Finite Element Modelling Software Package

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DESIGN STUDY REPORT

INTRODUCTION
Geotechnical considerations of tunnel construction project will be evaluated here. This tunnel is 4 km
long and will be an extension to London metro tunnel. Due to special characteristics of soil profile in
London determination of effects due to tunnelling is a critical task. This tunnel will be modelled at
three cross sections as shown in Figure 1. Sections A and C are mid point of first and second 2 km
sections respectively while section B is taken across a historical area where 30 m deep piles are in
vicinity.
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20 m
4 km
30 m
Section C Section B Section A
Existing Ground
Figure 1 - Cross-section of proposed tunnel
Figure 2 - Cross-section of tunnels

TUNNEL CONSTRUCTION IN LONDON CLAY
Civil Engineers has been conducting researches on London Clay (LC) to identify its properties and to
use it for Engineering applications. London clay has formed by sedimentation of fossils and minerals
during several million years. This special type of clay layer covers most of the part of the capital of
England. This LC is mostly consisted with silt which contributes to the high volumetric change of LC
with the change of Moisture Content (MC) in water.
The city of London is built on this soft clay layer. This clay layer reaches up to 150 m deep from
ground level at some part of London. It is one of main reasons to scarcity of tall buildings in London
city. This LC is not popular for a good bearing capacity. But due to its less permeability it has been an
added advantage to construct tunnels underneath the city of London. This type of soil profile was the
main reason to rapid development of London underground railway Network.
NEW AUSTRIAN TUNNELLING METHOD (NATM)
Tunnel will be constructed in this method by excavating and concreting exposed tunnel. This method
provides a simple approach to tunnel construction with less capital cost, without any complex
construction equipment and processes. Necessity of very skilled work force, Slowness of construction
compared to shield construction, difficulties related to water and require stable soil or rock layers are
some the limitations of this NATM. Since NATM was primarily developed for tunnelling in rocks,
now it is being used with clayey soils. Therefore, it is important to study the behaviour of soils when
tunnelling with NATM (Dasari, Rawlings and Bolton, 1996).
FEM MODELING OF TUNNELS
Various methods have been adopted for tunnelling by different people. Limit state analysis and Limit
equilibrium analysis methods have been used in the past to study the effect on surrounding soil and
structures due to tunnelling. With the evolvement of computer technology use of computers in
Engineering analysis procedures has increased. To analyse these effects using computers Finite
Element Modelling is the most widely used method to idealize the soil and structural elements.
Usually structural elements are idealized by strut, plate and shell element using linear material models
in most of Civil Engineering applications. But when it comes to modelling the soil, it has been used
many constitutive models with different approaches due to complex behaviour of different types of
soils. Mohr – Coulomb model, Soil hardening model, and modified Cam-clay model are few of those
constitutive models.
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IDEALIZATION OF CONSTRUCTION OF TUNNEL
PLAXIS
Plaxis software will be used to analyse the construction of this tunnel as the Finite Element Modelling
software package. Due to unavailability of Plaxis 3D software Plaxis 2D software was used to analyse
the effect on surroundings due to construction of this 4 km tunnel.
When modelling an actual 3D scenario in to a 2D model various assumptions and techniques must be
used. In Plaxis 2D, Plain Strain and Axe-symmetric idealization methods are available to idealize the
structure. Due to unavailability of Axially symmetric structure Plain strain model was used to idealize
the construction procedure.
SELECTION OF CROSS-SECTIONS
To simulate the actual conditions using plane strain method of idealization a cross section must be
identified. Since this is a considerably long (4 km) construction project 3 cross-sections had to be
modelled to assess settlements and impacts on surrounding structures. Selection of these cross-sections
were done according to the severity of induced effect on the surroundings.
Cross-sections A –
This cross-section was selected at the middle of first 2 km section of the proposed tunnel as shown in
figure 1. It is located at 1 km from the start of the tunnel. Top of the tunnel lining will be located at a
depth of 22.5 m from the existing ground.
Cross-section B –
A historical site and 30 m deep piles were in the vicinity of the proposed tunnel. Since those structures
could be affected by the tunnel construction analysis of this area is a must. Therefore, an analysis
section was selected at the mid point of the section. These historical site and piles are located at a
distance of 2 km from the start of the tunnel. There will be 25 m depth to the top of the lining of the
tunnel from existing ground.
Cross-section C –
This section was selected at the middle of second 2 km section of the proposed tunnel as shown in
figure 1. It is located at 3 km from the start of the tunnel. Top of the tunnel lining will be located at a
depth of 27.5 m from the existing ground.
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CROSS-SECTION DIMENSIONS
Even though soil has infinite dimensions compared to tunnel, a finite area should be selected for the
model. To select that finite area, area beyond the selected area should have a minimal effect due to
simulations. When simulating an excavation usually breath of the model taken as 1.5 time the depth of
the excavation. To determine the depth of the model, effect of stress bulb is taken into account. A
depth of 2 times the breath of a construction will be affected. These facts were considered in selecting
the dimensions of the simulated soil area.
 Depth of the model –
Depth to tunnel and diameter of a tunnel is fixed. Depth to the bottom of the model was taken as the
twice the diameter of tunnel due to pressure bulb will be developed to such depth. Since diameter of
the tunnels nearly 12 m depth was taken to the bottom of the model from the bottom of the tunnel
lining was 24 m. When that value added with the diameter of the tunnel and the depth to the tunnels
form existing ground surface total height of the model was 70 m.
 Width of the model –
Distance to the right and left boundaries from the tunnel was determined as 1.5 times the depth to the
tunnel from the ground level. When selecting these values effects caused by the tunnel construction
was negligible after these distances. Therefore, a minimum distance of 42 m was kept to the boundary
from both right and left side boundaries to the tunnel. When spacing between tunnels and diameter of
tunnels added to the model which has 100 m breath was developed using Plaxis 2D.
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70 m
100
m
D S
Figure 3 - Dimensions of the model

TUNNEL PROPERTIES
Shape of the tunnel was taken as circular. To determine the effect on surroundings due to size of tunnel
diameter and spacing between two tunnels, several models were created with different tunnel diameter
and space between two tunnels. Three diameter values were used with 1m gap between each value
while three inter tunnels space values were used with 1 m gap between each value in this analysis.
Therefore, 9 finite element models were build using Plaxis 2D at each cross-sections A, B & C. Values
used in this model building are shown in Table 1.
Table 1 - Used Tunnel Diameter and spacing between tunnels
Dimension Used values (m)
Diameter of a tunnel (D) 10, 11, 12
Spacing between tunnels (S) 5, 6, 7
Thickness of the tunnel lining was taken as 300 mm at every model. As per the model lining was
consisted of 6 precast blocks each subtending 600 at the centre of the tunnel.
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Figure 4 - Properties of the tunnel