THE IRKIGATIOX AGE. 



897 



A CELLULAR REINFORCED CON- 

 CRETE DAM* 



BY GEORGF J. BANCROFT 



In modern hydraulic practice there is a great demand for 

 a cheap substantial type of dam, having all the resistant quali- 

 ties of the monolithic type, without the great expense of that 

 type. I presume that the same demand has existed at all 

 times, but the large number of irrigation and power projects 

 now on foot have accentuated this demand. Several forms 

 of skeleton dams have been proposed and some of them built. 

 These dams, for the post part, consist of a sloping surface 

 of iron, concrete or wood, supported by a framework of the 

 same material. The weight of the water resting on the in- 

 clined surface imparts the necessary weight to the structure. 

 I think one of the principal objections to this type of dam is 

 that it looks unsafe. People living below a reservoir like to 

 feel that there is something more between them and destruc- 

 tion than a thin plane supported by a few posts. 



A dam is a comparatively simple mechanical device. A 

 canon dam with rock abutments is not unlike a bridge lying 

 on its side. A dam which is relatively long, so that the abut- 

 ments do not contribute to its resistance is not unlike a shelf 

 carrying a uniform load. In this case again the shelf is lying 

 on its side, the load is the horizontal thrust of the water and 

 gravity replaces the fastenings to the wall. 



In either case the modern plan of using a built-up struc- 

 ture would seem to promise economy. I see no more reason 

 in using a solid concrete dam than in using a solid bar of iron 

 for an automobile axle. The dimensions of a "gravity sec- 

 tion" or "heavy masonry" dam are determined, not from a 

 consideration of the strength of the material used in resisting 

 tensile or compressive stresses, but by making it of such size 

 that weight alone enables it to resist the overturning moment 

 of the water. 



In designing a dam to meet these conditions, I have taken 

 reinforced concrete as the most suitable material to furnish 

 strength, and earth or rock as the most suitable material to 

 furnish weight. By combining the two in a cellular form, I 

 believe I have evolved a type of dam that is safe, strong, self- 

 contained and cheap. 



Briefly, the dam is built in the general outline of a solid 

 concrete dam, but instead of being solid concrete, it is built 

 like a honey comb, the cells being vertical. The dam will 

 be somewhat thicker than a solid concrete dam, owing to the 

 difference in weight between earth and concrete. After the 

 concrete work is finished, the cells are filled with earth and 

 rocks laid down in water, so in the end the dam is practically 

 a solid mass. The accompanying half-tone gives a general 

 idea of the dam. It is a view of the dam from the rear or 

 down-stream side. 



Perhaps the greatest use of the new dam will be in canon 

 dam sites, where the dam is a combination of the gravity and 

 arch types. In such cases it is customary to design the dam 

 so that it will hold back the water of its own weight, and th,en 

 arch it against the water pressure to secure a large factor fff 

 safety. 



To illustrate the manner in which this dam works out, I 

 will take a specific instance. In this case the dam is 185 feet 

 high and 1,370 feet along the crest. 



The material in this dam is proportioned with due consid- 

 eration to all the strains that may come upon it. The prin- 

 cipal strains are : 



(a) The pressure of water when the reservoir is full. 



(b) The pressure of the earth filling when the reservoir 



is empty. 



(c) The weight of the superimposed material on the 



foundations. 



The dam is considered, for the sake of calculation, as con- 

 sisting essentially of a face wall supported in the rear by but- 

 tresses. The auxiliary walls which are parallel to the face 

 wall and which complete the enclosure of the cells are con- 

 sidered only as supports to prevent the buckling of the but- 

 tresses, as resistance to shear strain and as weight to resist 

 overturning. Their great stiffening effect on the entire struc- 



*Read at the meeting of the Colorado Scientific Socity, Oct. 1st, 

 1910. 



ture, and their support and assistance to resisting the strain 

 of the water pressure is not considered. Moreover, the 

 strength of the earth filling in shear and its supporting effect 

 in resisting transverse and longitudinal pressure is disre- 

 garded because I wished the structure to be strong enough 

 to withstand all strains without counting on this assistance. 



The computations are, therefore, as follows : 



First The proportioning of the dam as a whole so as to 

 resist overturning. 



Second The proportioning of the face wall. 



Third The proportioning and spacing of the buttresses. 



Fourth The proportioning and spacing of the walls par- 

 allel to the face wall, which we will call the auxiliary walls. 



In a measure, these problems are worked backward, for 

 the general form of the dam and the general nature of the 

 strains suggest a certain arrangement which is assumed at 

 the outset, although the proof of its fitness is the last thing 

 arrived at in the course of the calculations. Thus it is 

 assumed that the cells will be 20 feet, as measured longitudin- 

 ally pn the face wall, and will, of course, be narrowed as the 

 radial buttresses approach the center of curvature of .the dam. 

 As measured transversely to the dam, the first tier will be 

 20 feet, the second 25 feet, and the third and balance, 30 feet, 

 measurements being center to center of retaining walls. The 

 spacing of these walls was decided upon after several calcula- 

 tions to determine the maximum economy in the proportion- 

 ment of concrete and earth. The only way to decide this 

 matter seemed to be by the "cut and try" method, so five dif- 

 ferent designs were figured out, and the one presented gave 

 the best results. I think it is self-evident that the face part 

 of the dam should have more concrete and less earth-filling 

 than the rear part, and our "cut and try" calculations verified 

 this assumption. Several formulae were found which almost 

 fitted this case, and it is entirely possible that theoretic per- 

 fection may yet be attained, but the present design is suf- 

 ficiently attractive from a practical standpoint. 



As mentioned above, the nature of the several problems 

 continually involves using the ultimate result in the primary 

 calculation. It is therefore more simple, and better suited to 

 the purpose of this article, I think, to assume the entire design 

 as shown on the cross sections presented herewith, and pro- 

 ceed with the calculations to ascertain what the factors of 

 safety may be. 



First To ascertain the factor of safety of the entire dam 

 to resist overturning. 



To do this the dam is considered in progressively increas- 

 ing segments, beginning at the top and going down, the last 

 segment being the entire dam. The width of the base of each 

 segment is determined by the graphic method given by 

 Bulkely on page 184 of "Facts, Figures and Formulae for 

 Irrigation Engineers." The factor of safety consists in the 

 fact that the resultant falls in the middle third of the base 

 of the dam and also in the fact that the dam is arched against 

 the water pressure. 



It is evident that for the dam to yield, all the longitudinal 

 walls must be crushed by the longitudinal component of the 

 water thrust and that the buttress walls must be crushed by 

 the overturning movement. By calculations given later on, it 

 will be seen that the factor of safety in the buttresses is 8, 

 without reinforcing. To this must be added the factor of 

 safety protecting the crushing of the longitudinal walls. 

 These walls are supported every 20 feet, at least, by the trans- 

 verse walls so they cannot yield by buckling, neither can the 

 dam as a whole yield by buckling, if properly curved, as in 

 this case, and not too long in proportion to its thickness. 



For the purpose of finding out what factor of safety is 

 contributed by arching the dam against the water, two hori- 

 zontal segments will be considered, namely, the top 10 feet 

 and the bottom 10 feet. Measured at right angles to the line 

 of pressure, the upper segment is 1270 X 10' and the walls 

 meet the buttresses at an angle of 35 to the line of pressure. 



The strain then is 

 10 



X10 J -1270X62.5=3,968,750 Ibs. 

 2 

 62.5 being the weight of a cubic foot of water. 



This strain is met by two abutments, so it is proper to 

 divide this in two. 



3,968,750 



= 1,984,375 Ibs. 

 2 



As it does not meet the abutment parallel to the line of 



