23
Numerical study of the cross-sectional shape of shallow tunnels
subjected to impact and blast loading
Dhamne, R.
M. Tech Student, Department of Civil Engineering, IIT Delhi, New Delhi, 110016, India
Mishra, S.
Research Scholar, Department of Civil Engineering, IIT Delhi, New Delhi, 110016, India
Kumar, A.
Research Scholar, Department of Civil Engineering, IIT Delhi, New Delhi, 110016, India
Rao, K.S.
Professor, Department of Civil Engineering, IIT Delhi, New Delhi, 110016, India
E-mail (Corresponding Author): [email protected]
Abstract
Recently, external terrorist activities have become one of the most influential events on tunnel structure
safety because of the absence of proper mechanisms to detect these events in time to take preventive action.
Urban tunnels are highly susceptible to destruction under such attacks. In the present study, Abaqus/CAE
or “Complete abaqus environment” numerical tool based on finite element method is used to investigate the
dynamic response of different shapes of tunnels which are D-shapedand Circular under dynamic loading
conditions. In the study, peak impact load is simulated for different shapes of shallow tunnels and damage
behaviour and fracture propagation for each case is determined and compared. The effect of different
loading condition on lining and crown of the tunnel is also studied. For modeling blast load, explosive
Trinitrotoluene(TNT) is used in the analysis. Blast loading is incorporated by using Conventional weapons
(CONWEP) empirical model.The deformation at the crown of the tunnel is estimated along the tunnel
length.
Keywords:Impact loading, Finite Element Analysis, TNT, Tunnel Lining, Underground Tunnel, Abaqus
1. Introduction:
In many civil and mining engineering applications, underground tunnels are always
subjected to different loading conditions and in-situ stresses. These structures often have
to withstand not only static load but also impact and blast load due to worldwide
terrorism attack which become intensive and more frequent. Underground structures are
an integral part of infrastructures of modern society and are used for wide range of
applications. One of aspect in the protection of such type of structures is the accurate
prediction of impact and blast loading on structural elements using an advanced
numerical Finite element (FE) based tool Abaqus/CAE 6.13. For this it is necessary to
analyze the dynamic behaviour of underground structures subjected to impact and surface
explosion to ensure the safety of these structures. The numerical study has been carried
out to find best shape of tunnel which will have the ability to resist blast where
experimental determination of response of underground tunnels under blast loading often
becomes difficult due to socio-political issues. Therefore, advance numerical analysis of
tunnels subjected to blast loading is of utmost importance.
In the literature, many researchers have investigated the dynamic behaviour of rock-mass
and found that dynamic properties are very different from static case (e.g. Zhang and
Zhao 2014; Xia and Yao 2015; Li et al. 2014). Liu (2009) perform a dynamic analysis of
subway structures under blast loading where they found from numerical study which
performs on explicit three-dimensional finite element method that maximum lining stress
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occurred right after explosion, before the blast air pressure reduced to atmospheric
pressure.
Dynamic response of underground structures under effect of blast loading has been
studied by several researchers (e.g. Liu 2009; Liu 2011; Feldgun 2008).Yang et al. (2010)
has analyzed the dynamic responses of the operating metro tunnel in soft soil, using a
widely applied explicit dynamic nonlinear finite element software ANSYS/LS-DYNA.
They were presented the blast induced wave propagation in the soil and the tunnel and
the Von Mises effective stress and acceleration of tunnel lining and the safety of tunnel
lining was evaluated based on failure criterion. The numerical results indicate that the
upper part of tunnel lining cross-section with direction ranging from 0° to 22.5° and
horizontal distances 0 to 7 m away from the explosive center are the vulnerable areas, and
the metro tunnel might be safe when tunnel depth is more than 7 m and TNTcharge on
ground is more than 500 kg.Lu et al. (2005) and Gui and Chien (2006) used FE procedure
to perform the blast analysis of tunnels subjected to external blast loading. Mussa et al.
(2017) used ANSYS/LS-DYNA software to assess the damage of an underground box
tunnel by a surface explosion. Jose and Anju (2018)used ANSYS software to study
numerically cross-sectional shape of tunnel under blast effect. Subway tunnels under
explosive loads have been analyzed by Liu (2009) using FE method. Modelling of
explosive load was done by CONWEP model in Abaqus/CAE 6.13.Tiwariet al. (2014)
has analyzed the dynamic response of underground tunnel subjected to internal blast
loading using FE based numerical tool. They observed from their results that pressure
acting on the tunnel lining increases as the charge weight increases. Under impact loading
condition, modelling the responses of rock material is difficult. Hiermaier (2012)
presented a study which determines that two basic processes occur when rock material is
subjected under impact loading condition: change in mechanical behaviour of material as
a function of strain rate and evolution and propagation of shock waves.
Figure 1 Schematic Diagram of Strain Rate Regimes (in reciprocal seconds) and
Techniques (Omar 2013)
The specific objectives of the present study are to perform a three dimensional (3D)
nonlinear finite element analysis of cross-sectional shapes of shallow tunnels by
considering D-shaped and Circular with the same area and boundary conditions subjected
to impact and blast loading and to find the best shape of shallow tunnel which resist blast
and deformation to suitable extent. Herein, finite element model of rock mass and
concrete lining have been prepared using Lagrangian analysis tool in Abaqus/CAE 6.13.
Rock mass stress-strain behaviour has been modeled using Mohr-Columb criterion. Field
and Walley (2004) presented a study which gives an experimental technique for high rate
deformation and shock loading where one important point in Fig. 1. is the transition from
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One dimensional (1D) stress to 1D strain which occurs by increasing the strain rate.This
transition is due to inertial confinement of the material. The strain rate at which this
transition occurs depends on the density and size of the specimen. Therefore, larger
specimen with higher density results in lower transitional strain rates.
In case of blast loading the strain rate can reach upto 102 to 10
4 per second (Ngo and
Mendis, 2008) and for impact loading it can reach upto 104 to 10
8 per second.
2. Numerical Analysis:
Numerical analysis is carried out to find best shape of tunnels from different cross-
sectional shapes of tunnel which resist the effects of blast and impact where geometry
and other related data are shown below.
i. Geometry of Model:
The behaviour of rock-mass models subjected to impact and blast loads are observed with
the help of Abaqus/CAE 6.13. Full scale Models of rock-tunnel of size 30 m x 30 m x 35
m, with 5 m diameter of tunnel are used as a target having lining thickness as 0.17m.
Geometry of rock-mass model with cross-sectional shape of Circular tunnel which has
been used by Mishra et al. (2016) to analyze the effect of different loading condition on
tunnel lining in soft rock and Mishra et al. (2017) to analyze the effect of damage to
shallow tunnel under static and dynamic loading with same area and cover depth of 5 m
has been considered in this study. Geometry of Hammer and rock-mass model of D-
shaped tunnel along with lining are shown in Figure 2 to Figure 6 and Table 1 gives the
dimensions of different shapes as shown below.
ii. Input Parameters:
a) Hammer Properties:
A rigid hammer used for impact is of mild-steel dropped from a height of 1m on the rock-
mass to visualize the moment of hammer with predefined velocity of 4.68 m/sec.
Properties of hammer are specified below in Table 2.
Table 1
Dimension of Different Shapes
b) Material Properties:
The Mohr-Columb plasticity model is used for modeling the rock-mass. Material
Sr.
No.
Shape Diameter (m) Cover Depth (m)
1 5.0 7.5
2 Outer - 5.0
Inner - 4.7
-
3 Outer - 3.2
Inner - 3.0
-
4 Outer - 5.0 5.0
5 Outer - 3.2 5.0
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properties for synthetic rock-mass (GM1) has been taken from Mishra et al. (2018) where
they studied the effect of cover depth on deformation in tunnel lining when subjected to
impact load. For numerical analysis, the properties of the above material which has been
used is listed below in Table 3.
Table 2
Hammer Specification
Table 3
Index Properties of Laboratory Modeled Geo Material
Figure 2 Geometry of the
Hammer (m)
Figure 3 Geometry of Circular
Tunnel Lining (m)
Figure 4 Geometry of D-
Shaped Tunnel Lining
(m)
Figure 5 Geometry of Rock Model with
Circular Shape Tunnel (m)
Figure 6 Geometry of Rock Model with D-
Shaped Tunnel (m)
Sr.
No.
Parameters Values Units
1 Density 7800 Kg/m3
2 Young’s Modulus (E) 200 GPa
3 Poisson’s Ratio (ν) 0.3 -
4 Height of Fall 1 Meter
5 Tup Diameter 5 Meter
6 Hammer Velocity 4.68 m/sec
Material
Type
Modulus of
Elasticity
(GPa)
Poisson’s
Ratio
(ν)
Density
(Kg/m3)
Friction
Angle
Cohesion
(MPa)
UCS
(MPa)
GM1 3.675 0.163 1216.68 39.12 0.79 3.51
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iii. Meshing:
Global meshing size used for the rock-mass of Circular shape tunnel is 2 whereas for D-
shaped tunnel it is 3.2, for Circular lining 0.5 whereas for D-shaped lining it is 2.9 and for
hammer it is 0.5. An approximate element size used for the rock sample of both D-shaped
and Circular shape tunnels are same as 0.8, for lining which comprise both cross-
sectional shapes is 0.8 and for hammer it is 0.4. The individual meshing of the
components and mesh assembly is shown in Fig. 7.The eight-node brick element
(C3D8R) with reduced integration, hourglass control and finite membrane strains are
used in the FE mesh for rock model which are available in Abaqus/CAE 6.13.
In case of D-shaped tunnel, rock tunnel lining model comprises total of 73513 nodes and
66838 elements, including 1620 nodes and 792 elements for tunnel lining. For meshing
of hammer, total of 934 four-node rigid elements (R3D4) and 931 nodes are used. In case
of Circular shape tunnel, rock tunnel lining model comprises total of 41493 nodes and
37185elements, including 2130 nodes and 1680 elements for tunnel lining and same
meshing of hammer used for this shape.
Figure 7 Meshing of Individual Components and Rock-Tunnel Assembly
iv. Boundary Condition:
The rock-mass is considered fixed at the base and free at sides and top surface where this
effect of boundary condition has been analyzed experimentally by Mishra et al. (2018).
An assembly of rock-tunnel of D-shaped and Circular shape with boundary condition are
shown in Figure 8.
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Figure 8 Boundary Condition of Rock-Tunnel Assembly
v. Dynamic Analysis of Shallow Tunnels:
Tunnels are model under impact (dynamic) loading through drop-hammer assembly as
dropped height of hammer is mentioned in Table 2. Whereas for blast loading, standard
explosive TNT equivalent is model with the help of CONWEP empirical model. Hammer
used in impact for analysis is of mild steel and Johnson-Cook damage model is adopted
for that.
For modeling of steel, Johnson-Cook model is widely used for numerical analysis. It is an
elasto-visco plastic material model used for predicting flow and fracture behaviour of
target material.
�� = (� + �(���(1 + � log ��
�� ��(1 − ��� where�� = Yield Strength of Steel, �= Effective Plastic Strain, ��= Strain Rate, T =
Homologous Temperature.
3. Loading Condition:
To investigate the deformation behaviour of rock-mass, different zones along with their
distances are shown in Table 4.The mass of the hammer considered in analysis are 12.4
Kg, 20 Kg and 25 Kg. The different mass of the hammer adopted in the present numerical
study are on the basis of the scaling laws and laboratory experimentation performed on
the small scale models, as shown in Table 5.The experimented mass has been dropped
and variations in deformation along the tunnel length for two different cross-sectional
shapes of tunnel are computed. For blast analysis the mass of TNT equivalent used are
100 Kg, 250Kg, 500 Kg and 1000 Kg. A step time of 0.2 sec is used for impact and 0.03
sec is used for blast analysis which is sufficient to transfer the load in every points of
rock model and tunnel as well.
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Table 4
Different Zones and their Distances in Rock-Tunnel Model
Zones L1 L2 L3 L4 L3’ L2’ L1’
Distance (m) 0 11.67 14.583 17.5 20.417 23.333 35
Table 5
Different Loading Conditions
Load
Impact Blast
Mass of Hammer (Kg) Moment of Inertia (m4) TNT
Equivalent
(Kg) Mass of
Hammer
Mass of
Disc
Total
Mass I11 I22 I33
1 1.03 11.38 12.4 0.064531 0.244239 0.064531 100
2 1.03 19 20.03 0.107448 0.516607 0.107448 250
3 1.03 24 25.03 0.135539 0.788349 0.135539 500
4 - - - - - - 1000
i. Tunnels Subjected to Impact Loads:
Numerical analysis is a carried out for lined tunnels having a cross-sectional shape of D-
shaped and Circular shape by considering same rock mass (GM1) and crack initiation
with fracture propagation in model is computed under varying mass of drop hammer.
Maximum penetration of tunnel of both the cross-sectional shapes when subjected to
impact load of 20 Kg is shown in Figure 9 and Figure 10.
Figure 9 Maximum Penetration of Circular Figure 10 Maximum Penetration of D-
Shape Tunnel When Subjected to Shaped Tunnel When Subjected to
Impact Load Impact Load
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-0.02
-0.016
-0.012
-0.008
-0.004
3.7E-17
0 0.04 0.08 0.12 0.16 0.2
Dis
pla
cem
ent
(m)
Time (sec)
Circular
20
D-Shaped
20
Drop Weight, Kgs
(Numerical)
GM1, Lined
(Impact)
In this case on Circular shape tunnel of diameter 5 m and D-shaped tunnel of diameter
3.2 m under overburden of 5 m, hammer of mass is taken as 20 Kg and variation in
displacement with respect to time and change in velocity of hammer is shown in Figure
13 and Figure 14.
Figure 11 Contour Plots of Deformation
when Figure 12 Contour Plots of Deformation Circular Shape Tunnel Subjected
when D-Shaped Tunnel Subjected to
to Impact Load Impact Load
whereas contour plots of deformation of both cross-sectional shapes indicates that
maximum deformation obtained in D-shaped tunnel at the crown node due to impact of
hammer on the center part of rock-tunnel model. Variations indicated in negative
direction represent penetration of hammer in downward direction.
ii. Tunnels Subjected to Blast Loads:
Numerical blast analysis is carried out with the help of CONWEP empirical model
developed by Kingery and Bulmash (1984). For the blast analysis, TNT explosive
compound is used as a standard high explosive used to simulate the blast analysis in both
D-shaped and Circular Tunnels. Explosive charge used for the blast analysis are 100 Kg,
250 Kg, 500 Kg and 1000 Kg to visualize the effect of blast loads on tunnels of D-shaped
and Circular shape whereas variation of displacement with respect to time and change in
velocity of crown node with variation of blast loads are shown in Figure 17 & Figure 18.
Figure 13 Effect of Impact Load in both Shapes of Tunnel on Displacement with respect
to Time
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-0.9
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2V
elo
city
(m
/sec
)
Time (sec)
Circular
20
D-Shaped
20
Drop Weight, Kgs
(Numerical)
GM1, Lined
(Impact)
Figure 14 Effect of Impact Load in both Shapes of Tunnel on Velocity with respect to
Time
Figure 15 Contour Plots of Deformation when Circular Shape Tunnel Subjected to Blast
Load
Figure 16 Contour Plots of Deformation when D-Shaped Tunnel Subjected to Blast Load
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-0.04
-0.032
-0.024
-0.016
-0.008
8E-17
0 0.006 0.012 0.018 0.024 0.03
Dis
pla
cem
ent
(m)
Time (sec)
Circular1002505001000D-Shaped1002505001000
TNT Equivalent, Kgs
(Numerical)
GM1, Lined
(Blast)
-22
-18
-14
-10
-6
-2
2
6
0 0.006 0.012 0.018 0.024 0.03
Vel
oci
ty (
m/s
ec)
Time (sec)
Circular1002505001000D-shape100250500
TNT Equivalent, Kgs
(Numerical)
GM1, Lined
(Blast)
Figure 17 Effect of Blast Loads in Circular and D-Shaped Tunnels on Displacement with
respect to Time
4. Results and Discussion:
i. Dynamic Analysis:
In the present study, the numerical investigation of tunnels under impact and blast
loading condition are performed by considering two different cross-sectional shape of
tunnels i.e. Circular and D-shaped tunnels. To find the best shape of the tunnel, the
comparison between the two cross-sectional shape of the tunnel is carried out by keeping
same geometry and material property (GM1, i.e. a synthetic rock mass prepared in the
laboratory). The displacement of crown of tunnel along the tunnel axis are observed and
quantified. The deformation of lining along the length of the tunnel for two different
cross-sectional shapes under impact loading is shown in Figure 21.
Figure 18 Effect of Blast Loads in Circular and D-Shaped Tunnels on Velocity of crown
node with respect to Time
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-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0 5 10 15 20 25 30 35
Def
orm
ati
on
(cm
)
Distance along Tunnel Length (m)
Circular12.42025D-Shaped12.42025
Drop Weight, Kgs
(Numerical)
GM1, Lin
ed
(Impact)
0
5
10
15
20
25
30
35
40
0 0.006 0.012 0.018 0.024 0.03
Pre
ssu
re (
MP
a)
Time (sec)
D-Shaped
100
250
500
1000
TNT Equivalent, Kgs
(Numerical)
GM1, Lined
(Blast)
Figure 19Effect of Blast Loads in Circular Shape Tunnel on Pressure with respect to
Time
Figure 20Effect of Blast Loads in D-Shaped Tunnel on Pressure with respect to Time
Figure 21Effect of Impact loads in D-Shaped and Circular Shape Tunnel on Deformation
along Tunnel Length
-5
3
11
19
27
35
0 0.006 0.012 0.018 0.024 0.03
Pre
ssu
re (
MP
a)
Time (sec)
Circular
100
250
500
1000
TNT Equivalent, Kgs
(Numerical)
GM1, Lined
(Blast)
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-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0 5 10 15 20 25 30 35
Def
orm
ati
on
(cm
)
Distance along Tunnel Length (m)
Circular
100
250
500
1000
D-shaped
100
250
500
1000
TNT Equivalent, Kgs
(Numerical)
GM1, Lined
(Blast)
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0 5 10 15 20 25 30 35
Def
orm
ati
on
(cm
)
Distance along Tunnel Length (m)
Circular
V = -4.68 m/sec
V = -6.8 m/sec
V = -8.18 m/sec
D-shaped
V = -4.68 m/sec
V = -6.8 m/sec
V = -8.18 m/sec
Drop weight 25 Kgs
(Numerical)
GM1, Lined
(Impact)
Figure 22 Effect of Blast loads in D-Shaped and Circular Shape Tunnel on Deformation
along Tunnel Length
Figure 23 Effect of Hammer Velocity on Deformation along Tunnel Length
From the analysis it has been concluded that deformation on the center of tunnel lining at
17.5 m distance along the tunnel length is maximum in case of D-shaped tunnel rather
than Circular shape while in case of blast loads, deformation obtained on tunnel lining is
maximum than impact loading in D-shaped tunnel and Peak particle velocity of crown
node increases as intensity of blast increases. CONWEP empirical model developed an
overpressure in case of blast analysis. In Fig. 23. Effect of hammer velocity is also being
studied by varying velocity of hammer from -4.68 m/sec to -8.18 m/sec and observed
from the above study that deformation along the tunnel length increases as velocity of
hammer increases. This is because effect of hammer velocity strongly influences
impacted energy. D-shaped tunnel has achieved maximum deformation at maximum
velocity.
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-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0 5 10 15 20 25 30 35
Def
orm
ati
on
(cm
)
Distance along the Tunnel Length (m)
Impact
25 Kg
Blast
1000 Kg
Impact
25 Kg
Blast
1000 Kg
GM1, Lined
Figure 24 Effect of Impact and Blast load in Circular and D-Shaped Tunnel on
Deformation along Tunnel Length
5. Conclusion:
In the present study, an attempt is made to understand the deformation of tunnel lining of
two different cross-sectional shapes under impact and blast loading. The analysis is
performed by using FE based numerical tool i.e. Abaqus/CAE 6.13 and two different
cross-sectional shapes of tunnels i.e. D-shaped and Circular shape are chosen to find the
best shape of tunnel which resist blast and deformation on suitable extent. It is found that
most of the urban tunnels are constructed in soft or weathered rock mass as surrounding
material. In such conditions when subjected to high impact loads, rock mass with high
grade of weathering undergoes more deformation.
From the above result it is observed that concrete lining experiences maximum
deformation in D-shaped as compared to Circular shape at 17.5 m i.e. on center part of
tunnel lining. From this result it also observed that rock-tunnel model consists of both the
shapes experiences maximum deformation in case of blast loads rather than impact loads.
Finally, it can be concluded that in case of impact as well as blast load, Circular shape
tunnel is more stable than D-shaped tunnel as it undergoes less deformation observed on
center part of lining by dropping a maximum impact load of 25 Kg and 1000 Kg blast
load of TNT and both shapes of the tunnel follows the Gaussian distribution along the
length.
References:
1. Abaqus/Explicit User’s Manual, Version 6.13. Dassault Systems Simulia
Corporation, Providence, Rhode Island, USA.
2. Feldgun, V. R., Kochetkov, A. V., Karinski, Y. S. and Yankelevsky, D. Z. (2008).
Internal blast loading in a buried lined tunnel. International Journal of Impact
Engineering, 35(3), 172-183.https://doi.org/10.1016/j.ijimpeng.2007.01.001
3. Field, J. E., Walley, T. M., Proud, W. G., Goldrein, H. T. and Siviour, C. R.
(2004). Review of experimental techniques for high rate deformation and shock
studies. International journal of impact engineering, 30(7), 725-775.
https://doi.org/10.1016/j.ijimpeng.2004.03.005
Journal of Engineering Geology Volume XLIII, Nos. 1 & 2
A bi-annual Journal of ISEG June-December 2018
36
4. Gui, M. W. and Chien, M. C. (2006). Blast-resistant analysis for a tunnel passing
beneath Taipei Shongsan airport–a parametric study. Geotechnical and
Geological Engineering, 24(2), 227-248.https://doi.org/10.1007/s10706-004-
5723-x
5. Hiermaier, S. (2012). Integrated experimental-numerical characterization of
geological materials under shock and impact. Dynamic Web Programming and
HTML5, 71.
6. Jose and Anju (2018). Numerical Study of the Cross-Sectional Shape of Tunnel
Under Blast Effect Using Ansys. International Research Journal of Engineering
and Technology (IRJET), 5(5), 3582-3586.
7. Kingery CN and Bulmash G. (1984). Air blast parameters form TNT spherical air
burst and hemispherical surface air burst. Tech. ReportARBRL-TR-02555, US
Army Armament Research and Development Center, Ballistic Research Lab.
Aberdeen Proving Ground, Maryland.
8. Li, J. C., Li, H. B., Ma, G. W. and Zhou, Y. X. (2013). Assessment of
underground tunnel stability to adjacent tunnel explosion. Tunneling and
Underground Space Technology, 35, 227-234.
https://doi.org/10.1016/j.tust.2012.07.005
9. Li, X., Zou, Y. and Zhou, Z. (2014). Numerical simulation of the rock SHPB test
with a special shape striker based on the discrete element method. Rock
Mechanics and Rock Engineering, 47(5), 1693-1709.
10. Liu, H. (2009). Dynamic analysis of subway structures under blast
loading. Geotechnical and Geological Engineering, 27(6), 699.
https://doi.org/10.1007/s10706-009-9269-9
11. Liu, H. (2011). Soil-structure interaction and failure of cast-iron subway tunnels
subjected to medium internal blast loading. Journal of Performance of
Constructed Facilities, 26(5), 691-701.
12. Mishra, S., Rao, K. S. and Gupta, N. K. (2017). Damage to Shallow Tunnels
under Static and Dynamic Loading. 11th International Symposium on Plasticity
and Impact Mechanics, Implast,DOI: 10.1016/j.proeng. Article in Procedia
Engineering 173:1322-1329. https://doi.org/10.1016/j.proeng.2016.12.171
13. Mishra, S., Rao, K. S. and Gupta, N. K. (2017). Damage to Shallow Tunnels in
Different Geomaterials under Static and Dynamic Loading; TWST_2017_198.
Article in Thin Walled StructuresISSN: 0263-
8231.https://doi.org/10.1016/j.tws.2017.11.051
14. Mussa, M. H., Mutalib, A. A., Hamid, R., Naidu, S. R., Radzi, N. A. M. and
Abedini, M. (2017). Assessment of damage to an underground box tunnel by a
surface explosion. Tunneling and Underground Space Technology, 66, 64-76.
https://doi.org/10.1016/j.tust.2017.04.001
15. Ngo, T. and Mendis, P. (2008). Modelling reinforced concrete structures
subjected to impulsive loading using concrete lattice model. AA, 2, 1.
16. Omar, M., F. (2013). Static and dynamic mechanical properties of thermoplastic
material. Lambert academic publishing.https://www.lap-
publishing.com//system/covergenerator/build/85751
17. Rao K. S., Mishra, S. and Gupta N. K. (2016). Effect of Different Loading
Conditions on Tunnel Lining in Soft Rocks. ISRM International Symposium
“EUROCK 2016”, Cappadocia, Turkey. Taylor and Francis Group, London,
ISBN 978-1-138-03265-1.
18. Sharma, H., Mishra, S., Rao, K. S. and Gupta, N. K. (2018). Effect of Cover
Depth on Deformation in Tunnel Lining When Subjected to Impact Load.
Journal of Engineering Geology Volume XLIII, Nos. 1 & 2
A bi-annual Journal of ISEG June-December 2018
37
InISRM10th Asian Rock Mechanics Symposium, (ARMS 10).Suntec City,
Singapore.
19. Tiwari, R., Chakraborty, T. and Matsagar, V. (2014). Dynamic analysis of
underground tunnels subjected to internal blast loading. In Proceedings of the
World Congress of Computational Mechanics (WCCM XI), Barcelona, Spain, 20–
25.
20. Wang, Z., Lu, Y., Hao, H. and Chong, K. (2005). A full coupled numerical
analysis approach for buried structures subjected to subsurface blast. Computers
and Structures, 83(4-5), 339-356.https://doi.org/10.1016/j.compstruc.2004.08.014
21. Xia, K. and Yao, W. (2015). Dynamic rock tests using split Hopkinson (Kolsky)
bar system-A review. Journal of Rock Mechanics and Geotechnical
Engineering, 7(1), 27-59.https://doi.org/10.1016/j.jrmge.2014.07.008
22. Yang, Y., Xie, X. and Wang, R. (2010). Numerical simulation of dynamic
response of operating metro tunnel induced by ground explosion. Journal of rock
mechanics and geotechnical engineering, 2(4), 373-
384.https://doi.org/10.3724/SP.J.1235.2010.00373
23. Zhang, Q. B. and Zhao, J. (2014). A review of dynamic experimental techniques
and mechanical behaviour of rock materials. Rock mechanics and rock
engineering, 47(4), 1411-1478.