COASTAL ENGINEERING - Introduction to Soft Soil Geotechnique: Content, Context and Application - page 290

oscillations H b . Note, that the average free water level is lower, because of wave
deformation on the shallow zone before the breakwater slope (trochoidal form),
and the average water level at the back side is high due to internal set-up.
From Fig 16.21b one observes that the maximum head gradient is in the range of
20%. This leads to 0.20 = bq 2 , or q = (0.20/1.73) 0.5 = 0.20 k , which gives for the
apparent (linear) permeability k = 1.7 m/s. In a similar manner the apparent
permeability of 0.1 to 0.3 rock (filter 2b) becomes k = 1.2 m/s. Because of air
intrusion during high water a reduction is required, and for the 1 to 3 ton rock
(filter 2a) an approximate permeability of k = 0.9 m/s is assumed.
In case 2 the effective still water depth is D = 11 m, and in case 1 the finer core
is simulated by a reduced effective depth of D = 5.5 m. The dam width is L = 35 m,
the slope 34 o , the porosity is n = 0.4, the wave height is 6.5 m, the wave period T =
20 s, and the air intrusion coefficient is taken as c a = 4 (large waves are
considered). Results of formula (16.29) for case 1 and case 2 are given in the table
in Fig 16.22a, and they are in reasonable agreement with the results of the
numerical values, shown in Fig 16.22b. H b is significantly lower than found by
numerical simulation, particularly for case 2, probably due to reflection (closed-
end) and the assumption of a uniform velocity field over depth in the formulae.

case 1 case 1 case 1

case 2 case 2 case 2

H b = 3.20 m H b = 3.20 m H b = 3.20 m

H = 6.5 m H = 6.5 m H = 6.5 m

H b = 1.00 m H b = 1.00 m H b = 1.00 m

H = 6.5 m H = 6.5 m H = 6.5 m

S = 1.56 m S = 1.56 m S = 1.56 m

S = 1.19m S = 1.19m S = 1.19m

Figure 16.22b Isochrones of cyclic internal water table response by numerical simulation

case (1) case (2)

D m
2 m
F 1
;

5.5
8.9
0.90
0.82
1.75
0.91

11.0
12.6
0.77
0.29
1.17
1.91

S by formula (16.29)
H b by formula (16.28)

S m
H b m

S m
H b m

1.56
1.00

1.19
3.20

numerical

application 16.2
A dam is constructed on a permeable stratum of about 20m underlain by an
impermeable rock (Fig 16.23). A sheet piling of 10 metre height is installed at the
upstream face. The permeability is 50 m/day. Some streamlines are given. Sketch
the equipotential lines and determine the total discharge Q in m 3 /hr under the