IISRT ZMahantaesh TR

International Journal of Mechanical Civil and Control Engineering Vol. 1, Issue. 3, June 2015 ISSN (Online): 2394-8868

36

Study on Effect of Soil Type on Rectangular

Tunnels 1Mahantesh T R, 2Dr. J.K. Dattatreya

1PG Student, 2Research Professor,

Civil Engineering Department, Siddaganga Institute of Technology Karnataka, INDIA

Abstract Rectangular tunnel is consisting of top, bottom and

two vertical side walls built monolithically which forms the

square or rectangular single cell. These structures are mainly

used as underground tanks, subways, highway underpasses and

culverts. The box structure is highly indeterminate structure which is having continues support as directly rests on soil. Hence

to understand its true behavior, soil structure interaction should

take into account. This paper presents the finite element results

of parametric investigation of typical underground metro subway

station subject to various soil types by considering appropriate soil subgrade reaction. The finite element method was used to

analyze the structural behavior of typical metro subway station

under different loading conditions using SAP 2000. And the

structure was modeled using SHELL element and the LINE

element and results obtained from the 3D analysis using SHELL element and the plane frame analysis using BEAM or LINE

element were compared. Also study is carried out for various soil

types by considering appropriate soil subgrade reaction to know

the effect of type of soil on bending moment. The study reveals that the bottom slab is the element which is severely affected and

variation of bending moment in bottom slab is in the range of

50% to 70%, in some other load cases the bending moment also

changes the sign.

Keywords Box structures; Modulus of Subgrade

reaction,;Plane frame model; Rectangular tunnel; Soil structure

interaction; SAP 2000; Underground Metro Station.

I. INTRODUCTION

With the acceleration of INDIAs rapid economic

development and urbanization, city size continues to expand and traffic congestion is becoming increasingly prominent. As

an effective way to solve this problem, rail transit and public transit system represented by subways has received great

attention and more and more cities are under construction or planning of subways. Design of underground stations in

developed urban environments requires detailed understanding and consideration of the analysis type, site conditions,

constructability and construction sequencing as part of the

design process in order to produce appropriate design solutions. A rectangular box structure mainly consists of two

horizontal and two vertical slabs constructed monolithically are ideally suited for a road or railway transportation. These

structures are economical due to their rigidity and monolithic action and separate foundation are not required since the

bottom slab resting directly on the soil serves as raft slab.This

makes structure is highly indeterminate structure which is

having continues support as directly rests on soil. Although the functional requirements of these structures may not vary

greatly, the unique site conditions at each location can lead to

very different solutions. Dimensions of box type tunnels are in general greater than those of box culverts resulting in much

thicker walls and slabs for the box frame. Hence to understand its true behaviour the main parameters which influence

structural behaviour are varied and the results are studied. Structural behaviour of underground rectangular metro station

box is analysed under different loading conditions using FEM

tool SAP2000.Results obtained from plane frame analysis is compared with 3D analysis results obtained by using SHELL

element. Study is carried out related to variation in bending moment for different types of soil that usually encountered at

site

II. FINITE ELEMENT ANALYSIS

A. Load cases considered

The loading include the

1. Self-weight

2. Soil back fill over the structure

3. Live load

4. Lateral static earth pressure due to saturated soil (Ko)

5. Lateral active earth pressure due to saturated soil (Ka)

6. Lateral Hydrostatic pressure when is at ground water level is at ground level

7. Vertical Uplift pressure when ground water level is at Ground level

8. Lateral Seismic Earth pressure due to saturated soil.

B. Load Calculations

1. Self-weight

The self-weight of the structure is calculated in

SAP2000 by defining load patterns.

2. Soil Overburden Load


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The weight of the backfill on top of the box structure,

assumed to be of equivalent bulk density as the existing ground, typically g = 21 kN/m3 under

saturated conditions.

3. Earth pressure

i. Coefficient of lateral earth pressure at rest is calculated by Rankine earth pressure co efficient for

soil at rest KO= 1-SIN ().

ii. Coefficient of lateral earth pressure during active stage is calculated by Coulomb's theory.

4. Train live load

The train live loads are considered as per standard

train loading for the Metro corridor (IRC:6-2000 Code gives formula to impact factor). Impact factor, I, is calculated as per Indian Railway Standard Code (Refer

clause 2.4.1.1.a).

5. Seismic loads

The IS: 1893-1984 (Clause 6.1.3) provide that box culverts need not be designed for earthquake forces

Seismic loads are determined in accordance with work carried out by Cetin Soydemir and presented in his

1991 paper "Seismic design of rigid underground walls

in New England" (Proceedings: Second international conference on recent advances in geotechnical

earthquake engineering and soil dynamics, paper no. 4.6). This paper is a review and analysis of other

studies and concludes by presenting graphs for estimating lateral earth pressures. The graph for the

situation where the length, L, from the structure to the

nearest obstruction, is greater than 1 (which is always the case for this design), is shown below. The chain

line marked "Recommended" is used. The graph is prepared for an area of moderate seismicity, with a

design acceleration of 0.12g. It has the depth of the structure, as a proportion of the height, H, on the Y

axis, and the ratio of horizontal to vertical pressure (sx/gH) along the X axis. It can be seen that the

pressure ratio has a value of 0.12 above a depth of

0.5H, and reduces linearly from this value to half this value at the base of the structure.

An additional load to represent the seismic component of the water pressure on the wall is

calculated using the theory of Westergaard, which gives an approximate distribution of load as a parabola

with the horizontal pressure at respective depth.

Fig.1, Recommended Dynamic Soil Pressures against Rigid, Non-Yielding Walls for (ah = 0.12 g) by Cetin Soydemir.

6. Modulus of subgrade reaction

The modulus of subgrade reaction is a conceptual relationship between soil pressure and deflection that is widely used in the structural analysis of foundation members like continues footings, mat or raft foundations etc. The modulus of subgrade reaction is the ratio of stress to deformation. Soil medium is modeled linear springs and their stiffness is obtained modulus of subgrade reaction obtained from Table 9-1 Bowles, J.E. (1977) Foundation Analysis and Design.

Table.1, Range of modulus of subgrade reaction for different types of soil.

Soil

Ks (kN/m3)

Loose Sand 48000-16000

Medium Dense Sand 9600-80000

Dense Sand 64000-128000

Clayey Medium Dense Sand 32000-80000

Silty Medium Dense Sand 24000-48000

Clay 12000 to 480000 (depending upon bearing capacity)


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C. Modeling procedure in SAP2000

o The analysis is carried out using Finite Element

Analysis software SAP2000

o Material property defined as Isotropic.

o Defining Sectional properties and load patterns

are assigned to model.

o 4-noded thin shell element is assigned to area element.

o 2-noded Rectangular section beam is used in frame modelling.

o Supported condition are provided using area and

line springs for 3D analysis and 2D frame

analysis respectively which were calculated from

modulus of subgrade reaction.

o Model is run for analysis.

III. COMPARISION OF 3D AND PLANE FRAME MODEL

Many models are available to determine live a dead

load demands for underground structures load rating

problems. Determining which of the models to use can be a

daunting and difficult task. Being these structures are having

larger dimensions in the longitudinal direction the basic

assumption in analysis of the box structures is the

displacement and forces are uniform in the longitudinal

direction of the culvert. This assumption holds true for certain

type of loadings than others. For example soil loading applied

to the surface or pavement maybe considered as uniform in the

longitudinal direction. Solution therefore is independent of

one of the three orthogonal axes and can be formulated in

remaining two axes. Thus problem can be treated as two

dimensional.

But the spread of live load with depth is inherently a 3D

problem. Hence an attempt is made to compare the analysis

using BEAM element and SHELL element using FEA

package SAP 2000.Same modeling procedure is followed and

a conventional rectangular box structure of 10m width and 5m

height and unit length was considered.

Frame Models

Several modelling programs are available to analyse of

underground structures. The simplest of these are two

dimensional frame models. Two dimensional frame models

have many advantages. They are simple to construct with

often fewer than a dozen nodes; some even construct the

model automatically from a few culvert geometry properties.

Their structural stiffness matrices are smaller and therefore

require less computation time and introduce fewer errors.

They can deal with the behaviour of reinforced concrete by

using beam elements with Transformed moments of inertia.

The beam elements themselves are built around a proven and

well understood mechanics of materials model.

Finite Element Models

Underground structures load rating literature indicates that the

finite element analysis (FEA) method offers superior

capabilities for predicting box structures and soil-structures

behaviour. Finite element Codes allow for modelling phenomena not described by the underground structures

specific codes and for graphical investigations of the results

(Duane, Robinson, & Moore, 1986). The most popular soil

models can be integrated in the FEA code. Such models

include linear elastic models, elasto-plastic with Mohr-

Coulomb failure, soil hardening with stress dependent

stiffness and Mohr-Coulomb failure, Hardin, Duncan, and

bilinear. Duncan is the most popular (Kim &Yoo, 2005;

Kitane & McGrath, 2006). Though it is clear that FEA is the

analytical tool of choice for analysing underground structures,

the particular implementation of FEA must be determined.

Fig.2, Shows 2D plane frame model in SAP200P.


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Fig.3, Shows 3D model in SAP2000 using SHELL element.

Observations

Fig.4, Maximum center moments in Top slab,Bottom slab and Side wall using SHELL and BEAM element in SAP 2000.

Fig. 5, Maximum en moments in Top slab,Bottom slab and

Side wall using SHELL and BEAM element in SAP 2000.

Inference

From the above observations it is clear that

1. The spread of live load with depth is inherently a 3D problem and use of 2D frame model proves to be more

conservative and overestimate the end joint moments

ignoring the spread of live load on the wall surface.

2. The 3D model using shell element considers the spread of area loads even in the direction of 3-axis and results in higher wall moments at center of wall.

3. High estimated moments at the end corner of beam results in more ductile joints which are one of key parameter to special joints design which is highly

necessary of stability of these type structures.

4. The two dimensional frame models are simple models and very easy to analyze for static loading conditions.

5. And produce the very conservative results and very adoptable for design purposes.

IV. PARAMETRIC STUDY

The parametric study concentrate on variation of bending moment in a typical underground rectangular metro station box

on various soil types by considering appropriate soil subgrade reaction.

The station box has outer dimension of 22m x15m and

having concourse slab at 8m center to from the base slab and with a toe projection of 1m in bottom slab.

The same load cases and same method of FEM analysis is used for the load calculations, modelling and analysis.

Soil cases considered and their Modulus of Subgrade Reaction for vertical stiffness is listed below.

Soil Ks (kN/m3)

Loose Sand 16000

Clayey medium dens sand 32000

Medium dense sand 80000

Dense sand 128000


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Sectional Properties and Material Properties

Material property defined as Isotropic and Grade of concrete is M40.

Depth of

Base slab is 1.4m

Concourse slab is 0.7m

Top slab is 1m and

Wall thickness is 1.2m

RESULTS

Fig. 6, Shows variation of Bending moments in Bottom slab

and Top slab with respect to Modulus of subgrade reaction.

Observations

o With increase in value of modulus of subgrade

reaction values of bending moment in al structural

members decreases.

o Values of bending moments changes significantly in

bottom slab and negligible in top slab and side walls

as the values of modulus of sub grade reaction

changes from lower values to higher values.

o Bending moments of bottom slab are affected more as bottom slab directly lay on soil without any

additional foundation.

v. Conclusion

1. The Two-dimensional frame models produces very conservative Bending Moment results especially in the

bottom slab which in turn produces conservative design of joints and base slab.

2. The 3D model using shell element considers the spread of area loads even in the direction of 3-axis and results

in higher wall moments at centre of wall.

3. From the graph shown above it is evident that the positive bending moment (tension in bottom) in bottom

slab goes on decreasing as the value of modulus of subgrade reaction increases and for higher values of

modulus of subgrade reactions bending moments may results as for non-yielding supports.

4. Above problem being soil structure interaction problem the variation of bending moments in top slab

and side walls are in small magnitude and bottom slab

plays critical role in design of underground rectangular structures. Due attention should to bottom slab while

considering soil structure interaction.

5. While considering the seismic loading for underground structures Underground structures suffer minor damage from earthquakes compared to aboveground structures.

Deep tunnels are safer compared to shallow tunnels. So

for moderate seismic region the effect of earthquake is not critical but in sever seismic region it plays critical

role.

REFERENCES

[1] Bowles, J.E.(1977). Foundation analysis and design. 2nd ed.

McGraw-Hill, NY, 750 p.Brinkgreve RBJ et al., editors.(2002)

[2] Dowding, C. H., and Rozen, A., Damage to Rock Tunnels from Earthquake Shaking, "Journal of the Geotechnical Engineering Division, ASCE, Vol. 104, No. GT2, February1978.143

[3] Kuesel, T . R., Earthquake Design Criteria for Subways, Journal of the Structural Divisions,ASCE, Vol. 95, No. ST6, June 1969.

[4] Sharma, S., and Judd, W. R., Underground Opening Damage from Earthquakes, "Engineering Geology, 30, 1991.

[5] Wang, J. M., The Distribution of Earthquake Damage to Underground Facilities during the 1976 Tangshan Earthquake, Earthquake Spectra, Vol. 1, No. 4, 1985.

[6] Owen, G. N., and Scholl, R. E., Earthquake Engineering of Large Underground Structures, prepared for the Federal Highway Administration, FHWA/RD-80/195, 1981


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[7] AASHTO (American Association of State Highwaysand Transportation Officials), Standard Specifications for Highway Bridges, 17th Edition, 2002.

[8] IS:1893-1984, Criteria for Earthquake Resistant Design of Structures, Fourth Revision.

[9] Wang, J.-N., 1993. Seismic Design of Tunnels: A State-of-the-Art Approach, Monograph, monograph 7. Parsons, Brinckerhoff, Quade and Douglas Inc., New York.

[10] Cetin Soydemir 1991-Seismic Design of Rigid Underground Walls in New England. Proceedings: Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics.

[11] Geotechnical Interpretive Report 2001-Contract BMR/UG2 East -West Corridor Bangalore Metro Rail Project.

[12] Ciria report 91- early age thermal crack control in concrete.

[13] IS 456 : 2000 Indian Standard PLAIN AND REINFORCED CONCRETE -CODE OF Practice ( Fourth Revision ).

[14] Design Manual Report 2001-Contract BMR/UG2 East -West Corridor Bangalore Metro Rail Project.

[15] B.N. Sinha & R.P. Sharma., RCC Box Culvert Methodology and Designs including Computer method Journal of the Indian Roads Congress, October-December 2009, paper 555.

[16] IRC: 6-2000, Standard Specifications and Code of Practice for Road Bridges-Section:II Loads and Stresses.

[17] IRC:21-2000, Standard Specifications and Code of Practice for Road Bridges-Section:III Cement Concrete (Plain and Reinforced).

[18] SAP2000 (2000).SAP2000 Plus Version 7.4 Users Manual, Computersans,Structures.Inc.Berkelely,CA.

[19] Wood, J. H., Earthquake-Induced Soil Pressures on Structures, Report No. EERL 73-05,1973, California Institute of Technology.

[20] TxDOT. (2003). CULV5 - Concret Box Culvert Analysis Programe.. Austin:Texan.

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IISRT ZMahantaesh TR