Granular Materials in Civil Engineering: Recent Advances in the Physics of Their Mechanical Behavior and Applications to Engineering Works - Multiscale Geomechanics: From Soil to Engineering Projects - page 76

measures for steep abutments can be either to provide a flatter slope by excavations
or to build a zone of low-compressibility fill at the point of contact with the steep
abutment.
3.3.3.3.2. Scale effect on the horizontal contraction under the upstream slab
Another effect of the micromechanical settlements is the horizontal contractive
strains resulting from the wedging of the dam body between the abutments.
Horizontal contractive strains are induced by friction in the upstream concrete slab,
which may reach failure, as in the recent cases in Brazil, Lesotho, and China
(section 3.3.3.2).
For steep abutments inducing significant shearing at contact, the order of
magnitude of these shear strains at mid-height can be estimated from a basic 3D
analysis of the kinematics. Under pressure loading on the upstream face, the dam
will settle perpendicularly to this face and the central part will be confined between
the two converging abutments. The key parameter controlling the amplitude of this
phenomenon is the apparent rigidity modulus of the dam during reservoir filling.
This modulus can be related to the apparent rigidity modulus during construction by
use of statistical correlations [HUN 03]. The resulting contractive strains are easy to
estimate at mid-height, if we assume that initially horizontal directions in the dam
remain horizontal during straining.
This leads to the practical relation in Figure 3.22a, which links these contractive
strains to two adimensional variables:
− a dam deformability ratio, expressed here as a function of the apparent rigidity
modulus during construction, which is the only parameter usually known before
impounding;
− a valley shape ratio, expressed here as a function of the geometrical
characteristics of a vertical middle section of the valley, schematically represented
by a trapezoid.
Knowing that reinforced concrete reaches failure during uniaxial compression at
strain amplitude ε ~ 0.2%, the relation in Figure 3.22a allows us to construct a
diagram giving the risk of failure of the concrete slab. In this diagram, we have
plotted the corresponding locations of the characteristics of high dams having
recently suffered this type of damage (Barra-Grande, H = 185 m, and Campos-
Novos, H = 202 m, in Brazil; and Mohale, H = 145 m in Lesotho), as well as those
of dams without damage (Karahnjukar, H = 198 m, in Iceland; and El Cajon,
H = 189 m, in Mexico). The corresponding points are in fairly good agreement with
the observed behavior of these dams, which underlines the interest of such a
diagram.