Advanced numerical modelling of grey cast iron linings

Student: Agustín Ruiz López

Supervisors: Dr Aikaterini Tsiampousi and Dr. Jamie Standing

Start date: 1 October 2017

  1. 1.    Background to research

The London Underground network experienced great development during the 19th century and early 20th century with the construction of an extensive network of deep tunnels built with grey cast iron (GCI) linings (Craig and Muir Wood, 1978). As a consequence, it is not uncommon to encounter tunnels of this kind in the vicinity of proposed new underground structures such as excavations, deep foundations or tunnels. Due to the segmental nature of GCI tunnels, which comprise a succession of rings and segments bolted together, the prediction of movements and changes in structural forces caused by new construction involves some judgement of the tunnel stiffness. This can be significantly affected by the presence of the tunnel joints. Industry’s most common practice is to assess the tunnel forces by means of closed-form solutions assuming a continuous ring with either full bending stiffness (‘stiff ring’) or a reduced bending stiffness (‘flexible ring’) obtained from the reduction formula proposed by Muir Wood (1975).

The validity of the industry methods mentioned above has been recently assessed experimentally. A comprehensive laboratory investigation using a half-scale bolted GCI ring was conducted at Imperial College London between 2010 and 2014. The laboratory programme involved series of tests under distortion levels within serviceability limits (Yu et al., 2017) and large distortion tests until failure was reached (Afshan et al., 2017). The investigation gave insight into the influence of joints in the ring response and allowed for comparison between the response of the GCI ring and that of a continuous ring. Recommendations regarding the use of full or reduced bending stiffness were provided. The experimental investigation was a milestone in the understanding of GCI linings, however, due to practical limitations of laboratory testing the boundary conditions adopted were not completely representative of the tunnels in-situ condition. In order to confirm the experimental findings, further research should be conducted adopting more realistic boundary conditions.

There are situations where a numerical analysis, such as the finite element method, is required to understand better the interaction between the construction-induced ground movements and the existing tunnel. Numerical analysis allows the inherent complexities of the problem including the segmental nature of the lining to be modelled. Even though the lining is typically modelled with structural elements (e.g. beams or shells), it is possible to represent the tunnel joints with springs or by a small structural element. Either way, the nonlinear behaviour of the joint must be reproduced with an adequate constitutive relationship. In the case of longitudinal joints, several moment-rotation relationships (Janssen, 1983, Blom, 2002) have been proposed for concrete linings and the model suggested by Potts and Zdravkovic (2001) has been adopted for GCI joints, however, none of these models account for the presence of bolts, which potentially have a major effect on the joint behaviour.


  1. 2.    Research objectives

This PhD project aims to improve our understanding of segmental GCI linings by means of finite element analysis, using the program ICFEP (Potts and Zdravkovic, 1999). Particularly, the focus will be on developing tools for the engineering assessment of GCI tunnels, contributing to the enhancement of simple methods as well as developing advanced numerical analysis. Consequently, the project intends to fulfil the following objectives:

  • To develop an advanced 3D model of the segmental GCI ring and to validate it against the experimental investigation reported by Yu et al. (2017) and Afshan et al. (2017).
  • Once validated, the 3D model will be used to produce guidelines for practitioners in their assessment of GCI linings subjected to distortion and to characterize the rotational behaviour of bolted GCI joints under compressive hoop force.
  • To develop a joint model that accounts for the presence of the bolts and to implement it in ICFEP.
  • To investigate the influence of the tunnel joint model in geotechnical boundary value problems.
  • To integrate the newly developed joint model into a numerical scheme with the bedded-beam-spring method in order to produce a practical tool to estimate lining forces in GCI tunnels.


  1. 3.    References

Afshan, S., Yu, J., Standing, J., Vollum, R. & Potts, D. 2017. Ultimate capacity of a segmental grey cast iron tunnel lining ring subjected to large deformations. Tunnelling and Underground Space Technology, 64: 74-84.

Blom, C. 2002. Design philosophy of segmented linings for tunnels in soft soils. PhD Thesis, Delft University of Technology, the Netherlands.

Craig, R. & Muir Wood, A. 1978. A review of tunnel lining practice in the United Kingdom.

Janssen, P. 1983. Tragverhalten von Tunnelausbauten mit Gelenktübbings. PhD Thesis, Technische Universität Carolo-Wilhelmina zu Braunschweig, Braunschweig.

Muir Wood, A. 1975. The circular tunnel in elastic ground. Geotechnique, 25(1): 115-127.

Potts, D. M. & Zdravkovic, L. 1999. Finite element analysis in geotechnical engineering: theory, London, Thomas Telford.

Potts, D. M. & Zdravkovic, L. 2001. Finite element analysis in geotechnical engineering: application, London, Thomas Telford.

Yu, J., Standing, J., Vollum, R., Potts, D. & Burland, J. 2017. Experimental investigations of bolted segmental grey cast iron lining behaviour. Tunnelling and Underground Space Technology, 61: 161-178.