where N represents the ratio of prototype to model values of a quantity, should
be maintained. Assuming that the model stone has the same approximate shape
(∴ N K = 1), and because the model is undistorted (∴ Ncotθ = 1), the prior
D
relationship can be reduced to:
3
Nwr NH
NW =
(A10)
3
N (Sr - 1)
The rock placed in the model was limestone having a unit weight of
approximately 2,710 kg/cu m. The prototype armor was assumed to have an
identical unit weight of 2,710 kg/cu m. This is a conservative assumption because
rock sources used in rubble-mound structures in the Pacific Northwest are
typically igneous in origin with higher unit weights (2,850-3,000 kg/cu m).
Therefore, the scale of the unit weight of rock becomes unity, Nwr = 1 .
Assuming a seawater density of 1,025 kg/cu m, the scale of the specific
gravity term is:
⎛ 2710 ⎞
- 1⎟
⎜
⎝ 1025
⎠
=
=
= 0.961
(A11)
N (Sr - 1)
N⎛ w
⎞
⎛ 2710 ⎞
⎜ r - 1⎟
- 1⎟
⎜w
⎟
⎜
⎝ w
⎠
1000
⎝
⎠
The scale of the wave height is the model length scale (i.e., N H = 20);
therefore, the weight scale for the armor stone is:
(20)3
= 9,014 ≈ 20.813
=
(A12)
NW
3
(0.961)
To account for the fresh water used in the model, the weight of the stone
used in the model was roughly 12.5 percent lighter than that given by standard
Froude scaling. (According to standard Froude scaling, the scale for rock weight
would be 203 = 8,000.) The assumed specific gravity for the full-scale armor
stone was S r = 2.71.
All armor stone gradations used had a W50 = 2,426 lb. Select armor placed on
the upper portion of the spur had a gradation of 30 percent of W50 (nominally
(nominally 1.5 to 3.5 ft diam).
The prior relationships and a model specific gravity of Sr = 2.71 were used to
determine the model armor stone gradations as presented in Table A2 and
Figure A14. For test series A, which was a preliminary evaluation of armor
stability, a single gradation was used which was an initial approximation to the
A17
Appendix A
Stability Analysis of a Submerged Spur, North Jetty, Grays Harbor, WA
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