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Stress Analysis of Gravity Dam Founded on Rock Mass Having Stress Analysis of Gravity Dam Founded on Rock Mass Having

Horizontal Seam (A Case Study of Bargi Dam in Madhya Pradesh, Horizontal Seam (A Case Study of Bargi Dam in Madhya Pradesh,

India) India)

J. K. Jain Maulana Azad College of Technology, Bhopal, India

R. K. Khare Maulana Azad College of Technology, Bhopal, India

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Recommended Citation Recommended Citation Jain, J. K. and Khare, R. K., "Stress Analysis of Gravity Dam Founded on Rock Mass Having Horizontal Seam (A Case Study of Bargi Dam in Madhya Pradesh, India)" (1988). International Conference on Case Histories in Geotechnical Engineering. 62. https://scholarsmine.mst.edu/icchge/2icchge/2icchge-session6/62

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Proceedings: Second International Conference on Case Histories in Geotechnical Engineering, June 1-5, 1988, St. Louis, Mo., Paper No. 6.39

Stress Analysis of Gravity Dam Founded on Rock Mass Having Horizontal Seam (A Case Study of Bargi Dam in Madhya Pradesh, India) J.K. Jain Assistant Professor of Applied Mechanics, Maulana Azad College of Technology, Bhopal, India

R.K. Khare M. Tech. Student of Applied Mechanics, Maulana Azad College of Technology, Bhopal, India

SYNOPSIS: Under certain situations where horizontal seams of weaker material are detected below a depth of relatively competent rock and if it is decided to found the base of the dam on the rock below weak seam, the current practice of extending the triangular profile right down to base proves to be uneconomical both in terms of cost of excavation and quantity of concrete. In such situations for realistic assessments it becomes imperative to study the effect of foundation block having seam, on the behaviour of entire dam structure. With a view to assist the design of such dams, results of plane strain elastic finite element stress analysis for a typical Bargi dam in Madhya Pradesh, India, wher.e a horizontal seam of weaker material expected in the foundation block are presented in this paper considering gravity load hydrostatic pressure.

INTRODUCTION

Conventional design of gravity dams is based on the assumption that a gravity dam acts like a rigid triangular cantilever resting on the foundation and held in equilibrium under its own weight and the reservoir loading. The uplift forces are also taken into accounts. The distribution ~f vertical reaction at the base being assumed to be linear, the maximum stresses occur at the toe of the dam under reservoir full conditions. In some of the dams a situation often arises when seams of weaker material are detected at some depth below the dam base. If it is decided to excavate this soft rock and take base of the dam to the sound rock below weak seam, a vital question arises whether the base of the dam has to be extended. Many designers insists on increasing the base width so that a triangular profile is maintained. However, this procedure which leads to increase in excavation is not only uneconomical but at times also hazardous if further excavation tends to undermine valley slope with consequ­ent possibility of slides.

Such a situation arises in many dams constru­cted in hilly areas. In these cases, it be­comes imperative to consider the foundation block consisting of strong rock mass having seam of weaker material. Thus the analysis shall cater the effect of composite founda­tion block on the behaviour of entire dam structure. From the geological investiga­tions this type of situation is also assessed in case of Bargi dam in Madhya Pradesh,India, where a horizontal seam of relatively weaker material is expected at a competent depth below the foundation level of the dam. This gravity dam is founded on strong basaltic rock. The present study deals with stress analysis of this dam using plane strain elastic finite element technique considering gravity load and hydrostatic pressure.

1289

DETAILS OF PROBLEM

The 5380 metre long Bargi dam (1983) is constructed across the river Narmada in Vindh­ya mountain ranges of state of Madhya Prade~h, India. The 69 metre high and 870 metre long masonry section of dam is constructed betweeen two earthen sections of total 4510 metre length. The masonry section has 386 metre long and 49.5 metre high spillway portion equiped with twenty one radial gates of 13.7 m x 15.25 m size. The area around dam site possess dense, dark basaltic rock varying from 10 metre to 30 metre in depth. A thin layer of tuffaceous clay of about 0.5 m thickness is assessed at about 10 to 15 metre below the foundation level of the dam. The salient features of the non-overflow and overflow sections of the dam are shown in figures 1 and 2.

151, 121 Sl 46 31 15 16

EL 426·9

E:L 358

2 3 4 5 Et...

EL416

GIUVITY LOAD ANC HYORCSTt ... TIC PRESSURE

r-r-'1 0 5 10M

155 J'Z::;,

105 so

28 45 30

7 8 9 10 II 12 13 14

2 3 5 I U 5

FIG. 1 DETAILS AND DISCRETISATION OF NDN·OVERFLOW SECTION OF BIIRGI OO.M

Second International Conference on Case Histories in Geotechnical Engineering Missouri University of Science and Technology http://ICCHGE1984-2013.mst.edu

.e:L .. 407'51 '70 ~~

253 1\\~,'~51 GRAVITY LOAD AND HYDROSTATIC PRESSURE

244 I \ \ \ \. '\. "\. EL 392-42

212\ \ \ \ ~,,'{52 ,...-,--, 235 0 5 10M

... \ \\\~ 225

'\ \ \ ~0~?.25 196 217 EL 373

202 107 \ \.195"'~ - 16 EL 355·5 187173

,., 201

172159 171 , .. EL 358 134 109

~i 91 58 201 I 2 3 4 5 6 7 8 9 10 II 12 13 ~ 15 15 17 Ill

I 2 3 4 5 6 7 e 9 10 II 12 13 1415 16 17 IB FIG.2 DETAILS AND DISCRETISATimi OF OVERFUDW SECTION OF BARGI DAM

METHOD OF ANALYSIS

Though there are several methods of analysis of such class of problems but the finite ele­ment method possesses certain characterstics that takes advantage of special facilities offered by high speed computers. In particu­lar the method can be systematically progra­mmed to accomodate such complex and difficult problems as nonhomogeneous materials, non­linear stress strain behaviour, arbitrary loadings and complicated boundary conditions. Thus for the analysis of such problems the finite element method proves to be a valuable technique.

In the present study the stress analysis has been carried out for both non-overflow and overflow sections by discretising them into two dimensional four nodal quadrilateral ele­ments. In case of Plain strain analysis,each node will have two degrees of freedom thus total eight unknown d~flections per node are to be determined. Hence the displacement functions are to be chosen with eight coeffi­cients as

U =~l + ~2x +~XY +~4Y

v =<s + ~6x +~7xY +~8Y

(1)

(2)

The finite element method principally invol­ves the determination of stiffness of each element and then over all stiffness of the continuum for yielding unknown deformations. Thus the stiffness determination plays sign­ificant role in this method. In the present

case the stiffness of each element [Ke] is derived using the displacement coefficients given in equation (1) and (2) by conventional energy approach as

[Ke] = J [B]T [D] [B] dvol. ( 3) v

where [B] represents matrix of coefficients relating strain and displacements

and [D] represents the elasticity matrix interms of modulus of elasticity E and poisson's ratio and has the form

19

1290

1 _'lJ __

0 ( 1-:U)

[D]= E(l-:1) ) .2:L_ 1 0

(1- ) (l-2lJ) ( 1-'il )

0 0 {1-21>)

2 ( 1-lJ) J

The computation algorithm suggested by Desai (1977) is used to calculate [B],[D] and subse­quently the element stiffness matrix [Ke] for given mate rial properties, applied forees and boundary conditions. The overall stiffness of the structure is assembled which yields the nodal displacements. Stresses at the centro­ida! points of each element are calculated by using these nobal displacements.

Discretisation

The ·two masonry sections of Bargi dam are analysed for as~essed horizontal seam of 50 em thickness, 10 metre below the foundation level of the dam. The non-overflow section has been discretised into 234 four nodal quadrilateral elements while the overflow section has 194 elements with 270 and 228 nodes respectively. Smaller elements near the seam are considered for assessing the behaviour of seam. The dis­cretisation of non-overflow and overflow sect­ions are also shown in figures 1 and 2.

Loads

Dam weight i.e. gravity load and water press­ure in full reservoir condition are considered in stress analysis on dam. The uplift press­ure is duly accounted by readjusting the gra­vity load. While analysing the overflow sect­ion, an expected vertical crack at the upstre­am heel is also considered up to the seam le­vel for representation of ideal situation.

Material Properties

As suggested by Pant (1980), the material pro­perties of the masonry and hard rock mass on which dam is founded·-~re·~ssamed to'be'"Ballie~·· The values of various material constants for Wack and seam material are~tak~rt=as

·~asonryfRock .. r II ()'

Seam Material

Young's modulus 2.1 :·166 -~· 2.8 x105

t/m2 t/m2

Poisscn's ratio 0.2 0.15

Unit weight 2.3 t/m3 1.65 t/m3

Boundary.Conditions

In conventional design procedures the base of the dam is assumed fixed i.e. the displacements in the two

(4)

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6~

:t 1$11 (=:J -r:=r 5@ I

FIG.3 DISTRIBUTION OF NOilMAL 5TnE55E!'> IN NON-OVERFLOW SECTION (FOUNDATION WITIIOUT SEAM J

~ GllJ\VITY LOAD AND HYDROSTATIC PRESSURE

1~\ 4z 1

~·6 I

h,l

:eft! I I 4·~6 I

I 5h I

I I 1 5 ~~

542 ·c:r=;t 4. :c:

~ 2 0 10 ZO KG/CM

FIG. 4 OIS'TRIBUTION OF NORMAL STRESSES ltl NON-OVERFLOW SECTION C FOUNDATION WIT!! SEAM J

4 .•• \s.so \ 114 t5·3

GRAVITY LOAD AND HYDROSTATIC PRESSURE

>4\ ~··\ \' .q 8·2 8·97

\5~\ \e••\ \B·IB \ \~ !. r •.• t \,.., \ 1 •• + 0 I

9·'27

\_,.,9 . t43 ~.

QSi'o KG/CM2

COMPRESSION

TENSION

' ..• ' 0·9

FIG.S DISTRIBUTION OF PRINCIP.O,L STREssES IN NON-OVERFLOW SECTION ( FOUNDATION WITH SEAM )

1291

(lUAVITY LOAD AND IIYOnOSTI\TJC PHESSURE

0£5

112

riG.& DISTRIBUTION OF NORMAL STRESSES IN OVFRFLOW SECTION

C FOUNDATION Wll H §.E~·A"-M'-'-J -------------__1

~4·46 GRAVITY LOAD ANI) HYOROSfATIC PRESSURE

~4·63 2

1·6

0·67

0·66

0'79 I

1'25

2·63 I I I I

7-lil:::t::::: I

FIG.? DISTRIBUTION

~~:' " f.'.~~ l<.

~"'~;;-1(

' ' \ 1,

\

~5·8 ~

0 10 2Q KG/CM

~B·59 -.... :] I I 4-16 ]S>r--

3·5

2·89 I

: I

:.~~::= __..-9149 I I

·--··-OF SHEAR !;ln~:s'"~~s IN ilVF.flfLOW !;FCTION

( FOUNilATICN Wlll·l ,..~I·AM ) ---

GRAVITY LOAD AND HYDROSTATIC PRESSURE

o5JOKG/CM2

- COMPRESSION =TENSION

II·

' " ' " ·\ \ 'Z'""' , . "" '< '!'!?.?.

\ \ ,,. \ ' \ ' \ \ '\ " ...

' \ ,~~\ \ \MS \ \ \ \ \ ~,.

•• 10 •..

i

FIG.B DISTRIBUTION OF PRINCIPAL STRESSES IN OVERfLOW SECTION t FOUNDATION WITH SEAM J

Second International Conference on Case Histories in Geotechnical Engineering Missouri University of Science and Technology http://ICCHGE1984-2013.mst.edu

directions are assumed to be zero. But pract­ically complete fixity at the base can not be achieved and hence in the present analysis the base above the seam level is assumed flexible and below as fixed till 30 metre depth. The fixity is also assumed at 50 metre up and down -stream lengths of the base.

RESULT AND DISCUSSIONS

Though the present study is mainly focused towards studying the behaviour of gravity dam founded on hard rock mass with horizontal seam of weaker material in the foundation block, it also depicts the behaviour and stress varia­tions of gravity dams in general. Apart from the consideration of gravity load and hydros­tastic pressure, the analysis has also been done for extreme condition of empty reservoir, the chances of which are very remote. The no­rmal vertical stresses, shear stresses and consequently the two principal stresses are calculated at centroidal points of various elements and some typical results are shown in figures 3 to 8 whereas, detailed results are discussed by Khare (1987) in his M.Tech. Thesis.

Upon studying various stress distributions, following points are observed:

1. In the analysis of non-overflow section with gravity load only, it is observed that the stress distribution in the dam at higher levels is linear but it becomes nonlinear near the interface of the masonry base and the rock. The vertical stress near the heel reaches as high a value as 14.15 Kg/cm 2 when analysed without seam and 14,32 kg/cm2 whem analysed with seam. It is also seen that the distri­butions are nearly the same, except few local changes due to provision of seam. Similarly the effect of seam in case of shear and prin­cipal stresses is also negligible. The shear 2 stress touches the peak value of 5.0 kg/em whereas, the major principal stress reaches the value of 15.4 kg/cm2 •

2. In analysing the non-overflow section with gravity load and hydrostatic pressure, it is observed that the maximum values of vertical stress and principal stress are reduced by about 50% and 20% respectively whereas, the maximum shear stress is increased by about 10%, indicating negligible variations due to provi­sion of seam.

3. While analysising the overflow section for gravity load and hydrostatic pressure, the higher values of normal stresses are observed along the se~m with maximum value to the tune of 8.3 kg/em • The maximum shear stress value of 9.5 kg/cm 2 at toe and some tension at the heel section is also reported which can be easily taken care of.

CONCLUSIONS

Based on the observations made in analysis of Bagri dam following

the stress conclusions

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Can clearly be drawn:

1. The effect of 50 em. thick seam of tuffa­ceous material 10 metre below the foundation level of the dam and sandwiched between two layers of basaltic rock is negligible on the

behaviour of the entire dam structure except development of few higher values of shear st­resses at toe and tensions at the heel section which are generally taken care by provision of heavy reinforcement and shear keys.

2. The finite element method could be succ­essfully used in solving such difficult design problems which are not easily amenable to con­ventional methods of analysis.

ACKNUWLEDEMENT

The authors are grateful to Shri J.K.Tiwari Deputy Director, Bureau of Design of Hydel Irrigation Projects, Irrigation Department, Govt. of Madhya Pradesh, Bhopal, for providing necessary information and rendering help time to time in preparation of this research proje­ct. Thanks are also due to Shri O.N. Thaper, Director, Bureau of Design of Hydel Irrigation Projects, Irrigation Department, Govt. of Mad­hya Pradesh, Bhopal, for his valuable sugges­tions.

REFERENCES

Bargi Multipurpose Project Head Works (1983), Vol. 1 and 3, Irrigation Department, Govt. of Madhya Pradesh, Bhopal.

Desai, c.s. and J.F. Abel (1977), Introduction to Finite Element·Method, East west Publ~ca-

tion, New Delhi.

Khare, R.K. (1987), Some Gravity Dam (An Analysis Method), M.Tech. Thesis, Bhopal.

Design Aspects of by Finite Element Bhopal University,

Pant, B., D.K. Vaid, B. Thomas and S.K. Chou­dhary (1978), An Innovation in Gravity Dam Profile to Suit Local Foundation Conditions, Proceedings of 47th R and D Session of Central Bureau of Irrigation and Power, India.

Pant, B. and D.K. Vaid (1980), Some of Analysis and Design of Gravity Dam on Rock Ridge, Proceedings of 50th R Session of Bureau of Irrigation and

Aspects Founded and D Power,

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