# DESIGN OF GRAVITY DAMS

• Elementary profile of the gravity dam has already been discusse.
• It is not possible to adopt elementary profile as such, because of certain practical requirements.
• The preliminary design of gravity dams is done by two dimensional gravity method by considering the dam as being made of a number of cantilevers of unit length and acting independently of adjacent cantilevers.

(a) Effect of top width added at the apex of triangular profile.

• ABC is an elementary profile of the dam.
• Let a be the top width added at the apex.
• The effect of this added top width is that the resultant of the dam section would shift slightly towards U/S side when reservoir is empty.
• For all the dam sections lying below point H or section FHG the resultant would be shifted towards the U/S face of the line AE1.
• This shift in resultant causes development of tension at the toe when reservoir is empty.
• Hence to avoid the possibilities of tension at toe when dam is empty, some batter has to be provided to U/S face below the plane FHG.
• The depth (h’) of plane FHG can be found out as follows:

$FH= AN= \frac{2}{3}a$

$FG= 3\times FH= 3\times AN= 3\times \frac{2}{3}a= 2a$

$h{}’= AF= FG\sqrt{p-c}= 2a\sqrt{p-c}$

• c is the uplift pressure intensity coefficient.
• Thus upto height h’ no batter in the U/S face is required, but for larger depths U/S face has to be battered.
• Now, letus consider the case when reservoir is full of water.
• The vertical line NJ cuts the outer-third point line AE2 at point j. Hence resultant of all the dam section lying below the plane JK are again shifted to the U/S side.
• To bring the resultant back to the outer third point line, the slope of D/S force have to be flattered. Figure 13.13 shows the effect of top width of various sizes.
• From diagram it can be easily seen that with increase in the size of the top width, the

• batter of U/S face of the dam is increased while that of D/S face decreased.
• The total effect of addition of masonry at the top, actually causes reduction in overall volume of the masonry of the dam rather than increasing it.
• The most economical top width of the gravity dam is about 14 per cent of the height of the dam.
• In case of low dams increased top width may be provided from practical considerations such as provision of roadway on the top etc.

(b) Multiple step method of design of gravity dam.

• In this case, the total dam height is divided into various zones with the help of various horizontal sections.
• Each zone, starting from top of the dam, is deigned in such a way that all the stability requirement for it are fully satisfied.
• The total height may be divided into seven zones as shown in Fig. 13.14.
• Brief description of conditions for each zone are given one by one.

Zone I.

• This is the top most rectangular part of the dam lying above the full reservoir level.
• The height of this zone is controlled by the free board requirements and thickness is fixed on the basis of practical considerations.
• If ice is likely to deposit at the surface of the reservoir, the thickness and height of this zone is fixed on the basis of sliding of the zone due to ice pressure.

Zone II.

• This is the zone which has both of its faces vertical.
• The position of bottom of this zone (c.c.) is fixed, such that the resultant, passes through the outer third point of the plane c.c.

Zone III.

• In this zone U/S face is maintained vertical, whereas D/S face is given the slope.
• The position of the bottom of this zone (d.d.) is fixed in such a way that the resultant for reservoir full and empty conditions, pass through the outer middle third point and inner middle third point respectively.

Zone IV.

• In this zone U/S face of the dam is also battered like D/S face but batter of U/S face with vertical is very small.
• The position of the bottom of the zone (e.e.) is fixed in such a way that the maximum stress developed at toe for the condition when reservoir is full, reach the allowable limit of the stress for the material.
• The height of the dam above the bottom of zone IV (e.e.) is the height of the low dam.

Zone V.

• D/S slope is further flattened in this zone so that the maximum pressure at D/S toe remains within the working stress under reservoir full condition.
• The resultant for reservoir full, remains well within middle third point of the base of this zone.
• For the reservoir empty condition, the resultant cuts the U/S middle third point of the base of this zone in section ff and stress at heel reached the permissible limit.

Zone VI.

• In this zone, the resultant lines for both the conditions of reservoir, full and empty, well within the middle third points of the base of this zone.
• maximum stresses developed at toe for reservoir full condition and at heel for reservoir empty condition reach the maximum permissible value.

Zone VII.

• At the bottom of this zone the maximum compression at the D/S toe exceeds the permissible limit.
• This zone is generally eliminated by revising the design of the dam.
• If change in design is not possible, then this zone is made from superior materials so that it may sustain the increased stresses developed at toe and heel.

(c) Single step method for design of high dams.

• We have seen in multiple step method of design of the dam that upto bottom of zone IV, the dam is low gravity dam.
• But if we go beyond the height of low dam, U/S slope has very steep slope whereas D/S slope has convex shape outwards as shown in Fig. 13.16. Convexity outwards is not allowed.
• This convexity is avoided by designing the dam as a single block but conforming to the conditions laid down in zone VI. The shape

• of the high dam designed according to single-step method is shown in Fig. 13.16.
• In this method, the U/S face of the dam is maintained vertical for some depth which may be determined as given in Fig. 13.12 (a).
• Below this section, both U/S and D/S faces are given such slopes that for both the conditions of reservoir full and empty, the stresses at toe and heel at all the sections reach their maximum values.
• This condition can be accomplished by performing several trials in all sections.

• Figure 13.16 shows super-position of dam section, designed according to single step method over that designed according to multi-step method.
• It is very clear that cubic content of the dam designed by multi-step method in economical.
• Dam designed by multi-step method is fully stressed at all the heights lying below the height of the low dam.
• But in case of dam, designed according to single step, the section is understressed everywhere except at the base.
• From the discussions done uptill now, following inferences can be easily drawn.

1. Low dams should be designed by multi-step method as they prove economical.

2. High dams beyond zone VI should be designed by single step method so as to avoid convex curvature on the D/S face.

3. It may be economical to eliminate the zones V and VI by using more superior materials in the lower part of the dam, as in that case, permissible compressive stress will be more and hence higher stresses can be sustained by the dam.

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