non-linear load response. Modelling techniques well established in other
applications, e.g. finite element analysis (FEA), are therefore not widely
employed other than for more rigorous and specific design studies. The
principles of finite element modelling are referred to very briefly in
Section 3.2.8, in the context of concrete dam stress analysis.
The application of mathematical modelling to the study of specific
areas of behaviour, notably internal cracking and progressive failure in
embankments, is addressed comprehensively in Vaughan, Dounias and
Potts (1989), in Potts, Dounias and Vaughan (1990), and in Dounias,
Potts and Vaughan (1996). The first also addresses the influence of
core geometry, e.g. vertical or inclined, slender or wide, on embank-
ment dam behaviour. All are also relevant to more general considera-
tions of hydraulic fracturing and cracking, leading to potentially
catastrophic internal erosion, as exemplified by problems which
occurred at recently commissioned dams at Hyttejuvet (Finland) and
Balderhead (UK). The latter instance is discussed in Vaughan et al.
(1970).
(b) Hydraulic fracturing
The analysis of internal stresses is generally restricted to an assessment of
the risk of hydraulic fracturing or of internal cracking, e.g. as a result of
interface effects attributable to load transfer and strain incompatibility at
zone boundaries. This is addressed in some depth in Kulhawy and Gur-
towski (1976).
Hydraulic fracturing, with the risk of consequent internal erosion
and migration of fines, may initiate if the total stress, n, normal to any
plane within a soil mass is less than the local porewater pressure uw,
making allowance for the limited tensile strength, t, of the soil. The con-
dition for fracturing to occur is thus uwnton any internal plane.
Given that such a fracture initiates in the core the factors critical to
integrity are firstly whether the fracture propagates through the core and,
secondly, whether seepage velocities etc. are such that ongoing erosion
takes place. Development of the erosion process will depend upon
whether the fracture self-heals and/or the ability of the material immedi-
ately downstream to ‘trap’ fines migrating from the core. Erodibility of
soils is discussed in Atkinson, Charles and Mhach (1990) and in Sherard
and Dunnigan (1985).
A transverse vertical plane can be shown to be the critical orienta-
tion within the core, and transverse fracturing on such a vertical plane will
take place if, neglecting t,uwha, where hais the axial horizontal total
stress, i.e. parallel to the dam axis. The other critical plane is the trans-
verse horizontal plane. Fracturing will develop on the latter orientation
if vertical total stress, v, falls below uwas a result of arching of a
compressible core as a result of load transfer to relatively incompressible