Numerical study of the cross-sectional shape of shallow...

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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

Journal of Engineering Geology Volume XLIII, Nos. 1 & 2

A bi-annual Journal of ISEG June-December 2018

24

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



26

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)



34

-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

)


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

)


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.



35

-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.

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