In this paper, the field monitoring method is used to study the variation of rock mass pressure during the construction of a tunnel in phyllite stratum, and three functions are used to fit and analyze the variation of rock mass pressure with deformation, excavation time, and space. The results show the following (1) When the deformation increases significantly, the rock mass pressure decreases firstly and then increases. This is caused by the insufficient bearing capacity of the rock mass in the arch foot of the supporting structure after the excavation of the upper bench, which leads to a settlement of supporting structure and surrounding rock. (2) Compared with other kinds of fitting functions, the logistic function can better characterize the variation of the pressure of surrounding rock with deformation, excavation time, and distance from the face. This paper provides a reliable reference for the design and construction of the tunnel in phyllite stratum. The logistic function can be used to present and predict the change of rock mass pressure with deformation, excavation time, and space in similar rock mass conditions.
Rock mass pressure is the pressure acting on supporting structure, and it is caused by deformation or loosening of the surrounding rock after a tunnel is excavated. After the excavation of the tunnel, the initial stress field of the surrounding rock is disturbed, and the rock mass pressure enters the dynamic adjustment stage. In the soft surrounding rock, this stage lasts for a long time, and the stress and deformation of the tunnel are difficult to be stable for a long time, which is not good for the safety and stability of the overall structure of the tunnel [
By using the analytical method, many researchers proposed a new method or new coefficient to better predict the change of the rock mass pressure. Panet proposed a load release coefficient to describe the load variation during tunnel construction. It is found that the increase in load is due to the rheological behavior of the rock mass [
Model tests are also widely used to analyze the change of rock mass pressure. Li et al. used a comprehensive load release rate to study the load release process of tunnel excavation, results showed that the whole section should be taken as the research object, and the overall load release state of the section should be analyzed [
On-site monitoring plays an important role in the analysis of rock mass pressure during tunnel construction. Hu et al. found that the horizontal stress of the bias tunnel was over released and the measured pressure value of side walls was much larger than the calculated pressure value by comparing the on-site monitoring data with the theoretical calculation results [
In the past, a large number of researchers have obtained the law that the rock mass pressure decreases with the increase of surrounding rock deformation through numerical simulation and theoretical calculation [
The Mingyazi tunnel is located in Shaanxi province. It is a four-lane two-tunnel expressway project. The left line tunnel is 4949 m, and the right line tunnel is 4985 m. It is an extralong tunnel with a maximum buried depth of 320 m.
The monitoring measurement section is selected according to the field conditions. The right line has 9 deformation monitoring sections, including 1 stress monitoring section, and the station number of the stress monitoring section is YK214 + 011 (hereinafter referred to as 011 section). The main lithology of the monitoring section is gray-black carbon phyllite, with low stability and strength, which is easy to produce creep and be soften in water. It belongs to the grade V weak rock mass segment according to “Technical Specifications for Highway Tunnel Construction” (JTG/TF60-2009) [
The field geological condition of the Mingyazi tunnel.
Tunnel construction adopts three-bench and seven-step construction method, and its construction sequence is shown in Figure
Construction method of the Mingyazi tunnel.
The tunnel is supported by a composite lining. Grouted pipe spiling is used for presupport, the usually used rock bolts are not used, and the feet-lock anchor pipe is installed. The support parameters are shown in Figure
Support parameters of the Mingyazi tunnel.
According to the requirements of “Technical Specifications for Highway Tunnel Construction” (JTG/TF60-2009) [
On-site monitoring measurement project and method of the Mingyazi tunnel.
Number | Monitoring content | Instrument | Monitoring frequency | |
---|---|---|---|---|
1 | Clearance convergence | TOPCON (OS-600G) total station | 1–15 days | 1-2 times/day |
16 days-1 month | 1 time/day | |||
1 month later | 1-2 times/week | |||
2 | Crown settlement | TOPCON (OS-600G) total station | 1–15 days | 1-2 times/day |
16 days-1 month | 1 time/day | |||
1 month later | 1-2 times/week | |||
3 | Rock mass pressure and contact pressure | Pressure sensor | 1 time/day |
Measured points arrangement of arch settlement and clearance convergence.
Sensor arrangement for stress monitoring in initial support.
The relation between the rock mass pressure and settlement of the YK214 + 011 section is shown in Figures
Rock mass pressure and settlement curve of
Rock mass pressure and settlement curve of
Rock mass pressure and settlement curve of
Rock mass pressure and settlement curve of
Rock mass pressure and settlement curve of
Rock mass pressure of arch and clearance convergence curve of top heading.
Rock mass pressure of sidewalls and clearance convergence curve of the upper bench.
It can be seen from Figures
Figures
The rock mass pressure monitoring results of the YK214 + 011 section and the proportion of the rock mass pressure variation at each stage to the final measured values are shown in Table
Monitoring results of rock mass pressure in YK214 + 011 section/MPa.
Monitoring positions | Before upper bench excavation | Before lower bench excavation | Before the construction of invert | Before the construction of the secondary lining | Final monitoring value | ||||
---|---|---|---|---|---|---|---|---|---|
Rock mass pressure | Ratio (%) | Rock mass pressure | Ratio (%) | Rock mass pressure | Ratio (%) | Rock mass pressure | Ratio (%) | ||
0.034 | 17 | 0.080 | 39 | 0.174 | 84 | 0.196 | 95 | 0.206 | |
0.063 | 54 | 0.066 | 57 | 0.060 | 52 | 0.100 | 86 | 0.116 | |
— | — | — | — | — | — | — | — | — | |
0.013 | 25 | 0.015 | 29 | 0.019 | 37 | 0.052 | 100 | 0.052 | |
0.003 | 3 | 0.033 | 37 | 0.078 | 88 | 0.089 | 100 | 0.089 | |
— | — | 0.037 | 40 | 0.012 | 13 | 0.064 | 69 | 0.093 | |
— | — | 0.046 | 21 | 0.170 | 76 | 0.223 | 100 | 0.223 | |
— | — | — | — | — | — | 0.065 | 155 | 0.042 | |
— | — | — | — | — | — | — | — | — |
Temporal curve of rock mass pressure in YK214 + 011 section.
Distribution of rock mass pressure.
The average changing ratio of rock mass pressure in the construction stages of the arch and sidewalls in this section are shown in Figure
(a) Proportion of rock mass pressure changes in the arch. (b) Proportion of rock mass pressure changes on sidewalls.
It can be seen from Figure
It is interesting to note that after the construction of the upper bench and before the construction of the lower bench, the rock mass pressure at each part suddenly drops at the same time. This is caused by the insufficient support of rock mass at skewback (bottom of the constructed sidewalls). Due to the limited bearing capacity, supporting structure, and the rock mass move downwards together. As a result, after experiencing the deformation, rock mass pressure is decreased, and the loose rock mass around the tunnel becomes larger followed by further compaction of rock mass with rock mass pressure increase.
Figure
The change of rock mass pressure with distance to excavation face is shown in Figure
Space curve of rock mass pressure in YK214 + 011 section.
From Figure
The relation between rock mass pressure and distance to excavation face is found in Figure
Taking the YK214 + 011 section of the Mingyazi tunnel as an example, the relationship between the rock mass pressure and deformation, excavation time, and distance from the tunnel face is analyzed. Origin data analysis software is used to fit and analyze the rock mass pressure. In the analysis, logarithmic function, sigmoid function, and multiple functions are used to fit the data, and the optimal function is finally selected to characterize the variation of rock mass pressure. The logistic function is adopted to formulate the S-type function, and multifunction uses the cubic formulation to represent. The basic forms of the functions are shown in equation (
Fitting parameter range of rock mass pressure and settlement.
Function types | Basic form | Parameters | Value range |
---|---|---|---|
Logarithmic function | −10.127∼0.045 | ||
−1.184∼0.005 | |||
2941.362∼5151.256 | |||
Logistic function | 0.003∼0.027 | ||
0.046∼0.241 | |||
56.413∼82.275 | |||
18.718∼23.257 | |||
Multiple functions | −0.007∼0.019 | ||
−0.002∼0.006 | |||
−0.0002∼0.0001 | |||
−0.002∼0.001 |
Fitting is performed on the change of rock mass pressure with settlement and clearance convergence at the YK214 + 011 section. The representative fitting results are selected, as shown in Figures
Logarithmic function fitting results. (a) Fitting results of rock mass pressure and settlement (
Logistic function fitting results. (a) Fitting results of rock mass pressure and settlement (
Multiple function fitting results. (a) Fitting results of rock mass pressure and settlement (
Fitting correlation coefficient between rock mass pressure and settlement.
Function types | Results | |||||
---|---|---|---|---|---|---|
Logarithmic function | Correlation coefficient | 0.764 | 0.285 | 0.370 | 0.013 | 0.546 |
Logistic function | Correlation coefficient | 0.946 | 0.949 | 0.974 | 0.064 | 0.929 |
Multiple functions | Correlation coefficient | 0.941 | 0.868 | 0.965 | 0.619 | 0.932 |
Fitting correlation coefficient between rock mass pressure and clearance convergence.
Function types | Results | ||||
---|---|---|---|---|---|
Logarithmic function | Correlation coefficient | 0.259 | 0.534 | 0.071 | 0.713 |
Logistic function | Correlation coefficient | 0.948 | 0.975 | 0.103 | 0.968 |
Multiple functions | Correlation coefficient | 0.848 | 0.832 | 0.375 | 0.968 |
Fitting parameter range of rock mass pressure and clearance convergence.
Function types | Basic form | Parameters | Value range |
---|---|---|---|
Logarithmic function | −52.749∼−10.081 | ||
−5.891∼−1.205 | |||
3654.005∼7747.978 | |||
Logistic function | 0.003∼0.007 | ||
0.094∼0.276 | |||
177.585∼206.915 | |||
15.085∼17.577 | |||
Multiple functions | 0.002∼0.050 | ||
−0.001∼0.001 | |||
−0.00002∼0.00001 | |||
−0.0002∼0.0002 |
It can be seen from Tables
Considering the above factors, the fitting trend of logistic function with a higher correlation coefficient is more consistent with the measured data, and it has the minimum fluctuation of the constant range in characterizing the variation of rock mass pressure with deformation.
Representative fitting curves of the change of rock mass pressure with excavation time at YK214 + 011 section are shown in Figures
Logarithmic function fitting result. (a) Logarithmic function fitting result (
Logistic function fitting result. (a) Logistic function fitting result (
Multiple function fitting result. (a) Multiple function fitting result (
Correlation coefficient between rock mass pressure and excavation time.
Function types | Results | |||||
---|---|---|---|---|---|---|
Logarithmic function | Correlation coefficient | 0.931 | 0.538 | 0.067 | 0.478 | 0.911 |
Logistic function | Correlation coefficient | 0.982 | 0.796 | 0.323 | 0.704 | 0.952 |
Multiple functions | Correlation coefficient | 0.975 | 0.826 | 0.425 | 0.742 | 0.942 |
Range of parameters for rock mass pressure and excavation time.
Function types | Basic form | Parameters | Value range |
---|---|---|---|
Logarithmic function | −52.439∼0.017 | ||
−5.248∼−0.084 | |||
−24∼119.254 | |||
Logistic function | 0.014∼0.026 | ||
0.021∼0.233 | |||
456.969∼638.652 | |||
5.339∼11.030 | |||
Multiple functions | −0.006∼0.086 | ||
−0.0004∼0.0004 | |||
−0.00001∼0.00002 | |||
−0.00002∼0.00005 |
It can be seen from Table
In general, the quality of the fitting function needs to consider three factors: the correlation coefficient
The change of rock mass pressure with distance from the tunnel face is fitted and analyzed. The representative fitting results of each function are selected as shown in Figures
Logarithmic function fitting result. (a) Logarithmic function fitting result (
Logistic function fitting result. (a) Logistic function fitting result (
Multiple function fitting result. (a) Multiple function fitting result (
Fitting correlation coefficient between rock mass pressure and distance from the tunnel face.
Function types | Results | |||||
---|---|---|---|---|---|---|
Logarithmic function | Correlation coefficient | 0.931 | 0.737 | 0.067 | 0.468 | 0.910 |
Logistic function | Correlation coefficient | 0.982 | 0.764 | 0.323 | 0.711 | 0.952 |
Multiple functions | Correlation coefficient | 0.975 | 0.837 | 0.425 | 0.737 | 0.941 |
Range of fitting parameters of rock mass pressure and distance from the tunnel face.
Function types | Basic form | Parameters | Value range |
---|---|---|---|
Logarithmic function | −31.034∼0.019 | ||
−4.255∼−0.001 | |||
1465.809∼4976.583 | |||
Logistic function | 0.024∼0.049 | ||
0.090∼0.233 | |||
38.081∼58.231 | |||
2.600∼5.339 | |||
Multiple functions | −0.006∼0.086 | ||
−0.005∼0.004 | |||
−0.0001∼0.0002 | |||
−0.0003∼0.0003 |
It can be seen from Table
Considering above factors, when the logistic function is used to characterize the change of the rock mass pressure and the distance from the tunnel face, the correlation coefficient is higher, the trend of the fitting curve is more consistent with the actual situation, and the range of each constant term is easier to be determined.
In this paper, based on the measured rock mass pressure at the Mingyazi tunnel, the change of rock mass pressure in the construction process with tunnel deformation, construction process, excavation time, and distance from the tunnel face is analyzed. The following conclusions are obtained: The increase of rock mass pressure and deformation is inconsistent. When the clearance convergence and settlement experience a rapid growth, the rock mass pressure appears to increase first and then decrease. This is caused by the insufficient bearing capacity of the rock mass in the arch foot of the supporting structure after the excavation of the upper bench, which leads to a settlement of supporting structure and surrounding rock. During construction, the rock mass pressure is mostly 0.05∼0.23 MPa and changed slowly. After each process, the rock mass pressure adjustment time is long and reaches stable about 15 days after the secondary lining installation. It takes 65 to 70 days for the tunnel to stabilize after excavation and support. In the process of each construction stage, the change proportion of rock mass pressure is relatively uniform. When the supporting structure gets a full ring closure, the proportion of the rock mass pressure change value at each part accounted for 65% of the final monitoring value. Under construction, the space effect of the tunnel face is very significant. In the process of tunnel excavation, due to the constraints of the excavation surface, the surrounding rock cannot immediately release all the instantaneous elastic displacement, which is called the “space effect” of the excavation surface. When the test section is within two times of the diameter of the tunnel, the rock mass pressure is significantly affected by the excavation of the tunnel face. The spatial impact range is within three times the diameter of the tunnel (37 m), and the rheological properties of the rock mass dominate the changes afterwards. In view of the influence of rock rheological properties on rock pressure, further research is still needed. The logarithmic function, logistic function, and multiple functions are used to fit and analyze the relationship between rock mass pressure, deformation, excavation time, and distance from the tunnel face. It is found that the
The data used to support the findings of this study are included within the article.
The authors declare no conflicts of interest.
This research was funded by the National Key R&D Program of China (Grant no. 2018YFB1600100), the Key Project of National Natural Science Foundation of China (Grant no. 41831286), the Youth Project of National Natural Science Foundation of China (Grant nos. 51908052 and 51808049), Natural Science Foundation of Shaanxi Province (Grant no. 211421190347), and the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant no. 300102210216). These supports are gratefully acknowledged.