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Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE) PDF Download

Free board 

Free board is the vertical distance between the top of the dam and the sill water level. IS:6512-1984 recommends that the free board shall be wind set-up plus 4/3 times wave height above normal pool elevation or above maximum reservoir level corresponding to design flood, whichever gives higher crest elevation. Wind set-up is the shear displacement of water towards one end of a reservoir by wind blowing continuously – or in repeated regular gusts – from one direction. The Zuider Zee formula (Thomas, 1976) and recommended by IS: 6512-1984 may be used as a guide for the estimation of setup(S): 

S = V2FCosA / kD          (14)

Where 

S = Wind set-up, in m        

V = Velocity of wind over water in m/s        

F = Fetch, in km          

D = Average depth of reservoir, in m, along maximum fetch        

A = Angle of wind to fetch, may be taken as zero degrees for maximum set-up        

K = A constant, specified as about 62000 

Set-up of the reservoir will depend upon the period of time over which the wind blows, that is, at least 1hour, for a fetch of 3km or 3hours for a fetch of 20km. On a 80km fetch, a wind speed of 80 km/hour must last for at least 4hours, whereas for a wind speed of 40km/hour it must last around 8hours for maximum set-up. 

The free-board shall not be less than 1.0m above Maximum Water Level (MWL) corresponding to the design flood. If design flood is not same as Probable Maximum Flood (PMF), then the top of the dam shall not be lower than MWL corresponding to PMF. 

Stability analysis of gravity dams  

The stability analysis of gravity dams may be carried out by various methods, of which the gravity method is described here. In this method, the dam is considered to be made up of a number of vertical cantilevers which act independently for each other. The resultant of all horizontal and vertical forces including uplift should be balanced by an equal and opposite reaction at the foundation consisting of the total vertical reaction and the total horizontal shear and friction at the base and the resisting shear and friction of the passive wedge, if any. For the dam to be in static equilibrium, the location of this force is such that the summation of moments is equal to zero. The distribution of the vertical reaction is assumed as trapezoidal for convenience only. Otherwise, the problem of determining the actual stress distribution at the base of a dam is complicated by the horizontal reaction, internal stress relations, and other theoretical considerations. Moreover, variation of foundation materials with depth, cracks and fissures which affect the resistance of the foundation also make the problem more complex. The internal stresses and foundation pressures should be computed both with and without uplift to determine the worst condition.

The stability analysis of a dam section is carried out to check the safety with regard to 

  1. Rotation and overturning
  2. Translation and sliding
  3. Overstress and material failure

Stability against overturning

Before a gravity dam can overturn physically, there may be other types of failures, such as cracking of the upstream material due to tension, increase in uplift, crushing of the toe material and sliding. However, the check against overturning is made to be sure that the total stabilizing moments weigh out the de-stabilizing moments. The factor of safety against overturning may be taken as 1.5. As such, a gravity dam is considered safe also from the point of view of overturning if there is no tension on the upstream face. 

Stability against sliding 

Many of the loads on the dam act horizontally, like water pressure, horizontal earthquake forces, etc. These forces have to be resisted by frictional or shearing forces along horizontal or nearly-horizontal seams in foundation. The stability of a dam against sliding is evaluated by comparing the minimum total available resistance along the critical path of sliding (that is, along that plane or combination of plans which mobilizes the least resistance to sliding) to the total magnitude of the forces tending to induce sliding. 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE) 

Figure. 37: Stability against sliding along concrete dam - rock base interface. Good rock is assumed to exist below

Sliding resistance is also a function of the cohesion inherent in the materials at their contact and the angle of internal friction of the material at the surface of sliding. The junction plane between the dam and rock is rarely smooth. In fact, special efforts are made during construction to keep the interface as rough as possible. There may, however be some lower plane in the foundation where sliding is resisted by friction alone especially if the rock is markedly stratified and horizontally bedded. Figure 37 shows a typical dam profile with the bed-rock and foundation interface inclined at an angle α. Factor of Safety against sliding (F) along a plane may be computed from the following formula: 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)        (15) 

Where Fφ and Fc are the Partial Factor of Safety in respect of friction and Partial Factor of Safety of cohesion. IS: 6512-1984 recommends these values to be as given in the following table

Loading

Condition

Fφ

Fc

For dams and the contact plane with foundation

For foundation

Thoroughly

investigated

Others

A,B,C

1.5

3.6

4.0

4.5

D,E

1.2

2.4

2.7

3.0

F,G

1.0

1.2

1.35

1.5

 

The value of cohesion and internal friction may be estimated for the purpose of preliminary designs on the basis of available data on similar or comparable materials. For final designs, however, the value of cohesion and internal friction has to be determined by actual laboratory and field tests, as specified in the Bureau of Indian Standards code IS: 7746-1975 “Code of practice for in-situ shear test on rocks”. 

In the presence of a horizon with low shear resistance, for example, a thin clay seam or clay infill in a discontinuity (Figure 38), then it would be advisable to include downstream passive wedge resistance P, as a further component of the total resistance to sliding which can be mobilized. In this case, the Factor of Safety along sliding has to be found along plane B-B computing the net shear force and net cohesive force along this plane. The net shear force would now be equal to: 

(WCosα + ∑ ΗSinα ) tanφ    (16)

Where W is the weight of the wedge; αis the assumed angle of sliding failure, ∑Η is the net destabilizing horizontal moment; and φ is the internal friction within the rock at plane B-B. The net cohesive force along plane B-B is determined as equal to C.AB-B. Here, C is the cohesion of material and AB-B, the area, along plane B-B. 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)

Figure.33: Sliding against presence of weak seams resisted by passive wedge resistance

Failure against overstressing

A dam may fail if any of its part is overstressed and hence the stresses in any part of the dam must not exceed the allowable working stress of concrete. In order to ensure the safety of a concrete gravity dam against this sort of failure, the strength of concrete shall be such that it is more than the stresses anticipated in the structure by a safe margin. The maximum compressive stresses occur at heel (mostly during reservoir empty condition) or at toe (at reservoir full condition) and on planes normal to the face of the dam. The strength of concrete and masonary varies with age, the kind of cement and other ingredients and their proportions in the work can be determined only by experiment.

The calculation of the stresses in the body of a gravity dam follows from the basics of elastic theory, which is applied in a two-dimensional vertical plane, and assuming the block of the dam to be a cantilever in the vertical plane attached to the foundation. Although in such an analysis, it is assumed that the vertical stresses on horizontal planes vary uniformly and horizontal shear stresses vary parabolically, they are not 

strictly correct. Stress concentrations develop near heel and toe, and modest tensile stresses may develop at heel. The basic stresses that are required to be determined in a gravity dam analysis are discussed below:

Normal stresses on horizontal planes

On any horizontal plane, the vertical normal stress (σz) may be determined as: 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)               (17) 

Where 

∑V = Resultant vertical load above the plane considered  

T = Thickness of the dam block, that is, the length measured from heel to toe    

e = Eccentricity of the resultant load                

y = Distance from the neutral axis of the plane to the point where () is being determined 

At the heel, y = -T/2 and at toe, y = +T/2. Thus, at these points, the normal stresses are found out as under: 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)           (18) 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)            (19) 

The eccentricity e may be found out as: 

e = Net moment / Net vertical force            (20) 

Naturally, there would be tension on the upstream face if the overturning moments under the reservoir full condition increase such that e becomes greater than T/6. The total vertical stresses at the upstream and downstream faces are obtained by addition of external hydrostatic pressures. 

Shear stresses on horizontal planes    

Nearly equal and complimentary horizontal stress (τzy) and shear stresses (τyz) are developed at any point as a result of the variation in vertical normal stress over a horizontal plane (Figure 39). The following relation can be derived relating the stresses with the distance y measured from the centroid: 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)             (21)

Where  

τyz D = (σzD – pD) tanφD, the shear stress at downstream face 

τyz U = - (σzU – pU) tanφD, the shear stress at upstream face 

H = the height of the dam 

The shear stress is seen to vary parabolically from τyz U at the upstream face up to τyz D at the downstream face. 

Normal stresses on vertical planes 

These stresses, σy can be determined by consideration of the equilibrium of the horizontal shear forces operating above and below a hypothetical element within the dam (Figure 39). The difference in shear forces is balanced by the normal stresses on vertical planes. Boundary values of σy at upstream and downstream faces are given by the following relations: 

σ yU = Pu + (σ zU - Py) tan2φ U

 σ yD = Py + (σ zD - Py) tan2φ D

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)

Figure.39: State of stress in a concrete gravity dam 

Principal stresses 

These are the maximum and minimum stresses that may be developed at any point within the dam. Usually, these are denoted as σand σ3respectively, and are oriented at a certain angle to the reference horizontal or vertical lines. The magnitude of σ1 and σ3may be determined from the state of stress σzy and τyz at any point by the following formula: 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)            (24) 

The maximum and minimum shear stress is obtained from the following formula: 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)              (25) 

The upstream and downstream faces are each planes of zero shear, and therefore, are planes of principal stresses. The principal stresses at these faces are given by the following expressions: 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)(26) 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)                                            (27)

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)    (28) 

Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)                           (29) 

Permissible stresses in concrete 

According to IS: 6512-1984, the following have to be followed for allowable compressive and tensile stresses in concrete:

Compressive strength of concrete is determined by testing 150mm cubes. The strength of concrete should satisfy early load and construction requirements and at the age of one year, it should be four times the maximum computed stress in the dam or 14N/mm2, whichever is more. The allowable working stress in any part of the structure shall also not exceed 7N/mm2. No tensile stress is permitted on the upstream face of the dam for load combination B. Nominal tensile stresses are permitted for other load combinations and their permissible values should not exceed the values given in the following table: 

Load combinationPermissible tensile stress



G
0.01fc 0.02fc 0.02fc 0.04fc

Where fis the cube compressive strength of concrete. 

Small values of tension on the downstream face is permitted since it is improbable that a fully constructed dam is kept empty and downstream cracks which are not extensive and for limited depths from the surface may not be detrimental to the safety of the structure. 

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FAQs on Design and Construction of Concrete Gravity Dams (Part - 4) - Civil Engineering (CE)

1. What is the design process for concrete gravity dams?
Ans. The design process for concrete gravity dams involves several steps. First, the site is evaluated for geological and geotechnical considerations. Then, the dam's dimensions, including height, length, and thickness, are determined based on the reservoir's capacity and the load it needs to withstand. The dam is designed to resist various forces such as hydrostatic pressure, uplift, and earthquake loads. Structural analysis and stability calculations are performed to ensure the dam's safety and integrity. Finally, construction plans and specifications are prepared, considering factors like construction materials, joint detailing, and drainage systems.
2. What are the advantages of concrete gravity dams compared to other types of dams?
Ans. Concrete gravity dams offer several advantages over other types of dams. Firstly, they are highly durable and have a longer lifespan compared to earth or rockfill dams. Secondly, concrete gravity dams require less maintenance and are less susceptible to erosion or seepage. They also have excellent resistance to uplift forces and can withstand large water pressure. Moreover, concrete dams can be designed to incorporate hydropower generation facilities, allowing for the production of clean and renewable energy. Lastly, concrete gravity dams have a visually appealing and majestic appearance, often becoming iconic landmarks.
3. How are concrete gravity dams constructed?
Ans. The construction of concrete gravity dams involves several stages. First, the foundation is prepared by excavating and leveling the area. Then, a concrete base slab is constructed to provide a stable platform. The dam's main body is built using mass concrete, which is placed in layers and allowed to cure. Construction joints are provided to enable the dam to withstand temperature-related expansion and contraction. The dam's upstream face is usually given a smooth finish to enhance its hydraulic performance. Finally, auxiliary structures such as spillways, gates, and powerhouses are constructed to facilitate the dam's operation.
4. How are concrete gravity dams designed to withstand seismic forces?
Ans. Concrete gravity dams are designed to withstand seismic forces by considering various factors. Firstly, the dam's foundation is evaluated to ensure its stability during an earthquake. Then, the dam's geometry and cross-section are designed to provide sufficient strength and stiffness to resist the seismic loads. The use of reinforcement in critical areas, such as the dam's base and joints, helps enhance its resistance to seismic forces. Additionally, the presence of properly designed spillways and energy dissipation devices helps reduce the impact of seismic forces on the dam structure.
5. What are the key considerations for the construction of concrete gravity dams in mountainous regions?
Ans. Construction of concrete gravity dams in mountainous regions requires special considerations. Firstly, the geological conditions, including the type and quality of rock, must be thoroughly assessed to ensure a stable foundation. Secondly, the dam's design should account for the steep slopes and potential rockslides in the surrounding area. Adequate measures, such as rock anchors or stabilization techniques, may be required to enhance the dam's stability. Moreover, construction access and logistics become more challenging in mountainous terrain, necessitating careful planning and coordination. Finally, the impact of extreme weather conditions, such as heavy rainfall or snowmelt, on the dam's operation and safety must be carefully evaluated and addressed.
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