finite element analysis of 99.60 m high roller compacted concrete (rcc)

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),

ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

387

FINITE ELEMENT ANALYSIS OF 99.60 M HIGH ROLLER

COMPACTED CONCRETE (RCC) GRAVITY DAM - SPECIAL

EMPHASIS ON DYNAMIC ANALYSIS

KARIM M PATHAN

Consulting Structural Engineer,

Kasheef and Associates, Aurangabad -05, Maharashtra, India

E-mail: [email protected], [email protected]

ABSTRACT

Dams are supposed to be very important structures as they play a vital role in the

economical and social development of the area in which being constructed as well many a

times useful in Hydro power generation. The effect of failure of dam structures can be

imagined by studding the area covered by the dam on downstream side. Though, there are

very few cases of failure of dams, every designer shall think of zero probability of failure of

such structure. The Dam discussed here is Roller Compacted Concrete (RCC) Dam being

constructed over Vaitarna River Near Mumbai, India. The Non overflow section has 99.60 m

height which is very close to 100 m for which dynamic Analysis is desirable as per Indian

Code of practice. Most of the organizations analyze the dams by elastic method which gives

very rough results. The tolerance can be accepted in most of the cases as the factor of safety

used in dam design is 4 for concrete dams. Here Finite Element Approach is used to analyze

the dam which is proved to be the realistic for such structures. A comparison is done between

the equivalent static approach of seismic analysis with dynamic analysis by using time

history. The dynamic behavior is studied by using Time History of actual earthquake of

koyna ( Maharashtra , India ) and the proportioning is done to satisfy the stress limits.

Keywords: Finite Element Analysis, Dynamic Analysis, RCC, Gravity Dam, Stress Contours

1. INTRODUCTION

Gravity dams are very popular in these days due to ease to construction and

availability of machineries like concrete pumps and ready mix plants of huge capacity. The

Vaitarna dam described here is of RCC type. The dam body is designed to withstand the

water pressure, uplift forces and silt load, if any, along with the weight of the dam. As per the

Indian Standard Code of practice, dynamic analysis shall be done for dams with height

greater than 100m. The height of Vaitarna dam is very close to this value, hence dynamic

analysis is done by using time history of Koyna Earthquake of 10th

December 1967 with PGA

of 0.613g. The effects of equivalent static analysis and dynamic analysis are then compared.

INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND

TECHNOLOGY (IJCIET)

ISSN 0976 – 6308 (Print)

ISSN 0976 – 6316(Online)

Volume 3, Issue 2, July- December (2012), pp. 387-391

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2. SALIENT FEATURES OF THE RCC DAM

The dam is having foundation R.L.187.80m and T.B.L at R.L.287.40m. The Full

Reservoir level is at 285.00. Top width is kept as 8.0m whereas bottom width is 91.31m.

Upstream slope is 0.15:1.0 starting from top and downstream slope is 0.75:1.0 which starts

from R.L.278.97m. The Roller Compacted Concrete used is of G-75 Grade. The dam body

and surrounding rock is divided into 84 finite elements each.(See fig.1). The sizes of the

elements near the point of interest is kept smaller compared to the other elements.

Load 8X

Y

Z

Fig.1: Finite Element Model of the Dam

3. FINITE ELEMENT MODELING OF THE DAM

The dam body is modeled in STAADpro using the SOLID isoparametric finite

elements with eight nodes. Each node has three translational degrees of freedom. The

stiffness matrix of the solid element is evaluated by numerical integration with eight Gauss –

Legendre points.

The dam is analyzed for several basic loads and load combinations possibly met with

during its service. These are enlisted in table 1 below. The stresses induced are checked for

all the combinations and the dimensions are so framed that the factor of safety mentioned

above is maintained.



389

The base of the dam is to rest on rock and the extra excavation is to be filled with

concrete of same strength, the foundation rock of approximately equal to the height of dam is

modeled around and below the foundation level.

The Young’s modulus for concrete is used as 2.26 x 104 N/mm

2 and density 26.27

kN/m3. For the foundation rock these properties were 1.0 x 10

4 N/mm2 and 28.8 kN/m

3

respectively. Poisons ratio for concrete is 0.17 whereas for rock it is 0.16. Damping fraction

is assumed as 0.1, 0.2 and 0.3 for first three modes.

Table 1: Basic Loads and Load combinations used during the analysis

Sr.

No

Basic Loads Load Combinations

1 Self Weight ( Wg )

2 Hydrostatic pressure on upstream face ( Wp )

3 Uplift pressure ( Uw)

4 Silt Loads ( Sw)

5 Equivalent Static Analysis for Earthquake Loads

( ESA )

6 Hydrodynamic Effects due to sloshing ( Hd )

7 Time History loads ( Wt )

8 ( Wg+Wp+Sw+Uw+ESA+Hd)

9 ( Wg+Wp+Sw+Uw+Wt+Hd)

4. DYNAMIC RESPONSE OF THE DAM

Time history load is applied to the Finite Element model of the Dam by standard

software, STAADpro, with 500 pairs of time and acceleration of the Koyna Earthquake in

one of the horizontal direction. The finally reduced dimensions give maximum horizontal

displacement as 70.47 mm. The modes of vibration are shown in fig.2. Time period for the

first mode is found to be 0.5498s and frequency as 1.819 Hz.

The stress variation on the finally proposed section is studied for all load

combinations. The axial stress contours are shown in fig.3. Maximum normal stress induced

is 4.15 N/mm2 for the case with time history loading.

Mode Shape 1Load 6 : X

Y

Z

Mode Shape 2Load 6 :

XY

Z

Fig.2: Modes of Vibration for the Dam body



390

Load 7X

Y

Z

Load 8X

Y

Z

Fig.3: Stress Contours for the Dam Cross Section

5. RESULTS AND COMPARISON

Maximum normal stress in material is observed due to the time history load case

which is 4.15 N/mm2, whereas for Equivalent static analysis using Response Spectra Method

described in I.S.1893 gives maximum normal stress as 3.44 N/mm2. Thus dynamic analysis

governs. The tension induced in the body of dam in case of Time History loading is observed

as 2.8 N/mm2 whereas in case of Equivalent static analysis the tension is 1.16 N/mm

2. The

effect of soil structure interaction is to reduce the net tension in the body of the dam. The

deflection of the dam in case of time history loading is nearly three times of deflection due to

equivalent static analysis.

6. CONCLUSION

Dams being very important structure shall be designed with very great accuracy.

Finite Element method shall be preferred over the conventional elastic methods. The great

advantage is that, the stress variation through the whole body can be studied carefully and the

slopes can be designed according to the stress pattern. The points where slope changes, are

points of stress concentration. Such points can be observed carefully and taken care to avoid

over stressing. Moreever, the stress concentration near the gallery can be studied. As far as

dynamic analysis is considered, the stresses are more as compared to the equivalent static

analysis, hence shall be preferred while designing the important structures like dams.

REFERENCES

1. R. W. Clough, “The Finite Element Method in Plane Stress Analysis,” Proceedings of

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3. O. C. Zienkiewicz and Y. K. Cheung, “Finite Elements in the Solution of Field

Problems,” Engineer, Vol. 220, 1965, pp. 507–510.

4. Edword L Wilson, “Three Dimensional Static and Dynamic Analysis of Structures”,

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5. Roman Lewandowski, “Dynamic Analysis of Structures with Multiple Tuned mass

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Ash Stabilized Compressed Earth Block-A Sustainable Construction Building

Material – A Review” International Journal of Civil Engineering & Technology

(IJCIET), Volume3, Issue1, 2012, pp.1 - 14, Published by IAEME

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Redmud On The Properties Of Waste Plastic Fibre Reinforced Concrete An

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finite element analysis of 99.60 m high roller compacted concrete (rcc)

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