600 International Journal of Earth Sciences and Engineering

ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp 600-603

#020410331 Copyright © 2011 CAFET-INNOVA TECHNICAL SOCIETY. All rights reserved

3 D Stress Analysis around Large Openings in Concrete Gravity Dam

A. S. Shirkande Post-graduate student, Department of Civil Engineering, College of Engineering, Pune -5, Email: aceshirkande@gmail.com

V. B. Dawari Assistant Professor, Department of Civil Engineering, College of Engineering, Pune -5, Email: vbd.civil@coep.ac.in

ABSTRACT: The effect of openings is generally neglected in design of dam but it is considered when openings are

large. Large openings create critical zones for tensile stresses in dam. The work reported here comprise of analysis of

dam with large openings. The parameters considered are size and shape of large openings. Three models viz without

gallery, dam with regular size galleries and dam with large inspection gallery are considered for comparing the effect of

the size variation of inspection gallery on dam. The effect of different shapes of galleries like rectangular, square,

circular and horse shoe on stresses in dam is studied for various locations. Overall square shaped inspection gallery gives

minimum stress around gallery. Due to large openings, there is increase in stresses around the openings and in the dam.

Three dimensional finite element analyses are carried out using ANSYS 12.

KEY WORDS: Concrete Gravity Dam, large opening, Finite Element Method, Inspection Gallery.

INTRODUCTION:

A system of openings is provided within the body of dams

to serve various purposes. The layout, size and shape of

the openings are based on their requirements in dam.

Openings develop zone of tensile stresses since concrete is

not designed to take up any tension hence it become

necessary to reanalyze the dam section with openings. In

this paper the effect of size variation and shape variation

of large inspection gallery on dam are studied.

Large openings in dam

Opening is considered large when either of the following

is complied with:

a) d ≥ 6m or

b) Concrete cover anywhere around it is less than d.

(Where d is the maximum cross-sectional dimension)

Finite element analysis of the dam with large opening is

necessary to determine the general stress field, as large

openings are not considered in the IS: 12966: 1990.

MODELING OF DAM

For finite element analysis dam model representing the

actual 3-D behavior of the system is developed. Dam has

been modeled using eight noded brick element.

Finite element mesh for dam is achieved by considering

geometry after a detailed convergence study of the dam.

Khadakwasla dam profile as shown in fig. 1 is taken for

the study. Dam is considered in block of 30 m length.

Details of the dam profile are as follows:

Height = 32.34 m Base width = 17.45 m

Length = 1939 m Water level = 30.34 m

Top width = 2.74 m Base width = 17.45 m

U/S slope = 1V:0.050H D/S slope = 1V: 0.405H

Effect of size variation of inspection gallery

Theoretical limits of dam are influenced by openings with

different sizes. Finer mesh is provided around gallery for

accurate stress results. Sizes of openings in the dam are

given in Table 1 and Concrete cover of 2m is provided.

Fig.1: Khadakwasla dam profile

Table 1: Sizes of the openings

Dam model Drainage

gallery (m)

Inspection

gallery (m)

With regular sized opening 1.50X 2.25 1.50X 2.25

With large sized opening 1.50X 2.25 3.00X 3.50

Following three models as shown in fig. 2 are considered

for the analysis:

a) Dam without gallery,

b) Dam with regular sized openings: with equal size

of drainage and inspection gallery,

c) Dam with large inspection gallery and regular

sized drainage gallery.

Fig. 2: Dam models for effect of size variation

601 3 D Stress Analysis around Large Openings in Concrete Gravity Dam

International Journal of Earth Sciences and Engineering

ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp 600-603

Effect of Shape variation of large inspection gallery

Considering requirements of dam cross section, different

shapes for inspection gallery are generally provided. The

dam is modeled for different shapes keeping area of cross

section constant as shown in fig. 3 and 4. The effect of

different shapes of large inspection gallery on stresses in

dam is studied considering following dam models,

a) Without opening,

b) Rectangular opening,

c) Square opening,

d) Circular opening and

e) Horseshoe shaped opening.

Fig 3: Dam with Rectangular and Circular shaped opening

Fig. 4: Dam with Square and Horseshoe shaped opening

Table 2: Sizes of different shapes of Inspection galleries

Type Size Area (m2)

Rectangular 3.05 m x 4.00 m 12.25

Circular 3.95 m (diameter) 12.25

Square 3.50 m x 3.50 m 12.25

Horse shoe Diameter = 4.00 m

Base width = 3.00 m

Height = 2.60 m

12.25

For comparison of results between different shapes eight

key points or nodes around periphery of the gallery are

considered in clockwise manner as shown in Fig. 5. In the

dam without opening the stresses at nodes at same

position where gallery located are considered.

Fig. 5: Key points around different shapes of gallery

FINITE ELEMENT ANALYSIS OF THE DAM

In FEA of dam with various size and shapes of opening,

the stress field to which the opening is acted upon and

stress distribution around such opening due to the stress

field is determined. The gravity dam is analyzed for seven

load combinations as per IS 6512: 1984.

The static loadings on a concrete gravity dam include self-

weight of the dam, water pressure from the reservoir, and

uplift pressure from the foundation. Density of concrete is

taken as 2400 kg/m³. There is no tail water downstream of

dam. Seismic Coefficient Method is used for earthquake

analysis. Horizontal and vertical seismic coefficients are

obtained as 0.2 g and 0.1 g respectively. Modal Analysis

is carried out first to find out natural frequencies which

are used in the earthquake analysis. Harmonic response

analysis is used to determine steady-state response

considered for analysis using ANSYS 12.

EFFECT OF LARGE OPENINGS

Normal stresses are found out at toe, heel and top

upstream and top downstream. Stress results are obtained

at eight nodes around inspection gallery. Stresses at two

corners (Node no 1 and 5) and at centers of sides (Node

no. 2 and 6) of opening are represented for seven load

combinations as shown in fig. 7 and 8 for size variation

and in fig 10 and 11 for shape variation.

Effect of size variation: stress contours

Stress contours in fig. 6 show stress for normal operating

condition with earthquake. Tensile stresses are given by

positive signs and compressive stresses by negative signs.

a) Dam without Opening

b) Dam with Regular Opening

c) Dam with Large Opening

Fig. 6: Normal stresses in Longitudinal and Transverse

direction

602 A. S. Shirkande, V. B. Dawari

International Journal of Earth Sciences and Engineering

ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp 600-603

Graphical representation of normal stresses in

longitudinal and transverse direction:

Heel Toe

Top (Upstream) Top (Downstream)

Node No. 1 Node No. 2

Node No. 5 Node No. 6

Fig. 7: Comparison of stresses in longitudinal direction for

effect of size variation.

Heel Toe

Top (Upstream) Top (Downstream)

Node No. 1 Node No. 2

Node No. 5 Node No. 6

Fig. 8: Comparison of stresses in transverse direction for

effect of size variation

Results of stresses for the effect of size variation give

following observations:

1) Dam with large opening gives 40 -50 % more stresses

at heel and around gallery than dam without opening.

2) The stresses at top and bottom of the dam decrease with

increase in size by 10 -15%.

3) Tensile stresses around large opening found to be

increase in dam with large opening. It gives 20- 25% more

stresses than dam without opening.

4) From the deflection at different nodes in dam it is

observed that it is maximum at dam model with large

opening whereas it is very less in dam without gallery.

5) Stresses around opening in dam with large opening are

maximum (3.90 MPa) at node 6 for normal operating

condition with Earthquake and minimum (0.02 MPa) at

toe for normal operating condition.

Shape variation of large inspection gallery:

Stress contours show stresses for normal operating

condition with earthquake. Tensile stresses are given by

positive sign and compressive stresses by negative sign.

a) Rectangular shaped gallery

b) Square shaped gallery

603 3 D Stress Analysis around Large Openings in Concrete Gravity Dam

International Journal of Earth Sciences and Engineering

ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp 600-603

c) Horse-shoe shaped gallery

d) Circular shaped gallery

Fig. 9: Stresses in longitudinal and transverse direction

Graphical representation of normal stresses:

Node no.1 Node no.2

Node no.5 Node no.6

Fig. 10: Comparison of stresses in longitudinal direction

Node no.1 Node no. 2

Node no. 5 Node no. 6

Fig. 11: Comparison of stresses in transverse direction

Results of stresses for the effect of shape variation of

inspection gallery gives following observations:

1) Stresses around the horizontal large openings are 15 –

20% greater than that without opening. The stress

variation among different shapes is 5 -10 % only.

2) Dam with Square gallery gives minimum stresses at

all points except at bottom upstream corner. Overall

square gallery shows less stresses as compared to

others.

3) It is seen that at crown and invert point and side walls

show nearly equal values of stresses with 2 % average

variation. Vertical displacement is 10 % more in self

weight case than other cases i.e. water pressure and

uplift decreases the vertical displacement.

4) Results of displacement of different galleries are

nearly same in that square gives 5 % less than others.

5) Stresses around opening in dam with large opening

are maximum (4.40 MPa) at node 5 for normal

operating condition with earthquake and minimum

(0.50 MPa) at toe for normal operating condition.

CONCLUSIONS

It has been observed that large openings in the dam induce

higher stresses in the vicinity of them. In some cases,

these openings have contributed upto fifteen to seventeen

percent increase in stresses.

The variation according to different shapes is five to ten

percent. However, square galleries show less increase in

stresses as compared to other shapes.

REFERENCES

[1] Chen Jin Masoud Soltani, Xuehui An. (2005).

Experimental and numerical study of cracking

behavior of openings in concrete dams. Computers

and Structures, Nov. 8, 2004 Vol. 83, 525-535.

[2] Da Silva J.F. (2006). Optimization of concrete gravity

dams foundation drainage systems. Proc. 22nd

ICOLD- Barcelona, Spain.

[3] Dike Anirudhdha M. (1994). Finite Element Analysis

of Khadakwasla Dam. M. E. dissertation, University

of Pune, India.

[4] Mohamed Abd El Razek and Magdy M. Abo Elela.

(2001). Optimal Position of Drainage Gallery

underneath Gravity Dam. Proc. 6th International

Water Technology Conference, Alexandria, Egypt,

181-192.

[5] Wieland Martin and Malla Sujan, (2000). Earthquake

safety of an arch-gravity dam with a horizontal crack

in the upper portion of the dam. 12th WECC, 1779-

1787.