Probabilistic analysis of tunnel longitudinal performance based upon conditional random field simulation of soil properties

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Highlights

  • A probabilistic framework for tunnel longitudinal performance analysis is proposed.

  • A conditional random field theory-based site characterization method is outlined.

  • A tunnel longitudinal performance analysis model is presented.

  • The significance of the proposed framework is demonstrated through an illustrative example.

Abstract

Because of the inherent spatial variability of soil properties and the limited number of boreholes that can be afforded in a typical project, the soil properties at given geotechnical sites could not be known with certainty, which leads to an uncertainty in the predicted performance of a geotechnical system. For such uncertain system, probabilistic analysis is often used to assess its performance considering uncertainty. This paper presents a new framework for the probabilistic analysis of tunnel longitudinal performance. Within this framework, the conditional random field theory is adopted to simulate the spatial variation of soil properties along the tunnel longitudinal direction, in which the soil properties at borehole locations can be explicitly considered. Then, the tunnel longitudinal performance is analyzed with an advanced tunnel performance model, in which the influence of tunnel longitudinal behavior on the circumferential behavior of the tunnel cross section can be explicitly considered. With the aid of Monte Carlo simulation (MCS), tunnel longitudinal performance can readily be analyzed in a probabilistic manner; and, the variation of the tunnel performances (i.e., the structural safety and serviceability of the cross section) along the tunnel longitudinal direction could be assessed. The novelty and significance of this proposed framework, compared to the existing methods, are demonstrated through an illustrative example. Further, the influence of the borehole density (i.e., the number of boreholes per tunnel length) on the prediction of the tunnel longitudinal performance is analyzed through a parametric study.

Introduction

Shield tunnels, an important component of the modern transportation infrastructures, are being constructed in a fast pace around the world. As a reference, in Shanghai the metro tunnel system currently with a total mileage of 538 km, which takes up approximately 43% of the daily public transportation, is still growing (Huang and Zhang, 2016). From the perspective of a tunnel engineer, tunnel is a slender structure: the longitudinal length could be in hundreds or thousands of meters while the diameter could typically be less than 15 m. The longitudinal variation of the input parameters such as soil properties is quite likely over the tunnel longitudinal length, and the influence of this variation on the tunnel performances (measured herein in terms of the structural safety and serviceability of the cross sections) could not be ignored. The longitudinal variation of the input parameters would lead to the longitudinal variation of the tunnel performances, and this effect must be explicitly considered in the analysis and design of tunnels (ATRB, 2000, ITA, 2000, Koyama, 2003, Gong et al., 2015a, Gong et al., 2015b, Huang et al., 2015).

A comprehensive analysis of the tunnel longitudinal performance, which is referred to herein as the variation of the tunnel performances (i.e., the structural safety and serviceability of the cross section) along the tunnel longitudinal direction, requires a complete characterization of the input parameters (especially soil properties) along the tunnel longitudinal direction (Gong et al., 2015b). However, the soil properties could only be known at borehole locations and only a limited number of boreholes could be afforded in a specified project; whereas, the soil properties at other positions may have to be interpolated from those at borehole locations. Here, the spatial interpolation methods such as the linear interpolation methods could be employed (Schloeder et al., 2001, Kılıç et al., 2006, Samui and Sitharam, 2010). Note that while these spatial interpolation methods have been widely adopted in the current practice, they are deterministic approaches and they are not equipped to consider the inherent spatial variability of soil properties (Fenton, 1999b, Cho et al., 2004). To this end, the random field theory-based site characterization has long been advocated (Jaksa et al., 2005, Griffiths and Fenton, 2009, Gong et al., 2014a, Gong et al., 2016).

Within the random field theory-based site characterization, the statistical information of the random field of the soil property is first calibrated using the soil properties known at borehole locations. Then, the soil properties at the project site are randomly generated with the calibrated random field, the generated soil properties are readily taken as the inputs to the analysis of the performance of the geotechnical system. Although the random field theory is a powerful tool for the simulation of the inherent spatial variability of soil properties, the soil properties collected at borehole locations are not fully utilized in this conventional random field simulation, which may lead to an overestimate of the site variability (Li et al., 2015). For example, in the conventional random field simulation, the soil properties that are randomly sampled at borehole locations may be different from the collected borehole data. This is not ideal as the soil properties at borehole locations are certain; and, the generation of the random field must be constrained to reflect this known information. Hence, within the proposed framework for the probabilistic analysis of the tunnel longitudinal performance, the conditional random field theory (Chen et al., 2012, Li et al., 2015, Li et al., 2016) will be adopted, in which the simulation of the soil properties at borehole locations would be constrained by the borehole data.

It is worth noting that though the significance of tunnel longitudinal performance analysis has long been acknowledged (ATRB, 2000, ITA, 2000, Koyama, 2003), very limited studies have been undertaken to elucidate this aspect. The current tunnel design practice still depends on the deterministic analysis of a few critical tunnel cross sections adopting a plane strain assumption (Wood, 1975, Bobet, 2001, Lee et al., 2001, Lee and Ge, 2001). In this paper, a new framework for the probabilistic analysis of the tunnel longitudinal performance is proposed: (1) the conditional random field theory is adopted to simulate the inherent spatial variation of the soil properties (based upon the collected borehole database) along the tunnel longitudinal direction; (2) the soil properties generated from the conditional random field are taken as the inputs to the analysis of the variation of the tunnel performances (i.e., the structural safety and serviceability of the cross section) along the longitudinal direction; and (3) with the aid of Monte Carlo simulation (MCS), the tunnel longitudinal performance is analyzed probabilistically.

This paper is organized as follows. First, the conditional random field simulation of the soil properties based upon the collected borehole data is outlined. Second, the tunnel longitudinal performance analysis with a full characterization of the soil properties along the tunnel direction is presented. Third, a probabilistic framework for the tunnel longitudinal performance analysis is formulated. Fourth, an illustrative example of the tunnel longitudinal performance analysis is provided, through which the significance of the proposed framework is demonstrated. Fifth, the influence of the borehole density on the prediction of the tunnel longitudinal performance is analyzed through a parametric study. Finally, the concluding remarks are drawn based upon the results presented.

Section snippets

Conditional random field simulation of soil properties

It is known that a soil property at various locations (at a project site) is often correlated to some extent in both horizontal and vertical directions, and such spatial correlations generally decrease with the relative distance. This feature of soil properties can best be simulated utilizing the random field theory (Fenton, 1999b, Cho et al., 2004). As mentioned above, the soil properties at borehole locations are “known” through measurements (and thus considered “certain”). To this end, the

Tunnel longitudinal performance analysis

With a full characterization of the soil properties along the tunnel longitudinal direction, such as a realization of the conditional random field of the soil properties shown in Fig. 1(a), tunnel longitudinal performance could readily be analyzed. The model advanced in Gong et al. (2015b) is adopted in this study for the analysis of tunnel longitudinal performance. This model is summarized in the following two main steps.

Framework for probabilistic analysis of tunnel longitudinal performance

As noted previously, a complete characterization of the soil properties along the tunnel longitudinal direction, as shown in Fig. 1(a), cannot be available. In such a circumstance, the tunnel longitudinal performance can best be analyzed probabilistically. Here, a new framework for the probabilistic analysis of the tunnel longitudinal performance is proposed. This framework is outlined as follows:

Illustrative example

To demonstrate this new probabilistic framework for the tunnel longitudinal performance analysis, an example of a shield tunnel with a longitudinal length of 200 m is analyzed. The tunnel design parameters and soil parameters are assumed based upon typical designs of shield tunnels in Shanghai. In the probabilistic analysis of a geotechnical system, the input parameters are generally classified into two categories: uncertain parameters and certain (or deterministic) parameters. For illustration

Influence of the borehole density on the tunnel longitudinal performance analysis

It is expected that with the increase of the density of boreholes in the site investigation, the soil properties at the geotechnical site (of interest) can be more accurately characterized; and thus, the performance of the geotechnical system could be more accurately predicted. Although this concept is well acknowledged, few examples that illustrate this concept have been reported in literature (Qi et al., 2016). To illustrate this concept, a parametric study is conducted herein for studying

Concluding remarks

A probabilistic framework for the tunnel longitudinal performance analysis is proposed in this paper. Three components of this framework are: (1) use of the conditional random field theory to characterize the soil properties along the tunnel longitudinal direction, (2) variation of the tunnel performances (i.e., the structural safety and serviceability of the cross section) along the tunnel direction is analyzed with an advanced tunnel longitudinal performance model, and (3) tunnel longitudinal

Acknowledgments

This material is based upon the research partially supported by the Glenn Department of Civil Engineering and the Center for Risk Engineering & System Analytics (RESA) at Clemson University, the authors are however solely responsible for the results and opinions presented in this paper. The first author wishes to acknowledge the financial support provided by the Natural Science Foundation of China (No. 41702294). The second co-author and the last co-author also wish to acknowledge the financial

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