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

Abstract

The application discloses a kind of soft soil shield tunnel stratum displacement probability analysis method based on gap parameter, steps include: determining the relevant size parameter of soft soil shield tunnel to be analyzed;Determine the probability distribution model of equivalent three-dimensional gap related parameter, mean and variation coefficient, after random sampling, its theoretical solution is entered and its sample is obtained, obtain the tunneling parameter value at the cross section of the lining to be calculated, based on the multivariate probability distribution model of tunneling parameter, the edge distribution of shield posture related gap, mean and standard deviation are updated by Bayes, and its sample is obtained by random sampling, determine the probability distribution model of grouting filling rate, obtain the probability distribution of physical gap in combination with shield tail gap, and its sample is obtained by random sampling, the samples of three important components of gap parameter are summarized, input into stratum displacement calculation method based on gap parameter, to obtain the sample of stratum displacement, simplified probability analysis is carried out using Monte Carlo strategy.The method can predict the stratum displacement of soft soil shield tunnel from the probability point of view, and efficiently calculate the failure probability related to the stratum displacement of soft soil shield tunnel.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel engineering, and particularly relates to a soft soil shield tunnel stratum displacement probability analysis method based on a gap parameter. BACKGROUND

[0002] Once the shield tunnel body or the surrounding environment is damaged in shield construction, the development process is rapid, the damage range is large, the engineering function is mostly or entirely lost after the damage occurs and is difficult to repair, and the serious social impact and huge economic and property losses cannot be ignored. Therefore, the problem of stratum displacement caused by shield tunnel excavation has always been the focus of engineers. In order to effectively prevent the risk of excessive stratum displacement caused by shield tunnel, and to ensure the safety of the surrounding environment, it is necessary to analyze the stratum deformation probability of the shield tunnel.

[0003] The shield tunnel can be regarded as a highly nonlinear system, including a plurality of links and numerous parameters, and any link and parameter can affect the final stratum displacement. Influenced by human factors, external factors and the like, each link and parameter has strong uncertainty. Although many theoretical solutions or empirical solutions can efficiently calculate the stratum displacement, they 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 truly reflect the shield tunneling process, but often also involves high costs. In addition, the traditional displacement prediction method cannot rely on the field data to dynamically update the displacement, resulting in a waste of a large amount of field data. In recent years, many scholars have applied machine learning methods to the prediction of stratum displacement, but this method cannot reflect the internal mechanism of stratum deformation, and is limited to the uniqueness of stratum parameters, and the prediction effect may not be ideal. SUMMARY

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

[0005] The technical scheme for solving the above technical problems is as follows: a soft soil shield tunnel stratum displacement probability analysis method based on a gap parameter, comprising the following steps:

[0006] S1: determining the related size parameters of the soft soil shield tunnel to be analyzed;

[0007] S2: determining the probability distribution model, mean value and variation coefficient of the equivalent three-dimensional gap related parameters, and randomly sampling according to the statistical characteristics of the related parameters, and inputting into the theoretical formula of the equivalent three-dimensional gap to obtain samples of a specific sample size;

[0008] S3: Obtain the tunneling parameter value at the cross section of the tunnel lining, determine the shield posture related gap, obtain the mean and standard deviation of the updated shield posture related gap based on the multivariate probability distribution model of the shield posture related gap and the Bayesian updating process, update the edge distribution of the shield posture related gap, and randomly sample the updated edge distribution of the shield posture related gap 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 by combining the shield tail gap, and randomly sample the physical gap to obtain samples of a specific sample size;

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

[0011] Further, the related size parameters in step S1 include the tunnel axis burial depth, the tunnel diameter, and the shield tail gap.

[0012] Further, the related parameters in S2 include the soil chamber pressure, the soil bulk density, and the undrained shear strength.

[0013] Further, the tunneling parameter values in step S3 include the cylinder pressure, the articulated elongation, the total thrust, the cutter head speed, the soil chamber pressure, and the soil bulk density.

[0014] Further, when obtaining the sample of the shield posture related gap in step S3, first, the tunneling parameter values are normalized, and the general space parameters are converted to standard normal distribution space parameters according to the multivariate normal distribution model parameters, then the edge distribution of the shield posture related gap after Bayesian updating is calculated, the edge distribution is sampled, and finally the sample of the shield posture related gap is obtained.

[0015] Further, in step S4, the distribution of the 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 K-S test, and then the physical gap sample is generated based on the shield tail gap value.

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

[0017] G=S max -s

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

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

[0020]

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

[0022] Further, in the Bayesian updating process in step S3, first, the Bayesian updating is carried out in the standard normal distribution space, and then the updating in the general space is completed.

[0023] Further, the specific implementation mode of the semi-empirical solution is:

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

[0025]

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

[0027] The present application has the following beneficial effects: the soft soil shield tunnel stratum displacement probability analysis method based on the gap parameter provided by the present application,

[0028] (1) The method improves the traditional gap parameter method by combining the mechanical driving theoretical solution model with the data driven probability distribution model, realizes the probability analysis under the gap parameter framework, and applies the theoretical solution of the equivalent three-dimensional gap, which combines the empirical model that can reflect the unloading effect of soft soil and the progressive excavation cumulative deformation in front of the working face, to more accurately predict the equivalent three-dimensional gap parameter.

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

[0030] (3) The multivariate probability distribution model used in the method can update the shield posture related gap in time by using the field data, comprehensively considers the uncertainty of multiple factors in the shield tunneling process, can explain the fundamental reason of the deformation of the soft soil stratum during the shield tunnel excavation from the aspects of data and mechanism, and can efficiently predict the probability of stratum deformation, and provide substantial suggestions for field parameter control. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 Flow chart of the method of the present application;

[0032] Figure 2 Schematic diagram of the definition of the gap parameter of the present application;

[0033] Figure 3 Sampling results of the equivalent three-dimensional gap of the present application;

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

[0035] Figure 5 Sampling results of the shield posture related gap of the present application.

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

[0037] Figure 7 Sampling results of the physical gap of the present application;

[0038] Figure 8 Sampling results of the maximum ground settlement of the present application. DETAILED DESCRIPTION

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

[0040] As shown in Figures 1 to 8 A soft soil shield tunnel stratum displacement probability analysis method based on a gap parameter, comprising the following steps:

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

[0042] S2: determining the probability distribution model, the mean and the coefficient of variation of the parameters related to the equivalent three-dimensional gap, and randomly sampling according to the statistical characteristics of the related parameters, inputting into the theoretical formula of the equivalent three-dimensional gap to obtain a sample of a specific sample size. The related parameters include the soil chamber pressure, the soil bulk density and the undrained shear strength.

[0043] Specifically, according to the engineering background, the soil chamber pressure at this profile is 1.32 bar, and the average bulk density and undrained shear strength at the axis are 16.56 kN·m 2The soil cabin pressure, the specific gravity and the undrained shear strength are sampled and input into the theoretical formula of the equivalent three-dimensional gap to obtain 10,000 groups of samples of the equivalent three-dimensional gap.

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

[0045]

[0046] δ y1 = δ y1 + δ y2 '

[0047]

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

[0049] S3: Obtain the tunneling parameter values at the tunnel lining cross section to be calculated, determine the shield posture related gap, obtain the mean value and the standard deviation of the updated shield posture related gap based on the multivariate probability distribution model of the shield posture related gap and the Bayesian updating process, update the edge distribution of the shield posture related gap, and randomly sample the updated edge distribution of the shield posture related gap to obtain a sample of a specific sample size; the tunneling parameter values include the cylinder pressure, the articulated elongation, the total thrust, the cutter head speed, the soil cabin pressure and the soil specific gravity.

[0050] When the sample of the shield posture related gap is obtained in step S3, first, the tunneling parameter values are normalized, and the general space parameters are converted to standard normal distribution space parameters according to the multivariate normal distribution model parameters, then the edge distribution of the shield posture related gap after Bayesian updating is calculated, the edge distribution is sampled, and finally the sample of the shield posture related gap is obtained.

[0051] Specifically, according to the engineering data, the A group oil cylinder pressure at the section to be solved is 50 bar, the C group oil cylinder pressure is 70 bar, the D, C, A and B group articulated elongation is 69 mm, 102 mm, 63 mm and 86 mm respectively, the total thrust is 6400 kN, the cutter head speed is 1.2 r / min, the soil tank pressure is 1.32 bar, and the average specific gravity of the soil on the working face is 18.5 kN·m -3 First, the data is normalized and the Y space parameters are converted to the X space according to the multivariate normal distribution model parameters, the marginal distribution of the shield posture related gap after the Bayesian update is calculated, and the marginal distribution is sampled, and the sampling amount is still 10000, to obtain the sample of the shield posture related gap.

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

[0053]

[0054] Wherein, the mean vector of the standard normal probability density function is 0. According to the definition of the covariance matrix, the parameter covariance matrix of a group of parameters subject to the standard normal distribution is consistent with the correlation coefficient matrix, and the correlation coefficient matrix is as follows.

[0055] Table 1 correlation coefficient matrix

[0056]

[0057] The data in the original sample library is described by using a multivariate probability distribution model. One of the advantages of using a multivariate normal distribution model is that the calculation is very simple, and the calculation process is as follows: let U be an 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 , wherein C is the 11×11 correlation coefficient matrix given in Table 1. The corresponding standard normal distribution variable is X=LU, wherein X is the random variable vector (X 13 ) T . The transformed simulation sample is 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 = (X-b xi ) / a xi .

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

[0066] Table 2 Parameters of Johnson distribution family

[0067]

[0068] In the Bayesian updating process in step S3, first, the Bayesian updating is performed in the standard normal distribution space, and then the updating 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 spaces refer to the standard normal distribution space (X space) and the general space (Y space) in Johnson distribution family, respectively.

[0070] First, the Bayesian updating is performed in X space. Before updating, X i (i.e. any parameter in X space, i = 1 ~ 11) is subject to the standard normal distribution, and the corresponding mean μ and standard deviation σ are 0 and 1, respectively. After updating based on the known (X j , X k , …), X i is still normally distributed, but the mean μ i ' and the standard deviation σ i ' change, and their values are:

[0071]

[0072] To simplify the above two formulas, the covariance matrix C (i.e. the correlation coefficient matrix) and the updating data set X are introduced:

[0073]

[0074] The mean μ i ' and the standard deviation σ i ' can be written as:

[0075] μ i ' = C (12) C (22) -1 X (2)

[0076]

[0077] If the parameter to be updated is a set of parameters, then the result of the above formula is the covariance matrix of the set of parameters, and the standard deviation of the updated parameters can also be calculated according to the matrix.

[0078] Next, the update in Y space is completed. The updated μ i ' and the standard deviation σ i are substituted into the following conversion formula, that is, there is:

[0079]

[0080] where Z is a standard normal variable, and it is obvious that the updated probability distribution model and the prior distribution are both Johnson distribution families, and are of the same distribution type, and the distribution parameters of the updated distribution 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, combine the shield tail gap to obtain the probability distribution of the physical gap, and perform random sampling to obtain a sample of a specific sample size;

[0086] Fit the distribution of the grouting thickness in the tunnel detection radar data to obtain a normal distribution model of the grouting filling rate, verify by K-S test, and then generate physical gap samples 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 K-S test is performed on the goodness of fit, h is 0, and p is greater than 0.05, which means that at a 5% significance level, the sample can be accepted to conform to the original hypothesis that the distribution is acceptable, and 10000 groups of physical gap samples are generated based on the value of the shield tail gap.

[0088] S5: aggregate the three specific sample amounts of the gap parameters obtained in S2-S4, obtain samples of the gap parameters, input the samples into a stratum displacement calculation method based on the gap parameters or the stratum loss rate, obtain samples of the stratum displacement, and then perform a simplified probability analysis on the stratum displacement samples by using the Monte Carlo strategy.

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

[0090] G = S max -s

[0091] s is the allowable value of the maximum surface subsidence or uplift, and the failure probability P can be calculated from the function function and the displacement sample value f , and thus the probability analysis is carried out.

[0092] The specific implementation of the semi-empirical solution is as follows:

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

[0094]

[0095] where R is the radius of the tunnel, v is the Poisson's ratio of the soil, z is the vertical distance from any point in space to the surface, x is the horizontal distance from any point in space to the tunnel axis, and the equivalent stratum loss parameter is g is the gap parameter value.

[0096] The scheme is described in detail through specific parameter settings.

[0097] A soft soil shield tunnel stratum displacement probability analysis method based on gap parameters, the implementation flowchart is as shown in Figure 1 , wherein the definition of the gap parameter is as shown in Figure 2 , and the specific steps are as follows:

[0098] (1) Input the size parameters of the tunnel, and the 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 cabin pressure at this profile is 1.32 bar, the average unit weight and undrained shear strength at the axis are 16.56 kN·m 2 and 15.87 kPa respectively, the mean values of these deterministic parameters are determined, the variation coefficients of the soil cabin pressure, unit weight and undrained shear strength are 0.1, 0.05 and 0.4 respectively, and the probability distribution models of the three are normal distribution. The soil cabin pressure, unit weight and undrained shear strength are sampled and input into u*3D Theoretical formula, 10000 groups of u 3D are obtained, as shown in the figure. Figure 3

[0100] (3) The A group of oil cylinder pressure at the profile is 50bar, the C group of oil cylinder pressure is 70bar, the hinge elongation of D, C, A, B groups is 69mm, 102mm, 63mm, 86mm respectively, the total thrust is 6400kN, the cutter head rotating speed is 1.2r / min, the soil tank pressure is 1.32bar, the average specific weight on the working face is 18.5kN·m -3 / m, and the data is normalized to solve Y1-Y 10 , and 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 are obtained; then Y is converted into X according to the multivariate normal distribution model parameters, 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 are obtained.The edge distribution of the overbreak after updating is calculated by using the step of Bayesian updating in the application, and the updated mean value and standard deviation are μ x =-0.758, σ x =0.730, and the updated edge distribution parameters are a x =2.902, b x =-2.408, a y =0.777, and b y =-0.186. Figure 4 The edge distribution before and after the overbreak updating is shown, and the red arrow represents the measured data of the overbreak.The sampling amount is still 10000, and the sample of ω is shown in the figure. Figure 5

[0101] (4) The data of the grouting thickness in the tunnel detection radar case is fitted to obtain the probability distribution model of the grouting filling rate, as shown in the figure. Figure 6 The normal distribution parameters are μ=0.811 and σ=0.064.The K-S test is performed on the fitting degree, h is 0, and p is greater than 0.05, which indicates that the sample can accept the original hypothesis that the distribution is consistent at the 5% significance level. The value of the shield tail gap is generated to obtain 10000 groups of G p , as shown in the figure. Figure 7

[0102] (5) The samples of the three important components of the intermediate gap parameter in the previous three steps are summarized to obtain the sample of the gap parameter, which is input into the semi-empirical solution based on the gap parameter in the present application to obtain the displacement sample, as shown in the following formula: Figure 8 The measured results of S max The measured results of S are within the 95% confidence interval and are highly consistent with the median. The measured results of ω are also within the 95% confidence interval. The prediction results of the displacement by the simplified probability analysis method proposed in the present application are consistent with the actual situation.

[0103] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for analyzing the probability of stratum displacement of a soft soil shield tunnel based on a gap parameter, characterized in that, The method comprises the following steps: S1: determining relevant size parameters of soft soil shield tunnel to be analyzed; S2: determining a probability distribution model, a mean value and a coefficient of variation of a relevant parameter of an equivalent three-dimensional gap, and performing random sampling according to statistical characteristics of the relevant parameter, and inputting the relevant parameter into a theoretical formula of the equivalent three-dimensional gap to obtain a sample of a specific sample size; S3: obtaining an excavation parameter value at a tunnel lining cross section to be calculated, determining a shield posture related gap, obtaining a mean value and a standard deviation of the shield posture related gap based on a multivariate probability distribution model of the shield posture related gap and a Bayesian updating process, updating an edge distribution of the shield posture related gap, and performing random sampling on the updated edge distribution of the shield posture related gap to obtain a sample of a specific sample size; S4: determining a probability distribution model of a grouting filling rate, combining the shield tail gap to obtain a probability distribution of a physical gap, and performing random sampling on the physical gap to obtain a sample of a specific sample size; S5: collecting the samples of the three specific sample sizes of the gap parameters obtained in S2-S4, obtaining a sample of the gap parameters, inputting the sample into a stratum displacement calculation method based on the gap parameters or a stratum loss rate, obtaining a sample of stratum displacement, and performing simplified probability analysis on the stratum displacement by using a Monte Carlo strategy; The multivariate probability distribution model in step S3 is uniquely determined by a mean value vector and a covariance matrix: The mean value vector of the standard normal probability density function is 0. In the Bayesian updating process in step S3, Bayesian updating is first performed in a standard normal distribution space, and then updating in a general space is completed. The specific implementation mode of the semi-empirical solution is: After tunnel excavation, the vertical displacement and horizontal displacement of any point in the space are: wherein: R is the tunnel radius; ν is the Poisson's ratio of the soil mass; 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; and the equivalent strata loss parameter is , g is the gap parameter value; and H is the depth of the tunnel axis.

2. The gap parameter-based soft soil shield tunnel stratum displacement probability analysis method according to claim 1, characterized in that, The relevant size parameters in step S1 include a tunnel axis buried depth, a tunnel diameter and a shield tail gap. 3.The method of claim 1, wherein, The relevant parameters in step S2 include a soil cabin pressure, a soil specific gravity and an undrained shear strength. 4.The method according to claim 1, wherein, The excavation parameter values in step S3 include a cylinder pressure, an articulated elongation, a total thrust, a cutter head speed, a soil cabin pressure and a soil specific gravity.

5. The gap parameter-based soft soil shield tunnel stratum displacement probability analysis method according to claim 4, characterized in that, When the sample of the shield posture related gap is obtained in step S3, the excavation parameter values are first normalized, the general space parameters are converted to standard normal distribution space parameters according to the multivariate normal distribution model parameters, the edge distribution of the shield posture related gap after Bayesian updating is calculated, the edge distribution is sampled, and finally the sample of the shield posture related gap is obtained. 6.The method of claim 1, wherein, In step S4, the distribution of the 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 K-S test, and then the physical gap sample is generated based on the shield tail gap value.

7. The gap parameter based probabilistic analysis method for ground displacement of soft soil shield tunnel according to claim 1, wherein, In step S5, the samples of the three specific sample sizes of the gap parameters obtained in S2-S4 are collected to obtain the sample of the gap parameters, which is input into the semi-empirical solution based on the gap parameters to obtain the displacement sample, and a functional function is set: G = S max - s s The allowable value of the maximum settlement or uplift of the ground surface, from which the failure probability can be calculated from the performance function and the displacement sample value P f From which a probabilistic analysis is carried out.

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