Elsevier

Computers and Geotechnics

Volume 50, May 2013, Pages 41-54
Computers and Geotechnics

Stability of dual circular tunnels in cohesive-frictional soil subjected to surcharge loading

https://doi.org/10.1016/j.compgeo.2012.12.008Get rights and content

Abstract

The stability of dual circular tunnels in cohesive-frictional soils subjected to surcharge loading has been investigated theoretically and numerically assuming plane strain conditions. Despite the importance of this problem, previous research on the subject is very limited compared to that on single tunnels. At present, no generally accepted design or analysis method is available to evaluate the stability of dual circular tunnels/openings in cohesive-frictional soils. In the design stage, it is important to consider the interaction effects of dual circular tunnels. Unlike the case of a single tunnel, the centre-to-centre distance appears as a new problem parameter and plays a key role in tunnel stability. In this study, continuous loading is applied to the ground surface, and a smooth interface condition is modelled. For a series of tunnel diameter-to-depth ratios and material properties, rigorous lower- and upper-bound solutions for the ultimate surcharge loading are obtained by applying finite element limit analysis techniques. For practical suitability, the results are presented in the form of dimensionless stability charts and a table with the actual tunnel stability numbers closely bracketed from above and below. As an additional check on the solutions, upper-bound rigid-block mechanisms have been developed, and the predicted collapse loads from these are compared with those from finite element limit analysis. Finally, a discussion is presented regarding the location of the critical tunnel spacing between dual circular tunnels where interaction no longer occurs.

Introduction

Accurately assessing the stability of circular tunnels, pipelines and disused mine workings in cohesive-frictional soils is an important task due to the ubiquitous construction of buildings and tunnels in urban areas. The design of tunnels for roads and railways often utilises separate tunnels to carry traffic in opposite directions. In addition, in the expansion of pipelines, underground openings and transportation systems, new tunnels/openings have often been constructed near existing tunnels/openings. In practice, it is often observed that the construction of dual circular tunnels is a better option than a single large circular tunnel, due to the soil characteristics and geological conditions, as well as practical and economic concerns. Because many tunnels and pipelines already exist at deep levels, new tunnels and openings are now often constructed at shallow depths. In these cases, it is important to know how the stability and interaction effects of these tunnels/openings are affected by surcharge loading. Because no generally accepted design or analysis method is currently available for this problem, the goal of this study is to equip design engineers with simple design tools to determine the stability of dual circular tunnels in cohesive-frictional soils subjected to surcharge loading. Previously, the authors have investigated the stability of a circular tunnel in cohesive-frictional soil subjected to surcharge loading [1]. Compared to the case of a single circular tunnel, the effect of centre-to-centre distance is naturally a key factor in the behaviour of dual circular tunnels. In addition, it is assumed that the problem of interaction between dual tunnels is complex, due to the geometry of the tunnels and the properties of the lining and surrounding soils. Drained loading conditions are considered, and a continuous load is applied to the ground surface. For a series of tunnel diameter-to-depth ratios and material properties, rigorous lower- and upper-bound solutions for the ultimate surcharge loading are found by applying recently developed finite element limit analysis techniques [2], [3]. The results are presented as dimensionless stability charts for use by practising engineers, and the actual tunnel stability numbers closely bracket the true solution from above and below. As an additional check on the accuracy of the results, a variety of upper-bound rigid-block mechanisms are developed, and the solutions from these are compared with those from finite element limit analysis.

The stability of circular tunnels has been extensively studied at Cambridge since the 1970s; see, for example, the work reported by Cairncross [4], Atkinson and Cairncross [5], Mair [6], Seneviratne [7] and Davis et al. [8]. Before the 1990s, most published research on tunnel stability focused on the undrained stability of circular tunnels in clay. Later, theoretical solutions for circular tunnel problems under drained conditions were determined by Muhlhaus [9] and by Leca and Dormieux [10]. All of the theoretical studies mentioned so far have investigated the stability of single tunnels only. It would appear that there is very little information available on the interaction effects between dual tunnels. With respect to the research on dual tunnels, a series of centrifuge model tests and numerical simulations of unlined single and parallel tunnels was conducted under plane strain conditions to investigate tunnel stability, arching effects on the soil mass surrounding tunnels, ground movements and collapse mechanisms induced by tunnelling in clayey soil [11], [12]. Chehade and Shahrour [13] presented an analysis of the interaction between twin tunnels with a particular emphasis on the optimisation of both the relative positions of the twin tunnels and the construction procedure, using the finite element program PLAXIS. Osman [14] investigated the stability number of twin tunnels in an undrained clay layer using upper-bound calculations. He presented a new methodology for calculating an upper bound for twin tunnels based on the superposition of the plastic deformation mechanisms of each individual tunnel. Recently, Mirhabibi and Soroush [15] investigated the effect of surface buildings on the ground settlement of twin tunnels, using field data from the Shiraz metro line 1 and the ABAQUS finite element code. The interaction between buildings and the construction of twin tunnels has been studied less. The studies that have been performed on this subject have focused on developing a feasible methodology for estimating, during preliminary design phases, the settlement of surface buildings due to tunnelling.

The application of finite element limit analysis to the undrained stability of shallow tunnels was first considered by Sloan and Assadi [16], who investigated the case of a plane-strain circular tunnel in a cohesive soil whose shear strength varied linearly with depth using linear programming techniques. Later, Lyamin and Sloan [17] considered the stability of a plane-strain circular tunnel in a cohesive-frictional soil using a more efficient nonlinear programming technique. This method can accommodate large numbers of finite elements, resulting in very accurate solutions. To clarify the effects of interaction between tunnels, Wilson et al. [18] investigated the undrained stability of dual square tunnels using finite element limit analysis and upper-bound rigid-block methods. Stability charts were generated for a variety of tunnel depths, material properties and inter-shaft distances. Recently, Yamamoto et al. [19] studied the stability of dual circular tunnels in cohesive-frictional soils subjected to surcharge loading. Upper-bound rigid-block mechanisms were also developed, and the computed surcharge loads were compared with the results of finite element limit analysis. This paper presents the extension of this research in detail.

Section snippets

Problem description

The problem description is given in Fig. 1. The ground is modelled as a uniform Mohr–Coulomb material with cohesion c, friction angle and unit weight γ, assuming drained loading conditions. The dual circular tunnels are of diameter D, depth H, and centre-to-centre distance S, and deformation takes place under plane strain. The stability of the dual circular tunnels shown in Fig. 1 is described conveniently by the dimensionless load parameter σs/c′, which is a function of ϕ′, γD/c′, H/D and S/D,

Finite element limit analysis

Finite element limit analysis utilises the power of the lower- and upper-bound theorems of plasticity theory, coupled with finite elements, to provide rigorous bounds on collapse loads from both below and above. The underlying limit theorems assume small deformations and a perfectly plastic material with an associated flow rule. The use of a finite element discretisation of the soil, combined with mathematical optimisation to maximise the lower bound and minimise the upper bound, makes it

Upper-bound rigid-block analysis

Semi-analytical rigid-block methods were used to find upper-bound solutions for the cases considered. These provided an additional check on the limit analysis results. Three types of rigid-block mechanisms were constructed, as shown in Fig. 3. In this figure, Ai is the area of the rigid block i; Vi is the kinematically admissible velocity of block i; Vij is the velocity jump along the discontinuity between blocks i and j; lij is the distance between points i and j; w is the width of the ground

Results and discussion

Fig. 4, Fig. 5, Fig. 6, Fig. 7 show the plastic multiplier field, power dissipations(velocity plots) and rigid-block mechanisms for various cases. Note that velocity plot is shown only in Figs. 5b and 8b to indicate a better appreciation for the velocity distribution, instead of the power dissipation. The plastic multiplier field and power dissipation (velocity plot) are obtained from the finite element lower-bound and upper-bound analyses, and the optimum rigid-block mechanism is obtained from

Conclusions

The stability of plane strain dual circular tunnels in a cohesive-frictional soil subjected to surcharge loading has been investigated using upper-bound rigid-block analysis and finite element limit analysis. The results of these analyses have been presented in the form of dimensionless stability charts and a table. The lower and upper bounds obtained using finite element limit analysis bracket the actual ultimate surcharge load quite accurately for soils with moderate frictional angles. As an

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