the 
The sea level displacement, dD, being small, the difference in 
the quantity of sand represented by the two triangles ABC and A'B!C! 
in Figure 4 is considered as a difference of infinitesimals and there- 
fore is neglected. So, combining equations (2) and (3) 
dv 8Yg dD 
—_—_— = —-_—___-=— - 4 _—__ 4 
ony oe SET Ole: Bb. ide (4) 
It is seen that when dV/dt = 0 
Via cnaty 
b dD 
dyna = oe 
Vela BeSTDP ioe Ss 
where S is the average bottom slope. Note that this expression is 
independent of the beach profile and, therefore, implicitly takes into 
account bar formation. 
(b) The change of volume due to the perturbation and departure 
from the equilibrium profile. This departure is characterized by 
a change of slope. Therefore, the corresponding variation of sand 
volume (area AEG in Fig. 3) is 
Se ene) 3) 
t BTS aha on TOL eel 
in accordance with the previous assumption. Therefore, the total 
variation of sand volume, dV/dt, is (adding eqs. 4 and 5): 
dV _ 5 any. 5 oS 
qe Oo Ue) ae = Cle lee ay Mane (6) 
This variation of volume is due to the variation of littoral drift along 
ox-axis and the onshore-offshore motion. The following terms are included: 
(a) The discharge of sand leaving the beach per unit of width 
includes: 
(1) Qyw due to loss of sand by wind. 
(2) Qs 09D due to the quantity of silt contained in the 
bluff and which tends to move offshore by suspension. This 
loss occurs only in case of erosion (dy,/at < 0) and is equal 
to Qs =UKAB oye/ ot), where) Ka) iisiithespercentage) of silt ain 
the bluff. 
(3) QF due to the loss of sand from the beach by density 
current during a storm. QF is a function of the size dis- 
tribution and density of material. A beach of fine material 
(<0.1 tm) tends to erode more rapidly than a beach of coarse 
material (>1 mm). The coarse material tends to move along 
the shore while the fine sand moves offshore. 
15 
