We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Research & business

View Profile

Publication details for Professor Ashraf Osman

Osman, A. S., Bolton, M. D. & Mair, R.J. (2006). Predicting 2D ground movements around tunnels in undrained clay. Géotechnique 56(9): 597-604.

Author(s) from Durham


A new analytical method is introduced for calculating
displacements due to tunnelling. This is conceived within
the framework of the bound theorems of plasticity, but
allowing for soil strain-hardening. The ground displacements
due to tunnelling are idealised by a simple displacement
mechanism of distributed shearing in the plane of
the tunnel cross-section. The tunnel support pressure
corresponding to a certain volume loss is calculated from
energy balances of the work dissipated in distributed
shear, the potential energy loss of soil flowing into the
tunnel, and the work done by this soil against the tunnel
support pressure. The calculations are carried out in
steps of small volume loss accompanying small reduction
in support pressure, after each of which the tunnel
geometry is updated. In this way, each reduced tunnel
support pressure is related to a complete ground displacement
field. A simplified closed-form solution is also
provided for the prediction of maximum surface ground
settlement for the particular case of deep tunnelling. This
closed-form solution is obtained by integrating the vertical
equilibrium equation on the tunnel centreline from
the tunnel crown up to the ground surface. These two
analytical solutions have been validated against five previously
published centrifuge tests.


Addenbrooke, T. I., Potts, D. M., & Puzrin, A. M. (1997). The
influence of pre-failure soil stiffness on the numerical analysis
of tunnel construction. Ge´otechnique 47, No. 3, 693–712.
Burland, J. B. (1989). ‘Small is beautiful’: the stiffness of soils at
small strains. Ninth Laurits Bjerrum Memorial Lecture. Can.
Geotech. J. 26, No. 4, 449–516.
Gunn, M. J. (1993). The prediction of surface settlement profiles
due to tunnelling. In Predictive soil mechanics (eds G. T.
Houlsby and A. N. Schofield), Proceedings of Wroth Memorial
Symposium, pp. 304–314. London: Thomas Telford.
Houlsby, G. T & Wroth, C. P. (1991). Variation of shear modulus
of a clay with pressure and overconsolidation ratio. Soils Found.
31, No. 3, 138–143.
Jardine, R. J., Symes, M. J. & Burland, J. B. (1984). The measurement
of soil stiffness in the triaxial apparatus. Ge´otechnique 34,
No. 3, 323–340.
Loganathan, N. & Poulos, H. G. (1998). Analytical prediction for
tunneling-induced ground movements in clays. ASCE J. Geotech.
Geoenviron. Engng 124, No. 9, 846–856.
Mair, R. J. (1979). Centrifugal modelling of tunnel construction in
soft clay. PhD thesis, University of Cambridge.
Mair, R. J. & Taylor, R. N. (1997). Bored tunnelling in urban
environment. Proc. 14th Int. Conf. Soil Mech. Found. Engng,
Hamburg 4, 2353–2385.
Mair, R. J., Taylor, R. N. & Bracegirdle, A. (1993). Subsurface
settlement profiles above tunnels in clays. Ge´otechnique 43, No.
2, 315–320.
Osman, A. S., Mair, R. J. & Bolton, M. D. (2006). On the
kinematics of 2D tunnel collapse in undrained clay. Ge´otechnique
56, No. 9, 585–595.
Peck, R. B. (1969). Deep excavations and tunnelling in soft ground.
Proc. 7th Int. Conf. Soil Mech., Mexico City 3, 225–290.
Rankin, W. J. (1988). Ground movements resulting from urban
tunnelling. Proceedings of the conference on engineering geology
of underground movements, Nottingham, pp. 79–92.
Sagaseta, C. (1987). Analysis of undrained soil deformation due to
ground loss. Ge´otechnique 37, No. 3, 301–320.
Seneviratne, H. N. (1979). Deformations and pore pressure variations
around shallow tunnels in soft clay. PhD thesis, University
of Cambridge.
Sketchley, C. J. (1973). Behaviour of kaolin in plane-strain. PhD
thesis, University of Cambridge.
Verruijt, A. & Booker, J. R. (1996). Surface settlements due to
deformation of a tunnel in an elastic half plane. Ge´otechnique
46, No. 6, 753–756.