EM 1110-2-1100 (Part III)
30 Apr 02
(3) Variation of K with median grain size.
(a) Longshore sand transport data presented in Figure III-2-4 represent beaches with quartz-density grain
sizes ranging from ~0.2 mm to 1.0 mm, and wave heights ranging from 0.5 to 2.0 m. Bailard (1981, 1984)
developed an energy-based model, which presents K as a function of the breaker angle and the ratio of the
orbital velocity magnitude and the sediment fall speed, also based on the rms wave height at breaking.
Bailard calibrated the model using eight field and two laboratory data sets, and developed the following
K ' 0.05 % 2.6 sin2 (2αb) % 0.007 mb
where umb is the maximum oscillatory velocity magnitude, obtained from shallow-water wave theory as
and wf is the fall speed of the sediment, either calculated using the relationships described in Part III-1, or,
if the spherical grain assumption cannot be applied to the material, measured experimentally. Bailard
developed his relationship using the following data ranges: 2.5 # wf # 20.5 cm/sec; 0.2o # αb # 15o; and 33
# umb # 283 cm/sec. A comparison of observed and predicted K coefficients using Bailard's Equation 2-8 is
presented in Figure III-2-5, using the data sets on which Bailard based his calibration. Because Bailard's
relationship is based on a limited data set, predicted K coefficients may be highly variable. Bailard's
relationship for K is similar to a relationship presented by Walton (1979) and Walton and Chiu (1979), which
was compared to limited laboratory data.
(b) Others have proposed empirically based relationships for increasing K with decreasing grain size (or
equivalently, fall speed) (Bruno, Dean, and Gable 1980; Dean et al. 1982; Kamphuis et al. 1986; Dean 1987).
Komar (1988), after reexamining available field data, suggested that the previous relationships resulted from
two data sets with K values based on erroneous or questionable field data. Revising these K values, Komar
(1988) concluded that existing data suggests little dependence of the empirical K coefficient on sediment
grain sizes, at least for the range of sediments in the data set. Data from shingle beaches, however, indicated
a smaller K, but the data were too limited to establish a correlation. Komar stressed that K should depend on
sediment grain size, and the absence of such a trend in his analysis must result from the imperfect quality of
(c) Recently, del Valle, Medina, and Losada (1993) have presented an empirically based relationship for
the K parameter, adding sediment transport data representing a range in median sediment grain sizes (0.40
mm to 1.5 mm) from the Adra River Delta, Spain to the available database as modified by Komar (1988).
Del Valle, Medina, and Losada obtained wave parameters from buoy and visual observations, and sediment
transport rates were evaluated from aerial photographs documenting a 30-year period of shoreline evolution
for five locations along the delta. Results of their analysis reinforce a decreasing trend in the empirical
coefficient K with sediment grain size. Their empirical fit based on the corrections to the database as
suggested by Komar (1988) is shown in Figure III-2-6 and given in Equation III-2-10. The empirically based
relationship is to be applied with rms breaking wave height,
(&2.5 D50 )
K ' 1.4 e
Longshore Sediment Transport