Design and Construction of Concrete Gravity Dams (Part -2) - Civil Engineering (CE) PDF Download

Design of concrete gravity Dam sections    

Fundamentally a gravity dam should satisfy the following criteria:

1. It shall be safe against overturning at any horizontal position within the dam at the contact with the foundation or within the foundation.
2. It should be safe against sliding at any horizontal plane within the dam, at the contact with the foundation or along any geological feature within the foundation.
3. The section should be so proportional that the allowable stresses in both the concrete and the foundation should not exceed.

Safety of the dam structure is to be checked against possible loadings, which may be classified as primary, secondary or exceptional. The classification is made in terms of the applicability and/or for the relative importance of the load.

1. Primary loads are identified as universally applicable and of prime importance of the load.
2. Secondary loads are generally discretionary and of lesser magnitude like sediment load or thermal stresses due to mass concreting.
3. Exceptional loads are designed on the basis of limited general applicability or having low probability of occurrence like inertial loads associated with seismic activity. 

Technically a concrete gravity dam derives its stability from the force of gravity of the materials in the section and hence the name. The gravity dam has sufficient weight so as to withstand the forces and the overturning moment caused by the water impounded in the reservoir behind it. It transfers the loads to the foundations by cantilever action and hence good foundations are pre requisite for the gravity dam.

The forces that give stability to the dam include:

1. Weight of the dam  
2. Thrust of the tail water  

The forces that try to destabilize the dam include:

1. Reservoir water pressure  
2. Uplift  
3. Forces due to waves in the reservoir
4. Ice pr essure
5. Temperature str esses
6. Silt pr essure
7. Seismic for ces
8. Wind pr essure

The forces to be resisted by a gravity dam fall into two categories as given below:

1. Forces, such as weight of the dam and water pressure which are directly calculated from the unit weight of materials and properties of fluid pressure and
2. Forces such as uplift, earthquake loads ,silt pressure and ice pressure which are assumed only on the basis of assumptions of varying degree of  reliability. In fact to evaluate this category of forces, special care has to be taken and reliance placed on available data, experience and judgement.  

Figure 23: Different forces acting on a concrete gravity dam

Figure 23 shows the position and direction of the various forces expected in a concrete gravity dam. Forces like temperature stresses and wind pressure have not been shown. Ice pressures being uncommon in Indian context have been omitted.

For consideration of stability of a concrete dam, 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. However for convenience, the stability analysis is commonly carried out for the whole block.
2. That the vertical stress varies linearly from upstream face to the downstream face on any horizontal section. The Bureau of Indian Standards code IS 6512-1984 “Criteria for design of solid gravity dams” recommends that a gravity dam should be designed for the most adverse load condition of the seven given type using the safety factors prescribed. 

Depending upon the scope and details of the various project components, site conditions and construction programme one or more of the following loading conditions may be applicable and may need suitable modifications. The seven types of load combinations are as follows: 

1. Load combination A (construction condition): Dam completed but no water in reservoir or tailwater
2. Load combination B (normal operating conditions): Full reservoir elevation, normal dry weather tail water, normal uplift, ice and silt (if applicable)
3. 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)
4. Load combination D: Combination of A and earthquake  
5. Load combination E: Combination B, with earthquake but no ice
6. Load combination F: Combination C, but with extreme uplift, assuming the drainage holes to be Inoperative
7. Load combination G: Combination E but with extreme uplift (drains inoperative)

It would be useful to explain in a bit more detail the different loadings and the methods required to calculate them. These are explained in the following sections.  

Loadings for concrete Gravity Dams 

The significant loadings on a concrete gravity dam include the self-weight or dead load of the dam, the water pressure from the reservoir, and the uplift pressure from the foundation. There are other loadings, which either occur intermittently, like earthquake forces, or are smaller in magnitude, like the pressure exerted by the waves generated in the reservoir that his the upstream of the dam face. These loadings are explained in the following section. 

Dead load 

The dead load comprises of the weight of the concrete structure of the dam body in addition to pier gates and bridges, if any over the piers. The density of concrete may be considered as 2400 kg/m³. Since the cross section of a dam usually would not be simple, the analysis may be carried out by dividing the section into several triangles and rectangles and the dead load (self weight) of each of these sections (considering unit width or the block width) computed separately and then added up. For finding out the moment of the dead load (required for calculating stresses), the moments due to the separate sub–parts may be calculated individually and then summed up.

Water pressure on dam

The pressure due to water in the reservoir and that of the tailwater acting on vertical planes on the upstream and downstream side of the dam respectively may be calculated by the law of hydrostatics. Thus, the pressure at any depth h is given by γh kN/m² acting normal to the surface. When the dam has a sloping upstream face, the water pressure can be resolved into its horizontal and vertical componenets, the vertical component being given by the weight of the water prism on the upstream face and acts vertically downward through the centre of gravity of the water area supported on the dam face. 

In spillway section, when the gates are closed, the water pressure can be worked out in the same manner as for non–overflow sections except for vertical load of water on the dam itself. During overflow, the top portion of the pressure triangle gets truncated and a trapezium of pressure acts (Figure 24). 

The pressure due to tailwater is obtained in a similar manner as for the upstream reservoir water.

In case of low overflow dams, the dynamic effect of the velocity of approach may be significant and deserve consideration. 

Uplift pressures

Uplift forces occur as internal pressure in pores, cracks and seams within the body of the dam, at the contact between the dam and its foundation and within the foundation. The recent trends for evaluating uplift forces is based on the phenomenon of seepage through permeable material. Water under pressure enters the pores and fissures of the foundation material and joints in the dam. The uplift is supposed to act on the whole width plane, that is being considered, either at the base or at any position within the dam. The uplift pressure on the upstream end of the considered horizontal plane is taken as γ_hu where h_u is the depth of water above the plane. On the downstream the value is γ_hd where h_d is again the depth of water above the plane.

Figure 25. Uplift pressure at base and at any genera! plane in the dam body. Drainage holes are not considered. 

Figure 25 illustrates the uplift pressure on a concrete gravity dam’s non overflow section through two planes – one at the base and the other at the horizontal plane which is above the tail water level. In Figure 25, the drainage holes either in the body of the dam, or within the foundation has not been considered. If the effects of the drainage holes are considered, then the uplift pressure diagram gets modified as shown in Figure 26. If there is crack at any plane of the dam, or at the base then the uplift pressure diagram gets further modified as shown in Figure27. 

As such, the uplift pressure is assumed to act throughout the base area. Further it is also assumed that they remain unaffected by earthquakes. 

Silt pressure 

The weight and the pressure of the submerged silt are to be considered in addition to weight and pressure of water. The weight of the silt acts vertically on the slope and pressure horizontally, in a similar fashion to the corresponding forces due to water. It is recommended that the submerged density of silt for calculating horizontal pressure may be taken as 1360 kg/m³. Equivalently, for calculating vertical force, the same may be taken as 1925 kg/m³.