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Experimental and numerical investigation of the dynamic response of tunnel

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Article  in  Structures · September 2020

DOI: 10.1016/j.istruc.2020.08.055

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 Structures 29 (2021) 2162–2173

Contents lists available at ScienceDirect

Structures
journal homepage: www.elsevier.com/locate/structures

Experimental and numerical investigation of the dynamic response of

tunnel in soft rocks
Swapnil Mishra a, *, Ankesh Kumar b, K.S. Rao c, N.K. Gupta d
a
Department of Civil Engineering, School of Technology, Pandit Deendayal Petroleum University, Gandhinagar, Gujarat 382007, India
b
Department of Civil Engineering, S.V. National Institute of Technology Surat, Surat, Gujarat 395007, India
c
Department of Civil Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India
d
Department of Applied Mechanics, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi, 110016, India

A R T I C L E I N F O A B S T R A C T

Keywords: Underground structures are proven to be one of the vital part of modern transportation system. With the growing
Blast and impact loading importance of tunnels for mobility, they are being subjected to threats of severe terrorist activities. Urban tunnels
Deformations are mainly located in the upper few kilometers and are highly susceptible to deformations even at very low strain
Physical modeling
rates. Therefore, in the present study, an attempt is made to understand the behavior and pattern of tunnel
Tunnel damage
damage subjected to the different dynamic loading conditions, through the simulation of natural as well as
artificial stress states such as loads due to overburden, impact, and blast. The new methodology is proposed to
overcome the difficulties of field test during a surface blast. In the present study, the combination of experimental
and numerical approaches is used to analysis and design tunnels under impact and blast loads. The investigation
is carried out in four steps; firstly, the impact testing is performed in the laboratory on small-scale physical
models of tunnel prepared using proper scaling laws. Secondly, the numerical investigation of the physical model
is performed under laboratory conditions, and then the experimental and numerical results are compared for the
validation purpose. Thirdly, the numerical analysis of impact loading on prototype is carried out. The tunnel
deformation results of small scale model and prototype under impact loading are compared for the validation of
the prototype model. Finally, the effect of blast loading on the tunnel deformation of the prototype is investi­
gated. It is found from the numerical simulations that the deformation at the tunnel crown in prototype under
impact loading is 10 times more than that of a small scale physical model. It is also observed that the deformation
of tunnel crown in prototype under impact load is equal to that of blast load due to 500 kg TNT. Therefore, it can
be concluded that the methodology proposed in the present work can be utilized by the practicing engineers and
academicians for the safe and economical design of tunnels subjected to impact and blast loading.

and in-situ stresses. The metro tunnels in highly populated cities are one
1. Introduction of the cheapest and safest modes of the transportation system. These
tunnels are constructed at shallow depth: therefore, they are highly
The increase in population coupled with rapid growth and indus­ susceptible to deformations due to external loading. The underground
trialization has increased the demand for infrastructural facilities. structures not only withstand static load but also impact and blast load
However, the limitation of space above ground has prompted the utili­ due to current terrorism activities. Impact loading at the surface causes
zation of underground space for several civil and military purposes such damage to the underground tunnel running beneath and affects the
as subways, railways, highways, and water and sewage conveyance. The transportation system and human lives. Thus, problems to the surface
major application of underground space is for the metro tunnel, which tunnel under dynamic loading attract concerns from all over the world.
turned out to be a lifeline for cities. Tunnels also play a crucial role in Dynamic loading conditions arise mainly due to earthquakes or due
connecting the mountainous regions (Himalayas) with the other parts of to blast loading and terrorist activities. Therefore, in the present study,
the country. In many civil and mining engineering applications, un­ an attempt has made to quantify the amount of deformations caused to
derground tunnels are always subjected to different loading conditions the tunnel lining when subjected to surface impact or blast loads.

* Corresponding author.
E-mail addresses: swapnil.mishra@sot.pdpu.ac.in (S. Mishra), ankesh@amd.svnit.ac.in (A. Kumar), raoks@civil.iitd.ac.in (K.S. Rao), nkgupta@am.iitd.ac.in
(N.K. Gupta).

https://doi.org/10.1016/j.istruc.2020.08.055
Received 31 January 2020; Received in revised form 29 July 2020; Accepted 18 August 2020
Available online 23 September 2020
2352-0124/© 2020 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
S. Mishra et al. Structures 29 (2021) 2162–2173

moderately deep tunnels because it is overground at some places and

Nomenclature underground at other sites, hence the transition from overground to
underground represents the variation in cover depth. Farther, due to this
C/D cover depth to Diameter ratio transition, the tunnels are passing through the soil, weathered rock, and
ɸ angle of internal friction intact hard rock type of geomaterials. Therefore, the specific objective of
c cohesion the present study is to quantify the amount of deformations caused to the
ρ density of soft rock tunnel lining when subjected to surface impact or blast loads. But, the
E modulus of elasticity field experimentation to investigate the effect of blast loading on tunnel
x distance from centre of tunnel deformation is very risky, costly, and unachievable in civilian research;
UCS uniaxial compressive strength therefore a new methodology is developed to carry out such in­
ʋ Poisson’s ratio vestigations. The present methodology is the combination of both
experimental and numerical techniques; thus, the synthetic rock mass is
modeled to represent soft/highly fracture rock for the experimentation
purpose. An impact testing facility is developed in the laboratory to
Recently, external terrorist activities have become one of the most sig­ carry out drop weight experimentation on physical models (small scale
nificant events on tunnel structure safety because of the absence of models). Further, the extensive numerical study is carried out using a
proper mechanisms to detect these events in time to take preventive FEM tool after validating it through experimental results. Finally, the
action. Urban tunnels, such as Delhi metro tunnels, are highly suscep­ numerical simulation is carried out to investigate the effect of impact
tible to destruction under such attacks. One of the aspect in protecting and blast loads on the prototype models.
such structures is the accurate prediction of impact and blast loading on
structural elements using an advanced Finite element (FE) based tool 2. Methodology
Abaqus/CAE 6.13 [1]. Many researchers have investigated the dynamic
behaviour of rock-mass for material modeling, and found that the dy­ 2.1. Material characterization
namic properties are very different from the static case [2–4]. The dy­
namic analysis of subway structures and other underground structures In the present research, three geo-materials are modeled, covering
under the effect of blast loading has been studied by several researchers the range of very low strength rockmass (from soil to soil-forming rocks
[5–7]. Yang et al. [8] analyzed the dynamic responses of the operating like mudstones, sandstones, highly weathered quartzite or basalt). The
metro tunnel in soft soil by using a widely applied explicit dynamic material is selected on the basis of its stress–strain behaviour, and the
nonlinear finite element software ANSYS/LS-DYNA. The numerical re­ material should have unconfined compressive strength (UCS) more than
sults indicate that the upper part of tunnel lining cross-section with di­ 1 MPa. The synthetic/representative rock mass is prepared in the labo­
rection ranging from 0◦ to 22.5◦ and horizontal distances 0 to 7 m away ratory from distinct materials like PoP, Kaolinite clay, Badarpur sand,
from the explosive centre is the vulnerable area. The metro tunnel might and mica (Fig. 1). To achieve the desired strength representing weak
be safe when the tunnel depth is more than 7 m, and the TNT charge on rockmass, the materials are mixed in different proportions and moisture
the ground is more than 500 kg. Mishra [9] analysed the effect of surface contents. The petrological study is conducted for constituent materials,
blast caused by 100 to 1000 kg TNT on tunnels embedded in the ground and mineral composition is determined for each material (Figs. 2a and
with varying C/D ratio. It is observed that the tunnels are safe for TNT 2b). It is observed that the model material is having the highest amount
charge less than 500 kg and C/D ratio greater than 1.0. Many researchers of quartz and K-feldspar due to the presence of sand, whereas halloysite
have used FE procedure to perform the dynamic analysis of tunnels and gypsum are present due to PoP. The materials are mixed in different
subjected to external blast loading [10,11]. Mussa et al. [12] used proportions, as shown in Table 1, and the mixed materials are named as
ANSYS/LS-DYNA software to assess the damage to an underground box Plaster of Paris (PoP), GM1, GM2, and GM3. Further, the specimens of L/
tunnel due to surface explosion. Jose and Anju [13] used ANSYS soft­ D ratio of 2 are also prepared to understand the physical properties and
ware to study numerically the cross-sectional shape of tunnel under blast mechanical behaviour under different loading conditions (uniaxial and
effect. Liu [5] investigated the subway tunnels under explosive loads by triaxial). Fig. 3a shows the failure pattern of the samples tested under
using the FE method, and modelled the explosive load by using CON­ uniaxial loading and Fig. 3b shows the stress - strain response of each
WEP model in Abaqus/CAE 6.13. synthetic rock. It is observed from the experimentation that the PoP
Tiwari et al. [14] analyzed the dynamic response of an underground sample is having the highest strength, and GM3 material is having lest
tunnel in weathered rock mass subjected to internal blast loading using strength.
FE based numerical tool. The investigation suggested that the distur­ It is observed that the strength is decreasing with an increase in the
bance on the ground surface is highest in highly weathered rock, due to clay content, and it can be seen from the test results that the stress –
which the existing structures will get affected. Mishra et al. [15,16] strain behaviour of the material is changing from brittle to elastoplastic.
determined the deformation zones in the tunnel’s lining and crown The change in material behaviour is observed due to a reduction in PoP
under static and impact loads through extensive experimental and nu­ content and an increase in clay content. Hence, the synthetic model
merical investigations. The effect of geometric, mechanical, and phys­ materials are finalized as GM1, GM2, and GM3.
ical parameters on the tunnel crown deformation under impact loading
are examined in detail. Sharma et al. [17] conducted numerical analysis 2.2. Physical modeling
on the small scale tunnel models under varying impact loads with
different C/D ratios, and it is concluded that the effect of external blast The physical modeling is carried out for different rock tunnel models
loading decreases with an increase in C/D ratio. Further, Dhamne et al. with a model size of 35 cm × 30 cm × 30 cm and tunnel diameter of 5
[18] explained the effect of different shapes of underground structures cm. The size of the rock tunnel model is chosen on the basis of proper
when subjected to impact loading conditions. Hence, it is necessary to scaling laws, as shown in Tables 2 and 3. The casting of physical models
analyze the dynamic behaviour of shallow underground structures is carried out by three model materials (GM1, GM2, and GM3) by
subjected to impact and surface explosion to ensure these structures’ varying the C/D ratio from 0.5 to 1.0. The casted models are kept for 28
safety. days for curing. In the present study, both lined and unlined tunnel
In the present study, the case of shallow and moderately deep tunnels models are prepared.
(0–20 m cover depth), which are mostly present in the metro cities, is The site of the railway tunnel project at T-48 Quazigund tunnel in
considered. The Delhi metro rail network is an example of the shallow / Katra, Jammu, is considered as a prototype, from where the properties of

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Fig. 1. Constituents for preparing synthetic rockmass.

Fig. 2a. Morphological study: SEM Analysis.

Fig. 2b. Mineral composition of the materials: XRD Analysis.

surrounding rockmass and tunnel lining are chosen for fixing the model
Table 1
specifications. The ratio of elastic modulus of lining material to the
Composition of selected synthetic rockmass.
elastic modulus of surrounding rock (Elining/Erock) is kept constant for
Material PoP (% by GM1 (% by GM2 (% by GM3 (% by model studies, to represent in-situ weak and weathered rocks at shallow
weight) weight) weight) weight)
depths. The rockmass present at the T-48 Quazigund tunnel consists of
Plaster of paris 100 50 50 40 the fractures carbonaceous phyllite and quartzitic phyllite. The elastic
(PoP)
modulus (Erock) of carbonaceous phyllite is reported as 33.00 GPa. As far
Sand – 40 35 35
Clay – 10 15 15
as the lining is concerned, shotcreting is done using M− 30 grade con­
Mica – – – 10 crete. The elastic modulus of the lining material is reported as 27.39
Water content 60 45 60 60 GPa. It is found that the elastic modulus ratio calculated from field data
is 0.83. The approximate value of elastic modulus of lining used in
physical modeling is determined using the following equation:

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Fig. 3a. Samples failed during testing.

Fig. 3b. Stress-Strain behaviour of laboratory modeled geomaterial.

( ) ( )
Elining Elining
Table 2 = (1)
Erock Erock Physical
Scaling of the different parameters of the model. Field Model

Parameter Model value where prototype is 1.0 Unit Further, the selection of lining material and thickness of lining used
Length 1/N m
for physical modeling is decided on the basis of proper scaling of the
Velocity 1 m/s structural interaction of real field conditions. Finally, PVC hollow tube is
Volume 1/ N3 m3 selected as a lining material for scaled studies. The lining thickness of the
Mass N3 kg tunnel in the physical model is fixed by comparing the ratio of lining
Force 1/N2 kN
thickness with the ratio of tunnel diameter of real field condition and
Pressure 1 MPa
Deformation 1 M physical model. The ratio of lining thickness and tunnel diameter of the
Energy 1/N3 J T-48 railway tunnel project gives a constant value, which is then
equated with the ratio of lining thickness and tunnel diameter of the
physical model. Since the diameter of the model is already fixed hence,
Table 3 tlining is computed. The casted rock tunnel models are shown in Fig. 4.
Dimensions of the full scale prototype model adopted in the present study. The C/D ratio of 1.0 represents the tunnel located at 5 cm depth from the
surface (where C is cover depth and D is the tunnel diameter).
Rock – tunnel model Small scale model Prototype

Dimension Surrounding rock 30 cm × 30 cm × 35 30 m × 30 m × 35 m 3. Experimentation

mass cm
Tunnel Length 35 cm, Length 35 m,
Diameter 5 cm Diameter 5 m 3.1. Development of ITF facility
Hammer Small scale model Prototype
Material Solid rigid object Solid rigid object The Impact testing facility is developed and fabricated in the labo­
Mass of the hammer 20 kg 20 × 106 kg
ratory, at IIT Delhi, to conduct impact testing on small scale tunnel
Velocity 4.68 m/s 8 m/s
Mesh size Small scale model Prototype models. The machine has 40 kg of dead weight capacity, and automatic
Rockmass 0.008 0.8 pneumatic actuator to release load hanger carrying different dead
Hammer 0.004 0.4 weights (in the form of discs weights). The ITF facility is based on the
law of conservation of energy, and the velocity of drop hammer is

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S. Mishra et al. Structures 29 (2021) 2162–2173

Fig. 4. Geometric design of casted rock tunnel model with varying C/D ratio.

calculated by using Eq. (2). The ITF has been used to understand the
Table 4
dynamic behavior of tunnel subjected to impact loads. Along with ITF,
Rock tunnel models subjected to different drop loads.
the compressor unit and data logger unit are used in the experimentation
for measuring the tunnel deformations and loads. Drop Weights on Rock Tunnel Model (kg)

Unlined Small Scale Tunnel Lined Small Scale Tunnel

v = (2gh)0.5 (2)
C/D ratio GM1 GM2 GM3 GM1 GM2 GM3

where ‘v’ is the velocity of hammer in m/sec and h is the height of fall 1.0 20.0 15.0 12.4 25.0 15.0 15.0
which is measured as 1.12 m for this analysis. 0.7 15.0 10.0 10.0 17.6 12.4 12.4
0.5 5.8 7.4 5.8 12.4 10.0 7.4

3.2. Testing procedure

Table 5
The experimentation is carried out on the samples with different C/D
Different zones and their distances in rock-tunnel mode.
ratios by varying drop weights. Firstly, the casted models are drilled
Zones L1 L2 L3 L4 L3′ L2′ L1′
from the bottom, at three chosen locations, for the attachment of
deformation sensors (LVDT’s). After attaching the deformation sensor to Distances (cm) 0.00 11.67 14.58 17.50 20.42 23.33 35.00
the physical model, it is placed on the loading platform, as shown in
Fig. 5. The impact load is dropped on the physical models of different
shown in Table 5. In the present investigation, the impact energy is
material and C/D ratios, and the cases considered for testing are shown
varied by varying the mass of the hammer. In the case of GM1 material
in Table 4. The calibration of load sensor and displacement sensor is also
and C/D of 1.0, 0.7, and 0.5, the impact load of 20.0, 15.0, and 5.8 kg are
performed prior to every impact loading test.
considered for unlined tunnels, and 25.0, 17.6 and 12.4 kg are consid­
To investigate the deformation behavior of rock mass, the displace­
ered for lined tunnels. Similarly, for GM2 and GM3 materials, different
ment at different locations is measured along the tunnel’s length, as
drop weights are impacted for the lined and unlined cases.
The impacting unit consists of a cylindrical-hemispherical nosed
drop hammer of 5 cm tup diameter attached with the load assembly, and
the disc weight may be added according to the requirement (Fig. 5). The
impact energy is controlled by weight of disc attached with the hammer,
and drop hammer’s falling height. For the measurement of deformation
along the tunnel length under impact loading, 3-AC slim line LVDTs (±5
mm) are used and placed at L/2, L/3 and 7L/12 positions from the
corner.

Fig. 5. Impact testing facility (ITF). Fig. 6. Deformation profile of the tunnel with GM1 synthetic rock for C/D 1.0.

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3.3. Experimental results for rock models, which are available in Abaqus/Explicit code. The rock
tunnel model comprises total of 92,518 nodes and 84,908 elements,
The deformations are measured at the tunnel’s crown on three including 2698 nodes and 2100 elements for lining. For meshing of
different locations and results are plotted for the same. The results for hammer, total of 912 four-node rigid elements (R3D4) and 900 nodes
GM1 synthetic rock for the lined and unlined tunnel are shown in Fig. 6. are used. The contour plots of deformations for unlined and lined tun­
It is found that the maximum deformation occurs at the point of loading. nels in GM1 material under different drop weights are shown in Figs. 9
Further, the punching and shear failure is also obtained at the impact and 10, respectively. The drop weights considered for the unlined tunnel
location for each drop weight. It is observed that the unlined tunnel are 12.4, 15.0, and 20.0 kg, whereas the drop weights for the lined
experiences massive deformation under very small drop energies as tunnel are 17.6, 20.0, and 25.0 kg. It is observed from the contour plots
compared to lined tunnels. The value of crown deformation is low for that the spread zone is less for unlined tunnels as compared to lined
lined tunnel due to the resistance offered by the lining material. Similar tunnels for C/D ratio of 1.0 in GM1 material. Similar type of contour plot
type of results are obtained for the other cases, and the results from the and deformation behaviour is obtained for the other geomaterials.
experimentation are used for the validation of the numerical model. The variation of deformation along the tunnel length through
experimental and numerical analysis for the lined and unlined tunnel
4. Numerical analyses and validation under different impact loads in GM1 material for C/D ratio of 1.0 is
shown in Figs. 11 and 12, respectively. The crown’s deformation value
In the present study, the numerical investigation is performed and obtained through experimentation and numerical analysis in an unlined
the obtained results are compared with the experimental results. The tunnel with C/D ratio of 1.0 under 20 kg of impact load for GM1 material
testing on small scale physical models is vital for the validation of the is 1.7 mm and 1.5 mm respectively. Similarly, the crown deformation
numerical model. The 3D FE model of the tunnel in rock mass, and drop obtained through experimentation and numerical techniques for the
hammer are modeled using ABAQUS explicit code and lagrangian ele­ lined tunnel in GM1 material for C/D ratio of 1.0 is 1.51 mm and 1.43
ments. The dimensions of the numerical model and Finite Element mesh mm, respectively. It is observed that the deformation of the tunnel
of rock mass are shown in Figs. 7 and 8, respectively. The top surface of crown increases with an increase in the drop weight. It is worth noting
the physical model is kept free to deform in all the directions, whereas that the pattern and the magnitude of vertical deformation computed
the bottom surface is restricted against both vertical and horizontal from the numerical model are in good agreement with that of physical
deformations for the dynamic analysis. All the side surfaces of the modeling for both lined and unlined tunnels in GM1 material. The dif­
physical model are allowed for vertical displacements and restrained ference between the numerical and experimental results is due to the
against horizontal displacements. Further, in the dynamic case the constitutive model and assumptions considered in the present investi­
coupled Eulerian - Lagrangian analysis is performed, and the non- gation. It is found that the numerical analysis predicts values on a
reflecting outflow boundary condition is defined at the Eulerian slightly higher side than the experimental results due to different as­
boundary to counter the wave reflection. sumptions on which analyses are based. Hence, the deformation value
The input parameters to model the drop hammer, tunnel lining, and obtained from numerical analysis for unlined and lined tunnels can be
surrounding rock are shown in Table 6. The rockmass is assumed as a considered as representative values for the design of the tunnels. It is
homogeneous, isotropic, and continuous material, and it is modelled also established that the fracture of rockmass under impact loads are
using the Mohr-Coloumb plasticity model, which allows the material to mainly due to tensile and shear failure. Further, the effect of load re­
harden or soften isotropically. Whereas, the lining and hammer are duces as the distance between the point of measurement and loading
assumed as elastic material in the analysis. Further, proper meshing is position increases.
done for different parts separately, as represented in Fig. 8(a)–(d). The The deformation at the crown of shallow tunnels in different geo­
global mesh size of 0.004 is adopted for the hammer, and the mesh size materials with C/D ratio of 1.0 and, subjected to drop weight of 10 kg, is
of 0.008 is applied to rockmass and tunnel lining. The hammer is given a shown in Fig. 13. It is found that the zone of influence along the tunnel
free fall under a gravitational effect from a height of 1.12 m. length is small in the case of GM1 material as compared to other syn­
The acceleration due to gravity ‘g’ of 9.81 m/s2 is applied to the thetic materials (GM2 and GM3), this behaviour is observed due to the
hammer to simulate the free-fall condition. For calculating the ham­ brittle nature of GM1 material. The crown deformation is maximum for
mer’s inertial properties, the drop weight disc of 2 cm thickness and 25 tunnels in GM3 material and minimum in the case of GM1 material. The
cm diameter are placed above the hammer. The inertial properties are crown deformation values obtained through experiments for the tunnel
applied at the hammer’s bottom most point by considering it as the in GM1, GM2, and GM3 material are 0.37, 0.6, and 0.95 mm respec­
reference point. tively. Similarly, the crown deformation values obtained through nu­
The eight-node brick element (C3D8R) with reduced integration, merical simulation for tunnel in GM1, GM2, and GM3 material are 0.4,
hourglass control, and finite membrane strains are used in the FE mesh 0.8, and 1.3 mm. The observed behaviour is due to the presence of pores

Fig. 7. Geometrical design of rock tunnel models.

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Fig. 8. Meshing of the Elements.

Table 6
Input parameters for model materials.
Material types Elasticity modulus (GPa) Poisson’s ratio (ν) Density (kg/m3) Friction angle (deg) Cohesion (MPa) UCS (MPa)

GM1 3.675 0.163 1216 39.12 0.790 3.51

GM2 2.809 0.216 1094 31.40 0.627 1.97
GM3 2.480 0.277 1105 22.65 0.400 1.14
PVC Lining 3.000 0.400 1400 – – –

and fissures, which are reducing the strength of GM2 and GM3 material, reduce as the brittleness of the material increases. The difference in the
and hence representing weak weathered rockmass. Further, the punch­ experimental and numerical results is more prominent for the cover
ing at the top surface of the physical models is also observed, and it is depth of 25 mm as compared to 35 and 50 mm; this is because the
very high in the case of weak rockmass, due to the collapse of the air deformation velocity at the crown is much higher for 25 mm than other
voids. The length of affect area in the direction of tunnel axis is 50 mm cover depths. It is also found that the effect of static material properties
for GM1 material and 100 mm for GM2 and GM3 material, which shows decreases with an increase in cover depth.
that the massive damage will take place inside the tunnels in weak
rockmass. 5. Prototype analysis
The effect of cover depth on the deformation of the crown of the
tunnel in GM2 material subjected to the drop weight of 12.4 kg is shown The testing of small-scale models is indispensable for complex
in Fig. 14. It is observed that the tunnels with more cover depth are not structural systems that are difficult to analyze theoretically and
affected much in the vertical direction because of the cushioning action. numerically or study experimentally. Impact tests are conducted on a
The deformations at the bottom of the tunnel lining are negligible in all small-scale model to obtain the response characteristics of a geometri­
the cases; therefore, it can be concluded that the heel of the tunnel is safe cally similar full-scale prototype which is the actual system of interest. In
for the given impact energy. Whereas, for cover depths of 35 and 25 mm, order to represent in-situ conditions, small models are scaled up to
large deformations are encountered in the vertical direction. The predict field deformations of tunnels in weak or weathered rockmass.
negligible deformation is also noticed at the bottom of the tunnel lining The dimensions of the rock tunnel model’s geometry, lining thickness,
for higher drop loads in numerical simulations. The deformation at the and mesh size are increased by 100 times, whereas the impact energy
top of the tunnel lining surrounded by different rock mass under varying applied on the prototype is 106 times that of the scaled model.
impact loads are measured experimentally as well as numerically and
compared. Further, it is worth to mention that for high cover depth (50
5.1. Geometry and meshing
and 35 mm), the deformation values of experimental and numerical
results are similar. Hence, the present study suggests that the tunnel
After adopting proper scaling laws, a 3D FE prototype model of
lining for shallow tunnels should be designed to resist the blast loads.
surrounding rockmass and tunnel is modeled with dimension 35 m × 30
Further, it can be concluded that the crown deformation and zone of
m × 30 m using the Abaqus/CAE tool with Langrangian elements. A 35
influence are dependent on the coupled effect of friction angle and
m long tunnel with a diameter of 5 m and a lining thickness of 150 mm is
cohesion of the rock mass. It is also concluded that the crack dimensions
created in a rock domain of 35 m long, and 30 m × 30 m cross-section,

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Fig. 10. Deformation contours for lined tunnels with C/D ratio of 1.0 under
Fig. 9. Deformation contours for unlined tunnels with C/D ratio of 1.0 under drop weights of (a) 17.6 kg (b) 20.0 kg and (c) 25.0 kg.
drop weights of (a) 12.4 kg (b) 15.0 kg and (c) 20.0 kg.

the central axis of the tunnel is placed at a depth of 5 m below the ground
surface.
In the present study, the rockmass with varying cover depth, con­
crete lining, their assembly, and hammer are developed through 3D part
option of Abaqus/CAE FE tool and are shown in Fig. 15 (a)–(f). The FE
mesh of the rock, tunnel lining, and hammer is considered 100 times the
small scaled models in both the cases of impact and blasting i.e., 0.8 m
for rockmass and tunnel lining, and 0.4 m for hammer or drop weight.
The contact between tunnel linings and rockmass is modeled with the
general contact option in Abaqus, with hard contact in the normal di­
rection and frictionless contact in the tangential direction. Due to sym­
metry about the YZ and YX planes in the numerical model, change in the
deformations, velocity and stress with respect to time is recorded at
desired locations of the tunnel in accordance with the location of the Fig. 11. Comparison of deformation profile obtained from numerical and
LVDT’s as discussed in small scale model section. experimental analysis for lined tunnel in GM1 material with C/D ratio of 1.0.

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5.2. Boundary condition

In order to minimize the reflection of the shock wave from the

rockmass boundaries, rockmass domain is considered much larger than
the size of the tunnel. The domain size is determined through boundary
convergence studies. The bottom boundary of the rock domain is fixed in
all Cartesian directions, x, y and z to signify bedrock. The XZ plane is
encastered while other planes are set free for both translational and
rotational motions in both impact and blast studies.

5.3. Constitutive modeling

As discussed in the small-scaled model’s case of buried circular

tunnel, rockmass is modeled by using Mohr-Coulomb plasticity model,
Fig. 12. Comparison of deformation profile obtained from numerical and whereas concrete lining is modeled using the concrete damage plasticity
experimental analysis for unlined tunnel in GM1 material with C/D ratio of 1.0. model [19–21]. In the present study, M30 grade concrete is adopted as a
lining material. In the concrete damaged plasticity model, stress–strain
relation is given by
( )
σ t = (1 − dt )Del0 : ε − εplt (3)
( )
σ c = (1 − dc )Del0 : ε − εplc (4)

where c and t represent compression and tension behavior, respectively.

Here, σ c and σ t are compressive and tensile stress vectors; εpl pl
c and εt are
plastic strains; dc and dt are the damage variables that are considered
functions of plastic strain; Del0 is the undamaged initial elastic modulus.
For the concrete damage model, the yield function is proposed by Lub­
liner et al. [22] and later modified by Lee and Fenves [23]. The yield
function is presented as
(√̅̅̅̅̅̅̅̅ √̅̅̅̅̅̅̅̅ ) 〈 〉 〈 〉
F= 3/2 s : s − 3αp + β ̂ σ max − γ − ̂
σ max − (1 − ∝)σ c = 0 (5)

(σ b0 /σ c0 )− 1 3(1− Kc )
where ∝ = 2(σ b0 /σ c0 )− 1, β = σc
− ∝) − (1 +∝), γ = 2Kc − 1 , σ c = (1−σcdt ) and
σt (1
σ t = (1−σtdt )where ̂
σ max represents maximum principal effective stress; s is
the deviatoric stress tensor; σb0 /σ c0 is the ratio of initial equibiaxial
Fig. 13. Variation of deformation profiles of lined tunnel with different ma­ compressive yield stress to initial uniaxial compressive yield stress; dt is
terials for 10.0 kg drop weight and C/D ratio of 1.0. the damage variable and Kc is the ratio of the second deviatoric stress
invariant on the tensile meridian to that on the compressive meridian at
initial crushing for any given value of effective mean stress, p =
(σ1 +σ2 +σ3 )/3.
The concrete damaged plasticity model assumes a non-associated
plastic flow, therefore the plastic potential function Gp used for this
model is given by
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
( )̅
3
GP = (εσ t0 tanψ ) + 2
s : s − ptanψ (6)
2

where ψ is the dilation angle at mean stress-deviatoric stress plane; σt0 is

the uniaxial tensile stress at failure, and ε is the eccentricity parameter. If
ε = 0, then GP represents straight line. The material properties of plain
concrete used in the study are shown in Table 7.

5.4. Prototype models subjected to impact loading

The velocity of the drop hammer in the prototype study is changed so

that the velocity at the tunnel crown in the prototype becomes equiva­
lent to a small scale model. In the case of a small scale model, the ve­
locity at the tunnel crown in GM1 material for C/D ratio = 1.0 is 0.45 m/
Fig. 14. Effect of cover depth on the deformation profiles of unlined tunnel in s, and the velocity of the hammer is 4.68 m/s. As per scaling laws, the
GM2 material for 12.4 kg drop weight. velocity of the tunnel crown deformation should be same in both small
scale and prototype models. Therefore, the velocity of crown deforma­
tion in prototype is considered as 0.45 m/s, and the velocity of the
hammer required to obtain the corresponding crown deformation ve­
locity is found to be 8 m/s. It is observed that the hammer’s velocity in

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Fig. 15. Geometrical design of hammer and rock tunnel model, model with C/D, (a) 1.0, (b) 0.7, (c) 0.5 (d) Hammer (e) Assembly (f) Lining thickness (All dim. in m).

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S. Mishra et al. Structures 29 (2021) 2162–2173

Table 7
Material properties for concrete (Tiwari et al. 2016)
Density (ρc ;kg/m3) 2400 Elastic modulus (Ec; GPa) 27.4

Poisson’s ratio (ʋc) 0.2 Compressive strength (fck; MPa) 30

Friction angle (φ) 32o Kc 0.7
Eccentricity (ε) 0.1 Viscosity parameter 0.0001
σb0 /σc0 1.16 Dilation angle (Ψ) 20o

the prototype is approximately 1.7 times the velocity of the hammer in a

small scale model. The deformation of the tunnel crown immediately
below the impact loading location for a lined tunnel in GM1 material at
C/D ratio of 1.0 is 0.008 m. In contrast, the deformation in the case of a
small scale model is 0.9 × 10− 3 m. Hence, it can be concluded that the
deformation in the case of the prototype is approximately 10 times the
deformation in a small scale model.

5.5. Shallow tunnels under blast loading

The blast load experienced by the tunnel is due to internal and Fig. 16. Variation of crown deformation of tunnel in GM1 material with C/D =
external explosions, which can severely damage the tunnel lining. The 1.0 under blast loading.
damage to the tunnel lining is aggravated if the tunnels are at very
shallow depth, such as Delhi metro tunnels. Nevertheless, the chances of 1000 kg) are detonated on the ground surface above the existing tunnel.
an explosion inside an underground structure are significantly less The results are obtained for lined tunnels with C/D ratio of 1.0 in GM1
because of the current technological advancement, which can detect the material. The variation of tunnel crown deformation along the tunnel
carrier of explosive material very quickly inside the tunnel. However, length under different blast loading is shown in Fig. 16. It is found that
many researchers have determined the dynamic response of under­ the deformation of the tunnel crown increases with an increase in the
ground tunnels subjected to internal blast [5–10,19–21]. On the con­ TNT amount. The deformation of tunnel crown under 100, 250, 500, and
trary, external blasts are more prominent to occur and cause excessive 1000 kg of TNT is 0.0025, 0.006, 0.007, and 0.033 m respectively. The
destruction because of the difficulties in monitoring and preventing such comparison of tunnel crown deformation under blast load and impact
activities. Further, the database on full-scale field experimentation to load is shown in Table 8. It is observed that the deformation at the crown
investigate the impact of blast loading on tunnel crown deformation is of the prototype lined tunnel under 500 kg of blast loading is approxi­
very limited because such an experiment is extremely risky, costly, and mately equal to the impact loading. Therefore, it can be concluded that
unachievable in civilian research. Hence, in the present investigation, the damage to the tunnel crown due to blast loading can be simulated by
the numerical study of a prototype is carried out by creating surficial carrying out the impact loading investigations.
detonation over a circular tunnel buried at C/D ratio of 1.0 in GM1 The limitations associated with the conduct of field experimentation
material, and the effect of different explosive weights of TNT (100, 250, have forced scientists to search for the alternative method, therefore a
500 and 1000 kg) on the tunnel is examined. new methodology is developed to carry out such investigations. The
present methodology is the combination of both experimental and nu­
5.5.1. Constitutive modeling of blast load merical techniques. Firstly, the small scale physical models are prepared
Dynamic load due to detonation result in strain rates of the order of using proper scaling laws, and then the impact testing is performed on
10− 1 to 103 s− 1, which indicate short time dynamic behavior of the the physical model. Secondly, the numerical investigation of the phys­
materials involved. The materials are characterized mainly by a great ical model is performed under laboratory conditions, and then the
over strength and increased stiffness compared to static properties (low experimental and numerical results are compared for the validation
strain rate). Different models are available to allocate blast loading over purpose. Thirdly, the numerical investigation of impact loading on the
underground structures, but in the present investigation, a universally prototype is carried out, and the tunnel deformation results of small
accepted empirical model of blast (CONWEP) is used for modeling sur­ scale model and prototype under impact loading are compared for the
face and air blast. The CONWEP is the acronym of the Conventional validation of the prototype model. Finally, the effect of blast loading on
Weapons Effects Programme, a study made by USACE (USACE, 1986), to the tunnel deformation of the prototype is investigated.
simulate of the effects of a blast produced by conventional explosives.
Because of the simplicity, this model is widely used by scholars for
determining blast overpressure and its decay with time. The peak
overpressure calculated in the CONWEP model is given by
Table 8
( )
P(t) = Pr .cos2 θ + Pi 1 + cos2 θ − 2cosθ (7) Comparison of tunnel crown deformation for the lined tunnel of C/D ratio of 1.0
in GM1 material under blast and impact load.
where θ is the angle of incidence, defined by the tangent to the
Type of loading Deformation at tunnel
tangent’s surface and wavefront. Since reflected pressure from the sur­ crown (m)
face is also taken into account in CONWEP, therefore total blast pressure
Blast loading (TNT, 100 0.0025
is applied as the sum of incident and reflected pressure. Pr represents kg) 250 0.006
reflected pressure, and Pi is the incident pressure. It is noticed in CON­ 500 0.007
WEP that the model computes reflected pressure values and applies 1000 0.033
these to the surface of detonations by incorporating the angle of inci­ Impact loading Small scale model 0.0009
dence of the blast wave. (Experimental)
Small scale model 0.001
5.5.2. Tunnels subjected to blast load (Numerical)
Prototype (Numerical) 0.008
In this study, four different weights of explosives (100, 250, 500, and

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6. Conclusion References

Underground structures are constructed in different possible ground [1] Abaqus/Explicit User’s Manual, version 6.14. Dassault Systemes Simulia
Corporation, Providence, 2011.
conditions ranging from soft ground to massive jointed rock. In the [2] Zhang QB, Zhao J. A review of dynamic experimental techniques and mechanical
present study, an attempt is made to simulate the in-situ condition behaviour of rock materials. Rock Mech Rock Eng 2014;47(4):1411–78.
through the physical and numerical modeling. Extensive experimenta­ [3] Xia K, Yao W. Dynamic rock tests using split Hopkinson (Kolsky) bar system–a
review. J Rock Mech Geotech Eng 2015;7(1):27–59.
tion is performed for the validation of numerical modeling. Further, the [4] Li X, Zou Y, Zhou Z. Numerical simulation of the rock SHPB test with a special
assessment of deformations at different locations is carried out by shape striker based on the discrete element method. Rock Mech Rock Eng 2014;47
varying cover depth and drop energies. It is observed that the numerical (5):1693–709.
[5] Liu H. Dynamic analysis of subway structures under blast loading. Geotech Geol
analysis for small scale models is in good agreement with the experi­ Eng 2009;27(6):699.
mentation. The extent of the damage along the tunnel length depends on [6] Liu H. Soil-structure interaction and failure of cast-iron subway tunnels subjected
different factors like cover depth, the intensity of drop loads, and me­ to medium internal blast loading. J Perform Constr Facil 2012;26(5):691–701.
[7] Feldgun VR, Kochetkov AV, Karinski YS, Yankelevsky DZ. Internal blast loading in
chanical strength of the surrounding rockmass. It is observed that when
a buried lined tunnel. Int J Impact Eng 2008;35(3):172–83.
the hammer strikes to the top surface of the rock tunnel model, it started [8] Yang Y, Xie X, Wang R. Numerical simulation of dynamic response of operating
to penetrate the top surface up to a certain distance before the rebound metro tunnel induced by ground explosion. J Rock Mech Geotech Eng 2010;2(4):
of the hammer is observed. Due to this, the total impact energy imparted 373–84.
[9] Mishra S. Physical and Numerical Modeling of Tunnels under Blast and Impact
by drop hammer is equal to the difference between the kinetic energy of Loads. Ph.D. Thesis. Department of Civil Engineering, Indian Institute of
the hammer before striking and after striking. For lined tunnels with Technology Delhi, 2019.
varying surrounding rockmass and drop energies, the difference be­ [10] Lu Y. Underground blast induced ground shock and it’s modelling using artificial
neural network. Comput Geotech 2005;32(3):164–78.
tween the ranges of deformations obtained numerically is 2–7% more [11] Gui MW, Chien MC. Blast-resistant analysis for a tunnel passing beneath Taipei
than that of the deformations obtained experimentally. This difference is Shongsan airport–a parametric study. Geotech Geol Eng 2006;24(2):227–48.
considerable in unlined tunnels, particularly for unlined tunnels with C/ [12] Mussa MH, Mutalib AA, Hamid R, Naidu SR, Radzi NA, Abedini M. Assessment of
damage to an underground box tunnel by a surface explosion. Tunn Undergr Space
D 1.0 in GM1 material, the difference varies from 10 to 15%. Technol 2017;1(66):64–76.
In the present study, the effect of impact and blast load on the pro­ [13] Jose J, Anju V. Numerical study of the Cross-Sectional Shape of Tunnel under Blast
totype is also investigated. It is observed that the velocity of the crown Effect Using Ansys. Int Res J Eng Technol (IRJET) 2018;5(5):3582–6.
[14] Tiwari R, Chakraborty T, Matsagar V. Dynamic analysis of underground tunnels
deformation in the prototype and small scale model should be the same. subjected to internal blast loading. In World Congress of Computational Mechanics
It is found that the deformation in the case of a prototype subjected to (WCCM XI), Barcelona 2014 Jul 25.
impact loading is approximately 10 times the deformation in a small [15] Mishra S, Rao KS, Gupta NK, Kumar A. Damage to shallow tunnels under static and
dynamic loading. Procedia Eng 2017 Jan;1(173):1322–9.
scale model. It can be concluded from the investigation that the blast
[16] Mishra S, Rao KS, Gupta NK, Kumar A. Damage to shallow tunnels in different
loading can be simulated by carrying out the impact loading in­ geomaterials under static and dynamic loading. Thin-Walled Struct 2018;1(126):
vestigations. Further, the field experimentation to investigate the effect 138–49.
of blast loading on tunnel deformation is very risky, costly, and [17] Sharma H, Mishra S, Rao KS, Gupta NK. Effect of Cover Depth on Deformation in
Tunnel Lining When Subjected to Impact Load. In ISRM International Symposium-
unachievable; therefore, a new methodology is developed to carry out 10th Asian Rock Mechanics Symposium 2018 Jan 1. International Society for Rock
such investigations. The developed methodology is the combination of Mechanics and Rock Engineering.
both experimental and numerical techniques. The methodology pro­ [18] Dhamne R, Mishra S, Kumar A, Rao KS. Numerical study of the cross-sectional
shape of shallow tunnels subjected to impact and blast loading. In EGCON 2018
posed in the present study can be used by the academicians and engi­ National Conference on Prospects and Retrospect in Engineering Geology,
neers to validate the numerical models under impact loads. After Geophysics and Instrumentation, Hyderabad, India 2018.
validation, the numerical models can be scaled to represent the real site [19] Tiwari R, Chakraborty T, Matsagar V. Dynamic analysis of tunnel in soil subjected
to internal blast loading. Geotech Geol Eng 2017;35(4):1491–512.
conditions. However, the scope of the present work is limited to the [20] Tiwari R, Chakraborty T, Matsagar V. Dynamic analysis of a twin tunnel in soil
intact and homogeneous weak rockmass. subjected to internal blast loading. Indian Geotech J 2016;46(4):369–80.
[21] Tiwari R, Chakraborty T, Matsagar V. Dynamic analysis of tunnel in weathered
rock subjected to internal blast loading. Rock Mech Rock Eng 2016;49(11):
Declaration of Competing Interest 4441–58.
[22] Lubliner J, Oliver J, Oller S, Oñate E. A plastic-damage model for concrete. Int J
The authors declare that they have no known competing financial Solids Struct 1989;25(3):299–326.
[23] Lee J, Fenves GL. Plastic-damage model for cyclic loading of concrete structures.
interests or personal relationships that could have appeared to influence
J Eng Mech 1998;124(8):892–900.
the work reported in this paper.

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