THE IRRIGATION AGE. 



859 



and a secondary line of sheet-piling with a depth of penetra- 

 tion of about 15 ft. under the extreme toe, which should be 

 curved up so as to form a trough at a depth of about 5 ft. 

 below the bed of the river, for a water-cushion. Then, at a 

 point about 200 or 250 ft. down stream, construct a srmller 

 dam, about 15 or 16 ft. in height, with a line of main sheet- 

 piling having a depth of penetration of 30 ft., and embodying 

 all other features of design in accordance with the special 

 features outlined in this paper, to back up the water against 

 the main dam for a proper depth of water-cushion. The 

 seepage flow, which would probably find its way under the 

 main dam in considerable quantities, would issue from the 

 section of confined river bed between the two dams, where 

 the depth and length of the water-cushion thus provided pre- 

 vents the removal of any sand, because, even during periods 

 of storm flow, the violent abrasive force of the flood passing 

 over the dam would be effectually broken by the extra depth 

 of water-cushion which is provided by the concrete trough 

 at the toe of the dam. 



In calculating the proportions of a dam which is to be 

 founded on sand, there is involved the consideration of the 

 hydrostatic pressure against the under side of the dam. 



The calculations for the cross-section of a masonry dam 

 founded on bed-rock are based on the assumption of an abso- 

 lutely water-tight contact between the footings and the bed- 

 rock, therefore the entire cross-sectional weight of the dam 

 may be use in calculating the moment of resistance to over- 

 turning. 



In a dam of such proportions that the resultant of forces 

 passes close to the toe, the effect of water working its way 

 under the footings at points of defective contact, or through 

 defective joints in the lower courses of masonry, might pro- 

 duce a change in the direction of the resultant such that it 

 would pass outside of the toe. That section of the dam 



would then be in unstable equilibrium, and, unless restrained 

 by other forces, would overturn. 



In considering the forces which may act on a dam resting 

 on sand, saturation of the foundation, with upward hydro- 

 static pressure, is an accepted fact, and, therefore, must be 

 considered as a definite element in the calculations. 



As stated previously, the combined effect of friction and 

 capillary attraction offers such marked resistance to the flow 

 of water through sand that the velocity which results from 

 any head, or inclination of surface, is infinitesimal, in com- 

 parison with the velocity which would result under similar 

 conditions of head in a body of free water, flowing in afl 

 open channel, or through a pipe. The transmission of hy- 

 drostatic pressure through a similar medium is similarly re- 

 sisted, to a slight degree, as will be shown. 



The removal of the soil above a stratum of dense clay, 

 which in turn overlies a stratum of water-bearing sand or 

 gravel under artesian pressure, will disclose a moist degree 

 of saturation of the clay such that water will accumulate in 

 small pockets, or sumps, which may be bored or dug to 

 shallow depths of 1 or 2 ft. into the clay. The seepage 

 flow which is thus indicated is absorbed by the soil above 

 by capillary attraction, and is evaporated from the surface ; 

 however, no hydrostatic pressure, of measurable magnitude, 

 would be exerted against the footing of any structure resting 

 on such a stratum of clay. 



Hydrostatic pressure is directly proportional to the head 

 of water, and time is not a factor in determining its magni- 

 tude, hence the coefficient of friction becomes zero. Clay 

 contains a relatively large proportion of voids of infinitesimal 

 size, and, while high head of water pressing against the un- 

 der side of the stratum of clay which is confined between the 

 porous strata would undoubtedly transmit the hydrostatic 

 pressure of measurable magnitude through such stratum of 



clay, it is evident that, under moderate heads, the force of 

 capillary attraction (in interstices of such infinitesimal size 

 that they would almost warrant an assumption of molecular 

 friction), is of sufficient magnitude to counteract and prac- 

 tically nullify the effect of hydrostatic pressure. 



It may be concluded, therefore, that the force with which 

 hydrostatic pressure is transmitted through alluvial soils is 

 modified by a coefficient which varies as the square, cube, 

 or perhaps the "nth" power of the effective size of the inter- 

 stices, or, inversely as such function of the effective size of 

 the grains. 



For the practical purposes of this paper, the probable 

 existence of such a coefficient may be disregarded, because, 

 for the interstices of the sizes which are ordinarily found 

 in sand of 40 per cent porosity, its probable value becomes so 

 small as to be negligible. 



The hydrostatic pressure against the under side of any 

 dam of the type and general dimensions illustrated in Figs. 1 

 and 2 is governed by the head of water on the down-stream 

 side of the dam, because the pressure which is transmitted 

 under the curtain-wall of sheet-piling, from the head of 

 water above the dam, is afforded lateral outlet, therefore 

 its intensity is limited to the depth of resistance, or head, 

 opposing such outlet on the down-stream side. 



The hydrostatic uplift per square foot of surface against 

 the base of a dam of the type and general proportions rec- 

 ommended in this paper, therefore, will vary between 25 and 

 40 per cent of that which would result from the head of 

 water on the up-stream side. 



Figure 2 illustrates the general proportions of the spill- 

 way section of a dam of the type discussed herein, with all 

 dimensions given in terms of H, the height of the crest above 

 the bed of the river, and assuming a length of spillway such 



1 



that the maximum height of overflow will not exceed H. 



5 



The resultant, which is obtained when the calculated 

 weight of the section of concrete is reduced by the total 

 amount of hydrostatic uplift due to a down-stream head = 

 0.3 H, intersects the base practically in the center, as is 

 shown by the solid line. This would indicate that the design 

 may be modified so as to involve less concrete, but the quan- 

 tity to be thus saved, in the total cost of a low dam, will 

 not outweigh the desirability of such a factor of stability 

 in a structure of this class. 



Fig. 4. 



The dotted line indicates the resultant which would be 

 obtained if the weight of the concrete were reduced by an 

 amount equal to the full hydrostatic uplift which would re- 

 sult from a head equal to the maximum up-stream head = 

 1.3 H. This resultant intersects the base outside of the mid- 

 dle third, but well within the toe. 



The sloping portion of the top of the dam, on the up- 

 stream side of the crest, is desirable to facilitate the passage 

 of ice and floating debris over the crest, and to reduce the 

 moment of ice thrust during periods of extreme cold when 

 the entire flow of the stream may be diverted for power 

 purposes. 



Any increase in the width of the base, with the addi- 

 tional material on the up-stream side of the dam, so as to 

 lengthen the inclined portion, affects the moment of stability 

 (Continued on page 880.) 



