Ground Displacements and Stresses around Single and Twin Tunnels using Analytical and Numerical Approaches

PhD;2023;Civil Engineering

Significant emphasis is given nowadays on exploring underground space- in the form of
tunnels- for (i) fast commuting in urban areas, (ii) connectivity to remote areas under different
weather conditions, (iii) military and strategical advantages, (iv) housing missiles, nuclear
facilities, oil storage facilities and research observatories, (v) water supply and sewage drains.
To determine the response of tunnels, geotechnical engineers often utilize several analytical
and numerical based approaches. Extensive work seems to have been carried out in literature
by using different numerical tools, especially, the finite elements (FE), to study the response
of ground to shallow tunnelling. Similarly, numerous analytical works have been reported on
tunnels in predicting the stress and displacement response. The ground response, especially the
ground surface vertical settlement, becomes critically important to geotechnical, structural and
tunnelling engineers. In the present thesis, it has been attempted to apply analytical and finite
element (FE) based approaches with an objective of predicting ground displacements and
stresses due to laying of single and twin tunnels in soft ground. The objective of this research
is to solve single and twin tunnel problems incorporating the presence of pseudo-static
earthquake body forces. It is aimed to (i) develop new analytical solutions enabling to
incorporate ground volume loss (GVL) and buoyant force problems for tunnels in weightless
and ponderable (weighty) media, and to (ii) use the FE method to develop design charts for
ground surface settlement for single and twin lined (supported) and unlined (unsupported)
tunnels. The plane strain formulation, considering the tunnel as very long as compared to its
cross-section, helps to reduce the difficulties of the modelling of the problem since the threedimensional analysis often becomes quite complicated. The study deals with planar tunnelling
problems in linearly elastic and linearly elastic perfect plastic medium. For developing the
analytical based solutions, computer codes have been written in MATLAB, while for the numerical FE based models, the commercially available codes OPTUM G2 and PLAXIS 2D
have been employed.
In the initial section of the work, the analytical solutions based on the Airy’s stress function
method (ASFM) and complex variable method (CVM) have been determined. The ASFM has
been used to obtain solution for a non-uniformly deforming lined circular tunnel in an elastic
medium. The non-uniform radial displacement around the tunnel periphery for a given GVL
was modelled by using the Gaussian distribution function. To simplify the analytical
formulation, the soil-liner interface was assumed to be frictionless. The horizontal and vertical
ground displacements (u, v), the radial & circumferential stresses (σr and σθ ) in soil media, and
the axial forces and the bending moments in the liner were computed. The results were
thoroughly compared and validated with the FE based solutions and with field measurements
from various recorded tunnelling case-studies.
The CVM has been applied to obtain analytical solutions for an unlined single circular
tunnel deforming non-uniformly (i) in a weightless medium, and (ii) in a ponderable medium
without and with horizontal earthquake body forces. The effects of various parameters, namely,
pseudo-static earthquake acceleration (αh) in horizontal direction, ground volume loss (���),
cover to diameter ratio, the ratio (wt) of weight of liner to weight of soil excavated on ground
displacements and stresses have been examined. For these analytical solutions, necessary analytical and numerical solutions presented in this thesis will be useful for predicting ground
displacements and stresses for single and twin tunnel problems.
validation has been provided by comparing the results with that obtained on the basis of the FE
based analyses. It was observed that (i) the shallow tunnels generally cause more ground
settlements as compared to deeper tunnels, (ii) a higher magnitude of GVL leads to greater
ground surface settlements, (iii) heave gets generated on unloading (excavation) of the tunnel
cavity for lower magnitude of wt, and (iv) the pseudo-static earthquake horizontal body forces
cause the deformations and stresses to become asymmetric about the tunnel’s centreline and it
leads to significant changes in horizontal displacement patterns.