CN111783308A - A method of accurately predicting the displacement of surrounding rock of tunnel - Google Patents

Abstract

The invention discloses a method for accurately predicting the displacement of surrounding rock of a tunnel. According to the "Technical Regulations for Monitoring and Measurement of Railway Tunnels (Q/CR 9218‑2015)", three types of displacement duration models, including exponential model, logarithmic model, and hyperbolic model, are given at the same time for regression analysis; The above three types of models are respectively tested for the significance of the regression model and the regression coefficient; after passing the significance test of the regression model and the regression coefficient, the model with the smallest residual sum of squares is used as the regression model; the present invention can avoid using the exponential model, Regression of a type of model in logarithmic model and hyperbolic model can avoid the use of insignificant models for regression, and the model with the best regression effect can be used as the regression model. The best regression effect means that the regression value is closest to the measured value. .

Description

A method of accurately predicting the displacement of surrounding rock of tunnel

technical field

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

Background technique

For tunnel engineering, displacement monitoring and measurement items such as surface subsidence, vault subsidence and peripheral convergence are mandatory items and are also an important part of the new Austrian method of construction. In the process of tunnel construction, the time-displacement scatter diagrams are generally drawn for the measured displacements according to time, and then an approved mathematical model is selected for fitting and analysis. Select the exponential model, logarithmic model and hyperbolic model given by CR9218-2015), and then carry out a prediction analysis on the maximum or final displacement, and compare and analyze it with the control reference value given in the technical regulations for tunnel monitoring and measurement. Combined with the tunnel construction conditions, the working conditions of the surrounding rock and lining support structure of the tunnel are comprehensively analyzed and studied. If the cumulative displacement curve obtained by fitting tends to a constant value with time, it indicates that the surrounding rock of the tunnel is in a stable state, and the lining support structure is reliable; otherwise, it indicates that the surrounding rock of the tunnel and the lining support structure are in an unstable state. status, appropriate remedial measures should be taken in a timely manner. It can be seen that the accurate prediction of the displacement of the surrounding rock of the tunnel is very important for the safety evaluation of the tunnel construction.

In the process of regression fitting of tunnel surrounding rock displacement, by reviewing the existing literature, the following three problems were found. 1. Some literatures only use one of the above three types of models for regression; 2. Some literatures use regression fitting No significance test was carried out in the process; 3. Although some literatures used the above three types of models for regression, the final model was selected based on the correlation coefficient.

Therefore, it is urgent to develop a method to accurately predict the displacement of the surrounding rock of the tunnel to solve the above problems.

SUMMARY OF THE INVENTION

In order to solve the problems raised in the above background art. The invention provides a method for accurately predicting the displacement of surrounding rock of a tunnel.

To achieve the above object, the present invention provides the following technical solutions:

A method for accurately predicting the displacement of surrounding rock of a tunnel, comprising the following steps:

S1. After tunnel excavation, timely collect displacement data such as surface settlement, vault subsidence and surrounding convergence, record the time, and draw a time-displacement scatter diagram;

S2. According to the "Technical Regulations for Monitoring and Measurement of Railway Tunnels (Q/CR9218-2015)", the three types of displacement duration models of exponential model, logarithmic model and hyperbolic model are simultaneously regression analysis;

S3, according to the relevant theory of probability theory and mathematical statistics, respectively carry out the significance test of the regression model and the regression coefficient for the above three types of models, and judge whether it passes, if it passes, go to step S4, if it does not pass, go to step S5;

S4. After passing the significance test of the regression model and the regression coefficient, the model with the smallest residual sum of squares is used as the regression model;

S5. After failing to pass the significance test of the regression model and the regression coefficient, kick out the regression model.

In steps S2, S3, S4, and S5: "use three types of displacement duration models to perform regression at the same time, test the significance of the regression model and regression coefficient, and use the model with the smallest residual sum of squares as the regression model" These three analysis processes Indispensable.

Compared with the prior art, the beneficial effects of the present invention are:

After adopting the present invention, step S2 can avoid using a type of model among exponential models, logarithmic models, and hyperbolic models for regression, and can avoid using models with poor regression effects for regression; step S3 can avoid using insignificant models. Regression is performed; in step S4, the model with the best regression effect can be used as the regression model, and the best regression effect means that the regression value is closest to the measured value. The correlation coefficient represents the closeness of the linear correlation between the dependent variable and the independent variable. The closer the correlation coefficient is to 1, the closer the linear correlation between the dependent variable and the independent variable. It can be seen that the correlation coefficient cannot represent the degree of deviation between the measured value and the regression value. In order to select the regression model closest to the measured value, the selection can be based on the residual sum of squares. The smaller the residual sum of squares, the closer the regression value is to the actual measurement. value, the better the regression effect is.

Description of drawings

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

Fig. 2 is a time-displacement scatter plot of the convergence around the Xiaba tunnel DK238+620 of the present invention.

Fig. 3 is the nonlinear curve fitting module diagram of the origin software of the present invention.

FIG. 4 is a new function diagram of the origin software of the present invention.

FIG. 5 is a diagram of a dialog box for inputting a function form into the origin software according to the present invention.

FIG. 6 is a dialog box diagram of the origin software of the present invention to complete the regression analysis.

FIG. 7 is an exponential model diagram obtained by regression of the present invention.

Fig. 8 is a logarithmic model diagram obtained by regression of the present invention.

Fig. 9 is a hyperbolic model diagram obtained by regression of the present invention.

FIG. 10 is a comparison diagram of an exponential model, a logarithmic model, and a hyperbolic model of the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

The present invention provides the following technical solutions:

As shown in Figure 1, it is a method for accurately predicting the displacement of surrounding rock of a tunnel, which includes:

S1. After tunnel excavation, timely collect displacement data such as surface settlement, vault subsidence and surrounding convergence, record the time, and draw a time-displacement scatter diagram;

S2. According to the "Technical Regulations for Monitoring and Measurement of Railway Tunnels (Q/CR9218-2015)", the three types of displacement duration models of exponential model, logarithmic model and hyperbolic model are simultaneously regression analysis;

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 the deformation value; A and B are the regression coefficients; t is the observation time (d) of the measuring point.

S3, according to the relevant theory of probability theory and mathematical statistics, respectively carry out the significance test of the regression model and the regression coefficient for the above three types of models, and judge whether it passes, if it passes, go to step S4, if it does not pass, go to step S5;

S4. After passing the significance test of the regression model and the regression coefficient, the model with the smallest residual sum of squares is used as the regression model;

S5. After failing to pass the significance test of the regression model and the regression coefficient, kick out the regression model.

In steps S2, S3, S4, and S5: "use three types of displacement duration models to perform regression at the same time, test the significance of the regression model and regression coefficient, and use the model with the smallest residual sum of squares as the regression model" These three analysis processes Indispensable.

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

Step 1: After the tunnel is excavated, timely collect displacement data such as surface settlement, vault subsidence and surrounding convergence, record the time, and draw a time-displacement scatter plot. Specifically:

Displacement data such as surface subsidence, vault subsidence and peripheral convergence are collected according to the monitoring and measurement frequencies given in the Technical Regulations for Monitoring and Measurement of Railway Tunnels (Q/CR9218-2015). , and plot a time-displacement scatterplot. The present invention takes the surrounding convergence data at the mileage DK238+620 of the Xiaba tunnel of the newly built Xuyong-Bijie Railway (Sichuan-Yunnan section) as an example.

Table 1 Convergence around DK238+620 of Xiaba Tunnel

Step 2: Simultaneously perform regression analysis on three types of displacement duration models: exponential model, logarithmic model and hyperbolic model. Specifically:

Use the nonlinear curve fitting module of the origin software (see Figure 3), then select the new function (see Figure 4), and input the functional forms of the exponential model, logarithmic model, and hyperbolic model respectively (see Figure 5), and finally Click Fit to complete the regression analysis (see Figure 6), and regress the obtained exponential model (see Figure 7), logarithmic model (see Figure 8), and hyperbolic model (see Figure 9).

Step 3: According to the relevant theory of probability theory and mathematical statistics, carry out the significance test of the regression model and regression coefficient for the above three types of models, and judge whether they pass, specifically:

The origin software gives the results of the significance test while giving the results of the regression model. The significance test results of the regression model and regression coefficient of the exponential model are shown in Table 2 and Table 3, respectively. The logarithmic model regression model and the regression coefficient significance test results are shown in Table 4 and Table 5, respectively. The results of the significance test of the regression model and regression coefficient of the hyperbolic model are shown in Table 6 and Table 7, respectively.

Table 2 Exponential model regression model significance test results

Table 3 The results of the significance test of the regression coefficient of the exponential model

Table 4 Logarithmic model regression model significance test results

Table 5 Logarithmic model regression coefficient significance test results

Table 6 The results of the significance test of the regression model of the hyperbolic model

Table 7 The results of the significance test of the regression coefficient of the hyperbolic model

It can be seen from Tables 2 to 7 that the values in the last column are all less than 0.05, that is, the p values corresponding to the exponential model, logarithmic model, hyperbolic model regression model and regression coefficient are all less than 0.05. Therefore, they all passed the significance test of the regression model and regression coefficient.

Step 4: After passing the significance test of the regression model and regression coefficients, the model with the smallest residual sum of squares is used as the regression model. Specifically:

It can be seen from Table 2 that when the exponential model is used to regress the measured values in Table 1, the residual sum of squares is 251.86; it can be seen from Table 4 that when the logarithmic model is used to regress the measured values in Table 1, the residual sum of squares is 876.22 ; It can be seen from Table 6 that when the hyperbolic model is used to regress the measured values in Table 1, the residual sum of squares is 593.76. That is, when the exponential model is used for regression, the residual sum of squares is the smallest, that is, the regression value at this time is the closest to the measured value, that is, the displacement predicted based on this model is the most accurate. The comparison results of the above three types of models are shown in Figure 10.

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

Claims (1)

1. a method for accurately predicting the displacement of surrounding rock of a tunnel, is characterized in that, comprises the following steps: S1. After tunnel excavation, timely collect displacement data such as surface settlement, vault subsidence and surrounding convergence, record the time, and draw a time-displacement scatter diagram; S2. According to the "Technical Regulations for Monitoring and Measurement of Railway Tunnels (Q/CR 9218-2015)", three types of displacement duration models of exponential model, logarithmic model and hyperbolic model are given at the same time for regression analysis; S3, according to the relevant theory of probability theory and mathematical statistics, respectively carry out the significance test of the regression model and the regression coefficient for the above three types of models, and judge whether it passes, if it passes, go to step S4, if it does not pass, go to step S5; S4. After passing the significance test of the regression model and the regression coefficient, the model with the smallest residual sum of squares is used as the regression model; S5. After failing to pass the significance test of the regression model and the regression coefficient, kick out the regression model.

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