COMBINATION OF LOADING FOR DESIGN GRAVITY DAM

COMBINATION OF LOADING FOR DESIGN GRAVITY DAMDr.P.SarathANUGravity dam design should be based on the most adverse load combination A, B, C, D, E, F or G given below using the safety factors prescribed.

Load Combination A (Construction Condition) - Dam completed but no water in reservoir and no tailwater.

Load Combination B (Normal Operating Condition) - Full reservoir elevation, normal dry weather tailwater, normal uplift; ice and silt (if applicable). Load Combination C (Flood Discharge Condition) - Reservoir at maximum flood pool elevation, all gates open, tailwater at flood elevation, normal uplift, and silt (if applicable ).

Load Combination D - Combination A, with earthquake.

Load Combination E - Combination B, with earthquake but no ice.

Load Combination F - Combination C, but with extreme uplift (drains inoperative).

Load Combination G - Combination E, but with extreme uplift (drains inoperative).Requirements for StabilityFollowing are the modes of failure of a gravity dam:

1. Overturning2. Sliding3. Compression or Crushing4. Tension.Therefore, the design shall satisfy the following requirements of stability:

1. The dam shall be safe against sliding on any plane or combination of planes within the dam, at the foundation or within the foundation;

2. The dam shall be safe against overturning at any plane within the dam, at the base, or at any plane below the base; and

3. The safe unit stresses in the concrete or masonry of the dam or in the foundation material shall not be exceeded.For consideration of stability the following assumptions are made:1. That the dam is composed of individual transverse vertical elements each of which carries its load to the foundation without transfer of load from or to adjacent elements.

(NOTE - However. in the stability analysis of a gravity dam, it becomes frequently necessary to make an analysis of the whole block, wherever special features of foundation and large openings so indicate); and

2. That the vertical stress varies linearly from upstream face to downstream face on any horizontal section.In the absence of any force other than the forces due to water, an elementary profile will be triangular in section, having zero width at the water level,

where water pressure is zero, and a maximum base width b, where the maximum water pressure acts.Elementary Profile of a Gravity DamThus, the section of the elementary profile is of the same shape as the hydrostatic pressure distribution diagram. For reservoir empty condition, a right angled triangular profile as shown in Fig.,

This is so because the weight of the dam acts at distance b/3 from the upstream face and is closer to it. If any triangular profile,

other than the right angled one, is provided, its weight will act still closer to the upstream face to provide a higher stabilizing force,

but tension will be developed at the toe when the dam is empty.We shall consider main three forces (weight of the dam, water pressure, and uplift pressure) acting on the elementary profile of a gravity dam viz., W = bHc/ 2, PH = w H2/ 2, Pu= CbHw /2

where C = uplift pressure intensity factor.

Base width of the elementary profileThe base width of the elementary profile can be found under two criteria:

No Tensile Stress Criterion, and (2) No Sliding Criterion.Practical Profile of a Gravity DamThe elementary profile of the gravity dam is only a theoretical profile. However such a profile is not possible in practice because of the provision of

(i) top width or roadway at the top, (ii) additional loads due to the roadway, and (iii) freeboard.Freeboard: Freeboard is the margin provided between the top of dam and H.F.L. in the reservoir to prevent the splashing of the waves over the non-overflow section.

It incidentally also takes care of any unforeseen floods in the reservoir.

The freeboard adopted shall be one and a half times the corresponding wave height hw above normal pool elevation or maximum reservoir level, whichever gives the higher crest elevation for the dam.

The freeboard above maximum reservoir level shall, however, be in no case less than 0.9 m. Wind velocities of 120 km/h over water in the case of full pool condition and 80 km/h over water in case of maximum reservoir condition are generally assumed for calculation of wave heights.

However, modern practice is to provide a maximum free board equal to 3 to 4 % of the dam height, though free board equal to 5 % or more might prove economical.Limiting Height of a Gravity DamThe only variable in the expression for the principal stress 1 at the toe is H. The maximum value of this principal stress should not exceed the allowable stress per for the material ie 1 per. In the limiting case 1 = Hw (Sc C +1)= per

Limit of low gravity damHlimHigh Gravity zone

From which, the limiting height Hlim is given by Hlim = per / w (Sc C +1)

For finding the limiting height Hlim, it is usual not to consider the uplift. Hence, putting C = 0, we get, Hlim = per / w (Sc+1)

If the height of the dam is more than Hlim, the maximum compressive stress will exceed the permissible stress and that condition is undesirable.This equation for the limiting height defines the distinction between a low and a high gravity dam. A low gravity dam is the one in which the height H is less than Hlim so that maximum compressive stress is not greater than the allowable stress.

For a concrete dam (Sc= 2.40 and per = 3.0 N/mm2), the limiting height is about 88 m.If higher grade concrete (per = 3.0 N/mm2) is used then the limiting height would be more. If the height of the dam to be constructed is more than that Hlim , the dam is known as high gravity dam.

For such a dam, the section will have to be given extra slopes to the upstream and downstream sides, below the limiting height, to bring the compressive stress within the permissible limits, as illustrated in Fig.THANK YOU