684 MODELS IN HYDRAULIC ENGINEERING
tangible rather than a solely mathematical representation of structural
response. Modelling techniques were developed and perfected in the
period 1950–65, essentially for multicurvature and complex concrete dams,
against limitations imposed on the application of sophisticated mathe-
matical analyses by non-availability of the necessary computing power.
Provided that a physical model is constructed in strict accord with the
appropriate laws of similitude (Section 16.1.3) it will function as a structural
analogue, yielding a valid prediction of prototype deformation and stress
distribution. In practice, as with hydraulic models, limitations are imposed
by conflicting requirements for compliance with the different laws of simili-
tude, most notably those relating to model material characteristics and load
response. Structural models are also relatively inflexible in practice, and
investigation of the effects of a change in geometry or structural detail, e.g.
the presence of joints in a concrete dam, or a change in any major parame-
ter, may require construction of a completely new model. For these and
other reasons computational methods (Chapters 2 and 3 and Section 16.1.2)
have largely displaced physical modelling techniques. Consideration of the
latter is therefore restricted here to the essential principles only.
Structural modelling of dams almost invariably relates to a static
loading condition. The relevant relationships are, therefore, those govern-
ing the stress () and force (P) ratios respectively (Table 16.1), i.e.
MM MlandMPM M^3 l.
For any material, the Poisson ratio, v, and the linear strain, , are
dimensionless parameters, and thus for structural similitude of model(subscript m) and prototype (subscript p) (^) p (^) m and vpvm. From
Hooke’s law the consequence of these statements is
MMEM (16.15a)
or, for M 1,
MME(M Ml). (16.15b)
The dominant stresses in a dam are those generated by hydrostatic loads,
including seepage and uplift, by structural self-weight and, if secondary
stresses are considered, the effects of temperature or of foundation defor-
mation. Difficulties inherent in simultaneously satisfying requirements for
material and structural similitude and reconciling scale ratios for geome-
try, stress and weight have been alluded to and are readily apparent, given
that the objective is for the model to correctly predict prototype deforma-
tion and stress.