Hindawi Advances in Civil Engineering Volume 2020, Article ID 9120983, 12 pages https://doi.org/10.1155/2020/9120983 Research Article Distribution Features of the Minimum Rock Cover Thickness of the Surrounding Rock Self-Stability of the Metro Tunnel in the Soil-Rock Dualistic Stratum Ziguang Zhang ,1 Tao Xu,2 Guangyong Cao ,1 and Xiaofeng Liu2 1Anhui Province Key Laboratory of Building Structure and Underground Engineering, Anhui Jianzhu University, Hefei, China 2Anhui Sijian Holding Group Co., Ltd., Hefei, China Correspondence should be addressed to Ziguang Zhang; [email protected] Received 1 November 2019; Revised 28 January 2020; Accepted 27 March 2020; Published 8 July 2020 Academic Editor: Flavio Stochino Copyright © 2020 Ziguang Zhang et al. +is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Based on the maximum value of the self-stability of surrounding rock, the key issues affecting the distribution of the minimum mock cover thickness of the surrounding rock self-stability (MRCT-SRS) of the metro tunnel in the soil-rock dualistic stratum are discussed. +e MRCT-SRS was studied for different soft stratum thicknesses Hs and excavation spans D based on cusp catastrophe theory. Moreover, the 3D spatial distribution was determined, and the fitted curves were constructed according to the MRCT-SRS, Hs, and D. +is facilitated the assessment of the stability of the surrounding rock in the excavation of a metro tunnel. Combined with the construction practices used for the Qingdao metro project, the validity of the obtained MRCT-SRS has been verified by the inverse analysis of the monitored data from the metro tunnel. Furthermore, the application of the MRCT-SRS in determining the reasonable buried depth of a metro line has been explored. +e research results have provided theoretical support and scientific basis for the preparation, revision, and improvement of the relevant codes, standards, and guidelines for metro tunnel planning and design. 1. Introduction Many scholars have studied the relationship between the stability of the surrounding rock and the rock cover +e fundamental goal of an excellent metro tunnel design thickness. Sun et al. [1] used an example of a metro station in scheme is to make full use of the self-stability of the sur- Qingdao to determine the safety factor of a tunnel in sur- rounding rock. Recently, many subsurface metro tunnels rounding rock at different buried depths by using the have been carried out in the soil-rock dualistic stratum in strength reduction method. +ey also considered the safety cities, such as Qingdao [1], Dalian [2], Guangzhou [3], factor equal to 1 as the basis for judging the surrounding Chongqing [4], and Guiyang [5]. When a metro tunnel is rock self-stability of the metro tunnel and determined the excavated in the urban area where the buried depth of the relationship between the minimum rock cover thickness and bedrock is shallow and the soft soil stratum thickness is thin, the soil stratum thickness. Yang and Xiao [6] established the the tunnel should be placed in the rock stratum and cusp catastrophe model of the safety thickness of a karst maintained such that the minimum rock cover thickness tunnel floor and derived the expression for the critical safety meets the requirements of the self-stability of the rock thickness. Xu et al. [7] designed a study based on the surrounding. In this case, the construction of a metro tunnel Qingdao Jiaozhou Bay Subsea Tunnel using two mutually can greatly reduce the tunnel support measures, save con- verified discrimination methods: the minimum vertical struction costs, reduce the tunnel construction safety risk displacement of the tunnel vault and the maximum safety and construction difficulty, and reduce the impact on the factor of the tunnel surrounding rock. +ey then studied the surrounding environment. minimum rock cover thickness of the subsea tunnel and 2 Advances in Civil Engineering x Ground surface α H Hs Hr D h Top page o β I Balanced surface Middle page II Bottom page α Figure 2: Analysis model. I stability of the tunnel surrounding rock and obtain the safety factor. Based on the measured deformation data of the o β surrounding rock, Ren et al. [17] established the catastrophe Control plane model of the tunnel surrounding rock cusp by using ca- II tastrophe theory and deduced the instability criterion of the Bifurcation set surrounding rock. Wang et al. [18] used the cusp catastrophe Figure 1: Balance-curved surface and bifurcation set of the cusp model to study the stability of gas storage pillars in layered catastrophe mode. salt caverns. Zhang and Han [19] used catastrophe theory to study the collapse mechanism and possible collapse block shape of a shallow, unlined tunnel. Zhou [20] et al. estab- considered that the minimum rock cover thickness of a lished a model based on the cusp catastrophe theory and subsea tunnel is the reasonable and effective thickness of the analyzed the stability of the support system in the goaf of tunnel. Wang et al. [8] pointed out that the reasonable room pillar gypsum. Zhang et al. [21] and Huang and Zhang buried depth of the metro station in the soil-rock dualistic [22] used catastrophe theory to study the instability stratum should be determined by using the double index mechanism of a shallow tunnel. system of the overburden thickness-span ratio and the rock +e problem of the minimum mock cover thickness of cover thickness-span ratio and noted that the rock cover the surrounding rock self-stability (MRCT-SRS) of the thickness-span ratio is more sensitive to the safety of tunnel tunnel has been studied by many scholars, who have used construction than the overburden thickness-span ratio. Qiu numerical calculations to analyze the stress, the deforma- et al. [9] studied the relationship between the minimum rock tion, and the safety factor. However, based on cusp catas- cover thickness and the surrounding rock stability of the trophe theory, rarely no relevant report has been found on subsea tunnel by the numerical method. Zhang et al. [10] the MRCT-SRS of the metro tunnel in the soil-rock dualistic discussed and expounded upon the issues of the surrounding stratum. +is paper based on the calculation and analysis of rock self-stability of the metro tunnel in the soil-rock du- the MRCT-SRS under different soft stratum thickness Hs alistic stratum from the three aspects of the stress, the and excavation span D was studied based on cusp catas- displacement, and the safety factor. Wang et al. [11] studied trophe theory and numerical calculation, the 3D spatial the conversion timing of tunnel excavation method in upper distribution was drawn, and the fitted curves was con- soft and lower hard strata based on displacement direction structed among MRCT-SRS, Hs, and D, which facilitated the angle theory under different working conditions. assessment on the stability of the surrounding rock in ex- +e catastrophe theory was put forward by +om, a cavation of metro tunnel. Combined with the construction French scholar, in the 1970s [12] and was then expanded into practice of Qingdao metro project, the validity of the ob- a perfect system by Trotman and Zeeman [13], Zeeman et al. tained MRCT-SRS has been verified by the inverse analysis [14], and Poston and Stewart [15]. Catastrophe theory is a on the data monitored for metro tunnel, and the application mathematical method used to study the phenomenon of of MRCT-SRS in determining the reasonable buried depth of discontinuity in nature. +e cusp catastrophe model is one of metro line has been expounded. +e research results can seven primary catastrophe models in catastrophe theory, provide theoretical support for the design of reasonable which has been widely used in the study of tunnel sur- depth of the vertical section of metro tunnel in soil-rock rounding rock stability, and it has achieved ideal results dualistic stratum and further offer a scientific basis for the [16–22]. Xia et al. [16] used cusp catastrophe theory and the preparation, revision, and improvement of relevant codes, discontinuous deformation analysis method to study the standards, and guidelines. Advances in Civil Engineering 3 Table 1: +e physical and mechanical parameters. Types of stratum Cohesion (MPa) Internal friction angle (°) Modulus of elasticity (GPa) Poisson’s ratio Density (kg/m3) Soft soil stratum 0.032 20 0.05 0.38 22.5 Rock stratum 0.60 35 5.0 0.25 24.5 Start Numerical calulation,unit grid division, and model loading and unloading for metro tunnel in soil-rock dualistic stratum Select a large Hr for elastic-plastic calulation with DP4 yield S model to derive 0 i = i + 1 Make elastic-plastic calculation with various Hr to derive Si Derive a fitting equation between Hr and Si N Identify any mutation in the vault vertical displacement for the surrounding rock Y Take such Hr in mutation as the minimum of MRCT-SRS End Figure 3: MRCT-SRS calculation process for metro tunnel. 2. Methodology and Research Process An equation for the cusp catastrophe model for the balanced curved surface has been obtained after first de- 2.1. Cusp Catastrophe (eory. +e cusp catastrophe model riving the potential function (1) with respect to x as follows: uses the simplest catastrophe mode with lag, divergence, and _ 3 other behaviors, which is unique to the high-order catas- V(x) � 4x + 2ux + v: (2) trophe model. +e critical interface is easy to construct and has a strong geometric rationale. Of the seven primary +e cusp catastrophe model uses a continuous balanced catastrophe models used in catastrophe theory, the cusp surface with a 3D phase space, the interior of which is folded catastrophe model is the one with the most extensive ap- into upper, middle, and lower pages, as shown in Figure 1.