step S5, the samples of three specific sample amounts of the gap parameters obtained in S2-S4 are summarized to obtain the samples of the gap parameters, which are input into the semi-empirical solution based on the gap parameters to obtain the displacement samples, and the function is set:

[0090] G=S max -s

[0091] s is the maximum allowable value of ground settlement or uplift. The failure probability P can be calculated from the performance function and displacement sample values. f , and thus conduct probability analysis.

[0092] The specific implementation method of the above semi-empirical solution is:

[0093] After tunnel excavation, the vertical displacement and horizontal displacement of any point in space are:

[0094]

[0095] Where: R is the radius of the tunnel; ν is the Poisson's ratio of the soil; z is the vertical distance from any point in space to the ground surface; x is the horizontal distance from any point in space to the tunnel axis; the equivalent formation loss parameter is g is the gap parameter value.

[0096] This scheme is described in detail through specific parameter settings;

[0097] A probability analysis method for ground displacement in soft soil shield tunnel based on gap parameters, the implementation flow chart is as follows Figure 1 As shown, the definition of the gap parameter is as follows Figure 2 As shown, the specific steps are as follows:

[0098] (1) Input the dimension parameters of the tunnel. The proposed calculated profile tunnel axis burial depth is 10.24 m, the tunnel diameter is 6.31 m, and the shield tail gap is 110 mm.

[0099] (2) According to the engineering background, the soil pressure at the section is 1.32 bar, and the average gravity and undrained shear strength at the axis are 16.56 kN·m 2 and 15.87 kPa, the deterministic parameter value is regarded as the mean, the coefficient of variation of soil pressure, gravity and undrained shear strength are 0.1, 0.05 and 0.4 respectively, and the probability distribution models of the three are all normal distribution. Sampling soil pressure, gravity and undrained shear strength are input into u*3D In the theoretical formula, we get 10,000 sets of u* 3D Samples such as Figure 3 shown.

[0100] (3) The pressure of the cylinder of group A at the proposed section is 50 bar, the pressure of the cylinder of group C is 70 bar, the articulated extensions of groups D, C, A, and B are 69 mm, 102 mm, 63 mm, and 86 mm, respectively, the total thrust is 6400 kN, the cutterhead speed is 1.2 r / min, the soil tank pressure is 1.32 bar, and the average gravity on the tunnel face is 18.5 kN·m -3 First, normalize the data to solve Y1~Y 10 , get Y1=0.189, Y2=0.076, Y3=0.515, Y4=0.520, Y5=0.537, Y6=0.503, Y7=0, Y8=0.220, Y9=0.331, Y 10 =0.684; then convert Y to X according to the multivariate normal distribution model parameters, and obtain X1=-0.362, X2=-0.267, X3=0.077, X4=-0.599, X5=1.151, X6=-0.225, X7=-0.973, X8=0.8, X9=-1.266, X 10 =-0.2053. The Bayesian update step in the present invention is used to calculate the marginal distribution after over-digging update. The updated mean and standard deviation are μ x =-0.758,σ x =0.730, the updated marginal distribution parameters are a x =2.902, b x =-2.408, a y =0.777, b y =-0.186. Figure 4 The marginal distribution before and after the over-digging update is shown. The red arrows represent the measured data of over-digging. Sampling the marginal distribution, the sampling size is still 10000, and the sample of ω is obtained, as shown in Figure 5 shown.

[0101] (4) Fitting the data of grouting thickness in the tunnel detection radar case to obtain the probability distribution model of grouting filling rate, such as Figure 6 As shown, the normal distribution parameters are μ = 0.811, σ = 0.064. The KS test of goodness of fit is performed, h is 0, and p is greater than 0.05, indicating that the original hypothesis that the sample conforms to the distribution can be accepted at the 5% significance level. Based on the value of the shield tail gap, 10,000 groups of G p Samples such as Figure 7 shown.

[0102] (5) Summarize the samples of the three important components of the gap parameter in the first three steps to obtain the samples of the gap parameter, and input them into the semi-empirical solution based on the gap parameter in the present invention to obtain the displacement sample, such as Figure 8 As shown. max The measured result of is within the 95% confidence interval and is highly consistent with the median. The measured result of ω is also within the 95% confidence interval. The predicted result of displacement by the simplified probability analysis method proposed in the present invention is in line with reality.

[0103] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for probabilistic analysis of stratum displacement in soft soil shield tunnels based on gap parameters, characterized in that: The following steps are involved: S1: Determine the relevant dimensional parameters of the soft soil shield tunnel to be analyzed; S2: Determine the probability distribution model, mean and coefficient of variation of parameters related to the equivalent three-dimensional gap, and perform random sampling based on the statistical characteristics of the related parameters, input them into the theoretical formula of the equivalent three-dimensional gap, and obtain samples of a specific sample size; S3: Obtain the excavation parameter values ​​at the cross section of the tunnel lining to be calculated, determine the shield attitude related gap, obtain the mean and standard deviation of the updated shield attitude related gap based on the multivariate probability distribution model of the shield attitude related gap and the Bayesian update process, update the edge distribution of the shield attitude related gap, and randomly sample the updated shield attitude related gap edge distribution to obtain samples of a specific sample size; S4: determine the probability distribution model of the grouting filling rate, obtain the probability distribution of the physical gap in combination with the shield tail gap, perform random sampling on it, and obtain samples of a specific sample size; S5: Summarize the three specific sample quantities of gap parameters obtained in S2-S4, obtain samples of gap parameters, input the samples into the formation displacement calculation method based on gap parameters or formation loss rate, obtain samples of formation displacement, and then use the Monte Carlo strategy to perform simplified probability analysis on the samples of formation displacement.

2. The method for probabilistic analysis of stratum displacement in soft soil shield tunnel based on gap parameters according to claim 1 is characterized in that: The relevant size parameters in step S1 include the tunnel axis burial depth, tunnel diameter, and shield tail clearance.

3. The method for probabilistic analysis of stratum displacement in soft soil shield tunnel based on gap parameters according to claim 1 is characterized in that: The relevant parameters in S2 include soil compartment pressure, soil weight, and undrained shear strength.

4. The method for probabilistic analysis of stratum displacement in soft soil shield tunnel based on gap parameters according to claim 1 is characterized in that: The excavation parameter values ​​in step S3 include cylinder pressure, articulation extension, total thrust, cutter head speed, soil compartment pressure, and soil weight.

5. The method for probabilistic analysis of stratum displacement in soft soil shield tunnel based on gap parameters according to claim 4 is characterized in that: When obtaining samples of shield attitude related gaps in step S3, the excavation parameter values ​​are first normalized, and the general spatial parameters are converted into standard normal distribution spatial parameters according to the multivariate normal distribution model parameters. Then, the marginal distribution of the shield attitude related gaps after Bayesian update is calculated, and the marginal distribution is sampled to finally obtain samples of the shield attitude related gaps.

6. The method for probabilistic analysis of stratum displacement in soft soil shield tunnel based on gap parameters according to claim 1, characterized in that: In step S4, the distribution of grouting thickness in the tunnel detection radar data is fitted to obtain a normal distribution model of the grouting filling rate, which is verified by the KS test, and then a physical gap sample is generated based on the shield tail gap value.

7. The method for probabilistic analysis of stratum displacement in soft soil shield tunnel based on gap parameters according to claim 1 is characterized in that: In step S5, the samples of three specific sample amounts of the gap parameters obtained in S2-S4 are summarized to obtain the samples of the gap parameters, which are input into the semi-empirical solution based on the gap parameters to obtain the displacement samples, and the function is set: G=S max -s s is the maximum allowable value of ground settlement or uplift. The failure probability P can be calculated from the performance function and displacement sample values. f , and thus conduct probability analysis.

8. The method for probabilistic analysis of stratum displacement in soft soil shield tunnel based on gap parameters according to claim 5 is characterized in that: The multivariate probability distribution model in step S3 is uniquely determined by the mean vector and the covariance matrix: Among them, the mean vector of the standard normal probability density function is 0.

9. The method for probabilistic analysis of stratum displacement in soft soil shield tunnel based on gap parameters according to claim 8, characterized in that: In the Bayesian update process in step S3, the Bayesian update is first performed in the standard normal distribution space, and then the update in the general space is completed.

10. The method for probabilistic analysis of stratum displacement in soft soil shield tunnel based on gap parameters according to claim 7, characterized in that: The specific implementation method of the semi-empirical solution is: After tunnel excavation, the vertical displacement and horizontal displacement of any point in space are: Where: R is the radius of the tunnel; ν is the Poisson's ratio of the soil; z is the vertical distance from any point in space to the ground surface; x is the horizontal distance from any point in space to the tunnel axis; the equivalent formation loss parameter is g is the gap parameter value.

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