Beam–spring structural analysis for the design of a tunnel pre-reinforcement support system
Highlights
► We suggest a beam–spring structural analysis model to optimize the design parameters. ► A simple but robust finite element program code is developed based on the structural model. ► The developed code is verified with commercial software and three case studies are carried out. ► The developed structural model and analysis system provides consistent design criteria. ► The developed code can be used for quantity estimation for the umbrella arching method.
Introduction
The construction of a large underground space is risky because of the difficulties in predicting arching effects and estimating various underground parameters. Multi-section excavation and short advance length, which minimize the sudden load transfer due to excavation, are conventionally used to stabilize tunnel faces. To minimize the seepage force acting on the tunnel face, groundwater ahead of it is often drained through horizontal probe core drilling. Moreover, auxiliary pre-reinforcement support systems such as waterproof grouting and the reinforced protective umbrella method (RPUM) have been used to strengthen the stiffness of the ground and for waterproofing ahead of the tunnel face. Recently, pre-reinforcement support systems have been combined with the conventional excavation method (or New Austrian Tunneling Method, NATM) in stabilizing tunnel faces.
Researchers have suggested various techniques for auxiliary support systems, such as the RPUM, which has the advantage of combining a modern fore-poling system with the grouting injection method [1]. This method is used in the pre-excavation design of projects such as small-section tunneling through weathered or crashed zones and the construction of large underground spaces. Furthermore, to decrease the risk of a collapse or failure in large excavation caverns and shallow tunnels, researchers have developed various techniques and construction methods. Among them is a tunneling method involving an advanced reinforcement system in which a double steel pipe is used for waterproofing and a urethane injection is used for reinforcement. Another is the Trevi jet method, which involves the use of cement grout in constructing an arch-shell structure around the tunnel crown. There is also steel-pipe-reinforced multistep grouting, in which a beam arch is constructed around the tunnel crown with large diameter steel pipes and multilayer cement grouting. This auxiliary support system has been given various names, e.g., “pipe fore-pole umbrella” [2], “umbrella arch method” [3], “long-span steel pipe fore-poling method” [4], and “steel pipe canopy” [5]. In our study, we called it the steel-pipe-reinforced umbrella arching method (SPRUAM). Considering that the modern NATM tunneling process is mechanized and involves the use of large machines such as jumbo drills, shotcrete spraying machines, and loading and transport equipment, an auxiliary pre-reinforcement support system such as the SPRUAM is needed to secure sufficient space for the operation of the machines.
Various researchers have mathematically modeled the structural stability of tunnels. Zienkiewicz and Pande [6] used a multilaminate model to derive a constitutive equation. The multilaminate model became the foundation of the homogenization constitutive equation derived by Bernaud [7] for rock-bolted ground; this model can be used to simulate the anisotropic elastic behavior of a pre-reinforced zone. Moreover, Bae et al. [8] used the homogenization technique to simulate the SPRUAM.
In recent years, predefined structural elements embedded in commercial software have been used to model each component of a reinforcement system. This approach has been facilitated by the evolution of computers and the development of special finite element method (FEM) software for underground reinforcement. The model used for assessing the SPRUAM was developed many years ago. Kotake et al. [9] considered a reinforced zone as a shell element, and later, beam elements were used to simulate the inserted pipes of the shell element to model the reinforced zone. In the simulation, the weighted Young's modulus of the steel pipes – i.e., the Young's modulus of the pipes weighted by an area ratio – was used. Furthermore, Song et al. [10] carried out a 3D finite element (FE) analysis of the effect of the pipe length, installation angle, overlap length, and particularly the tunnel size and ground condition. However, this analytical approach significantly depends on the intuition and experience of the designer and the results also depend on the size and shape of the FEs and the boundary conditions. Moreover, the processes involved require considerable time and manual labor.
Although the SPRUAM significantly reduces the construction time and cost, the design guidelines have not been clearly defined or standardized and its use mostly depends on the judgment of engineers and case histories. Hence, our study proposes a new analytical technique that can be used to evaluate the stability of the steel pipes. With a few reasonable assumptions, we derived a simplified beam-spring structural analysis model and developed FE software that can be used to calculate the bending moments and shear forces of the steel pipe. We also verified the reliability of the software by comparing its output with those of commercially available structural analysis software.
Section snippets
Monitoring data of the SPRUAM
Fig. 1 shows the bending moment data of the Maiko tunnel in Kobe, Japan [11]. The bending moment was measured at 1 m intervals and a, b, c, and d denote the bending moments in the unsupported section. It can be observed that the behavior of the bending moment is similar to that of a beam simply supported on two pivots and subjected to a distributed load—i.e., with one support ahead of the tunnel face and the other beyond the unsupported section. The location of the support beyond the unsupported
Considerations of design analysis
Using Eq. (1), we performed a preliminary stability assessment of the steel pipe by considering the core support behind the tunnel face.
To estimate the earth pressure (Pv) acting on the steel pipe, the loosening earth pressure (W) was estimated. To do this, we adopted Terzaghi's loosening earth pressure model for a tunnel in shallow and weak ground. It must be noted, however, that in a case where the overburden pressure is high, Terzaghi's loosening earth pressure model cannot be used to
Case studies in representative grounds
Case studies on the SPRUAM were conducted in three ground conditions representative of those in which the reinforcement method is generally used, namely, weathered rock, highly weathered rock, and weathered soil. The material properties of the grounds and the design variables are presented in Table 7.
The tunnel section, support characteristics, and longitudinal section of the steel pipes were identical for the three cases. The depths of the tunnels varied from 10 m to 40 m (i.e., 10, 20, 30, and
Conclusions
With a few reasonable assumptions, our study derived a beam-spring structural analysis model for the quantitative design of the steel-pipe-reinforced umbrella arching method (SPRUAM). The analysis of the model showed good agreement with field observations and was thus verified as being reliable for simulating the behavior of the shear forces and bending moments of the SPRUAM steel pipes. On the basis of the derived model, we also developed and verified simplified FE analysis software that can
Acknowledgments
This work was supported by INHA UNIVERSITY Research Grant (INHA-46436) and by the Jijoong Construction Company.
References (18)
Design and construction of mountain tunnels in Japan
Tunnel Underground Space Technol
(2003)- et al.
Optimization of a pre-improvement support system for large underground excavation.
Tunnel Underground Space Technol
(2006) - et al.
Evaluation of the load on shield tunnel lining in gravel.
Tunnel Underground Space Technol
(2003) Analysis of structural interaction in tunnels using the convergence–confinement approach
Tunnel Underground Space Technol
(2003)- Barisone G, Pigorini B, Pelizza S. Umbrella arch method for tunnelling in difficult conditions-analysis of Italian...
- Hoek E. Numerical modelling for shallow tunnels in weak rock. 2004. Available at:...
- Kim CY, Kim KY, Hong SW, Bae GJ, Shin HS. Interpretation of field measurements and numerical analyses on pipe umbrella...
- Gibbs PW, Lowrie J, Kieffer DS, McQueen L. M5 east—design of a shallow soft ground shotcrete motorway tunnel. In:...
- et al.
Time-dependent multilaminate model of rocks—a numerical study of deformation and failure of rock masses
Int J Numer Anal Methods Geomech
(1997)
Cited by (44)
Insights into the ground response characteristics of shallow tunnels with large cross-section using different pre-supports
2024, International Journal of Rock Mechanics and Mining SciencesStudy on mechanical characteristics of pipe umbrella support in shallow buried tunnels
2024, Tunnelling and Underground Space TechnologyStudy on the whole process application of advanced grouting pipe shed support under urban complex stratum conditions
2023, Geomechanics for Energy and the EnvironmentA comparative numerical analysis of design variation plans for a shallow tunnel in very soft ground after a sudden accident
2022, Engineering Failure AnalysisCitation Excerpt :As a new design philosophy, ground reinforcement, shotcrete and bolts (both on the tunnel face and at the crown) are often adopted in shallow tunnels to control ground movement [5–11]. These pre-reinforcement support systems combined with the conventional excavation method, e.g., New Austrian Tunneling Method (NATM) [12–15], are usually resorted to ensure the tunnel safety [11,16–20]. The forms of support systems for shallow tunneling are various, i.e., steel ribs [4,21,22], umbrella arch method [23,24], pipe fore-poling method [25–27].
Effect of pipe characteristics in umbrella arch method on controlling tunneling-induced settlements in soft grounds
2020, Journal of Rock Mechanics and Geotechnical EngineeringCitation Excerpt :They later developed a second–order equation for distributed load through a semi-analytical solution in which, it is assumed, the beam lays on the elastic foundation (Oke et al., 2016). Song et al. (2013) developed a finite element software package to evaluate various conditions and variables of the UAM. The developed model was instrumental in estimating the quantity of forepoling steel pipes needed for the UAM at an early stage of the tunnel design protocol.