GROUND SUBSIDENCE DUE TO SHALLOW TUNNELING IN SOFT GROUND

Abstract

Construction of metro underground transportation network forms part of the basic infrastructure development which becomes essential in large metropolitan cities for dealing with the growing problem of mass rapid transit. Metro underground tunnels are built usually with a low overburden and close to the surface and beneath populated areas, thereby aggrandizing the consequences of failure. Litigations related to structural damage caused by the ground subsidence and the claims for a just compensation have become a common problem associated with such metro underground projects. Assessment of the influence of tunneling on above ground structures has therefore become a very important and a crucial issue in metro cities. Excavation of shallow bored tunnels invariably induces some amount of ground movement which is reflected at the ground surface in the form of a settlement trough. Adjacent structures within this zone of subsidence experience some deformation; in some cases even resulting in distress in these structures The worldwide use of various tunneling techniques has generated an increased activity in the investigation of tunneling induced ground movements. This includes settlement damageto both the surface and subsurface structures which exist adjacent and in close proximity to the tunnel and it is the assessment of such damage that warrants the need for more accurate prediction of tunneling induced ground movements. In this present study, the problem of ground subsidence due to shallow tunneling and associated damage to surface structures has been thoroughly investigated. Emphasis has been laid on simulation of tunnel excavation process, placement of lining, soil-structure interaction and soil-lining interaction effects. Empirically, the transverse surface settlement trough immediately following the tunnel construction is well described by a Gaussian distribution curve or Error iii function (Schmidt, 1969; Peck, 1969). The longitudinal settlement trough can also be represented by a cumulative probability curve, as proposed by Attewell and Woodman (1982). Empirical rules for prediction of ground movements due to tunneling can lead to reasonably good estimation of ground subsidence profiles but only in greenfield condition, in situations with similar past experiences and with average ground conditions. However, presence of surface structures modifies the subsidence trough and an appropriate soil-tunnel-structure interaction analysis becomes necessary for a realistic assessment. Numerical solutions based on threedimensional Boundary Element Method (Hisatake et al., 1989), Artificial Neural Network (ANN) (Kim et al., 1999), Discrete Element Method (DEM) and Finite Difference Method (FDM) (Alejano et al., 1999) have been employed for the prediction of ground surface subsidence prediction due to shallow tunnel excavation. However, the most popular amongst the numerical approaches is the Finite Element Method as it can deal with factors like soil non-linearity, anisotropy, dilatancy, excavation simulation and soil-structure interaction etc. In addition, finite element method yields results both at the boundary as well as at any point within the domain making ita more versatile tool for analyzing such a problem ofground movement due to shallow tunneling. In the present study, a detailed investigation has been carried out for predicting the ground response due to tunneling. This includes: i) Ground subsidence analysis has been carried out for one real time tunneling project by conventional Deconfinement Modeling Method, considering the soil surrounding the tunnel to behave in a linearly elastic manner. Three new approaches namely, Concentric Convergence Method, Tunnel Invert Method and the Elliptical Convergence Method based on the prescribed displacement approach of linear elastic finite element analysis have been suggested for prediction ofground subsidence due to tunneling. IV ii) An exhaustive parametric study has been conducted for prediction of ground subsidence profile considering linear elastic soil behavior and analyze the effect of: elastic properties of soil, tunnel depth, volume loss, lateral distance of surface structure from the tunnel, relative stiffness between structure and raft and that between raft and the soil and also the presence of multiple surface structures. The effect of non-homogeneity of soil and the interference due to twin tunneling has also been investigated. iii) Within the framework of linear elastic finite element analysis, a full 3-D soiltunnel- surface structure interaction analysis has been carried out for predicting the tunneling induced ground subsidence. A modified stiffness approach for 2-D idealization of an otherwise 3-D soil-structure interaction problem has been suggested for the ease of design engineers. iv) The problem of prediction of ground subsidence due to excavation of tunnel has also been dealt with by considering the elasto-plastic material behavior. The Drucker-Prager yield criterion with non-associative flow theory of plasticity has been adopted. A formulation has been developed for simulation of excavation within the framework of elasto-plastic analysis, which has then been applied to three real time tunneling projects. Parametric studies have been carried out to have an insight into the effect of : elastic properties, dilatancy angle of soil and diameter and depth of tunnel on the subsidence trough. Development of the zone of yielding at various stages of deconfinement has also been investigated. Attempt has been made to study the behavior of soil masswith respect to stresses developed for the case of a single tunnel in green field condition as well as for twin tunnels with surface structure. v) To the best of knowledge of this author, General 2-D Contact Analysis has been applied for the first time to analyze the soil-tunnel lining interaction problem. Augmented Lagrangian approach with interfacial friction has been employed for the 2-D contact analysis by treating the lining as a rigid target surface and the excavated boundary as a deformable contact surface. Due to the intrinsic similarity between friction and classical elasto-plasticity, the constitutive model for friction has been constructed following the same formalism. The friction forces have been assumed to follow the Coulomb law, with a slip criterion treated in the context of a standard return mapping algorithm. vi) Tunneling induced subsidence problem is, in essence, a three dimensional in nature. However, enormous computational resources and time are required for a full 3-D elasto-plastic analysis of the problem. Therefore, literature with examples of real time tunneling projects treated as a 3-D approximation is scant. In this study, an attempt has been made to conduct a full 3-D elastoplastic analysis with step-by-step simulation of excavation and the sequence of construction applied to a real time tunneling project. Step-by-step advancement of tunnel heading in the forward direction followed by simulation ofgap closure and finally sequential placement of rigid lining have been simulated. It became therefore possible to predict transverse as well as the longitudinal subsidence troughs for various stages of excavation of the tunnel. The aspect of development of stresses in the soil mass with the advancement oftunnel heading has also been thoroughly investigated. vii) Generally, the consequence ofground subsidence due to shallow tunneling is the resulting damage to adjacent surface structures. Therefore, damage study has been conducted taking into consideration linearity as well as non-linearity ofsurface framed structure and the soil mass. For a heavily built up area, a number of surface structures are likely to be present near the tunnel. As such various cases, namely, (i) a single centrally placed structure, (ii) one adjacent vi structure on one side of a centrally placed structure and (iii) structures on either side of a centrally placed heavy structure have been considered in the analysis. Various configurations of adjacent structures have been adopted in order to study the effect of structural stiffness and loads on the degree of structural damage due to tunneling. Investigations based on linear elastic finite element analysis conclude thati) Conventional linear elastic finite element analysis based on Deconfinement Modeling Approach predicts wider and shallower ground subsidence trough. Maximum subsidence above the tunnel crown has been under predicted by 47% for a real time tunneling project like the BART tunneling project in San Francisco, USA. ii) All the three methods based on prescribed displacement approach of linear elastic finite element analysis, which have been suggested here namely, Concentric Convergence Method, Tunnel Invert Method and the Elliptical Convergence Method improve the prediction of ground subsidence. Though the Elliptical Convergence Method over predicts maximum subsidence by about 50%, the shape of the settlement trough is very well predicted when compared with the observed one. iii) Various parametric studies suggest that presence of surface structures modifies the ground subsidence trough significantly. Moreover, two closely spaced tunnels display interference between them, the maximum stress concentration at the tunnel opening being about four times. iv) 3-D linear elastic analysis reveals that for a surface structure, structural members which have the largest strain energy before tunneling need not continue to possess the largest strain energy after tunneling. The increase in vi 1 maximum strain energy due to excavation of tunnel in the structural members may be as high as 800 percent, v) Modified Stiffness Approach suggested in this study is essentially a 2-D analysis, which can be employed satisfactorily for an otherwise 3-D soilstructure interaction problem. Structural response in terms of the kinematic variables and the structural member forces derived from Modified Stiffness Approach match reasonably well with those from a full 3-D analysis. It is, however, well known that soil mass behaves linear elastically only up to a very small stress range beyond which it enters into the plastic state. Therefore, all the above mentioned conclusions do not preclude this basic inherent limitation of the assumption of linear elastic material behavior. The formulation proposed for the simulation of excavation by elasto-plastic finite element analysis with non-hardening Drucker-Prager yield criterion and a non-associative flow rule predicts the subsidence profile reasonably well. This has been amply clear from the study of three real time tunneling cases namely, BART Subway System, San Francisco, USA, Frankfurt Subway System, Germany and Thunder Bay Tunnel, Ontario, Canada. The important facts brought out by the elasto-plastic analysis include: i) For an unlined tunnel, smaller the diameter, shallower and flatter would be the subsidence trough. Higher dilatancy angle of soil leads to higher volume increase during shearing which results in lesser subsidence. When dilatancy angle is reduced from 33° to 0°, the maximum subsidence shows an increase by as much as 46%. ii) Elasto-plastic finite element analysis leads to location of yield zones around the tunnel. Yielding starts initially near the springing points and then gradually spreads to tunnel invert and tunnel crown with increasing deconfinement. Extent ofthe plastic zone around the tunnel periphery is a function of friction angle of soil. viii iii) Elasto-plastic analysis does not show a very high stress concentration around the tunnel periphery vis-a-vis the elastic analysis. For twin tunnels excavated close to one another, stress relaxation up to 26 percent can instead be observed at the periphery of the second tunnel after the excavation of both the tunnels is accomplished. iv) General contact analysis with rigid tunnel lining as the target surface and the deformable excavated boundary as the contact surface further improves the prediction ofground subsidence. a) With sticking contact analysis, the maximum subsidence is over predicted by only 0.3 percent and the overall subsidence profile also matches very well with the observed one. b) Ground subsidence decreases with an increase in the lining surface roughness. Coefficient of friction at the interface of soil and the tunnel lining is an important parameter for obtaining a realistic behavior. c) In contact analysis, unsymmetrical stiffness matrix solver is more efficient than a symmetrical one, especially at advance stages of deconfinement. d) General contact analysis yields normal and shear stresses along the soil-lining interface, which is otherwise not possible from conventional analysis without taking into consideration the soil-lining interaction. These values of normal and shear stresses may be used for tunnel support system design. v) A fully 3-D elasto-plastic analysis with simulation of step-by-step excavation and the sequence of construction can predict ground subsidence pretty well. For the BART Subway System, the maximum subsidence predicted is 2.2 percent lower than the observed maximum and the lateral subsidence profile also matches significantly within the limits of engineering accuracy. IX Longitudinal subsidence trough can be obtained at any stage of advancement of the excavated tunnel face from such an analysis only. vi) It is essential to consider the elasto-plastic behavior of both the structure and the supporting soil mass if the severity of damage to the surface structures is to be made in a realistic manner. vii) A lightweight and flexible structure adjacent to a heavy structure may suffer more damage due to tunnel excavation and as such may need attention while performing damage studies. viii) For prediction of the severity of structural damage, the Damage Classification System proposed by Burland et al. (1977) and quantified by Boscardin and Cording (1989) in terms of range of values of limiting tensile strain are extremely useful. Further generalization of building damage categories in terms of limiting horizontal strain and deflection ratio suggested by Burland (1995) and Mair (1996) respectively for a range of values of L/H ratio are recommended for use in estimating the severity of structural damage.