CN111783308A

CN111783308A - Method for accurately predicting tunnel surrounding rock displacement

Info

Publication number: CN111783308A
Application number: CN202010651430.5A
Authority: CN
Inventors: 何川; 蒙伟; 晏启祥; 封坤; 郭德平; 孙晋锋; 唐进才; 廖烟开; 王皋; 冯智; 李雨强; 青松勇
Original assignee: Xuzhen Railway Co ltd; Southwest Jiaotong University
Current assignee: Xuzhen Railway Co ltd; Southwest Jiaotong University
Priority date: 2020-07-08
Filing date: 2020-07-08
Publication date: 2020-10-16

Abstract

The invention discloses a method for accurately predicting tunnel surrounding rock displacement, which comprises the steps of collecting displacement data of surface subsidence, vault subsidence, periphery convergence and the like in time after a tunnel is excavated, recording time, and drawing a time-displacement scatter diagram; performing regression analysis simultaneously according to an exponential model, a logarithmic model and a hyperbolic model given in technical specification for monitoring and measuring the railway tunnel (Q/CR 9218-; according to the probability theory and the theory related to mathematical statistics, the three models are respectively subjected to the significance test of a regression model and a regression coefficient; after the regression model and the significance test of the regression coefficient are passed, the model with the minimum residual square sum is used as the regression model; the invention can avoid adopting one type of model of exponential model, logarithmic model and hyperbolic model to carry out regression, can avoid adopting an unobvious model to carry out regression, and can use the model with the best regression effect as the regression model, wherein the best regression effect means that the regression value is closest to the measured value.

Description

Method for accurately predicting tunnel surrounding rock displacement

Technical Field

The invention belongs to the technical field of tunnel engineering, and particularly relates to a method for accurately predicting tunnel surrounding rock displacement.

Background

For tunnel engineering, displacement monitoring and measuring items such as surface subsidence, vault subsidence and peripheral convergence belong to indispensable measuring items and also belong to important components of new Austrian construction. In the tunnel construction process, time-displacement scatter diagrams are generally drawn according to time for the measured displacements, approved mathematical models are selected for fitting analysis, the mathematical models can be selected according to index models, logarithm models and hyperbolic models given by technical regulations for railway tunnel monitoring and measuring (Q/CR9218-2015), then the maximum or final displacement is subjected to prediction analysis and is compared and analyzed with control reference values given by technical regulations for tunnel monitoring and measuring, and the working states of tunnel surrounding rocks and lining supporting structures are comprehensively analyzed and researched in combination with tunnel construction conditions. If the fitted accumulated displacement curve tends to a fixed value along with time, the tunnel surrounding rock is in a stable state, and the lining supporting structure is reliable; otherwise, indicating that the tunnel surrounding rock and the lining supporting structure are in an unstable state, and taking corresponding remedial measures in time. Therefore, the accurate prediction of the tunnel surrounding rock displacement is of great importance to the safety evaluation of tunnel construction.

In the regression fitting process of tunnel surrounding rock displacement, the following three problems are found by reviewing the existing literature, wherein 1, part of the literature only adopts one type of model in the three types of models to carry out regression; 2. part of the literature was not tested for significance during the regression fitting process; 3. some documents use the above three types of models to perform regression, but select the final model based on the correlation coefficient.

Therefore, it is urgently needed to develop a method for accurately predicting the displacement of the surrounding rock of the tunnel to solve the above problems.

Disclosure of Invention

To solve the problems set forth in the background art described above. The invention provides a method for accurately predicting tunnel surrounding rock displacement.

In order to achieve the purpose, the invention provides the following technical scheme:

a method for accurately predicting tunnel surrounding rock displacement comprises the following steps:

s1, after the tunnel is excavated, collecting displacement data such as surface subsidence, vault subsidence and peripheral convergence in time, recording time, and drawing a time-displacement scatter diagram;

s2, carrying out regression analysis simultaneously according to an exponential model, a logarithmic model and a hyperbolic model given in technical specification Q/CR9218-2015 for railway tunnel monitoring and measuring;

s3, according to the probability theory and the mathematical statistics correlation theory, respectively carrying out significance test on the regression model and the regression coefficient on the three models, and judging whether the three models pass or not, if the three models pass, the step S4 is carried out, and if the three models do not pass, the step S5 is carried out;

s4, after the significance test of the regression model and the regression coefficient is carried out, the model with the minimum residual square sum is used as the regression model;

and S5, kicking off the regression model after not passing the significance test of the regression model and the regression coefficient.

In steps S2, S3, S4, S5: the three analysis processes of adopting three types of displacement duration models to carry out regression simultaneously, carrying out significance test on the regression model and regression coefficients and adopting a model with minimum residual square sum as the regression model are all absent.

Compared with the prior art, the invention has the beneficial effects that:

after the method is adopted, step S2 can avoid adopting one type of model of exponential model, logarithmic model and hyperbolic model for regression, namely can avoid adopting a model with poor regression effect for regression; step S3 may avoid using insignificant models for regression; in step S4, the model with the best regression effect, i.e., the regression value closest to the measured value, may be used as the regression model. The correlation coefficient represents the closeness of the linear correlation between the dependent variable and the independent variable, and the closer the correlation coefficient is to 1, the closer the linear correlation relationship between the dependent variable and the independent variable is. It can be seen that the correlation coefficient cannot represent the degree of deviation between the measured value and the regression value, and for selecting the regression model closest to the measured value, the selection can be performed according to the sum of squares of the residuals, the smaller the sum of squares of the residuals is, the closer the regression value is to the measured value is, and the better the regression effect is.

Drawings

FIG. 1 is a flow chart of a method for accurately predicting tunnel surrounding rock displacement according to the present invention.

Fig. 2 is a time-displacement scatter diagram of the peripheral convergence of the lower dam tunnel DK238+620 according to the present invention.

FIG. 3 is a block diagram of the nonlinear curve fitting module of origin software according to the present invention.

FIG. 4 is a diagram of the new functions of origin software according to the present invention.

FIG. 5 is a block diagram of a dialog for entering a functional form into origin software in accordance with the present invention.

FIG. 6 is a block diagram of the dialog of origin software for performing regression analysis in accordance with the present invention.

FIG. 7 is a diagram of an exponential model obtained by regression in accordance with the present invention.

FIG. 8 is a graph of the regression model of the present invention.

FIG. 9 is a hyperbolic model diagram obtained by regression in accordance with the present invention.

FIG. 10 is a comparison of exponential, logarithmic and hyperbolic models of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The invention provides the following technical scheme:

as shown in fig. 1, a method for accurately predicting displacement of surrounding rock of a tunnel includes:

the exponential model is:

U＝Ae^(-B/t)；

the logarithmic model is:

U＝Alg(1+t)+B；

the hyperbolic model is:

in the above formula: u is a deformation value; A. b is a regression coefficient; t is the observation time (d) of the measurement point.

Each of the above steps is explained below with reference to specific examples.

Step 1: after the tunnel is excavated, displacement data such as surface subsidence, vault subsidence and peripheral convergence are collected in time, time is recorded, and a time-displacement scatter diagram is drawn. The method specifically comprises the following steps:

according to the monitoring and measuring frequency given by technical specification of railway tunnel monitoring and measuring (Q/CR9218-2015), displacement data such as ground surface subsidence, vault subsidence and peripheral convergence are collected, instruments such as a high-precision total station can be adopted as a collecting tool, and a time-displacement scatter diagram is drawn. The invention takes the peripheral convergence data of the mileage DK238+620 of a lower dam tunnel of a newly-built Symphytus-Hengchu railway (Chuanchuan segment) as an example, the data is shown in a table 1, and a drawn time-displacement scatter diagram is shown in a table 2.

Table 1 perimeter convergence of lower dam tunnel DK238+620

Step 2: and (4) carrying out regression analysis on the displacement duration models of the exponential model, the logarithmic model and the hyperbolic model simultaneously. The method specifically comprises the following steps:

the nonlinear curve fitting module of origin software (see fig. 3) is adopted, then a new function (see fig. 4) is selected, the function forms of an exponential model, a logarithmic model and a hyperbolic model are respectively input (see fig. 5), finally, the regression analysis can be completed by clicking fitting (see fig. 6), and the exponential model (see fig. 7), the logarithmic model (see fig. 8) and the hyperbolic model (see fig. 9) obtained by regression are obtained.

And step 3: according to the probability theory and the theory related to mathematical statistics, the three models are respectively subjected to the significance test of the regression model and the regression coefficient, and whether the three models pass or not is judged, specifically:

origin software gives the results of the regression model and also the results of the significance test. The results of the significance tests for the exponential model regression model and the regression coefficients are shown in tables 2 and 3, respectively. The results of the significance tests on the logistic model regression model and the regression coefficients are shown in tables 4 and 5, respectively. The results of the significance tests on the hyperbolic model regression model and the regression coefficients are shown in tables 6 and 7, respectively.

TABLE 2 results of significance testing of regression models of exponential models

TABLE 3 significance test results of regression coefficients of exponential models

TABLE 4 results of significance testing of logistic model regression models

TABLE 5 significance test results for regression coefficients of log models

TABLE 6 hyperbolic model regression model significance test results

TABLE 7 hyperbolic model regression coefficient significance test results

As can be seen from tables 2 to 7, the values in the last column are all less than 0.05, i.e., the p-values for the exponential model, the logarithmic model, the hyperbolic model regression model, and the regression coefficients are all less than 0.05. Therefore, both the regression model and the significance test of the regression coefficients were passed.

And 4, step 4: after passing the significance test of the regression model and the regression coefficient, the model with the minimum sum of squared residuals was used as the regression model. The method specifically comprises the following steps:

as can be seen from table 2, when the measured values in table 1 were regressed by the exponential model, the sum of squares of the residuals was 251.86; as can be seen from table 4, when the logarithmic model is used to regress the measured values in table 1, the sum of squares of the residuals is 876.22; as can be seen from table 6, when the hyperbolic model is used to regress the actual measurement values in table 1, the sum of squares of the residuals is 593.76. Namely, the sum of the squares of the residuals is minimum when an exponential model is adopted for regression, namely, the regression value at the moment is closest to the measured value, namely, the displacement predicted based on the model is most accurate. The comparison results of the above three types of models are shown in FIG. 10.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims

1. A method for accurately predicting tunnel surrounding rock displacement is characterized by comprising the following steps:

s2, performing regression analysis simultaneously according to an exponential model, a logarithmic model and a hyperbolic model given in the technical specification for monitoring and measuring railway tunnels (Q/CR 9218-2015);