The forementioned assumptions are rephrased as rule/guideline for design of concrete gravity dam as described below:

• Rule 1:|
  Location of the resultant: No tension in any joint of the dam under all loading conditions (i.e. for full and empty reservoir).Thus, resultant of all forces (including uplift) must intersect the joint within the middle third.
• Rule 2 a:
  Resistance to sliding when shear is neglected: the tangent of the angle between the vertical and the resultant (including uplift) above horizontal plane shall be less than the allowable coefficient of frictional force „f‟. If empirical values are taken, factor of safety, Sf = 2.

Some values of Coefficient of friction f  

Surface  f 

Masonry on masonry or masonry 0.75

on good rock or concrete on 

Concrete

• Concrete or masonry on gravel  0.50 
• Concrete or masonry on sand  0.40 
• Concrete or masonry on clay  0.30 

However, the value of f for specific cases should be obtained by test 

P tan f 

For foundation on earth,Sf is taken as 3 

W  S f  

• Rule 2 b:
  Resistance to sliding when shear is considered q

The total friction resistance to sliding on any joint plus the ultimate shearing strength of the joint, must exceed the total horizontal force above the joint by a safe margin, i.e. 

P f W   r .S n . 

A S  

sf 

Where:

Sn – ultimate shearing strength of material         

Ssf = shear friction factor of safety     

A = cross sectional area of joints  

r = ratio of average to maximum shearing strength   

Recommended values   Ssf = 5, r = 0.5     

2        rSsf = 200 to 500t/m

While analyzing resistance to sliding, first compute tan and if tan > f apply Rule 2b. In that  case, Ssf should equal or exceed the allowable value. 

• Rule 3:
  Governing compressive stresses: P‟v, or P”v (maximum vertical stresses) are not the maximum stresses in the structure. The maximum stresses occur at the end joints, or inclined planes, normal to the face of the dam. Maximum stress for downstream face, reservoir full:
  Pi '   Pv' (1  tan 2  ' )

Maximum stress for upstream face, reservoir full
Pi "   Pv" (1  tan 2  " )

The inclined compressive stresses in the dam and foundation shall not exceed the allowable values.
Ultimate stress, ‟c = 14 to 31 MPa (after 28 days curing)
Working stress  c = ‟c/6

For foundation materials some indications for allowable stress are: 

Limestone -------------200 to 350 t/m3

Granite  -------------250 to 300t/m3

• Rule 4:
  Governing internal tension: The dam shall be designed and constructed in such a manner as to avoid or adequately provide for tension on interior planes, inclined, vertical or horizontal. 
• Rule 5:
  Margin of safety: all assumptions of forces acting on the dam shall be unquestionably on the safe side, all unit stresses adopted in design should provide an ample margin of safety against rupture and the shear-factors shall be considered. 
• Rule 6:
  Detail of design and methods of construction: all details shall support and confirm to the assumptions used in design; masonry should be of quality suited to the stresses adapted, protection against overflowing water shall be ample. 

Theoretical Versus Practical Section of a Dam

Considering only the two major forces acting on the dam, i.e. the weight of the dam and the hydrostatic water pressure, the required section of the dam for its stability will be a triangle of base width, 

H

B  

Where:

H = depth of water s = specific gravity of concrete

For this section, the resultant will pass through the upper middle third point of the base when the reservoir is empty and through the lower middle third point when the reservoir is full.

Practical Section

• The pointed crest of the theoretical dam is unstable to resist shock due to floating objects.
• There is need for a free board
• There is also need for top width for a roadway

For Practical Section

• Crest of the dam shall be a certain thickness depending on the height of the dam. For non overflow dams, most economical crest width  14 % of the height (10 – 15 %) is normal.
• Free board is provided and usually 3-4% of the dam height is used as a maximum height of the free board.