Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 2947628, 11 pages

http://dx.doi.org/10.1155/2016/2947628

## Uncertainty Analysis on Risk Assessment of Water Inrush in Karst Tunnels

^{1}State Key Laboratory of Disaster Prevention & Mitigation of Explosion & Impact, College of National Defense Engineering, PLA University of Science and Technology, Nanjing 210007, China^{2}High-Tech Institute, Fan Gong-ting South Street on the 12th, Qing Zhou, Shan Dong, China^{3}State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China

Received 26 June 2016; Accepted 27 October 2016

Academic Editor: David González

Copyright © 2016 Yiqing Hao et al. This 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.

#### Abstract

An improved attribute recognition method is reviewed and discussed to evaluate the risk of water inrush in karst tunnels. Due to the complex geology and hydrogeology, the methodology discusses the uncertainties related to the evaluation index and attribute measure. The uncertainties can be described by probability distributions. The values of evaluation index and attribute measure were employed through random numbers generated by Monte Carlo simulations and an attribute measure belt was chosen instead of the linearity attribute measure function. Considering the uncertainties of evaluation index and attribute measure, the probability distributions of four risk grades are calculated using random numbers generated by Monte Carlo simulation. According to the probability distribution, the risk level can be analyzed under different confidence coefficients. The method improvement is more accurate and feasible compared with the results derived from the attribute recognition model. Finally, the improved attribute recognition method was applied and verified in Longmenshan tunnel in China.

#### 1. Introduction

Risk management became an integral part of most underground projects during the late 1990s [1]. Water inrush is one of the major problems in underground construction projects, especially in karst regions. It severely endangers the safety of underground tunnel constructions and operations in China, resulting in tremendous casualties and economic loss. Water inrush in karst tunnel has to satisfy three necessary conditions of water source, karst conduit, and potential energy.

Water inrush can be described exactly by the potential energies of water leaking from karst conduit. Based on the mechanism of water inrush in karst tunnel, it can be categorized into geological flaws and no geological flaws [2]. The research of water inrush mainly focuses on three aspects: factor indexes, assessment with no geological flaws, and assessment with geological flaws.

There exist many perspectives on risk, and traditionally some of the perspectives have been seen as representing completely different frameworks, making the exchange of ideas and results difficult [3]. Risk assessment of water inrush with no geological flaws established the model by the theory of rock mass mechanics. Yao et al. [4] built numerical models for the roof fracture and seepage development rule using RFPA 2D and COMSOL to analyze the changes in fracture zone, stress, water pressure, and seepage vector with the advancement of working face, respectively.

Risk assessment of water inrush with geological flaws normally use neural network method, AHP, FAHP, GIS, fuzzy mathematical method, attribute mathematical method, and so on [5, 6]. Risk analysis provides a procedure, which should take into account the uncertainties [7–9]. Some scholars have solved the uncertainties in water inrush with the probability method. Jurado et al. developed a general probabilistic risk assessment (PRA) framework to quantify risks driven by groundwater to the safety of underground constructions [10]. Sousa and Einstein estimated the risk during tunnel construction using Bayesian Network [11]. X. P. Li and Y. N. Li [12] studied a forecasting system for water inrush based on GIS. Further, a case study on the diversion tunnel groups of Jinping II Hydropower Station based on GIS is provided by X. P. Li and Y. N. Li [13]. Wang et al. constructed a secondary fuzzy comprehensive evaluation system to evaluate the risk of floor water invasion [14]. Meng et al. put forward a coal floor water inrush risk assessment method based on a conventional water inrush coefficient, considering the lithology and structure features [15]. Li et al. developed a spatiotemporal dynamic model through an analysis of the factors influencing temporal changes of water inrush spreading in roadways [16]. Li et al. developed the methodology which consists of two attribute recognition models: one is for design stage, and the other is for construction stage [17].

In the risk assessment of water inrush in karst tunnels, the biggest problem is that the classification is different and the result is not rational. However, it can be effectively solved by the risk assessment model based on attribute comprehensive evaluation system, according to the principle of maximum membership degree law. Many literatures present a series of researches on the integrated attribute evaluation system model.

When using the model based on attribute synthetic evaluation system, the value of evaluation index and attribute measure influence the assessment results directly. Based on ordered partition class and attribute recognition criterion, the attribute synthetic evaluation system can effectively identify and perform comparative analysis. Also, the attribute synthetic evaluation system effectively overcomes some shortcomings of other identification methods such as fuzzy recognition theory and can effectively reduce the loss of information in a calculation. Therefore, the synthetic evaluation system attribute has been successfully applied to the risk predication, risk evaluation, and risk decision of water inrush in karst tunnel. Previous methods usually adopt a definite value. Nevertheless, the geology in karst regions is uncertain, and it has the stochastic character. Also, the attribute is uncertain too. So, there are two basic problems before the viewpoints on the stochastic rock engineering to analyze the risk assessment of water inrush.

(1) The uncertainty of geology induces the uncertainty of evaluation index value. The evaluation indices generally rely on objective factors such as hydrogeology and geology factors. The values of evaluation index are always different from each other even in the same condition. Therefore, the value of evaluation index must account for the randomness.

(2) Uncertainty of attribute measure: in the model based on attribute synthetic evaluation system, the attribute level of evaluation index is quantitatively depicted as a constant by the attribute measure. It is more reasonable using an interval compared to a constant to depict the attribute measure, ascribed to the uncertainty of attribute measure.

In this paper the statistical characteristic about the value of evaluation index and attribute measure is taken into account with respect to the uncertainty of risk assessment in water inrush. An improved attribute recognition approach is proposed to calculate probabilities of risk level utilizing attribute synthetic evaluation system and Monte Carlo sampling distribution. The results would be more scientific and reasonable compared to other methods.

#### 2. Probabilities of the Evaluation Indices Based on Geology

Indices and criteria for risk assessment of water inrush are based on the statistical information about geology in karst tunnels, and several influencing factors of water inrush are selected as the attribute evaluation indices. Formation lithology is normalized, and strata inclination is divided into Level III and Level IV in the range of . The specific indices and criteria are shown in Table 1 [17].