This document discusses a study on the effect of soil type on rectangular tunnels. A finite element analysis was conducted to analyze the structural behavior of a typical underground metro station subject to various soil types. The analysis considered different soil subgrade reactions to model soil-structure interaction. Both 3D shell element modeling and 2D plane frame modeling were used and results were compared. The study found that soil type significantly impacts bending moments in the bottom slab, with variations of 50-70% between soil types under some load cases. Loose sand produced the lowest bending moments while clay soils produced the highest.

1. International Journal of Mechanical Civil and Control Engineering
Vol. 1, Issue. 3, June 2015 ISSN (Online): 2394-8868
36
Study on Effect of Soil Type on Rectangular
Tunnels1
Mahantesh T R, 2
Dr. J.K. Dattatreya
1
PG Student, 2
Research Professor,
Civil Engineering Department, Siddaganga Institute of Technology
Karnataka, INDIA
Abstract— Rectangular tunnel is consisting of top, bottom and
two vertical side walls built monolithically which forms the
square or rectangular single cell. These structures are mainly
used as underground tanks, subways, highway underpasses and
culverts. The box structure is highly indeterminate structure
which is having continues support as directly rests on soil. Hence
to understand its true behavior, soil structure interaction should
take into account. This paper presents the finite element results
of parametric investigation of typical underground metro subway
station subject to various soil types by considering appropriate
soil subgrade reaction. The finite element method was used to
analyze the structural behavior of typical metro subway station
under different loading conditions using SAP 2000. And the
structure was modeled using SHELL element and the LINE
element and results obtained from the 3D analysis using SHELL
element and the plane frame analysis using BEAM or LINE
element were compared. Also study is carried out for various soil
types by considering appropriate soil subgrade reaction to know
the effect of type of soil on bending moment. The study reveals
that the bottom slab is the element which is severely affected and
variation of bending moment in bottom slab is in the range of
50% to 70%, in some other load cases the bending moment also
changes the sign.
Keywords—— Box structures; Modulus of Subgrade
reaction,;Plane frame model; Rectangular tunnel; Soil structure
interaction; SAP 2000; Underground Metro Station.
I. INTRODUCTION
With the acceleration of INDIA‟s rapid economic
development and urbanization, city size continues to expand
and traffic congestion is becoming increasingly prominent. As
an effective way to solve this problem, rail transit and public
transit system represented by subways has received great
attention and more and more cities are under construction or
planning of subways. Design of underground stations in
developed urban environments requires detailed understanding
and consideration of the analysis type, site conditions,
constructability and construction sequencing as part of the
design process in order to produce appropriate design
solutions. A rectangular box structure mainly consists of two
horizontal and two vertical slabs constructed monolithically are
ideally suited for a road or railway transportation. These
structures are economical due to their rigidity and monolithic
action and separate foundation are not required since the
bottom slab resting directly on the soil serves as raft slab.This
makes structure is highly indeterminate structure which is
having continues support as directly rests on soil. Although the
functional requirements of these structures may not vary
greatly, the unique site conditions at each location can lead to
very different solutions. Dimensions of boxtype tunnels are in
general greater than those of box culverts resulting in much
thicker walls and slabs for the boxframe. Hence to understand
its true behaviour the main parameters which influence
structural behaviour are varied and the results are studied.
Structural behaviour of underground rectangular metro station
box is analysed under different loading conditions using FEM
tool SAP2000.Results obtained from plane frame analysis is
compared with 3D analysis results obtained by using SHELL
element. Study is carried out related to variation in bending
moment for different types of soil that usually encountered at
site
II. FINITE ELEMENT ANALYSIS
A. Load cases considered
• The loading include the
1. Self-weight
2. Soil back fill over the structure
3. Live load
4. Lateral static earth pressure due to saturated soil (Ko)
5. Lateral active earth pressure due to saturated soil (Ka)
6. Lateral Hydrostatic pressure when is at ground water
level is at ground level
7. Vertical Uplift pressure when ground water level is at
Ground level
8. Lateral Seismic Earth pressure due to saturated soil.
B. Load Calculations
1. Self-weight
The self-weight of the structure is calculated in
SAP2000 by defining load patterns.
2. Soil Overburden Load

2. International Journal of Mechanical Civil and Control Engineering
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The weight of the backfill on top of the boxstructure,
assumed to be of equivalent bulk density as the
existing ground, typically g = 21 kN/m3 under
saturated conditions.
3. Earth pressure
i. Coefficient of lateral earth pressure at rest is
calculated by Rankine earth pressure co efficient for
soil at rest KO= 1-SIN (Ø).
ii. Coefficient of lateral earth pressure during active
stage is calculated by Coulomb's theory.
4. Train live load
The train live loads are considered as per standard
train loading for the Metro corridor (IRC:6-2000 Code
gives formula to impact factor). Impact factor, I, is
calculated as per Indian Railway Standard Code (Refer
clause 2.4.1.1.a).
5. Seismic loads
The IS: 1893-1984 (Clause 6.1.3) provide that box
culverts need not be designed for earthquake forces
Seismic loads are determined in accordance with work
carried out by Cetin Soydemir and presented in his
1991 paper "Seismic design of rigid underground walls
in New England" (Proceedings: Second international
conference on recent advances in geotechnical
earthquake engineering and soil dynamics, paper no.
4.6). This paper is a review and analysis of other
studies and concludes by presenting graphs for
estimating lateral earth pressures. The graph for the
situation where the length, L, from the structure to the
nearest obstruction, is greater than 1 (which is always
the case for this design), is shown below. The chain
line marked "Recommended" is used. The graph is
prepared for an area of moderate seismicity, with a
design acceleration of 0.12g. It has the depth of the
structure, as a proportion of the height, H, on the Y
axis, and the ratio of horizontal to vertical pressure
(sx/gH) along the X axis. It can be seen that the
pressure ratio has a value of 0.12 above a depth of
0.5H, and reduces linearly from this value to half this
value at the base of the structure.
An additional load to represent the seismic
component of the water pressure on the wall is
calculated using the theory of Westergaard, which
gives an approximate distribution of load as a parabola
with the horizontal pressure at respective depth.
Fig.1,Recommended Dynamic SoilPressuresagainst
Rigid, Non-Yielding Walls for (ah = 0.12 g) by Cetin
Soydemir.
6. Modulus of subgrade reaction
The modulus of subgrade reaction is a conceptual
relationship betweensoilpressure and deflection that is
widely used in the structural analysis of foundation
members like continues footings,mat orraft foundations
etc. The modulus of subgrade reaction is the ratio of
stress to deformation. Soil medium is modeled linear
springs and their stiffness is obtained modulus of
subgradereaction obtained fromTable 9-1 Bowles, J.E.
(1977) „„Foundation Analysis and Design.‟‟
Table.1, Range of modulus of subgrade reaction for
different types of soil.
Soil Ks (kN/m3)
Loose Sand 48000-16000
MediumDense Sand 9600-80000
Dense Sand 64000-128000
Clayey MediumDense Sand 32000-80000
Silty MediumDense Sand 24000-48000
Clay 12000 to 480000 (depending
upon bearing capacity)

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C. Modeling procedure in SAP2000
o The analysis is carried out using Finite Element
Analysis software SAP2000
o Material property defined as Isotropic.
o Defining Sectional properties and load patterns
are assigned to model.
o 4-noded thin shell element is assigned to area
element.
o 2-noded Rectangular section beam is used in
frame modelling.
o Supported condition are provided using area and
line springs for 3D analysis and 2D frame
analysis respectively which were calculated from
modulus of subgrade reaction.
o Model is run for analysis.
III. COMPARISION OF 3D AND PLANE FRAME MODEL
Many models are available to determine live a dead
load demands for underground structures load rating
problems. Determining which of the models to use can be a
daunting and difficult task. Being these structures are having
larger dimensions in the longitudinal direction the basic
assumption in analysis of the box structures is the
displacement and forces are uniform in the longitudinal
direction of the culvert. This assumption holds true for certain
type of loadings than others. For example soil loading applied
to the surface or pavement maybe considered as uniformin the
longitudinal direction. Solution therefore is independent of
one of the three orthogonal axes and can be formulated in
remaining two axes. Thus problem can be treated as two
dimensional.
But the spread of live load with depth is inherently a 3D
problem. Hence an attempt is made to compare the analysis
using BEAM element and SHELL element using FEA
package SAP 2000.Same modeling procedure is followed and
a conventional rectangular box structure of 10m width and 5m
height and unit length was considered.
Frame Models
Several modelling programs are available to analyse of
underground structures. The simplest of these are two
dimensional frame models. Two dimensional frame models
have many advantages. They are simple to construct with
often fewer than a dozen nodes; some even construct the
model automatically from a few culvert geometry properties.
Their structural stiffness matrices are smaller and therefore
require less computation time and introduce fewer errors.
They can deal with the behaviour of reinforced concrete by
using beam elements with Transformed moments of inertia.
The beam elements themselves are built around a proven and
well understood mechanics of materials model.
Finite Element Models
Underground structures load rating literature indicates that the
finite element analysis (FEA) method offers superior
capabilities for predicting box structures and soil-structures
behaviour. Finite element Codes allow for “modelling
phenomena not described by the underground structures
specific codes” and for graphical investigations of the results
(Duane, Robinson, & Moore, 1986). The most popular soil
models can be integrated in the FEA code. Such models
include linear elastic models, elasto-plastic with Mohr-
Coulomb failure, soil hardening with stress dependent
stiffness and Mohr-Coulomb failure, Hardin, Duncan, and
bilinear. Duncan is the most popular (Kim &Yoo, 2005;
Kitane & McGrath, 2006). Though it is clear that FEA is the
analytical tool of choice for analysing underground structures,
the particular implementation of FEA must be determined.
Fig.2, Shows 2D plane frame model in SAP200P.

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Fig.3, Shows 3D model in SAP2000 using SHELL element.
Observations
Fig.4, Maximum center moments in Top slab,Bottom slab and
Side wall using SHELL and BEAM element in SAP 2000.
Fig. 5, Maximum en moments in Top slab,Bottom slab and
Side wall using SHELL and BEAM element in SAP 2000.
Inference
From the above observations it is clear that
1. The spread of live load with depth is inherently a 3D
problem and use of 2D frame model proves to be more
conservative and overestimate the end joint moments
ignoring the spread of live load on the wall surface.
2. The 3D model using shellelement considers the spread
of area loads even in the direction of 3-axis and results
in higher wall moments at center of wall.
3. High estimated moments at the end corner of beam
results in more ductile joints which are one of key
parameter to special joints design which is highly
necessary of stability of these type structures.
4. The two dimensional frame models are simple models
and very easy to analyze for static loading conditions.
5. And produce the very conservative results and very
adoptable for design purposes.
IV. PARAMETRIC STUDY
The parametric study concentrate on variation of bending
moment in a typical underground rectangular metro station box
on various soil types by considering appropriate soil subgrade
reaction.
The station box has outer dimension of 22m x15m and
having concourse slab at 8m center to from the base slab and
with a toe projection of 1m in bottomslab.
The same load cases and same method of FEM analysis is
used for the load calculations, modelling and analysis.
Soil cases considered and their Modulus of Subgrade
Reaction for vertical stiffness is listed below.
Soil Ks (kN/m3)
Loose Sand 16000
Clayey medium dens sand 32000
Medium dense sand 80000
Dense sand 128000

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Sectional Properties and Material Properties
• Material property defined as Isotropic and Grade of
concrete is M40.
Depth of
Base slab is 1.4m
Concourse slab is 0.7m
Top slab is 1m and
Wall thickness is 1.2m
RESULTS
Fig. 6, Shows variation of Bending moments in Bottom slab
and Top slab with respect to Modulus of subgrade reaction.
Observations
o With increase in value of modulus of subgrade
reaction values of bending moment in al structural
members decreases.
o Values of bending moment‟s changes significantly in
bottom slab and negligible in top slab and side walls
as the values of modulus of sub grade reaction
changes from lower values to higher values.
o Bending moments of bottom slab are affected more
as bottom slab directly lay on soil without any
additional foundation.
v. Conclusion
1. The Two-dimensional frame models produces very
conservative Bending Moment results especially in the
bottom slab which in turn produces conservative
design of joints and base slab.
2. The 3D model using shellelement considers the spread
of area loads even in the direction of 3-axis and results
in higher wall moments at centre of wall.
3. From the graph shown above it is evident that the
positive bending moment (tension in bottom) in bottom
slab goes on decreasing as the value of modulus of
subgrade reaction increases and for higher values of
modulus of subgrade reactions bending moments may
results as for non-yielding supports.
4. Above problem being soil structure interaction
problem the variation of bending moments in top slab
and side walls are in small magnitude and bottomslab
plays critical role in design of underground rectangular
structures. Due attention should to bottom slab while
considering soil structure interaction.
5. While considering the seismic loading for underground
structures Underground structures suffer minor damage
from earthquakes compared to aboveground structures.
Deep tunnels are safer compared to shallow tunnels.So
for moderate seismic region the effect of earthquake is
not critical but in sever seismic region it plays critical
role.
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