LIMITING PRESSURE. In determining the stability against crushing, it is not wise to compute the factor of safety, since the computed value of the factor will depend upon the value assumed as the crushing strength of the masonry; and therefore it is better to state the maximum pressure and limit it to twice the mean.
As a preliminary to the actual designing of the section, it is neces sary to fix upon the maximum pressure per square unit to which it is proposed to subject the masonry. Of course, the allowable pressure depends upon the quality of the masonry, and also upon the conditions assumed in making the computations. It appears to be the custom, in practical computations, to neglect the vertical pressure on the inside face of the dam, i.e., to assume that equation 8, page 465, is zero. This assumption is always on the safe side, and makes the maximum pressure on the toe appear greater than it really is. Computed in this way, the maximum pressure on cyclopean rubble masonry in cement mortar in some of the great dams of the world is from 11 to 15 tons per sq. ft. (150 to 200 lb. per sq. in.).
The New Croton Dam (§ 964) was designed for a maximum pressure of 16.6 tons per sq. ft. (230 lb. per sq. in.) on massive rubble in portland-cement mortar, which pressure occurs when the reservoir is empty.
For data on the strength of stone and brick masonry, see § 581-84 and § 617-29, respectively.
The actual pressure at the toe will probably be less than that computed as above. It was assumed that the weight of the wall was uniformly distributed over the base; but if the batter is con siderable, it is probable that the pressure due to the weight of the wall will not vary uniformly from one side of the base to the other, but will be greater on the central portions. The actual maximum will, therefore, probably occur at some distance back from the toe. Neither the actual maximum nor the point at which it occurs can be determined.* Professor Rankine claims that the limiting pressure for the toe should be less than for the heel. Notice that the preceding method determines the maximum vertical pressure. When the maximum pressure on the heel occurs, the only force acting is the vertical pressure; but when the maximum on the toe occurs, the thrust of the water also is acting, and therefore the actual pressure is the resultant of the two. With the present state of our knowledge, we can not determine the effect of a horizontal component upon the vertical resistance of a block of stone, but it must weaken it somewhat.
The preceding theory of the stability is the one ordinarily used, but there are a few matters not included therein that require a brief mention.
The force of the wind was not included. If the wind blows up stream, the stability of the dam will be increased when the reservoir is full and decreased when it is empty. If the wind blows down stream, it will not affect the stability when the reservoir is empty; but when the reservoir is full, the wind will produce waves rather than add directly to the pressure against the back of the dam.
The importance of wave action will depend upon the location of the dam and the area of the reservoir. The pressure due to waves has not been investigated thoroughly, but their effect has been studied by noticing the size and the weight of bowlders that have been moved by the waves, and also by observing in a single locality the pressure recorded by a dynamometer.* By the latter method, on the shore of the open ocean, the pressure due to waves 20 feet high was found to be 6,083 lb. per sq. ft. on a dynamometer "near the surface" and 2,856 lb. per sq. ft. on a similar instrument "several feet lower;" and waves 6 feet high gave pressures of 1,256 and 3,041 lb. per sq. ft., respectively.
If ice forms on the water in the reservoir, it will exert a horizontal thrust against the dam which will increase the sliding force and also the tendency to overturn down stream. Of course, the thrust from the ice will depend upon the altitude and the latitude of the location of the reservoir. The pressure due to ice in any particular case is almost wholly a matter of judgment. A Board of Experts in 1888 recommended that the Quaker Bridge Dam, virtually the same as the New Croton Dam (I 964), situated 30 miles north of New York City, be designed to resist an ice thrust of 43,000 pounds per lineal foot ;t but the recommendation was not adopted. The moment of the thrust of the ice should be added to the moment of the overturning forces in the preceding analysis. The pressure of the ice may be eliminated by frequently breaking up the ice next to the up-stream face of the dam. The pressure of ice caused the failure of a masonry dam at St. Paul, Minn.; but none of the details are known.
The preceding analysis considers only shear in a horizontal plane and compression on a horizontal section; but it is proved in the mechanics of materials that a shear combines with a compression normal to it, and produces a greater compression in an inclined plane (see I 459). Therefore after a dam has been designed according to the foregoing analysis, to be perfectly sure of its stability it should be tested for shear along inclined planes and also vertical planes— particularly near the toe (the down-stream portion near the base). For a brief discussion of this phase of the subject, see Wegmann's Design and Construction of Dams, fifth edition, pages 8-10; School of Mines Quarterly, Vol. xxvit, pages 33-39; and Proceedings Insti tute of Civil Engineers (London), Vol. cLxxii, page 105, 126-29.
It is not known that any dam was ever designed in accordance with this modification of the ordinary theory; and it has not been proved that lams designed by the ordinary theory are unstable when tested by the more refined method of analysis just referred to.