GRAVITY DAM ANALYSIS 143

3.2.4 Stress analysis: gravity method

Straight gravity dams are generally analysed by the gravity method of stress
analysis. The approach is particularly suited to dams where adjacent mono-
liths or blocks are not linked by shear keys or by grouted transverse contrac-
tion joints (Section 3.5.4). The gravity method is, however, also suitable for
preliminary analysis of dams where such continuity is provided. More
sophisticated analytical methods are briefly referred to in Section 3.2.8.
Gravity stress analysis derives from elastic theory, and is applied to
two-dimensional vertical cantilever sections on the basis of the assump-
tions listed in Section 3.2.1. The stress analysis makes two further assump-
tions, namely

4. Vertical stresses on horizontal planes vary uniformly between
   upstream and downstream face (the ‘trapezoidal law’) and


5. Variation in horizontal shear stress across horizontal planes is parabolic.

Rigorous analytical techniques reveal that assumptions 4 and 5 are less appro-
priate for horizontal planes near base level (compare Figs 3.7(a) and 3.7(f )).
Stress concentrations develop near heel and toe, and modest tensile stresses
may be generated at the heel. Gravity stress analysis is, however, adequate for
the initial design of all but extremely large or geometrically complex gravity
dams. In the latter instances, the need to account for influences such as, inter
alia, dam and foundation deformation and interaction between adjacent
monoliths will require the use of advanced analytical methods which are the
province of specialist texts (e.g. USBR, 1976; Jansen, 1988).
The primary stresses determined in a comprehensive analysis by the
gravity method are as follows:

1. vertical normal stresses, z, on horizontal planes;


2. horizontal and vertical shear stresses, zyandyz;


3. horizontal normal stress, y, on vertical planes;


4. major and minor principal stresses,  1 and 3 (direction and magnitude).

Table 3.7 Comparative sliding stability factors; triangular gravity profile

Inclination of c0;30° ∑c∑H;0°
plane,
(degrees)

FSS FSF FLE■FSF FLE

05 0.71 0.68 0.74 0.86 0.89
0  0 0.66 0.87 0.87 1.00 1.00
0  5 0.55 1.07 1.10 1.13 1.18
 10 0.44 1.33 1.39 1.29 1.41
 15 0.34 1.52 1.79 1.44 1.75