WIT Press

A Note On The Search For ‘optimal’ Shapes Of Arch Dams


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221 - 231




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M. Fanelli & A. Fanelli


The ‘shape resistance’ of an arch dam affords a concrete volume substantially smaller than that of a gravity dam of equal height, at the expense of more stringent requirements for concrete quality, formwork, foundation treatments, geometric tracing and erection constraints. Minimisation of the concrete volume or, more generally, of total costs is pursued by ‘optimising’ the shape under a set of constraints. This requires defining a ‘structural model’, a set of ‘shape parameters’, the ‘constraints’ under which optimisation is to be achieved, the ‘design external load(s)’, an ‘objective function’ and an ‘algorithmic procedure’. Usually the number of shape parameters ranges from a dozen to 40 or more, to leave wide freedom of adaptation of the final shape to loads and constraints, and a unique distribution of design loads is assumed; hence heavy analyticalnumerical procedures leading to a unique ‘optimal’ shape. As the dam is called to withstand a large variety of external actions, the shape thus obtained cannot be ‘optimal’ for all cases; therefore the rationale for complex optimisation models may be questioned. The Authors claim that the number of shape parameters can be kept very small (from three to a few units) by adopting a simplified model complying from the start with the main constraints. This claim is supported by past experience: the shapes of arch dams designed in this way were found, indeed, to be very close to those obtained by more ‘rigorous’ approaches. Keywords: arch dams, shape optimisation, shape parameters, constraints, simplified models.


arch dams, shape optimisation, shape parameters, constraints, simplified models.