A novel dynamic impact pressure model of debris flows and its application on reliability analysis of the rock mass surrounding tunnels
Introduction
Debris flows are a common geological disaster in mountain areas and are characterized by the phenomena in which water-laden mixture masses of soil and fragmented rock rush down mountainsides, destroy and entrain objects in their paths, and form muddy deposits on valley floors. Tragedies caused by debris flows have attracted more and more attention by researchers (e.g. Cui et al., 2019; Fan et al., 2018; Hu et al., 2017; Lin et al., 2011; Liu et al., 2014; Peng et al., 2015; Staffler et al., 2008; Zhang and Zhang, 2017; Zhang et al., 2014; Zhou et al., 2015). In debris-flow-prone areas, the strategy of avoidance used to be applied in route selection studies of transportation facilities. With the development of highway network construction, however, obtaining a simple but perfect solution in route design has become increasingly difficult. Reconsidering the feasibility to build transportation facilities, e.g. bridges and tunnels, in areas that were originally considered not suitable enough, e.g. debris flow-prone areas, is now a common engineering challenge. Assessing the influence of the impact pressure exerted by potential debris flows on surrounding rock mass is one of the challenges of tunnel construction projects in debris flow prone areas and the assessment task is divided into two key issues.
The first key issue is how to build a simple but effective mathematical model for the impact pressure of debris flows. Previous studies have suggested various methods for describing the impact pressure exerted on obstacles: historical statistics (e.g. Hong et al., 2015; Kang and Kim, 2016), in situ tests (e.g. Bugnion et al., 2012), flume tests (e.g. Cui et al., 2015; Song et al., 2019; Yang et al., 2011; Zhou et al., 2019), numerical models (e.g. Chen and Zhang, 2015; Gao et al., 2017; Kang et al., 2018; Shen et al., 2018) and analytical or so called semi-empirical formulas (e.g. He et al., 2016; Hungr et al., 1984; Kim et al., 2018; Tan et al., 2019). The semi-empirical formulas have the unique advantages of simplicity and efficiency, and this article will focus on this type of approach. Without loss of generality, the semi-empirical formulas can be divided into two sub-types, namely hydrostatic models and hydrodynamic models. The first model was initially by Lichtenhahn (1973) and then gained continuous development (e.g. Armanini, 1997; Luna et al., 2012; Ouyang et al., 2015; Scotton and Deganutti, 1997). In this model, the debris flow impact pressure is considered as only one feature namely the maximum impact pressure, regardless of the change in pressure over time. So, this model is a typical pseudo-static model from the perspective of dynamics analysis. The latter model was initially by Mizuyama (1979) and then developed and discussed by many researchers (e.g. Armanini, 1997; Canelli et al., 2012; Cui et al., 2015; Ferrero et al., 2015; He et al., 2016; Kim et al., 2018; Rickenmann, 1999; Scotton and Deganutti, 1997; Vagnon et al., 2016; Vagnon and Segalini, 2016; Zanuttigh and Lamberti, 2007; Zeng et al., 2015; Zhao et al., 2018). The latter model is highly dependent on the acquisition of velocity data of debris flows. However, the physical process of debris flow involves many interactions, including solid-fluid interaction (Iverson, 1997), solid-grain interaction (Iverson et al., 1997), interaction with bed sediment (Iverson et al., 2011), interactions between adjacent layers (Iverson, 2012), and interactions with obstacles (Iverson et al., 2016), and these multiple interactions cause the velocity of debris flows to vary in time and space, making it difficult to achieve an analytical solution. Although previous experiments concerning velocity of debris flows have revealed certain characteristics to some extent, there are many challenges remaining to form useful mathematical models by using these scattered and isolated characteristics. In short, the unsolved theoretical obstacles limit the application of the hydrodynamic model.
The second key issue is how to perform stability assessment for the rock mass surrounding tunnels under given debris flows impact pressure models. Essentially, a debris flow impact pressure can be regarded as an external dynamic action exerted on the system of rock mass. Because a seismic load is also an external dynamic action applied on the rock mass system, the stability assessment methodology for rock mass under seismic conditions is also theoretically applicable to debris flow impact conditions. There have been many studies of dynamic stability assessment of the rock mass surrounding tunnels under seismic condition (e.g. Genis, 2010; Liu et al., 2018; Sahoo and Kumar, 2012; Shen et al., 2014; Xu et al., 2019; Yang et al., 2015). However, the single evaluation indicator of factor of safety (FOS) is inadequate to the requirements of dynamic conditions. It is generally accepted that evaluation from a perspective of reliability is more advanced than a simple stability analysis. However, due to the complexity of the problem, the research concerning dynamic reliability assessment in this field is limited (e.g. Kurgansky et al., 2012; Yan et al., 2005; Zhang and Zhang, 2019).
There is an increasing concern to study the resistance of rock mass and structures to impact of debris flows (e.g. Dong et al., 2018; Law et al., 2016; Li et al., 2017, Li et al., 2018; Yu et al., 2015). The purpose of this paper is to propose an effective mathematical model for the impact pressure of debris flows exerted on obstacles, and then to apply this model to carry out reliability analysis of the rock mass surrounding tunnels under conditions of debris flow impact. A new method for dynamic reliability analysis of the rock mass surrounding tunnels is also proposed. Finally, the results of a case study illustrate and confirm the advantages of the new methodologies.
Section snippets
Construction of new dynamic model
The new model is an advancement using the basic idea of previous hydrostatic models (e.g. Armanini, 1997; Lichtenhahn, 1973; Luna et al., 2012; Ouyang et al., 2015; Scotton and Deganutti, 1997). Fig. 1 illustrates the impact pressure of a debris flow on the contact surface. Without loss of generality, the impact pressure on the object surface is a function of time t and depth h as:where is the dynamic load on the buried point to be measured at time t and depth h, and k(t) is the
Instantaneous dynamic stability analysis
The instantaneous dynamic stability analysis plays a fundamental role in the framework of the entire dynamic reliability analysis of the rock mass surrounding tunnels, and provides quantitative data for the following reliability analysis procedure. Because the stress in a rock mass is constantly changing during the period of impact pressure of debris flow, every moment of the dynamic stress field reflects a unique instantaneous state of the rock mass. So, a quantitative stability evaluation for
Case profile
In order to test the new method, an example case of a dynamic impact of debris flow on the rock mass surrounding tunnels is presented. This case comes from the landslide-debris flow at Madaling in Jiangzhou Town, Duyun City, Guizhou Province, China (Qi et al., 2016; Zhao et al., 2016). The Madaling landslide was influenced by underground mining activities and induced by three heavy rainfall events on 17th May 2003, 18th May 2005, and 26th July 2007. Two secondary landslides, i.e. HP1 and
Drawbacks of previous displacement-based stability assessment method
For static stability cases, the stability evaluation relied mainly on assessment of whether the displacement exceeds the threshold on several pre-assigned key locations (e.g. Li et al., 2015; Ma et al., 2016; Wang et al., 2016; Zhu et al., 2010). Because different types of rock mass have various tolerances on displacement, it is hard to provide a unified experience threshold of displacement to determine whether failure will happen. So, the subjective selection of the threshold of displacement
Conclusions
This paper is dedicated to two innovations. First, a novel mathematical model for a dynamic impact pressure of debris flows is suggested. Second, a new method of reliability analysis is proposed to evaluate the dynamic impact of debris flows on the rock mass surrounding tunnels. The combination of these two innovations provides a new methodology to evaluate the reliability of surrounding rock mass under the condition of debris flow impact. The case study verified the effectiveness and
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The research work presented here and the preparation of this paper have been financially supported by the National Natural Science Foundation of China (NSFC; Grant Nos. 41572279, 41702328 and 41807271), China Postdoctoral Science Foundation (Grant Nos. 2012M521500 and 2014T70758), China Communications Construction Company Second Highway Consultant Co., Ltd. (Project No. 2017306034), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (Grant No
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