32 
s = ratio of specific gravity of sediment to that of water in which it is 
immersed (= 2.65) 
P = porosity (= 0.35) 
h. = depth of closure 
B = berm height 
It can be shown that in the absence of background erosion, the fraction of 
material remaining, M, in the region where fill is placed depends only on the 
parameter VG#/( in which ¢ is the length of the initially rectangular project and ¢ 
is time (see Figure 26). For values of M between 0.5 and unity, it can be shown 
that an approximate expression for the relationship in Figure 26 is 
We tee (3) 
yx ! 
within a 15-percent error band in /. This equation was employed to estimate 
the time interval for 50 percent of the placed material to be transported from the 
original project limits. The standard values listed previously for K, K, s, and p 
were used in all calculations. The length of the fill project, the depth of closure, 
and average berm height were taken as 4,100 ft (1,250 m), 29.5 ft (9.0 m), and 
10.4 ft (3.17 m), respectively. In the first test, 4, was taken equal to 2.0 ft 
(0.6 m) (the effective wave height at the Long Branch wave gauge), resulting in 
G equal to 22,924 sq yd/month (19,167 sq m/month). The interval to 50 percent 
of placed material remaining was estimated to be 16 months. In the second test, 
h, was taken equal to 3.0 ft (0.9 m) (the effective wave height at the Long 
Branch wave gauge shoaled to breaking conditions) to more accurately estimate 
breaking wave conditions. In this case, G was computed as 63,170 sq yd/month 
(52,818 sq m/month), and the interval to 50 percent of placed material remaining 
was estimated to be about 6 months. 
The preceding calculations indicate that end losses from the Monmouth 
Beach area should be rather large, if one can consider the Monmouth Beach 
region as an independent beach fill because of its protrusion seaward beyond 
adjacent beaches. Beach profile analyses indicate that approximately 
620,000 cu yd were placed between sta 264+00 and 282+00 during the period 
July-October 1994. Approximately | year later (November/December 1995), 
two emergency fill placements were undertaken, and approximately 
230,000 cu yd were placed within this region. Assuming these emergency fills 
replaced fill material transported out of the placement area indicates a 37-percent 
loss of the initial placement volume or 63-percent retention over a 13-month 
interval. Both analytical predictions indicate that expected losses exceed the 
measured losses. The smaller magnitude of measured beach-fill losses is likely 
due to the fill-retaining capacity of the groins located at the ends of the 
Monmouth Beach hot-spot region. 
Chapter 4 Beach-Fill End Losses 
