0416paper_long.pdf

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Abstract

This paper deals with the study of soil-structure interaction based on 2D and 3D finite element

analysis of tunnels by using the software GTS (Geotechnical and Tunnel Analysis System). For buriedStructures like tunnels, the underneath soil/rock is to be simulated by elastic spring while surroundingand overlying soil/rock by superimposed loads. GTS is state of the art software, which defines a newparadigm for tunnel engineering and other specific geotechnical structures. It is founded on the expertanalysis and exceptional graphic technologies. GTS enables the engineers to intuitively generatecomplex geotechnical models. Such modelling capabilities are armed with very strong analysisfeatures, powered by a uniquely developed multi-frontal solver providing the fastest analysis speed. In3D finite element analysis of tunnels, the values of forces and moments are less than 2D FEA.Therefore, It can be concluded that the tunnel designed by using Terzaghis method & 2D FEA is onthe safer side but uneconomical. Also, the difference in values of forces and moments, between 3DFEA and 2D FEA, has been found to be more in large sections than small sections.

Also it is found that 2D finite element analysis of tunnels conserves simplicity and can be run on a

relatively normal computer, yet it tends to yield less accurate results. While 3D finite element analysisof buried structures require additional efforts, yet it gives a more realistic solution of soil-structure

interaction and the availability of modern geotechnical engineering software (GTS) and speedy

computers has facilitated the work. Moreover a single analysis gives stresses and forces both in soil

and structures. Therefore, it is concluded that the tunnels should be designed by 3D finite element

method.

Keywords: Tunnel, GTS, soil-structure interaction , finite element analysis,

1

Introduction

The analysis and design of buried structures is one of the most complicated and difficult subjects.With the advent of large-span flexible designs, buried structures are increasingly being used for large

culverts, tunnels and underground tanks. The engineer must understand the unusual behavior of such

structures and recognize the inherent difficulties in their design. The most important concept in

understanding buried structures is that the structural actions of the liner (that is the tunnel) and the

soil cannot be separated (Swoboda et al., 1987). The magnitudes of the interplay between soil and

structure depend on the boundary loadings. Moreover, the relative stiffness of soil and liner is not a

simple relationship, but is different in axial and flexural modes of deformation and is also dependent

Comparison of 2D & 3D finite element analysis of tunnels based onsoil-structure interaction using GTS

Liaqat Ali Qureshi, Kashif AminUnversity of Engineering & Technology, Taxila, Pakistan

Tahir Sultan & M. Ilyas ShBahaudin Zakariya University, Multan, Pakistan


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measurements demonstrate the ability of the bounding surface model to solve problems of tunneling

in saturated porous medium.

2

Analysis of tunnels

The analysis deals with the study of soil-structure interaction with the help of GTS (software) for twotypical sizes (10/x 10/ & 26/x 22/) of tunnels, based on 2D and 3D finite element analysis.

2.1

Properties of materials

The rock with the following material properties is taken to study the interaction of tunnels with the

surrounding material:

Modulus of elasticity of rock =229,740 ksf

Poissons ratio = 0.33

Unit weight (dry) = 0.1686 kcf

Unit weight (saturated) = 0.1686 kcf

Cohesion = 5.22 ksf

Friction angle = 30o

Tensile strength = 83.5 ksf

Initial stress parameters = 0.5

Modulus of subgrade reaction =2500 ksf

RQD = 50% - 75%

2.2

Loads on 10/x 10

/tunnel

Load on the model made up in 2D finite element analysis was calculated using Terzaghis theory:

Roof load = 0.4 (B +Ht)

r = 0.4 x 0.1686 x (12+12) = 1.624 ksf

B =10 + 1 + 1 = 12/ Ht = 10 + 2 = 12

/

Wall load h= kor = 0.5 x 1.62 = 0.81 ksf

Only self weight was applied in the model comprising 3D finite elements.

2.3

Loads on 26/x 22

/tunnel

Load on the model made up of 2D Finite Elements was also calculated using Terzaghis Theory:

Roof load = 0.4 (B +Ht)

r = 0.4 x 0.1686 x (30+25.91) = 3.77 ksf

B = 26 + 2 + 2 = 30/ Ht = 21.91+4 = 25.91

/

Wall load h= kor = 0.5 x 3.77 = 1.885 ksf

Only self weight was applied in the model comprising 3D finite elements.

2.4 Tunnel geometry

The 2D finite element model has been developed by using shell elements. Linear elastic springs are

provided under all nodes of base slab equal to the product of contributing area and co-efficient of


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modulus of sub grade reaction. For stability of structure, translations in principle horizontal directions

are kept fixed and springs are provided only in vertical direction. All the three rotations are kept free.

(Figure 1).

In 3D finite elements model, the tunnel has been developed by using shell elements and thesurrounding rock has been modeled by using solid elements. For stability of structure, translations in

three principle directions are kept fixed. All the three rotations are kept free. (Figure 1).

2.5 Loads on 2D finite elements model

The load of overlying rock calculated by Terzaghis method is applied as uniformly distributed on the

roof and triangularly distributed load on the walls (Figure 2).

Figure 2. Loads on 2D finite element model

2.6

2D & 3D Finite Element Analysis

2D & 3D finite element analysis was carried out on the basis of transverse moments and shear forces

in top slab, walls and base slab of both typical sizes of tunnels (10/x 10/ & 26/x 22/). Some typical

results are shown in figures 3 8.

Figure 1. Geometry of 2D (left) & 3D (right) finite element models


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Figure 3. Transverse moments in top slab in 2D (left) & 3D (right) FE models for 10/x 10/tunnel

Figure 4. Shear forces in base in 2D (left) & 3D (right) models for 10/x 10/tunnel

Fi ure 5. Transverse moments in walls in 2D left & 3D ri ht FE models for 10/ x 10/tunnel


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Figure 6. Transverse moments in top slab in 2D (left) & 3D (right) FE models for 26/x 22/tunnel

Figure 7. Transverse moments in walls in 2D (left) & 3D (right) FE models for 26/x 22/tunnel

Figure 8. Shear force in base in 2D (left) & 3D (right) FE models for 26/x 22/tunnel


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3

Comparison of results

3.1

Comparison of results for 10/x 10

/tunnel

The results of 2D finite element analysis of 10/ x 10/ tunnel are compared with 3D finite element

analysis of same section as follows:

In 3D FEA, negative transverse moment in top slab is reduced by 33.3%, positive transversemoment is reduced by 58.7%, and shear force is reduced by 1.25% as compared with 2D FEA.

In 3D FEA, negative transverse moment in walls is reduced by 22 %, and shear force is increased

by 80% as compared with 2D FEA.

In 3D FEA, negative transverse moment in base slab is reduced by 20.8 %, positive transverse

moment is reduced by 77.8 %, and shear force is reduced by 76 % as compared with 2D FEA.

Figure 9. Transverse moments in 2D FEA (left) & 3D FEA (right).

3.2

Comparison of results for 26/x 22/tunnel

The results of 2D finite element analysis of 26/ x 22/ tunnel are compared with 3D finite element

analysis of same section as follows:

Figure 10. Transverse moments in 2D FEA

-8.44 k-ft

+7.34 k-ft

-8.29 k-ft

-0.87 k-ft

-1.24 k-ft

+1.5 k-ft

-6.68 k-ft

+1.64 k-ft

-6.46 k-ft

+0.77 k-ft

-0.80 k-ft

+0.62k-ft

-71.0 k-ft

+66.5 k-ft

-71.7 k-ft

-15.0 k-ft

-16.9 k-ft

+15.53 k-ft


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In 3D FEA, negative transverse moment in top slab is reduced by 69 % and positive transverse

moment is reduced by 73.7 % as compared with 2D FEA.

In 3D FEA, negative transverse moment in walls is reduced by 3.64 % as compared with 2D FEA.

In 3D FEA, negative transverse moment in base slab is reduced by 2.3 % and positive transverse

moment is reduced by 78.5 % as compared with 2D FEA.

Figure 11. Transverse moments in 3D FEA

4 Conclusions

In 3D finite element analysis of tunnels, the values of forces and moments are less than 2D FEA.

Therefore, it can be concluded that the tunnel designed by using Terzaghis method & 2D FEA is

on the safe side but uneconomical.

The difference in the values of forces and moments, between 3D FEA and 2D FEA, in all type of

structures, studied in this research, has been found to be more in large sections than small sections.

The buried structures can be more accurately and safely designed by 3D finite element analysis.

References

SWOBODA, G., LAABMAYER, F., AND MADER I., 1987. Principles and developments in shallow tunnel construction,Part 2, Computers and Geotechnics,3(1), 61-68.

READ, R.S., CHANDLER, N.A., AND DZIK, E.J. 1998, In situ strength criteria for tunnel design in highly-stressed rockmasses.Int.Journal of Rock Mechanics and Mining Sciences, 35(3), 261-278.

KJARTANSON, G.A., HEILERS, R.A., LOHNES, AND KLAIBER, F.W., 1998.Soil-Structure Interaction - Analysis of theLongitudinal Uplift of Culverts.Journal of Geotechnical and Geoenvironmental Engineerin, 124(2), 128-139.

ARUP., 2003. Finite Element Modeling of 3D Geotechnical Problems and Comparison with Simple Solutions, A Research

Project of the Department of Civil, Environmental and Geomatic Engineering of University College London.

FRANZIUS, J.N. AND POTTS, D. M., 2005. Influence of Mesh Geometry on Three-Dimensional Finite-Element Analysisof Tunnel Excavation,Iternational Journal of Geomech, 5(3), 256-266.

LEE, K.M. AND ROWE, R.K., 1990. Finite element modeling of the three-dimensional ground deformations due totunneling in soft cohesive soils. Computers and Geotechnics,10(2), 111-138.

EBERHARDT, E., 2001. Finite Element modeling of three-dimension stress rotation ahead of an advancing tunnel face.Int.

Journal of Rock Mechanics and Mining Sciences,38(4), 499-518.

MIGLIAZZAA, M., CHIORBOLIB, M. AND GIANIA, G.P., 2008. Comparison of analytical method, 3D finite elementmodel with experimental subsidence measurements resulting from the extension of the Milan underground. Availableonline

QASSUN, S., MOHAMMED SHAFIQU, MOHAMMAD TAHA, R. AND ZAMRI, H. 2008. Finite Element Analysis ofTunnels using Elastoplastic-Viscoplastic Bounding Surface Model.ARPN Journal of Engineering and Applied Sciences,

3(3), 178-188.

SURJADINATA, J., HULL, T.S., CARTER, J.P., AND POULOS, H.G., 2006. Combined Finite- and Boundary-ElementAnalysis of the Effects of Tunneling on Single Piles,International Journal of Geomechanics, 6 (5), 245-252.

-69.4 k-ft

+14.33 k-ft

-69.1 k-ft

+6.69 k-ft

-5.24 k-ft

+4.08k-ft

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