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ORIGINAL RESEARCH article

Front. Earth Sci., 04 August 2022
Sec. Geohazards and Georisks
Volume 10 - 2022 | https://doi.org/10.3389/feart.2022.967328

Developing an evaluation model based on unascertained measurement for evaluation of tunnel squeezing

www.frontiersin.orgCong Wei1 www.frontiersin.orgShuangli Zhu1* www.frontiersin.orgChao Chen1,2* www.frontiersin.orgJian Zhou1
  • 1School of Resources and Safety Engineering, Central South University, Changsha, China
  • 2Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Trondheim, Norway

Tunnel squeezing brought great difficulties to the construction and severely threatened the safety of on-site operators. The researches regarding large deformation evaluation have been widely developed, but actual conditions of tunnels are considerably complex, producing a large variety of uncertainty information existing in the evaluation process. Therefore, we constructed an unascertained measurement model incorporating four membership functions for evaluation of tunnel squeezing based on the collected datasets. Simultaneously, information entropy was introduced to objectively calculate the index importance for each index. For the first group data (GPI), the accuracy associated with four membership functions are 100%, 83.33%, 50%, and 83.33%, respectively, while the accuracy of GPII are 70%、77.5%、67.5%, and 70%, respectively. Linear function and parabolic function show better performance on uncertainty information interpretation according to the classification results. The results revealed that the uncertainty model constructed in this study can enrich the available uncertainty evaluation system.

Introduction

Various technologies related to tunnel engineering have been greatly developed, such as ventilation technology, support technology, excavation technology, operation management, rock characteristics (Wang et al., 2021b; Du et al., 2022; Wang et al., 2022; Yu et al., 2022), prediction and prevention of geological disasters (Feng et al., 2015; Wang et al., 2021a; Feng et al., 2022; Zhou et al., 2021a; Zhou et al., 2021b), among which geological disasters are the main risk factors in engineering. In recent years, with the excavation of various tunnels in underground at great depth, the hazards regarding large deformation of surrounding rock frequently occurred. Currently, the scientific community gradually focused on the large deformation of excavated tunnels (Zhang et al., 2003; Singh et al., 2007; Chen, 2008; Lai et al., 2018; Sharma et al., 2020). Large deformation of surrounding rock can be divided into extrusion and expansion (Wood, 1972; Barton et al., 1974; Jethwa et al., 1984; Barla, 1995; Barla, 2001; He et al., 2002). The former occurs in soft rocks with high geostress, while the latter mainly occurs in rock mass with strong expansion properties. The stress redistribution caused by excavation exceeds the ultimate shear stress, resulting in a large-scale plastic failure zone in the surrounding rock of the tunnel (Gioda and Cividini, 1996; Panet, 1996; Barla, 2001; Singh et al., 2007; Dwivedi et al., 2013). Most of the large deformation of surrounding rock occurs in deep and long soft rock tunnels, e.g., in China, Zhegushan Highway Tunnel, Guanjiao Tunnel, Jiazhuqing Tunnel, Dazhailing Tunnel, the China-Laos railway tunnel, etc. The above-mentioned tunnels all suffered from large deformation to some extent, which brought great difficulties to the construction. In addition, the weak surrounding rock is more prone to squeeze and occur large deformation under the action of high in-situ stress. At this time, the surrounding rock ruptures and squeezes out of the tunnel boundary and further damages the supporting structure, which will seriously lead to tunnel collapse even cause damage to construction workers (Liu, 2004; Chen, 2008; Liu et al., 2008; Yu, 2020; Ren et al., 2021). The large deformation of surrounding rock is gradually accelerated with the development of time (Bhasin and Grimstad, 1996; Barla, 2001; Singh et al., 2007; Azizi et al., 2019). Therefore, the evaluation of tunnel squeezing is of great significance for improving the construction efficiency, reducing the cost, and ensuring the safety of the construction personnel (Aydan et al., 1993; Aydan et al., 1996; Hoek, 2001; Ghiasi et al., 2012; Panthi, 2013; Azizi et al., 2019).

The tunnel squeezing is a major engineering problem that needs to be solved urgently in this field. Many scholars tried to use different methods to evaluate the severity of large extrusion deformation (Dube et al., 1986; Jiang et al., 2004; Fatemi Aghda et al., 2016; Azizi et al., 2019; Liao et al., 2020). For example, Singh et al. (2007) evaluated the tunnel squeezing based on burial depth (H) and rock quality index (Q). Then, Goel et al. (1995) introduced the rock mass number N (the Q value of SRF = 1) into the fitting curve equation. Additionally, Liu et al. (2019) proposed an improved cloud model for the prediction of large deformation of surrounding rock in Mila Mountain Tunnel in Tibet based on the uncertainty and randomness of tunnel squeezing prediction. Although various methods associated with tunnel squeezing evaluation has been widely explored, the mechanism of this geological hazard is considerably complex, leading to a large variety of uncertainty exists in the evaluation of tunnel squeezing. (ISRM, 1995; Steiner, 1996; Malan and Basson, 1998; Palmstrom and Broch, 2006; Williams, 2010; Dwivedi et al., 2014; Farhadian and Nikvar-Hassani, 2020; Zhang et al., 2020).

In view of the wide application and robust uncertainty information interpretation of unascertained measurement theory in this field, e,g., stability evaluation, scheme optimization, risk assessment, and performance evaluation. This study aims to develop a hybrid model based on information entropy and unascertained measurement incorporating four membership functions to evaluate the tunnel squeezing, which is able to enrich the available risk evaluation methods for underground excavation projects.

Method description

There are n samples in the evaluation object space Y={y,1y2,...,yi,...,yn},(i=1,2,3,...,n), and each sample contains m predictors. X={x1,x2,...,xj,...,xm},(j=1,2,3,...,m) was used to represent the predictor space. There, yi={xi1,xi2,xi3,...,xij,...,xim},(yiY), where, xij(i=1,2,3,...,n;j=1,2,3,...,m) represents the jth predictor variable of the ith sample. Assuming that there are K evaluation levels for the degrees of deformation, therefore, the grade set can be shown as Ω={L1,L2,L3,...,Lk,...,LK},(k=1,2,3,...,K). It is worth noting that the evaluation space is an ordered segmentation category (Jing and Hua, 2008; Tu et al., 2008; Wang, 2019), that is, Lk+1>LK.

Single-index measurement matrix

According to the above yiY,(i=1,2,3,...,n) is the ith research sample in the evaluation system, and the predictor xjX,(j=1,2,3,...,m) reflects the characteristic of the research object. In this paper, yij,(i=1,2,3,...,n;j=1,2,3,...,m) was defined as the measure-valued of yi under the index xj. It is assumed that there are K evaluation levels for each measure-valued (yij), and the grade set is Ω={L1,L2,L3,...,Lk,...,LK},(k=1,2,3,...,K). Afterwards, we defined a possibility measure aijk=a(yijLk), it is known as the unascertained measure. It indicates the degree to which the measured value yij belongs to the kth evaluation level and satisfies the following three requirements at the same time: non-negativity, normalization equation and additivity, as shown in Eqs 13 respectively.

0a(yijLk)1(1)
a(yijΩ)=1(2)
a[yijk=1KLk]=k=1KyijLk(k=1,2,,K)(3)
(aijk)m×K=[ai11ai12ai1Kai21ai22ai2Kaim1aim2aimK](4)

The above Eq. 4 (aijk)m×K,(i=1,2,...,n;j=1,2,...,m;k=1,2,...,K) is the single-index measurement matrix of ith sample.

The single index measurement judgment matrix is calculated by the membership function. In this paper, we will use four types membership functions (Zhou et al., 2020b; Zhou et al., 2021a): linear, parabolic, exponential and sine functions, as shown in Eqs 58 respectively.

{ar(x)={xbr+1br+br+1br+1br(br<xbr+1)0(x>br+1)ar+1(x)={0(xbr)xbr+1brbrbr+1br(br<xbr+1)(5)
{ar(x)={1(xbrbr+1br)2(br<xbr+1)0(x>br+1)ar+1(x)={0(xbr)(xbrbr+1br)2(br<xbr+1)(6)
{ar(x)={11exbr1ebr+1br0(x>br+1)ar+1(x)={0(xbr)1exbr1ebr+1br(br<xbr+1)(7)
{ar(x)={1212sinπbr+1br(xbr+1br2)(br<xbr+1)0(x>br+1)ar+1(x)={0(xbr)12+12sinπbr+1br(xbr+1br2)(br<xbr+1)(8)

Where, ar(x) and ar+1(x) are the membership corresponding to grade Lk and Lk+1, respectively. br and br+1 are the left and right endpoints, respectively.

Information entropy theory

Based on the above single-index measurement matrix (Eq. 4), a more objective method is applied to determine the index weight in this paper, i.e., information entropy (Ruan et al., 2021). Wij represents the weight of jth index under ith sample, which can be calculated through Eq. 9.

Wij=ξijj=1mξij,(i=1,2,...,n;j=1,2,...,m)(9)

Where, 0Wij1,andj=1mWij=1. ξij(0ξij1) represents the value of entropy, which can be calculated via the single index measurement vectors aijk, referring to Eq. 10.

ξij=1+1lnK(k=1Kaijklnaijk)(10)

Then, the index weight vector of the ith sample can be expressed as: Wij=(Wi1,Wi2,...,Wij,...,Wim).

Comprehensive measurement matrix

The multi-index comprehensive measurement matrix is calculated as follows (Jia et al., 2019; Ma et al., 2021).

Aik=j=1mWijaijk,(i=1,2,...,n;k=1,2,...,K)(11)

Where, Aik=A(yiLk) is the multi-index comprehensive measurement vector. It represents the degree to which the evaluation sample yi belongs to the grade k. In addition, 0Aik1,andk=1KAik=k=1Kj=1mWijaijk=j=1m(k=1Kaijk)Wij=1.

(Aik)n×K=[A11A12A1KA21A22A2KAn1An2AnK](12)

Where, (Aik)n×K,(i=1,2,...,n;k=1,2,...,K) is the multi-index comprehensive measurement matrix. Then the multi-index comprehensive measurement vector of the ith sample can be expressed as: Ai=(Ai1,Ai2,...,Aik,...,AiK).

Credible identification principle

In order to determine the grade of individual sample, the credible identification principle was utilized. The grade of samples can be calculated through Eq. 13 based on the above-mentioned comprehensive multi-index measurement vectors (Shi et al., 2010).

Lik=min(k=1KAikλ,k=1,2,...,K)(13)

Where, Lik is the grade of sample ith, and LikΩ,(Ω={L1,L2,L3,...,Lk,...,LK}. λ(λ0.5), normally, λ=0.6 or λ=0.7 (Zhou et al., 2020a; Zhou et al., 2020b; Zhou et al., 2021b; Chen et al., 2021).

Sample score

Although the risk level of samples is judged through credible identification principle, it is difficult to further distinguish the severity of the tunnel deformation, that is, the large deformation cannot be quantitatively analyzed. There, each sample can be scored by the following equation.

SCi=k=1KNumkAik,(1kK;1in)(14)

where, SCi is the score of sample ith, Numk is the value assigned to grades {GR1,GR2,GR3,GR4}.

Squeezing evaluation using unascertained measurement

The influencing factors of tunnel squeezing are divided into objective and subjective factors, the former includes geological conditions, such as rock mass conditions, engineering geological conditions, and geo-hydrologic conditions; the latter refers to construction technology, survey and design. Studies shown that poor geological conditions are the main factors for tunnel squeezing, such as the strength of surrounding rock, in-situ stress, and groundwater. This study employed two sets of data collected from the literature to evaluate tunnel squeezing. For the first group of data, the construction of index system considers geological factors and construction technology, while only geological factors are taken into consideration for the second one. Simultaneously, we use GPI to represent the first set of data, and the second group data is described by GPII. The spatial location of datasets used in this study was shown in Figure 1.

FIGURE 1
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FIGURE 1. Spatial location of engineering cases used in this study.

The first group data is composed of six research samples, simultaneously, the evaluation results are categorized into four grades Ω(GPI)={L1,L2,L3,L4}, namely, no large deformation, slight large deformation, medium large deformation and strong large deformation. The initial data (Bai et al., 2021) of these six samples are listed in Tables 1, 2 is the classification standard corresponding to individual index. The first set of data includes 14 evaluation indicators, which can be generally divided into three categories: tunnel design and engineering construction factor (C1), the engineering geological condition (C2), the mechanical and physical properties of rock (C3). There are six second-level indicators in C1, four in C2 and four in C3, as shown in Figure 2.

TABLE 1
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TABLE 1. Engineering cases used for tunnel squeezing evaluation.

TABLE 2
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TABLE 2. The classification standards of tunnel squeezing.

FIGURE 2
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FIGURE 2. Index system of squeeze evaluation.

The second group was obtained from the Telmo Tunnel in the Chengdu-Kunming Railway double track (Wang, 2019), which is a deep-buried tunnel with poor surrounding rock conditions. Combine the current railway tunnel deformation classification standard and previous tunnel deformation research, five factors, i.e., the rock uniaxial compressive strength (Rc), the integrity coefficient of rock mass (RQD), the groundwater condition (GW), the angle between the main structural plane and the axis of the tunnel (θ), and the structural surface state (P) are considered as the evaluation indexes, as shown in Figure 2. The evaluation set Ω(GPII)={L1,L2,L3,L4,L5} is denoted as no large deformation, slight large deformation, medium large deformation, strong large deformation and severe large deformation. The related samples and classification standards (Wang, 2019) are presented in Tables 3, 4, respectively.

TABLE 3
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TABLE 3. Engineering cases of tunnel squeezing.

TABLE 4
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TABLE 4. Classification standard for tunnel squeezing.

Single index measurement of samples

Firstly, based on the four different membership functions shown in Eqs 58, the index measurement matrix calculated by different membership functions are obtained. In Figures 3A,B, different membership functions, corresponding to profit and cost index, respectively, are displayed, which can easily calculate the index membership incorporating Eqs 58. The single-index measurement matrix of the first and second group data can be represented by GPI:(aijk)m×K,(i=1,2,...,n,n=6;j=1,2,...,m,m=14;k=1,2,...,K,K=4) and GPII:(aijk)m×K,(i=1,2,...,n,n=40;j=1,2,...,m,m=5;k=1,2,...,K,K=5) respectively.

FIGURE 3
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FIGURE 3. Membership function for different indexes. (A) Membership function of benefit index, and (B) Membership function of cost index.

Finally, taking sample 1 (GPI:y1) of the first set of data as an example, the single index measurement matrix of sample1 is listed in Eqs 1417.

GPI:(a1jK)14×4linear=[001000.530.4700100100010001000000.480.5210000010010000.80.20100010001000](14a)
GPI:(a1jk)14×4parabolic=[001000.7790.22100100100010001000000.7300.27010000010010000.960.040100010001000](15)
GPI:(a1jk)14×4exponential=[001000.8960.16400100100010001000001010000010010000.0820.9180100010001000](16)
GPI(a1jk)14×4sine=[001000.5470.45300100100010001000000.4690.53110000010010000.9050.0950100010001000](17)

Index weight of squeezing evaluation

In this study, information entropy is introduced to calculate the index weight coefficients of each sample referring to Eqs 9, 10. There, only the weights calculated by linear function are visualized, as shown in Figure 4.

FIGURE 4
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FIGURE 4. Index weights calculated through linear membership function.

Determination of squeezing grade

For the first sample of first group, the multi-index comprehensive measurement vectors calculated through the linear function are listed GPI:A1k=(A11,A12,...,A1k,...,A1K)=(A11,A12,...,A14)=(0.5538,0.2197,0.2060,0.0206). Similarly, the multi-index comprehensive evaluation vectors of sample one calculated by the remaining three measurement functions (i.e., parabolic, exponential and sine function) are shown in Table 5. In this paper, the classification standard of the first group is set as 0.55, that is λI=0.55, and λII=0.6 for second one. Therefore, according to the comprehensive measurement vector in Table 5, the deformation grade of sample one can be identified through Eq. 13. For instance, incorporating the calculation results of the linear function into Eq. 13: A11+A12=0.5538>0.55, it can be clear that the risk level of sample one is L1. The grade of sample one is calculated as L2 while using parabolic function, exponential function and sine function, as shown in Table 5. According to the above criteria, the remaining samples are evaluated, and the results are listed in Figure 5; Table 6. Similarly, the squeezing level of dataset two also can be calculated as shown in Figure 6. Both sets of data show that the evaluation performance of exponential function is not ideal, and both are lower than the other three membership functions.

TABLE 5
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TABLE 5. Comprehensive unascertained measure based on linear function.

FIGURE 5
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FIGURE 5. Accumulated measurement of proposed model calculated by four functions.

TABLE 6
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TABLE 6. Evaluation results of unascertained measurement (GPI).

FIGURE 6
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FIGURE 6. Evaluation results obtained through four membership functions.

Sample score for tunnel squeezing

For most comprehensive evaluation models, risk level judgment of samples can be high-efficiently calculated, however, few models are able to quantify the samples simultaneously. Sample score can easily distinguish the risk state of samples at the same grade, which is beneficial to take more accurate measures to prevent geological hazards for on-site engineering issues. There, the scores of samples existing in the two groups data are shown in Table 7; Figure 7, making it possible to identify the most dangerous sample in the dataset. In Figure 7, the score of sample 29 is highest in comparison with other samples, that is, this sample is more likely to occur large deformation.

TABLE 7
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TABLE 7. Quantitative scoring of individual sample about tunnel squeezing (GPI).

FIGURE 7
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FIGURE 7. Sample score associated with tunnel squeeze.

Conclusion

In this paper, two sets of data with different evaluation index system are collected, and the unascertained measurement theory is used to comprehensively evaluate the tunnel squeezing. The calculation of this hybrid model includes single-index measurement matrix, index weight coefficient and comprehensive measurement matrix. Ultimately, credible identification principle is used to evaluate the risk level. The main conclusions are listed as following:

(1) Four membership functions are used in this paper: linear, parabolic, exponential, and sine function. The accuracy of the first datasets are: 100%, 83.33%, 50%, and 83.33%, respectively, while the accuracy of second dataset are: 70%, 77.5%, 67.5%, and 70%, respectively.

(2) Two groups of data evaluate the tunnel squeezing through constructing different dataset. For the first dataset, sample five is the most dangerous sample while sample 29 is the most dangerous one for the other dataset.

(3) The factors affecting the large deformation of surrounding rock are complex, not only related to the mechanical properties of rock and engineering geological factors, but also related to the construction conditions. There is high uncertainty in the evaluation of large deformation of surrounding rock, more models should be explored to remove various uncertainty existing in the evaluation process in the next research.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding authors.

Author contributions

Writing—original draft preparation, CW, JZ, CC, and SZ; Modelling, CC and CW; Writing—review and editing, CW, JZ, and CC. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Science Foundation of China (42177164 and 41807259) the Distinguished Youth Science Foundation of Hunan Province of China (2022JJ10073) and the Innovation-Driven Project of Central South University (No. 2020CX040). The authors gratefully acknowledge financial support from the China Scholarship Council (Grant No. 202206370030).

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Keywords: Squeezing, Unascertained measurement, Information entropy, Classification, Risk evaluation

Citation: Wei C, Zhu S, Chen C and Zhou J (2022) Developing an evaluation model based on unascertained measurement for evaluation of tunnel squeezing. Front. Earth Sci. 10:967328. doi: 10.3389/feart.2022.967328

Received: 12 June 2022; Accepted: 05 July 2022;
Published: 04 August 2022.

Edited by:

Guang-Liang Feng, Institute of Rock and Soil Mechanics (CAS), China

Reviewed by:

Tao Zhou, Shenzhen University, China
Lishuai Jiang, Shandong University of Science and Technology, China

Copyright © 2022 Wei, Zhu, Chen and Zhou. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Shuangli Zhu, 195512078@csu.edu.cn; Chao Chen, csuchenchao@csu.edu.cn, chao_chen_best@hotmail.com

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