Seismic analysis and design of cut-and-cover structures

Seismic analysis and design of cut-and-cover

structures Prashant Kumar#1, Nishant Kumar#2, Sunil Saharan#3

#Department of Civil Engineering1, 2,3, College of Engineering Roorkee, Uttarakhand, India1,

Sharda University, Noida, Uttar Pradesh. India2,3

[email protected] [email protected] [email protected]

Abstract— Underlying structures are used for a various purpose

in many areas such as transportation, underground areas,

metro stations and water transportation. The serviceability and

durability of buried structures is vital in many cases following

an earthquake; that is, the earthquake should not impose such

damage leading to the loss of serviceability of the structure. The

paper presents a state-of-the-art review of the modern

understanding of the seismic behaviour of tunnels. This paper

also presents seismic response of highway tunnels through a

case study on Cut & Cover Tunnel, which is well approved and

subjected to earthquake. The seismic response of a section of the

tunnels is examined with 2-D finite element model and 3-D finite

element model. 2-D & 3-D FEM model are analyzed &

interpretation of stresses to get final design forces and

comparison of analysis results between 2-D & 3-D FEM model

has been done. It is observed that there is slight variation

between 2-D & 3-D FEM Displacement & Moment results

except for the load cases which includes seismic force.

Keywords— Seismic Analysis, Cut & Cover Tunnels, Finite

Element Analysis, Soil-Structure Interaction, Displacement

I. INTRODUCTION

Underground structures are becoming increasingly

popular because of the fast growth of the

population and decreasing of the ground space,

particularly in urban areas all over the world

including high seismic risk zones. Accordingly, in

many cases the design of such structures must

incorporate not only the static loading but the

earthquake loading as well. Underground

structures have distinct features that make their

seismic behaviour radically different from surface

structures in general, most notably due to (i) their

complete enclosure in soil or rock, and (ii) their

significant length (i.e. tunnels) [2] .In underground

structures, the response is mainly dominated by the

surrounding soil medium rather than the inertial

properties because of the very large inertia of the

ground with respect to that of the structure. Main

differences of the seismic response of underground

structures from those of the surface structures are

that the seismic effect is controlled by the

deformation imposed on the structure by the

ground, not by the forces or stresses and the inertia

of the surrounding soil is much larger relative to

the inertia of the structure for most underground

facilities. Therefore, the free-field deformation of

the ground and its interaction with the structure are

the main interests in the seismic design of

underground structures. The Construction of 4 lane

divided carriageway from Udhampur to Banihal

section of NH-1A, in the State of Jammu and

Kashmir consists of number of tunnels that are

proposed on this stretch (Nashri – Chennani

Tunnel, Chanderkote bypass Tunnel etc). The

longest tunnel is Nashri – Chennani Tunnel (about

9 km long). The proposed design of cut and cover

tunnel is part of Chanderkote bypass tunnel. The

total tunnel length is about 888m and it is proposed

for north bound traffic for Srinagar. The initial

115m length is proposed as cut and cover tunnel

due to shallow rock cover. Remaining length is

underground.

The Cut& Cover part of Chanderkote bypass

tunnel was studied in this project. The description

of tunnel is given below:-

The Engineering Journal of Application & Scopes, Volume 5, Issue 2, Dec 2020 ISSN No. 2456-0472

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Finished size of the cut & cover tunnel and

southern portal is shown in fig.1.

Fig.1. Cut & Cover Tunnel and South Portal – Cross-section (AUTO-

CADD)

Table 1. Details of Cut & Cover tunnel

Height of Tunnel 10.6 m

Width of Tunnel 11.6 m

Carriageway Width 7.5 m

Radius 5.1 m

The aim of the study is to evaluate the seismic

forces acting on the tunnel using WANG racking

method of deformation, to analyse and design

the cut & cover tunnel using 3D FEM STAAD Pro

model and to verify the 2D FEM results with 3D

FEM analysis

II. FINITE ELEMENT MODELLING

The Plate/Shell finite element is based on the

hybrid element formulation. The element can be 3-

noded (triangular) or 4-noded (quadrilateral). If all

the four nodes of a quadrilateral element do not lie

on one plane. It is advisable to model them as

triangular elements. The thickness of the element

may be different from one node to another.

“Surface structures” such as walls, slabs, plates

and shells may be modelled using finite elements.

The following geometry related modelling rules

are followed while using the plate/shell element.

1. The program automatically generates a

fictitious, centre node “O” at the element

centre.

2. While assigning nodes to an element in the

input data, it is essential that the nodes to be

specified clockwise. For better efficiency,

similar elements should be numbered

sequentially.

3. Element aspect ratio should not be excessive.

They should be on the order of 1:1 and

preferably less than 4:1.

4. Individual elements should not be distorted.

Angles between two adjacent elements sides

should not be much larger than 90 and never

larger than 180.

During the generation of element stiffness matrix,

the program verifies whether the elements are

same as the previous one or not. If it is same,

repetitive calculations are not performed. The

sequence in which the element stiffness matrix is

generated is the same as the sequence in which

elements are input in element incidences. Loads

are specified in the STAAD model. Design is

based on the most adverse combination of probable

load conditions. However, only those loads are

selected which have reasonable probability of

simultaneous occurrence. Loads taken into

consideration are Self-weight (SW) 2D/3D,

Superimposed dead load (SIDL) 2D/3D, Earth

Pressure (EP) 2D/3D, Water Pressure and

Buoyancy (WP) 2D/3D, Racking Force (RF)

2D/3D, Live Load (LL) 2D/3D. Analysis of

structure was performed for following load

combinations

• SW + EP = Load Case 101,201,301


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• SW + SIDL + EP= Load Case 102,202,302

• SW + SIDL + EP + SO= Load Case

103,203,303

• SW + SIDL + EP + SO + LL= Load Case

104,204,304

• SW + SIDL + EP + SO + LL + RF= Load

Case 105,205,305

• SW + SIDL + EP + WP= Load Case

111,211,311

• SW + SIDL + EP + WP + SO= Load Case

112,212,312

• SW + SIDL + EP + WP + SO + LL= Load

Case 113,213,313

• SW + SIDL + EP + WP + SO + LL + RF=

Load Case 114,214,314

Following are the Indian Standards used in the

analysis

• IRC 6:2014 Standard specifications and code

of practice for road bridges. [11]

• IRC: 112-2011, “Code of practice for concrete

road bridge”.[12]

• IS: 456-2002, “Code of Practice For Plain And

Reinforced Concrete”.[7]

• IS 1786 (2008): High strength deformed bars

and wires for concrete reinforcement.[13]

• IS 1893 PART 1 - Criteria for earthquake

resistant design of structures.[8]

• EN 1992-1-1 (2004) – Design of concrete

structures – Part 1-1.[9]

• Seismic design of tunnels-Jaw Nan Wang. [6]

The grade of concrete is M30 and density of

concrete is taken as 25kN/m3conforming to IS: 456.

The grade of steel is of Fe500 conforming to IS:

1786. Density of the reinforcement is taken as

7850 kg/m3. For the type of geological conditions

available at site, density of the soil assumed as

26kN/m3 and Poisson’s ratio of the surrounding

rock was assumed as 0.25. Permissible (allowable)

stresses for M30 grade of concrete is obtained from

Cl. 12.2.1, IRC 112 [12] and the mean value of

axial tensile strength of concrete is obtained from

Table 3.1 of Euro code EN 1992-1-1:2004 [9].

STAAD Pro V8i, finite element software was used

for the purpose of the structural analysis. Thick

shell element model of 10m length was developed

for the structure. Irregular meshing has been done

to cater the typical shape of the structure. Fig. 2

presents thick shell finite element model of the

structure.

Fig. 2. Thick shell model of Southern Portal (STAAD Pro V8i.)

III. RESULT AND DISCUSSION

Compressive Stress results are summarized in

table 2 and compared with the prescribed limits of

stresses, recommended by IS 456: 2000 & IRC

112:2011.

Table 2. Maximum compressive stress in concrete

S. No. Component Governing

Load Case

Max.

Compressive

stress (MPa)

in concrete

1 Top slab top

SW+SIDL+EP

S+WP+SO+LL

+RF

14.33

2 Top slab bottom SW+SIDL+EP

+SO+LL+RF 7.33


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3 Wall outside SW+SIDL+EP

+SO+LL+RF 12.83

4 Wall inside SW+SIDL+EP

+SO+LL+RF 12.03

5 Base slab top SW+SID+EP+

SO+LL+RF 7.43

6 Base slab

bottom

SW+SIDL+EP

S+WP+SO+LL

+RF

6.71

It can be observed from the results presented in

Table 3 recommended by IS 456:2000 & IRC

112:2011 that maximum compressive stresses are

well within the permissible stresses. Crack-width

results are summarised as below (Maximum

permissible crack width is taken as 0.2mm).

Table 3 Maximum crack width results

S.

No.

Component Governing Load Case Max. crack

width(mm)

1

Top slab top SW+SIDL+EPS+WP 0.058

2 Top slab

bottom

SW+SIDL+EP+SO 0.06

3 Wall outside SW+SIDL+EP+SO 0.12

4 Wall inside SW+SIDL+EPS+WP 0.19

5 Base slab top SW+SIDL+EP+SO+LL

+RF

0.19

6 Base slab

bottom

SW+SIDL+EPS+WP 0.13

The comparison between 2-D & 3-D FEM

Model results has been done and it was found that

there is little variation in displacement presented in

fig. 3 and fig. 4. The variation of displacement in

line graphs between 2-D FEM model and 3-D

FEM model for top slab, bottom slab, left wall and

right wall are shown in fig.5, fig.6, fig.7 and fig. 8

respectively

LOAD CASE 201

LOAD CASE

202

LOAD CASE 203

LOAD CASE 204 LOAD CASE

205

LOAD CASE 211

LOAD CASE 212

LOAD CASE

213

LOAD CASE 214

Fig.3. Displacement diagrams (2-D) (STAAD Pro V8i.)

LOAD CASE 201

LOAD CASE

202

LOAD CASE

203

LOAD CASE 204

LOAD CASE

205

LOAD CASE

211


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LOAD CASE 212

LOAD CASE

213

LOAD CASE

214

Fig.4. Displacement diagrams (3-D) (STAAD Pro V8i.)

Fig.5. Displacement variation of bottom slab (STAAD Pro V8i.)

Table.4 Displacement variation of bottom slab (STAAD Pro V8i.)

Load Case Displacement

Y mm (2-D)

Displacement

Y mm (3-D)

201 -1.039 -0.985

202 -1.273 -1.206

203 -1.472 -1.305

204 -1.62 -1.445

205 -1.62 -1.445

211 -0.468 -0.539

212 -0.666 -0.638

213 -0.814 -0.778

214 -0.814 -0.778

Fig.6. Displacement variation of right wall (STAAD Pro V8i.)

Table. 5 Displacement variation of right wall (STAAD Pro V8i.)


X mm (2-D)

Displacement

X mm (3-D)

201 -1.351 -1.431

202 -1.41 -1.49

203 0.688 0.734

204 0.634 0.678

205 6.244 6.63

211 -1.426 -1.785

212 0.673 0.44

213 0.619 0.384

214 6.229 6.336


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Fig.7. Displacement variation of top slab (STAAD Pro V8i.)

Table.6 Displacement variation of top slab (STAAD Pro V8i.)


Y mm (2-D)

Displacement

Y mm (3-D)

201 0.993 1.18

202 0.897 1.098

203 -3.905 -3.836

204 -3.924 -3.843

205 -3.924 -3.843

211 1.988 2.218

212 -2.814 -2.715

213 -2.834 -2.723

214 -2.834 -2.723

Fig. 8 .Displacement variation of left wall (STAAD Pro V8i.)

Table.7 Displacement variation of left wall (STAAD Pro V8i.)


X mm (2-D)

Displacement

X mm (3-D)

201 1.351 1.431

202 1.41 1.49

203 -0.688 -0.734

204 -0.634 -0.678

205 4.976 5.274

211 1.854 1.785

212 -0.244 -0.44

213 -0.19 -0.384

214 5.42 5.568

Fig.9 and Fig.10 shows the intensity of

equivalent lateral raking force using 2D and 3D

model respectively. Intensity of raking force for

2D model calculated is 111.6 KN/m and for 3D

model calculated is 121.5 KN/m

Fig.9. Equivalent lateral Racking Force corresponding to 2D model

(STAAD Pro V8i.)

Fig.10. Equivalent lateral Racking Force corresponding to 3D model

(STAAD Pro V8i.)

IV. CONCLUSIONS


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For the analysis and design of cut & cover tunnel,

3-D finite element analysis was conducted. Finite

element model replicate the entire geometry of the

tunnel. All feasible loads were considered for the

design as per IRC provision. It can be concluded

from the 2-D & 3-D analysis of tunnel that 2-D

modelling may not be ample to capture the actual

behaviour of the structure and the critical 3D

effects may be lost. There is very slight variation

between 2-D & 3-D FEM Displacement &

Moments results but 3-D FEM is more vigorous in

extracting forces from the stress contours. The

intensity of raking force calculated using 2D model

is 111.6 KN/m and using 3D model is 121.5 KN/m.

This slight dissimilarity is due to the fact that

raking displacement is lower for 2D analysis than

3D analysis as the 2D structure is more rigid.

From the results presented, it was also observed

that maximum compressive/tensile stresses are

well within the permissible stresses.

ACKNOWLEDGMENT

I would like to express my sincere thanks to

faculty and support staff of Department of Civil

Engineering, College of Engineering Roorkee for

providing the facilities to conduct the research on

the topic.

REFERENCES

[1] Faraji. S, Qingping. Z, Far. M, & Kordestani. H, “A Simplified

Method for the Seismic Analysis of Urban Transportation Tunnels”.

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[2] Hashash. Y, Hook. J, Schmidt. B, & Yao. J, “Seismic Design and

Analysis of Underground Structures, Tunnelling and Underground

Space Technology”, vol. 16, pp. 247-293, 2001

[3] J. Jimenez, “Free-Field racking deformation methodology applied to

the design of shallow tunnel structures in high risk seismic areas.

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[4] N. Newmark, “Problems in wave propagation in soil and rock”,

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[5] G.N. Owen & R.E Scholl, “Earthquake engineering of large

underground Structures”, Report no. FHWA RD-80 195. Federal

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[6] Wang. J, "Seismic Design of Tunnels - A Simple State-of-the-Art

Design Approach", William Barclay Parsons Fellowship, Parsons

Brinckerhoff, Monograph 7, 1993

[7] IS 456, Plain and Reinforced Concrete-Code of Practice (Fourth

Revision), Bureau of Indian Standards, New Delhi, 2000.

[8] IS 1893, Criteria for Earthquake Resistant Design of Structures-Part 1,

General Provisions and Buildings (fifth revision), Bureau of Indian

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[9] EN 1992-1-1, Euro code 2: Design of concrete structures - Part 1-1:

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[10] IRC: SP: 84, Manual of Specifications & Standards for four laning of

highways through public private partnership (first revision), Indian

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[11] IRC: 6, Standard Specifications and Code of Practices for Road

Bridges, Section-II, Loads and Stresses (Revised Edition), Indian

Road Congress, 2014.

[12] IRC: 112, Code of Practice for Concrete Road Bridges, Indian Road

Congress, 2014.

[13] IS 1786, High Strength Deformed Bars and Wires for Concrete

Reinforcement. Specification (Fourth Revision), Bureau of Indian

Standards, New Delhi, 2008.


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Seismic analysis and design of cut-and-cover structures

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