Proceedings, Coastal Sediments ' 9, ASCE, 1999, 860 875.
9
EQUILIBRIUM SHAPE OF HEADLAND-BAY BEACHES
FOR ENGINEERING DESIGN
Luis J. Moreno1, Nicholas C. Kraus2, M. ASCE
The equilibrium shoreline form of crenulate or headland-bay
Abstract:
beaches was identified in the 1940s and is widely accepted by coastal
geomorphologists and engineers. However, little quantitative verification of
the standard functional shoreline forms, the logarithmic-spiral shape and
parabolic shape, has been made. In addition, limited guidance is available for
applying the functional shapes in engineering practice. In this paper, we
investigate the two shapes by fitting to 46 beaches in Spain and in the North
America covering from large regional scale to small project scale. Software
is described which automates the fitting. A new function, called the
hyperbolic-tangent shape, is introduced for engineering applications. The
hyperbolic-tangent shape is easy to fit, and its controlling parameters have
simple geometric interpretation. Guidance is given for interpreting and fitting
the three headland-bay beach functions, with background data listed.
INTRODUCTION AND BACKGROUND
The concept of an equilibrium shape of crenulate or headland-bay beaches was
introduced by Krumbein (1944), followed by the work of Silvester (1960) for
engineering applications and by Yasso (1965) for fitting of a logarithmic spiral to data.
Headland control, leading to a crenulate-shaped equilibrium beach planform, has been
advocated for engineering use by Silvester and Ho (1972) and Silvester and Hsu (1993)
as a naturally functioning and preferable means of shore protection.
Coastal Defense Program Director, CEDEX, Ministerio de Fomento, Antonio Lpez, 81, 28026
Madrid, SPAIN. Luis.Moreno@cedex.es
Senior Research Scientist, U.S. Army Engineer Waterways Experiment Station, Coastal and
Hydraulics Laboratory, 3909 Halls Ferry Road, Vicksburg, Mississippi 39180 USA.
n.kraus@cerc.wes.army.mil
Moreno & Kraus
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