Paper No. A111

A COMPARISON OF STATIC AND DYNAMIC RESPONSES

OF 2D AND 3D IDEALIZATION OF A CONCRTE GRAVITY

DAM

Abhilash Urs K.R.

1 and A.D. Pandey

2

1Nagadi Consultants,abhilashurs77@gmail.com 2Indian Institute of Technology Roorkee,adpanfeq@gmail.com

ABSTRACT

The analysis of concrete gravity dams is carried out by two dimensional and the three dimensional

FEM idealizations. The two dimensional idealization of a plain strain representation is the most

generic approximation that can be made. The two dimensional plane stress idealization permits the

evaluation of each monolith depending on its individual characteristics. The three dimensional

idealization provides a very elaborate model requiring, immense computational effort and time. The

purpose of this paper is to compare and contrast the performance of two dimensional and three

dimensional model of representative monolith of the idealized concrete gravity dam with respect to

their performance when the dam is taken as a single entity. The studies conducted in the present

context were restricted to gravity load analysis, hydrostatic analysis, free vibration characteristics and

response spectrum analysis. The results of the analysis conducted indicated that the two dimensional

models may be used for preliminary estimates, but three dimensional model of the dam taken as an

entity provides a stable basis for analytical assessment of design forces as well as performance

parameters.

INTRODUCTION

Dam has been idealized based on the sections of a concrete gravity dam yet to be built. Due to the

tremendous growth in agricultural and industrial activities in last few decades, small towns in the

region of the dam have grown in population and size and are putting immense pressure on natural

resource. Availability of water has become a major concern. The area has immense rain water

potential, so a scheme was devised, to store the water at a gorge and distribute it through canals. A

15MW hydro power project is also proposed at the dam site. Thus it was decided to construct a dam

across the river near a specified village, and a pick up weir at some distance from dam. As many as

five alternatives have been discussed and considered at various levels:

1. Rock fill dam with upstream concrete membrane.

2. Rock fill dam with clay core.

3. Hollow concrete gravity dam.

4. Solid concrete gravity dam.

5. Roller compacted concrete gravity dam.

The last mentioned was finally chosen as the type of dam to be built at the site.

SAILENT FEATURES OF PROJECT SITE

The river basin forms an important water regime in south-eastern Himalaya where it originates.

Some of the important details of dam have been discussed in brief below. Sections of the dam and

profile of the valley are shown from Fig1 to Fig 3.

Structural Details

Dam:

1) Type Roller compacted concrete gravity dam

2) Height above river bed 130m

3) Top level 765m

4) Length at the top 480m

Spillway:

1) Type of spillway Ogee spillway

2) Water way 4 bays of 13.25m each

3) Crest level 750m

Fig.1 Non over flow section of dam Fig.2 Over flow section of dam

Fig.3. Valley profile of the proposed dam.

MATHEMATICL MODELS ADOPTED

General Description of 2-Dimensional Dam Model

Dam, being considered for the analysis is a roller compacted concrete dam. Hence, the dam and the

foundation are modeled as 2D plain stress model with finite thickness for the finite element analysis.

Thicknesses of the individual monoliths considered for the analysis have been specified as thickness

in the analysis. Plane stress element considered from Ansys is Plane 82; a brief description is given

below. Plane 82 is an 8 node structural solid having two degrees of freedom at each node. The

element may be used as a plane element or as an axisymmetric element.

Fig.4Plane 82 geometry

The element is defined by four nodes having two degrees of freedom at each node: translations in the

nodal x and y directions. This element was preferred to Plane 42 as to model the spillway of dam with

8-node elements, which have compatible displacement shapes and are well suited to model curved

boundaries.

General Description of 3-Dimensional Dam Model

Three dimensional modeling has been done using element solid 95 in the Ansys. SOLID95 elements

have compatible displacement shapes and are well suited to model curved boundaries. To account for

the modeling of overflow section of the dam this was found to be convenient. The element is defined

by 20 nodes having three degrees of freedom per node: translations in the nodal x, y, and z directions

Fig.5. Solid 95 geometry

Geometrical Description of 2-Dimensional and 3-Dimensional Model

Two individual monoliths have been modeled and analyzed using Ansys tool;

a) Tallest non overflow section monolith no 14.

b) Tallest overflow section monolith no 16.

.

Fig.6 3D individual Monoliths 14, 16. and concrete gravity dam fixed base model

Three dimensional modeling has been done in two stages for finite element analysis. 1. Individual monoliths considered as specified earlier have been modeled in 3D without foundation.

2. Entire dam has been modeled with the effect of foundation discontinuities and without foundation.

Schematic view of the models adopted for all the monoliths and the dam in fixed base case have been

shown in Fig 6.

Material Properties

Density of concrete for the dam has been assumed as 2500 kg/m3.Specified characteristic compressive

strength of 150 mm Cube at 28 Days of ordinary M20 concrete is 20 N/mm2 as per IS 456:2000 Indian

standard plain and reinforced concrete -code of practice. Tensile strength of the concrete is assumed

as follows;

fckfcr 7.0 N/mm2

(1)

Modulus of Elasticity of concrete is assumed as follows;

fckEc 5000 N/mm2, (2)

Ec is the short term static modulus of elasticity in N/mm2.Hence, the tensile strength of concrete for

M20 from equation above is 3.13x 106 N/m

2 and modulus of elasticity is 2x 10

10 N/m

2. Poisson’s ratio

of concrete has been assumed as 0.2.

RESULTS AND DISCUSSIONS:

Gravity Analysis

Fig.7. 2-dimensional 14 and 16 monolith fixed base gravity stress in Y direction

Fig.8. Section from 3-dimensional individual 14 and 16 fixed base monoliths gravity stress in Y

direction

Fig.9. Section of 14 and 16 monoliths from dam as a single entity gravity stress in y direction

Hydrostatic Analysis

Fig.10. 2-dimensional 14 and 16 monolith fixed base hydrostatic stress in Y direction

Fig.11. Section from 3-dimensional individual 14 and 16 fixed base monoliths hydrostatic stress in y

direction

Fig.12. Section of 14 and 16 monoliths from dam as a single entity hydrostatic stress in y direction

Results of gravity and hydrostatic analysis

The graphs and contour plots of stresses shown above are reflecting well about the stress profile at the

base. Compressive stress and the tensile stress at the base of the dam have not exceeded the

permissible compressive and tensile strength of concrete in static analysis. As displacement in Y

direction is predominant in gravity, crest displacements (m) in normal Y direction at the top most

point in upstream side have been shown in all the 3 cases:

Table.1. Crest displacement of the monoliths in gravity analysis

2-dimensional 3-dimensional individual 3-dimensional fixed base dam

14 - 0.79191E-02 -0.72495E-02 -0.60358E-02

16 -0.81451E-02 -0.76910E-02 -0.67665E-02

As the hydrostatic load is a lateral load, crest displacements (m) in normal X direction at the top most

point in point in upstream side have been shown in all the 3 cases:

Table.2. Crest displacement of the monoliths in hydrostatic analysis

2-dimensional 3-dimensional individual 3-dimensional fixed base dam

14 0.21114E-02 0.14704E-01 0.20419E-01

16 0.36081E-02 0.17215E-01 0.14333E-01

MODAL ANALYSIS

Modal participation factor and effective mass for 15 time periods, corresponding to each case, in X, Y

directions for 2 dimensional and X, Y, Z directions for 3 dimensional have been found from Ansys.

As first mode shape is prominent, it has been shown in the Table 3.

Table.3. Mode Participation Factors

2-dimensional in X direction mode period Partic.factor ratio effective mass

14 1 0.3007 10264 1 1.05E+08

16 1 0.2840 13620 1 1.85E+08

3-dimensional individual in Z

direction mode period Partic.factor ratio effective mass

14 1 1.1359 11112 1 1.23E+08

16 1 1.3173 13460 1 1.81E+08

mode period Partic.factor ratio effective mass

3-dimensional fixed base dam

in X direction

1

0.2506

34679

1 1.20E+09

RESPONSE SPECTRUM METHOD

Square root of sum of squares method has been adopted for the analysis. A modal analysis has been

done followed by spectral analysis and the stresses have been compared of all the cases considered.

The design horizontal seismic coefficient Ah is determined by the following expression, Clause 6.4.2

of IS 1893 (Part 1): 1984,

Ah = (Z/2) (I/R) (Sa/g) (3)

Dam is assumed to be situated in seismic zone 4, hence Z =0.24.

RESPONSE SPECTRUM ANALYSIS

Fig.13.2-dimensional 14 and 16 monolith fixed base SRSS stress in Y direction

Fig.14. Section from 3-dimensional individual 14 and 16 fixed base monoliths SRSS stress in y

direction

Fig.15. Section of 14 and 16 monoliths from dam as a single entity SRSS stress in y direction

CONCLUSIONS

On the basis of the studies conducted on the two dimensional and three dimensional individual

monolith idealizations as well as the gravity dam taken as a single entity, as indicated in earlier

sections the following conclusions can be drawn.

1. For fixed based condition, the two dimensional and three dimensional individual idealizations

exhibit greater vertical displacements when compared to dams taken as an entity under the

action of gravity loads. However, under the action of the hydro static loads, the horizontal

displacements in the three dimensional model of the dam taken as an entity are larger.

2. The corresponding states of stresses for displacements as indicated above were such that

three dimensional individual monoliths exhibit the largest stresses.

3. The free vibration characteristics for the models adopted, with fixed base indicate a

reasonable consistency between similar modes of vibration. However, the three dimensional

individual monoliths have a tendency to vibrate in lateral and transverse directions in a

manner which cannot be replicated by the two dimensional model and is highly unlikely to

contribute towards the total response of the dam taken as an entity.

4. The SRSS stresses obtained from the response spectrum analysis indicate that the two

dimensional model is the most conservative.

References

1. Ansys Basic Analysis Procedure Guide, (2005),Version 10, Ansys. Inc

2. IS 456:2000 Indian standard plain and reinforced concrete -code of practice

(Fourth

Revision), Bureau of Indian Standards,New Delhi 2002.

3. IS 1893:2002, Criteria for Earthquake Resistant Design of Structures Part 1. General

Provisions and Buildings (Fifth Revision), Bureau of Indian Standards, New Delhi 2005.

4. “Status report on pre-construction stage geological investigations of proposed concrete

gravity dam project”, (2001).