Probabilistic analysis of tunnel longitudinal performance based upon conditional random field simulation of soil properties
Graphical abstract
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
References (60)
Effects of spatial variability of soil properties on slope stability
Eng. Geol.
(2007)- et al.
Optimization of site exploration program for improved prediction of tunneling-induced ground settlement in clays
Comput. Geotech.
(2014) - et al.
Robust geotechnical design of shield-driven tunnels
Comput. Geotech.
(2014) - et al.
Improved analytical model for circumferential behavior of jointed shield tunnels considering the longitudinal differential settlement
Tunn. Undergr. Space Technol.
(2015) - et al.
Simplified procedure for finite element analysis of the longitudinal performance of shield tunnels considering spatial soil variability in longitudinal direction
Comput. Geotech.
(2015) - et al.
Resilience analysis of shield tunnel lining under extreme surcharge: characterization and field application
Tunn. Undergr. Space Technol.
(2016) - et al.
Flattening of jointed shield-driven tunnel induced by longitudinal differential settlements
Tunn. Undergr. Space Technol.
(2012) - et al.
Microzonation of Zeytinburnu region with respect to soil amplification: a case study
Eng. Geol.
(2006) Present status and technology of shield tunneling method in Japan
Tunnel. Undergr. Space Technol.
(2003)- et al.
Estimation of parameters in geotechnical back analysis – I. Maximum likelihood approach
Comput. Geotech.
(1996)
Uncertainty reduction and sampling efficiency in slope designs using 3D conditional random fields
Comput. Geotech.
Analysis of shearing effect on tunnel induced by load transfer along longitudinal direction
Tunn. Undergr. Space Technol.
Simulation of geologic uncertainty using coupled Markov chain
Eng. Geol.
Bayesian identification of random field model using indirect test data
Eng. Geol.
Probabilistic analysis of shield-driven tunnel in multiple strata considering stratigraphic uncertainty
Struct. Saf.
Bayesian approach for probabilistic characterization of sand friction angles
Eng. Geol.
Probabilistic geotechnical analysis of energy piles in granular soils
Eng. Geol.
Influence of multi-layered soil formation on shield tunnel lining behavior
Tunn. Undergr. Space Technol.
Tunnelling through a frequently changing and mixed ground: a case history in Singapore
Tunn. Undergr. Space Technol.
Analytical solutions for shallow tunnels in saturated ground
J. Eng. Mech.
Finding knees in bi-objective optimization
Bayesian approach for probabilistic site characterization using cone penetration tests
J. Geotech. Geoenviron. Eng.
Bayesian model comparison and selection of spatial correlation functions for soil parameters
Struct. Saf.
Characterization of random fields and their impact on the mechanics of geosystems at multiple scales
Int. J. Numer. Anal. Meth. Geomech.
Reducing shear strength uncertainties in clays by bivariate correlations
Can. Geotech. J.
Statistical characterization of random field parameters using frequentist and Bayesian approaches
Can. Geotech. J.
Spatial variability in soils: high resolution assessment with electrical needle probe
J. Geotech. Geoenviron. Eng.
Understanding knee points in bicriteria problems and their implications as preferred solution principles
Eng. Optim.
Error evaluation of three random-field generators
J. Eng. Mech.
Cited by (95)
The influence of spatial variation on the design of foundations of immersed tunnels: Advanced probabilistic analysis
2024, Tunnelling and Underground Space TechnologyProbabilistic evaluation for excavation-induced longitudinal responses of existing shield tunnel in spatially random soils
2024, Computers and GeotechnicsAnalysis of tunneling-induced ground movements in spatially variable soil under the influence of existing building
2024, Computers and GeotechnicsRandom analysis method for nonlinear interaction between shield tunnel and spatially variable soil
2024, Computers and Geotechnics