858 



THE IRRIGATION AGE. 



piling is exerted equally in all directions, but, we are here 

 concerned only with the force which acts in an upward di- 

 rection. The tendency of this force to buoy up the mass of 

 sand is resisted by the excess weight, or specific gravity, of 

 the solid particles which compose the body of sand, after 

 deducting the percentage of voids which are taken up by 

 the water. 



Let h = Maximum head of water on upstream side, 

 d = Depth of penetration of sheet-piling, 

 j = Specific gravity of material penetrated, 

 x = Proportion of solids. 



For average sand, j = 2.65 and x = 1 0.40 = ().(>() 

 h h h 



Then b = - - = 0.629 h, 



s X -1- 2.65 X 0.6 1.59 



which is the theoretic penetration. 



This equation provides for the depth of penetration at 

 which the excess hydrostatic pressure on the up-stream side 

 is theoretically counterbalanced by the specific gravity of the 

 depth of material on the down-stream side, in sand of such 

 size and porosity that the* combined effect of friction and 

 capillary attraction is a maximum. 



A length of sheet-piling which provides for a depth of 

 penetration equal to the maximum head at flood-stage, there- 

 fore, involves a factor af safety of only 1.59 (with a tight 

 wall of sheet-piling in perfect alignment) applied to the the- 

 oretic minimum. This is manifestly inadequate for such 

 variable and uncertain conditions as are likely to be en- 

 countered. 



Where the workmanship, alignment, and depth of pene- 

 tration of a curtain-wall of sheet-piling are such as to insure 

 that there will be no marked "leakage'' flow through open- 

 ings, or places of variable density, silt and, matter carried 

 in suspension by the current of the stream will settle in the 

 quiet pool of water impounded by the dam, and gradually 

 seal up the interstices in the sand, until the bed of the stream 

 becomes practically impervious. This has been thoroughly 

 demonstrated in irrigation canals constructed in sandy soil, 

 and by the fact that the graded sands used in the filter beds 

 of many of our larger cities require frequent renewals, or 

 removal, for the purpose of washing out such accumulations, 

 in order that even the customary slow rate of percolation 

 may be maintained. 



No material, other than solid bed-rock, offers a more 

 secure support than sand which is properly confined ; there- 

 fore, to make it serve as a safe foundation for a permanent 

 dam is entirely a problem of making adequate provision 

 against the only disturbing element a current of flowing 

 water. 



For dams which are to be constructed on a sand founda- 

 tion, and embody the special features of construction recom- 

 mended in a subsequent part of this paper, the writer sug- 

 gests the following empirical rules : 



d = 2.5 /;. For heads up to 8 ft (I) 



d = 2 h. For heads up to 15 ft (II) 



d = 1.6/1. As the minimum, in any case.. (Ill) 



Equation (III) uses the proportion of excess weight, due 

 to the specific gravity of the sand, as a coefficient instead of 

 as a divisor. It provides a factor of safety of 2.5 under 

 normal conditions of low head, and, as the velocity of seep- 

 age flow through sand probably varies as some function of 

 the square root of the head, the factor of safety is corre- 

 spondingly increased for higher heads. 



Special Features of Construction. The horizontal dis- 

 tance through which seepage water must flow, after passing 

 under a line of sheet-piling, before it reaches an outlet at 

 the surface, is an important element in retarding its force 

 to such extent that there will be no erosion, or movement, 

 of the sand composing the surface of the river bed. It is 

 especially important below spillways, or dams of the overfall 

 type, where the velocity of current from the overflow of the 

 dam may already be such that erosion of the finer particles of 

 sand takes place ; therefore, the added impetus of upward 

 percolation would produce a dangerous condition of erosion 

 and the inevitable destruction of the dam. 



An apron below a dam serves, not only to resist the 

 shock of abrasion of falling water, but also to seal the bed 

 of the stream, so that the seepage water which finds its way 

 under the curtain-wall of sheet-piling, must flow diagonally 

 upward beyond the limits of the apron before issuing. The 

 width of such apron, therefore, is an important element in 



fixing the practical factor of safety of the structure, and 

 should not be overlooked. 



Aprons for spillways, diversion weirs, and dams of the 

 overfall type, should be submerged, so as to form a water- 

 cushion to absorb the shocks of falling water, ice, and debris. 

 'Such water-cushion should have a depth equal to one-quarter, 

 and preferably one-third, of the total height of overfall, and 

 a down-stream width of not less than \ l / 2 times the total 

 height of overfall, with the outer edge forming an apron, 

 sloping upward, and extending down stream for a distance 

 of not less than 1% to 2 times the length of sheet-piling used 

 in the main curtain-wall, ending with, and supported on, a 

 secondary line of sheet-piling of from one-third to one-half 

 the depth of penetration of the curtain-wall. 



A special feature of construction, which provides for 

 considerable economy in the quantity of concrete required 

 for a wide apron and, at the same time, provides a greater 

 element of safety against the force of seepage flow than a 

 solid concrete apron of the dimensions stated above, is illus- 

 trated in Fig. 1. 



The submerged apron should be constructed in the form 

 of a trough, with a depth of not less than one-fourth, and 

 a down-stream width of \ l /2 times the height of the overfall, 

 and the outer edge should be finished off at, or slightly below 

 the elevation of the bed of the stream. At a point down 

 stream, a distance of about twice the length of the main 

 sheet-piling used (or 4 or 5 times the head), there should 

 be driven a second cut-off wall of tight sheet-piling with a 

 depth of penetration of about one-half that of the main cur- 

 tain-wall, parallel to the line of the dam, to support a sub- 

 stantial concrete curb which should be finished off at the 

 elevation of the bed of the stream. 



The writer wishes to emphasize the statement that : One 

 of the most serious problems involved in the design and con- 

 struction of dams for rivers with beds of shifting sands is 

 that of providing adequate protection against dangerous ero- 

 sion of the river bed for some distance below the dam where 

 the erosive action of the current is dangerously magnified by 

 reason of the upward force of seepage flow, under the varia- 

 ble hydrostatic pressure communicated from the head of 

 water impounded on the upper side of the dam. 



In the design suggested in Fig. 1, the open space between 

 the edge of the trough forming the water-cushion and the 

 concrete curb supported by the secondary line of sheet-piling 

 provides an open space for the escape of the seepage flow 

 which finds its way under the curtain-wall, while the concrete 

 curb prevents the erosion and removal of the sand, which, 

 in this confined section of the river bed, is subject to the 

 combined forces of upward and horizontal currents. 



The approximate general dimensions suggested apply to 

 lew dams of the diversion-weir class, such as are used to 

 divert water from wide and shallow streams for purposes of 

 irrigation and power ; and the importance of careful and 

 conscientious workmanship on every detail of construction 

 in sand is so self-evident that special mention seems to be 

 unnecessary. 



Every dam or diversion weir should be designed in ac- 

 cordance with the practical demands of the exact local con- 

 ditions which prevail. This involves modifications of any set 

 of general rules, especially for higher heads, that is, for 

 dams which, in sandy rivers, will raise the level of the water 

 more than 12 or 15 ft. For low dams there is a variety 

 of shapes, or cross-sections, from which to choose; but, for 

 higher heads, economy in the matter of the materials in- 

 volved narrows down the choice in the direction of the 

 curved or ogee form of cross-section. 



Under the general rules previously stated, a dam which 

 is designed to raise the level of the water 50 ft., in a river 

 having a bed of sand of unlimited depth, would require a cur- 

 tain-wall of sheet-piling having a depth of penetration of not 

 less than 80 ft. below the bed of the stream, as the minimum. 

 A dam of this height would probably be designed with an 

 ogee form of curved cross-section. The impracticability of 

 driving a line of wooden sheet-piling to such depth in sand 

 and gravel, and the expense of providing a curtain-wall of 

 steel sheet-piling to such lengths, would suggest 'a careful 

 analysis of modifications, for the possiblity of eliminating 

 a portion of such construction without impairing its sta- 

 blity and permanence. 



Ample assurance of safety could be attained by using a 

 line of steel sheet-piling of such length as to provide a depth 

 of penetration of 50 ft. under the up-stream side of the dam, 



