Indian Geotechnical Conference (IGC-2010)igs/ldh/files/igc 2015 pune/THEME 4... · In this study, finite element analysis of a rock tunnel has been carried out by 2D modeling and

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50th INDIAN GEOTECHNICAL CONFERENCE

17th – 19th DECEMBER 2015, Pune, Maharashtra, India

Venue: College of Engineering (Estd. 1854), Pune, India

FRACTURED AND UNFRACTURED ANALYSIS OF A ROCK TUNNEL BY FINITE ELEMENT METHOD

Imran Ahmad Khan1, Kumar Venkatesh2, R. K. Srivastava3

ABSTRACT

Tunnels are important part of our modern infrastructure system. There is a tremendous need of a tunnelling system due to scarcity of land for proper transport of people, vehicles and materials such as water, oil etc. The need of tunnels may arise also when a more direct, faster, less obtrusive movement is required. Obstruction may be mountain, soil, any water body, dense traffic and urban area. Therefore according to their purpose a tunnel may be a railway tunnel, highway tunnel, pedestrian tunnel, navigation tunnel, subway tunnel, hydroelectric power station tunnels, water supply tunnels, sewer tunnels etc. A tunnel can be constructed by numerous ways such as cut cover method, sequential excavation method, boring technique by TBM. The cross sections of tunnels may be circular, semi circular, multi curve, horse shoe, cathedral arch, arched, flat roofed, elliptical. Therefore proper analysis of tunnels is extremely important. There are different approaches for the analysis of tunnels such as analytical approaches, observational approaches, physical modelling, empirical approaches, and numerical modelling. Finite element method, finite difference method, boundary element method, discrete element method, beam element method are some of the methods employed in the numerical modelling and analysis of tunnels. In this study, finite element analysis of a rock tunnel has been carried out by 2D modeling and meshing. Fractured and unfractured rock mass with tunnel has been considered for analysis. Interactive behavior between tunnel lining and rock has been studied with the variation of stresses and deformation. The models have been used to investigate the stress concentration along with deformation in the vertical, horizontal and radial axis. Parametric study considering different tunnel cross sections has also been performed. In addition to above comparative study has also been carried out to consider the type of tunnel section suitable for such condition i.e. circular, semi-circular, or horse shoe in both fractured and unfractured rocks. The outcome of finite element analysis represents that in unfractured rock, the most suitable section from vertical stress point of view is horse shoe and from deformation point of view, the suitable section is semi circular. The results also depicts that in fractured rock, the most

1Imran Ahmad Khan, Research Scholar, Civil Engineering Department, Motilal Nehru National Institute Of Technology,

Allahabad, India, [email protected] 2Kumar Venkatesh, Assistant Professor, Civil Engineering Department, Motilal Nehru National Institute Of Technology,

Allahabad, India, [email protected] 3R. K. Srivastava, Professor, Civil Engineering Department, Motilal Nehru National Institute Of Technology, Allahabad, India,

[email protected]

mailto:imranzhcet@

mailto:[email protected]


Imran Ahmad Khan, Kumar Venkatesh, R. K. Srivastava

suitable section from both point of view is semi circular. The following figure and graph shows the variation of deformations as a result obtained from the finite element analysis of the circular tunnel model with the help of ABAQUS software. Keywords: tunnel, rock, finite element method

Variation of deformations for circular section tunnel in fractured dolomite rock

Variation of deformations for different cross sections of tunnel in fractured and unfractured rock conditions along vertical section

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0 5 10 15 20 25

dis

pla

cem

en

t (m

)

distance (m)

circular(uf)

circular(f)

horseshoe(uf)horsrshoe (f)

semicircular(uf)semicircular(f)

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FRACTURED AND UNFRACTURED ANALYSIS OF A ROCK TUNNEL BY FINITE ELEMENT METHOD

Imran Ahmad Khan, Research Scholar, CED, MNNIT, Allahabad, India, [email protected] Kumar Venkatesh, Assistant Professor, CED, MNNIT, Allahabad, India, [email protected] R. K. Srivastava, Professor, CED, MNNIT, Allahabad, India, [email protected] ABSTRACT: In this study, finite element analysis of a rock tunnel has been carried out by 2D modeling and meshing. Fractured and unfractured rock mass with tunnel has been considered for analysis. Interactive behavior between tunnel lining and rock has been studied with the variation of stresses and deformation. The models have been used to investigate the stress concentration along with deformation in the vertical, horizontal and radial axis. Parametric study considering different tunnel cross sections has also been performed. In addition to above comparative study has also been carried out to consider the type of tunnel section suitable for such condition i.e. circular, semi-circular, or horse shoe in both fractured and unfractured rocks. The outcome of finite element analysis represents that in unfractured rock, the most suitable section from vertical stress point of view is horse shoe and from deformation point of view, the suitable section is semi circular. The results also depicts that in fractured rock, the most suitable section from both point of view is semi circular. INTRODUCTION Tunnels are important part of our modern infrastructure system. There is a tremendous need of a tunnelling system due to scarcity of land for proper transport of people, vehicles and materials such as water, oil etc. The need of tunnels may arise also when a more direct, faster, less obtrusive movement is required. Obstruction may be mountain, soil, any water body, dense traffic and urban area. Therefore according to their purpose a tunnel may be a railway tunnel, highway tunnel, pedestrian tunnel, navigation tunnel, subway tunnel, hydroelectric power station tunnels, water supply tunnels, sewer tunnels etc. A tunnel can be constructed by numerous ways such as cut cover method, sequential excavation method, boring technique by TBM. The cross sections of tunnels may be circular, semi circular, multi curve, horse shoe, cathedral arch, arched, flat roofed, elliptical. Therefore proper analysis of tunnels is extremely important. There are different approaches for the analysis of tunnels such as analytical approaches, observational approaches, physical modelling, empirical approaches, and numerical modelling.

Finite element method, finite difference method, boundary element method, discrete element method, beam element method are some of the methods employed in the numerical modelling and analysis of tunnels. In this paper finite element method has been used for modelling and meshing of tunnels in 2D for the observation of vertical stresses and deformations along different sections of the tunnel excavated in rock. Parametric study has also been performed considering different cross sections of the tunnel and fractured conditions. Finally a comparative study with respect to which type of tunnel section is more suitable in both fractured and unfractured rock conditions. Finite Element Modelling and Meshing For the modelling and meshing purpose finite element software ABAQUS has been used. The rock is considered to be a block of size 100 × 40 × 50 m. Three cross sections of the tunnel are considered for the analysis purpose namely circular, semi circular, and horse shoe. The diameter of the tunnel in first 2 sections is 10 m. Geometry of the sections are given in the figure 1.





Fig. 1 Geometry of different tunnels

Lining thickness is considered to be 0.75 m. Lining specifications are given in the table 1 :

Table1 Lining properties [13]

Lining material

Density Modulus of

elasticity

Poisson’s

ratio

Concrete 2400 kg/m3

2.75e10 N/m2

0.2

Rock is considered with specifications in the table 2 :

Table 2 Rock properties [14]

Rock name

Density

Modulus of elasticity

Poisson’s

ratio Dolomite 2700

kg/m3

4.0e10

N/m2

0.29

Boundary Conditions A set of boundary conditions was defined for the model to provide stability to the structural system. The analysis model was established with a fixed boundary at the bottom and roller supports on sides, such that the displacement in the x-direction at the two vertical sides of the model is equal to zero (ux =0). The displacement in the y-direction at the bottom horizontal boundary of the model is equal to zero (uy=0). Loading conditions Self weight of the rock including lining is considered for the analysis in all the cases. Meshing Finite element meshing is done with description given in the table 3:

Table 3 Details of meshing for 2D analysis Tunnel section

Total no. of nodes

Total no. of elements

Element shape

Element type

Circular 209 187 Linear quadrilateral

CPS4R*

Semi circular

277 259 Linear quadrilateral

CPS4R*

Horse shoe

220 197 Linear quadrilateral

CPS4R*

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CPS4R* A 4 node bilinear plane stress quadrilateral, reduced integration, hourglass control.

Fig. 2 Meshing of different tunnels

2D Analysis of Fractured rock In this analysis, fractured rocks are taken into consideration. A 2 dimensional plane strain analysis is done considering the same rock type, rock geometry, tunnel cross sections, lining property, boundary conditions and loading as in the case of 2D unfractured analysis. The fracture properties are given in the table 4 :

Table 4 Fracture properties of rocks

Mode of crack Width of crack

Vertical height of

crack Opening mode 10 mm 38 m

Fig. 3 uniform fracture condition in different rock

tunnels

Meshing Finite element meshing is done with description given in the table 5:

Table 5 Details of meshing fractured rock in 2D analysis

Tunnel section

Total no. of nodes

Total no. of elements

Element shape

Element type

Circular

392

355

Linear quadrilateral

CPS4R*

Semi circular

320

286


CPS4R*

Horse shoe

417

377


CPS4R*

CPS4R* A 4 node bilinear plane stress quadrilateral, reduced integration, hourglass control.


Fig. 4 Finite element meshing of different

fractured tunnels in 2D

Results Results Obtained from 2D Analysis of Unfractured Rock Circular section

Fig. 5(a) Variation of vertical stress for circular

section tunnel in unfractured rock

Fig. 5(b) Variation of deformation for circular

section tunnel in unfractured rock Horse shoe section

Fig. 6 Variation of vertical stress and deformation

for horse shoe section tunnel in unfractured rock

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Semi circular section

Fig. 7 Variation of vertical stress and deformation for semi circular section tunnel in unfractured rock

Results Obtained from 2D Analysis of Fractured Rock


for circular section tunnel in fractured rock



for horse shoe section tunnel in fractured rock

Fig.10 Variation of vertical stress and deformation

for semi circular section tunnel in fractured rock

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Vertical section

Horizontal section

Inclined section Fig.11 Variation of vertical stresses in unfractured rock and lining considering different sections of tunnel

Vertical section

Horizontal section

Inclined section

Fig. 12 Variation of deformations in unfractured rock and lining considering different sections of tunnel

0

50000

100000

150000

200000

250000

300000

350000

0 10 20 30

stre

ss (

N/m

2)

distance (m)

circular

horse shoe

semicircular

0

200000

400000

600000

800000

1000000

1200000

-5 0 5 10 15 20

stre

ss (

N/m

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horse shoe

semi circular

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200000

300000

400000

500000

600000

700000

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ss (

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semicircular

0.00076

0.00077

0.00078

0.00079

0.0008

0.00081

0.00082

0.00083

0.00084

0.00085

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pla

cem

en

t (m

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distance (m)

circular

horseshoe

semicircular

0.00056

0.00057

0.00058

0.00059

0.0006

0.00061

0.00062

0.00063

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pla

cem

en

t (m

)

distance (m)

circular

horseshoe

semicircular

0.0007

0.00072

0.00074

0.00076

0.00078

0.0008

0.00082

0.00084

0 10 20 30

dis

pla

cem

en

t (m

)

distance (m)

circular

horseshoe

semicircular


Vertical section

Horizontal section

Inclined section

Fig. 13 Variation of vertical stress for different sections of tunnel in fractured and unfractured rock

Vertical section

Horizontal section

Inclined section

Fig. 14 Variation of deformations for different sections of tunnel in fractured and unfractured rock

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200000

400000

600000

800000

1000000

1200000

0 10 20 30

stre

ss (

N/m

2)

distance (m)

circular (uf)

circular (f)

horse shoe(uf)

horse shoe(f)

semi circular(uf)

semi circular(f)

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200000

400000

600000

800000

1000000

1200000

1400000

1600000

-10 0 10 20

stre

ss (

N/m

2)

distance (m)

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circular (f)

horse shoe(uf)

horse shoe (f)

semi circular(uf)

semi circular(f)

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1000000

2000000

3000000

4000000

5000000

6000000

0 10 20 30

stre

ss (

N/m

2)

distance (m)

circular (uf)

circular (f)

horse shoe(uf)

horse shoe(f)

semicircular (uf)

semicircular (f)

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0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

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dis

pla

cem

en

t (m

)

distance (m)

circular (uf)

circular (f)

horse shoe(uf)

horsr shoe(f)

semicircular (uf)

semicircular (f)

0.0005

0.00052

0.00054

0.00056

0.00058

0.0006

0.00062

0.00064

-10 0 10 20

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pla

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en

t (m

)

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circular (f)

horse shoe(uf)

horse shoe (f)

semi circular(uf)

semi circular(f)

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0.0006

0.0008

0.001

0.0012

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The maximum vertical stress and maximum deformation for different types of tunnels are given in the following table:

Table 6 Maximum vertical stresses and maximum deformations for different tunnels

Tunnel(in

unfractured

rock)

Max. stress (×106

N/m2)

Location

of max.

stress

Max. deforma

tion (mm)

Location of

max.

deformation

Circular 1.061 wall 0.830 crown Horse shoe 1.072 wall 0.845 crown Semi circular

1.250 wall 0.829 crown

Discussions In the models, there is significant change in the vertical stresses near the lining region. The vertical stresses are decreasing after reaching a maximum value near lining region in all the sections. The vertical stresses are having a maximum value in horse shoe tunnel while considering the vertical and inclined section. The vertical stresses are having a maximum value in circular tunnel while considering the horizontal section. For vertical and inclined section, the vertical stresses are minimum for semi circular tunnel. For horizontal section, the vertical stresses are minimum for horse shoe tunnel. The deformations are decreasing continuously in a vertical section in all types of tunnel. The deformations are increasing after reaching a minimum value in all the tunnels while considering the inclined section. The deformations are increasing near the lining region for circular and horse shoe tunnel while considering the horizontal section but it is decreasing for semi circular tunnel. The deformations are having a maximum value in horse shoe tunnel while

considering any section. The deformations are minimum for semi circular tunnel while considering any section. The deformations in unfractured rock are more than fractured rock in horizontal and inclined section due to location of the crack. In fractured rock, maximum vertical stresses in vertical and horizontal sections are observed in semi circular tunnel. In fractured rock, maximum vertical stresses in inclined section are observed in circular tunnel. In fractured rock, minimum vertical stresses in vertical section are observed in circular tunnel. In fractured rock, minimum vertical stresses in horizontal section are observed in horse shoe tunnel. In fractured rock, minimum vertical stresses in inclined section are observed in semi circular tunnel. In fractured rock, maximum deformations in any section are observed in horse shoe tunnel. In fractured rock, minimum deformations in vertical section are observed in semi circular tunnel. In fractured rock, minimum deformations in horizontal section are observed in semi circular tunnel. In fractured rock, minimum deformations in inclined section are observed in circular tunnel. CONCLUSIONS On the basis of present study it can be concluded that in case of unfractured rock, the horizontal section is most critical due to vertical stresses in all type of tunnels. Vertical stress in circular tunnel is maximum whereas it is minimum for horse shoe tunnel. Therefore, comparing the vertical stress distribution in horizontal section it may be concluded that horse shoe tunnel is better. If deformation is considered and compared the most critical section is crown of the tunnel. From the present study it is clear that deformations are maximum for horse shoe tunnel but the deformations are minimum for semi circular tunnel. So in unfractured rock, the most suitable section from deformation point of view is semi circular. The most critical section in case of fractured rock is inclined section of the tunnel which is associated with crown of the tunnel. The vertical stresses are maximum for circular tunnel in inclined section but it is minimum for semi circular

Tunnel(in fractured rock)

Max. stress (×106

N/m2)

Location of max. stress

Max. deformat

ion (mm)

Location of max.

deformation

Circular 2.774 crown 1.082 crown Horse shoe

3.132 crown 1.238 crown

Semi circular

3.236 crown 1.020 crown


tunnel. So the most suitable tunnel in fractured rock is semi circular. Considering deformation point crown of the tunnel is critical along vertical section. Deformations are maximum for horse shoe tunnel but the deformations are minimum for semi circular tunnel. So in fractured rock, the most suitable section from deformation point of view is semi circular. REFERENCES

1. A. Elsayed, Study of Rock-Lining Interaction for Circular Tunnels Using Finite Element Analysis, Jordan Journal of Civil Engineering, Volume 5, No. 1, 2011.

2. A.M. El-Shihy, S.S. Abd El-Salam and H.M. El-Aassar, "Finite Element Analysis of open R.C. Tunnels" Proceeding of International Symposium on Tunneling in Congested Cities, January 28-29, ,Cairo, Egypt, PP. 301-319, 1991.

3. ABAQUS, 2001. ABAQUS/Standard User’s Manual. Hibbitt, Karlsson &

Sorensen, Inc. 4. Addenbrooke, T.I., Potts, D.M., Puzrin,

A.M., 1997. The influence of prefailure soil stiffness on the numerical analysis of tunnel construction. Geotechnique 47 (3), 693–712.

5. Asano, T., Ishihara, M., Kiyota, Y., Kurosawa, H., Ebisu, S., 2003. An observational excavation control method for adjacent mountain tunnels. Tunnelling and Underground Space Technology 18, 291–301.

6. Brown E.T., 1987, Analytical and computational methods in engineering rock mechanics, Allen & Unwin Ltd, London, UK.

7. Curran, J.H., Hammah, R.E., Yacoub, T.E., 2003. A two-dimensional approach for designing tunnel support in weak rock. In: Proceedings of the 56th Canadian Geotechnical Conference, Winnepeg, Manitoba, Canada, October 2003, pp. 1–6.

8. Galli, G., Grimaldi, A., Leonardi, A., 2004. Three-dimensional modeling of tunnel excavation and lining. Computers and Geotechnics 31, 171–183.

9. Keshvarian K., 2003, Seismic isolation of tunnels, M.Sc. thesis, Sahand University of Technology, Tabriz, Iran.

10. Ozgur Satıcı, Bahtiyar Unver, Assessment

of tunnel portal stability at jointed rock mass: A comparative case study, Computers and Geotechnics 64 (2015) 72–

82. 11. Potts, D.M., Zdravkovic, L., 2001. Finite

Element Analysis in Geotechnical Engineering Application. Thomas-Telford, London, p. 427.

12. S. Elavenil, A.Vanuvamalai, Analysis Of Tunnel For Different Subsoil Condition, International Journal of Civil Engineering applications Research, Vol 03, Issue 02, May-Aug 2012.

13. Sevim, Nonlinear earthquake behaviour of highway tunnels, Nat. Hazards Earth Syst. Sci., 11, 2755–2763, 2011.

14. T Ramamurthy, Engineering in Rocks for Slopes, Foundations, and Tunnels

15. Xiaojun Li, Zhiguo Yan, Zhen Wang, Hehua Zhu, Experimental and analytical study on longitudinal joint opening of concrete segmental lining, Tunnelling and Underground Space Technology 46 (2015) 52–63.

Documents

Indian Geotechnical Conference (IGC-2010)igs/ldh/files/igc 2015 pune/THEME 4... · In this study, finite element analysis of a rock tunnel has been carried out by 2D modeling and