A Treatise On The Principles And Practice Of Harbour Engineering

BREAKWATER DESIGN. 139 concentrated and F is the force of impact in statical units of pressure. If the block be small, and if its entire vertical surface encounter the full stroke of the wave, it is not unjustifiable to assume that the value of x is — or the semi-height of the block. It is, of course, a matter of conjecture, but evidently it represents the extreme condition of things in an unfavourable sense, and therefore is a reliable basis of calculation. But over surfaces of considerable extent the hypothesis of uniform intensity of pressure is not strictly tenable, and indeed, in certain cases, is very far from representing the actual effect of wave impact. The équivalent pressures at various points of an extensive surface are equally variable. The maximum occurs approximately at mean water level, and the force decreases above and below this point, probably in the ratio corresponding to ordinates of a para- bolic curve. Now, the stability of a block is a function of (d— 1) times the volume, for the moment of resistance to overturning is the product of the effective weight into a moiety of the width of the base. For critical equilibrium, therefore, we have :— Fæ=wA. If, then, W varies as (d - 1) V, it is noteworthy that any increase in d in- volves a much greater increase in W. Thus, if d be increased, say, from 2 to 3, the value of W is increased from V to 2V, an increment, in the one case, of 50 per cent., and in the other of 100 per cent. Hence the great importance to be attached to the use, for sea work, of materials having a high specific gravity. Although the influence of the bed-joint, in so far as it affords tensional resistance to the overturning action, is wisely neglected, on the other hand, it is not safe or desirable to ignore the effect of the corresponding compression upon the inner edge or line about which overturning may take place. The resultant of the overturning force and the gravitation of the wall will often produce a very powerful and concentrated pressure upon a small area of the bed-joint, which may be beyond its capacity to resist. Thus, if the line of action of the resultant fall upon one or other of the two points which trisect the base, the intensity of pressure on the edge nearer the point is twice as great as the mean of the pressure over the whole area, and for any further eccentricity of the resultant, the ratio is greatly magnified. The following expression serves to convey a value for the intensity of pressure, p, on the nearer edge in terms of the eccentricity (z), the length (Z) of the base-line, and the mean pressure (a) :— Gaz * p=a+_. The maximum value of p consistent with safety is about 10 to 12 tons per square foot on Portland cement concrete, 8 to 10 tons on hard rock, 4 to 5 tons on rubble masonry, and from 2 to 3 tons on gravel, sand, or clay. * See Dock Engineering, p. 176.