{tshtxt fenty Mhm^tm 
 
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 1903 
 
Cornell University Library 
 arY693 
 
 Two reports on researches concerning the 
 
 3 1924 032 181 103 
 olin.anx 
 
The original of this book is in 
 the Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924032181103 
 
City of New York. 
 
 Aqueduct Commission. 
 
 Two Reports 
 
 ON RESEARCHES CONCERNING THE DESIGN AND CONSTRUCTION 
 
 OF HIGH MASONRY DAMS, IN VIEW OF THE 
 
 PROPOSED BUILDING OF 
 
 Quaker Bridge Dam, 
 
 BY 
 
 B. S. CHURCH, AND A. FT E LEY, 
 
 Chief Engineer. Consulting Engineer. 
 
 1887. 
 
R K PO RT 
 
 OF 
 
 B. S. C HXJ RCH, 
 
 CHIEF Engineer. 
 
New York, July 28, 1887. 
 
 To the Honorable Aqueduct Commissioners : 
 
 Gentlemen: I herewith respectfully submit the Report called for by your 
 Resolutions of March 24, 1886, and June 22, 1887, on the subject of High 
 Masonry Dams, both curved and straight in form. 
 
 The plans presented for the straight Quaker Bridge structure were made 
 after long study of the forces and strains to be sustained, allowing for large" 
 factors of safety against overturning, crushing and sliding. The best proportions 
 and form consistent with safety and reasonable economy were designed, with great 
 care to meet all requirements of strength and stability. 
 
 The world's experience in the designing and construction of great dams, 
 together with the investigations and opinions of the highest authorities, in 
 Europe and America, werfe collected and considered in the plans prepared and 
 presented to the Commission. 
 
 The strength and cost of a straight dam, resisting hydraulic pressure, ice, 
 wind and wave action by its weight only, was compared by mathematical 
 results with the stability and cost of a dam in the form of a horizontal arch, 
 transmitting thrusts to the hill-sides. For the Quaker Bridge structure, the 
 strength, economy, and safety, of the straight dam, so far exceeded what was 
 obtainable by the curved form that I can only account for the construction on 
 a curve of so many large modern masonry dams, from the fact that only within 
 a few years has the question begun to receive the attention it deserves from 
 trained and experienced hydraulic engineers and authors. 
 
 The popular belief in masonry arches to bear great weight or pressure, 
 is justified when confined within reasonable limits. But no masonry bridge arch 
 of over 300 feet span has been constructed. 
 
 Beyond that length of span, the crushing strain, sustained by voussoirs, 
 exceeds safe limits on their mortar joints from the weight of the masonry alone, 
 without the added load the bridge should carry. 
 
It would therefore be out of the question to construct a masonry bridge 
 of the length of Quaker Bridge Dam (1350 feet long) as it would be over four 
 times the limit of safety in a possible span. The arch of a curved dam, however, 
 does not carry any part of its own weight (as in the case of a bridge), therefore 
 its strength of arch will bear only the water pressure against it from a full 
 reservoir. 
 
 I invite your attention to the following statements on the curved form. 
 
 1st. When the section of the Quaker Bridge Dam is of a required area 
 of cross section to resist reservoir pressure by its own weight, and is then built 
 on a curve, the dam cannot act as an arch. 
 
 Such a section (See E F G H, Sheet B) will closely approach the shape 
 of a right angle triangle, with its apex at the surface of the reservoir. 
 
 The water pressure against it, from a full reservoir, will be nothing at the 
 surface, and as the pressure increases, at successive depths, a corresponding 
 thickness of masonry in this section increases in due proportion down to its 
 base to sustain such pressure. 
 
 In order that arch-thrust may act to transmit pressure to the , hill-sides, an 
 elastic movement of the masonry, resulting from water pressure, must, of 
 necessity, take place to produce such thrust. 
 
 This approximate triangular section of masonry is of a form that will best 
 resist and practically stop such elastic movement, in the plane of the cross-section, 
 that transmits arch-thrust. It must be remembered, that the possible elastic 
 movement of the vertical transverse cross-section is insignificant when com- 
 pared with the longitudinal elastic yield through so long a dam. 
 
 In short, the stiffness of the triangular cross-section prevents the far greater 
 longitudinal elastic movement required to permit appreciable arch-thrust to 
 reach the hill-side. 
 
 ■ Therefore, a long, curved dam with a gravity section will resist hydraulic 
 pressure against it by its own weight, and not by arch action. 
 
 2nd. Let us next consider the effect of reducing the cross-section for a 
 curved dam at Quaker Bridge, by reducing its breadth of base and thickness of 
 masonry, to a degree that permits bending, or elastic movement, that will allow 
 the dam to act as an arch. Assume the thickness of the dam forming the arch 
 ring to be from 80 to 100 feet, and that it will be sufficiently elastic. We then 
 find that, with a radius of 900 feet, we will have a pressure on voussoir joints 
 of from 42 tons to the square foot with 80 feet breadth of section, to 39 tons with 
 100 feet breadth of section, on the supposition that the line of strain bisects 
 each joint. Such pressures are, however, beyond safe limit for hydraulic 
 masonry. Again, the elastic movement will throw the weight resultant near the 
 
end, or outside of the base, causing a tensile strain in horizontal joints of the 
 inside face, which should not occur, as it causes a tendency to rupture the 
 masonry and create leakage. 
 
 It is evident, therefore, that we cannot reduce the section or thickness of so 
 long and high a dam in order to force it to act as an arch, without causing 
 dangerous and complicated strains. 
 
 3rd. We must next consider the effect of increasing the cross-section or 
 thickness of the dam at Quaker Bridge, in view of broadening the voussoir joints 
 for reducing the thrust pressure of a curved dam of 900 feet radius, to 16 tons to 
 the square foot, the limit of pressure in the straight gravity plans, which have 
 been submitted to you. We find that it produces a section (A B C D Sheet B) 
 that is nearly double that required for a straight gravity dam, (E F G H) having 
 proportionately less tendency to act as an arch, than in the first mentioned case ; 
 while, at the same time, it adds 100 per cent, to the cost. 
 
 It, therefore, becomes evident that it is impossible to construct a curved 
 dam at Quaker Bridge which will act as an arch to any apperciable degree, and 
 consequently there is no valid reason for risking the complicating and serious 
 rupturing strains, which a curved da,m will produce ; or, for the increased expense 
 it would entail. 
 
 In order to verify the above statements and figures, I have worked out a 
 formula, and used it for the calculations on curved dams herein given, verifying 
 them by the formula of moments, where that formula became applicable. (See 
 Sheet A. Fig. i). 
 
 In a curved dam having a radius (R) sustaining a weight of water pressure 
 (W) and total pressure (p) on a voussoir joint of any span or cord (C), then we 
 
 have the formula (p^ — F^ )• 
 
 The demonstration of the above formula is as follows : (Fig. i). 
 
 Let A E and B E be drawn perpendicular to the radii A D, and B D, and 
 tangent to the curve A W B. Take E g equal to the weight (W) of water pressure 
 on a belt of the dam one foot in breadth, and the length of the cord. 
 
 From (g) draw g h and g i parallel to E B and E A. Then will E h g i 
 become a parallelogram of forces, and E h equals one component, normal to the 
 voussoir joints at A, and equals the total pressure (p) on that joint, 
 
 The triangle E h g is similar to the triangle A D B, their sides being perpen- 
 dicular to each other,therefore A B : E g : : A D : E h, or C : W : : R : p, and p=-p-. 
 The radius, weight and cord, or span, being known, the pressure p is found by 
 
this formula, which being divided by the area of the joint in square feet gives the 
 average pressure per square foot. 
 
 This formula proves the fact that, with a given radius, the total pressure on 
 each of the voussoir joints is equal and remains the same to all lengths of span, 
 from the length of a voussoir, to the total length of the dam, and that the pres- 
 sure on voussoir joints increases as the length of radius increases. If we assume 
 a value for (p), we can find the value of R by the above proportion, which becomes 
 
 Now, if we assume a rectangular section, equal to the area of the section 
 presented for the straight Quaker Bridge Dam, it will be loi feet in breadth, 
 limiting the pressure to i6 tons to the square foot, then (p) or the total pressure 
 on a voussoir joint, ten feet long on the extrados cord, will be 1616 tons at a depth 
 of 107 feet below the surface and (W) will be 51 tons for the same span of ten feet 
 on a belt one foot broad. 
 
 Then, by the formula, R= 'j equals 316.8 feet as the length of the radius 
 
 required to maintain the conditions. This radius will not be long enough to span 
 the Valley at the Quaker Bridge site, even with a half circle. 
 
 In other words, with the same area of section in the better shape to act as an 
 arch (because it admits of greater elastic movement), and with the same limit of 
 pressures that exists in the plans before you for the gravity Quaker Bridge 
 Dam, the radius must be so short that the dam cannot span the Valley. To 
 further illustrate the above statements and call your attention to another impor- 
 tant matter bearing on the subject of the Quaker Dam, I will suppose that the 
 Quaker Bridge Dam be built on a curve having a radius of 900 feet ; that instead 
 of being a dam, it is a wall 250 feet high, making a complete circuit forming a 
 well, resisting water pressure on its entire exterior circumference, 260 feet in depth, 
 as in Figure 2. 
 
 The youssoirs all being of equal size it is evident that the hydraulic pres- 
 sure (W) normal to the outer cord of each of the voussoirs, will be the same at any 
 fixed depth below water surface, and the total pressure on all the voussoir joints 
 will be equal. 
 
 The thrusts of all the voussoirs will balance each other and produce an 
 equilibrium of voussoir pressures in any horizontal plane, at any depth, all around 
 the circle, because the elastic movements to produce these pressures is perfectly 
 balanced. The pressure of (a), (Fig. 2) towards (b) equals (b) towards (a), and 
 the pressure of (e) towards (f) equals the pressure of (f) towards (e). etc. Now 
 a hill-side abutment may be substituted for voussoirs (a) or (e). 
 
Therefore with the same radius and section of dam, increasing the span, does 
 not increase the total pressure on voussoir joints as above stated. 
 
 In the complete circle, however, perfectly balanced elastic movement takes 
 place to produce uniform pressure on the several voussoir joints. 
 
 But when the thrust of a curved dam is sustained by unyielding hill-sides, the 
 hill-sides do not respond to the elastic movement (as in the case of voussoirs in 
 the complete circle), consequently the line of transmitted resultant pressure 
 through all the voussoirs cannot pass (as in the complete circle) uniformly 
 through the same part of the voussoir joints, but will take a direction approaching 
 to the line, d, d, d, in Fig. 3, because of the tendency of the arch to flatten, and 
 take the form of the dotted lines in Fig. 3 ; therefore, with a fixed radius, although 
 the total pressure on the voussoir joints does not increase with the span, the 
 resultant line of transmission of thrust does increase crushing strains. 
 
 It causes the line d, d, d, to fall near the ends of the joints tending to greatly 
 increase the strains, so unevenly distributed on the different joints, and also tends 
 to buckle and crack the arch, as well as to crush. 
 
 No experimental data or formulae exist to enable us to measure these arched 
 dam-thrust strains with any degree of accuracy. 
 
 It is probable that the line of strain near the centre and ends of the dam will 
 fall outside of the middle third of the joints, more than doubling the crushing 
 strain of 42 tons, given in the second case mentioned above, or over 82 tons to 
 the square foot. 
 
 Therefore, the building of any arched dam must be regarded as experimental 
 in character; it is far safer and less expensive to avoid such complications and 
 build straight dams to resist hydraulic pressure by their weight only. 
 
 The most reliable formulae for giving the maximum pressure on the outer and 
 inner toes of a gravity dam are not perfect, because no adequate experimental 
 data exist to give the elasticity of large masses of masonry and enable that factor 
 to be included in the formula, but we know that by neglecting such factor the 
 calculated strains exceed what will actually take place, and that we will, therefore, 
 be within safer limits than the formula indicates. Whereas, in the calculations for 
 curved dams, the reverse is true. 
 
 Many of the high dams we have obtained records of, are built on a curve, but 
 all except one act as gravity dams, and their arched form must weaken their 
 stability. 
 
 The only existing curved dam which can and does act as an arch, is the Zola 
 Dam, 205 feet long, 126 feet high, 41 feet broad at the base. 
 
 I believe that sooner or later it will fail, becoming ruptured and weakened by 
 
lO 
 
 the action of changing pressures from the drawing out and refilling of its reservoir 
 storage. 
 
 To sustain the above statements, I will refer to the following authors : Pelle- 
 treau advises that the arch form should not be used when the dam is more than 
 131 feet in height and length. 
 
 Delocre believes that the structure would cease to act as an arch when the 
 thickness of this arch would reach one-third of the radius, and calculates the limit 
 to be reached at a depth of 14.7 feet below the flow line and confines it to very 
 short spans. 
 
 Krantz gives the limit of the span at 131.2 feet with a radius of not more 
 than 65.6 feet. 
 
 Rankine suggests that in very short spans, a slight curve be introduced to 
 prevent the bending out of the top of the dam by water-pressure against it ; but 
 states that he has no confidence in calculations for stability for arch-thrust in long 
 dams, and intimates that the arch form is of doubtful utility even in short dams. 
 He insists that the section should be such as to resist overturning by its own 
 weight alone. 
 
 Mr. E. S. Chesbrough was sent to Europe by the Department of Public 
 Works to examine and report upon the principal dams existing there. From his 
 examinations and studies during his trip, he pronounced against the curved form ; 
 but his subsequent illness and death prevented the completion and presentation of 
 his report. I can, however, testify to his stating that opinion to me while I was 
 associated with him as Consulting Engineer in the Department of Public Works. 
 
 McMasters holds that, having established a profile that will resist the pressure 
 of water by its own weight, there is no valid reason for constructing it in the form 
 of an arch, and thereby increasing its length and the cost of its construction. 
 
 The standard authorities, both in Europe and in this country, agree that 
 in long and high dams the sectional profile should be capable of resisting water 
 pressures against it, by its own weight ; and that the curve increases the cost 
 without adding to its strength. 
 
 In fact, these general considerations militating against the arch have so 
 satisfied them that they have not considered it necessary to go into more elaborate 
 demonstrations. 
 
 Inasmuch, however, as the curved form has been pressed by several speakers 
 during the public hearings before this Commission, it becomes desirable that a 
 careful statement be given you of the inapplicability of a curved form for long and 
 high dams. 
 
 The horizontal, or bed joints in the stone masonry constructions are always 
 more perfectly filled and are stronger than the vertical joints. The weight of each 
 
II 
 
 stone maintains its bed and, as the load of superincumbent masonry increases upon 
 it, these joints become more firm and compact. 
 
 With the vertical joints this is not the case. In the straight dams, therefore, 
 the most complete and strongest bed joints bear all the strain from the reservoir 
 waterpressure against the dam, and the vertical joints of lesser strength are 
 relieved from strain, while the reverse is true of the curved form. 
 
 The plans for the Quaker Bridge Dam, submitted to this Commission, have 
 received, as its magnitude and importance deserve, a longer and far more 
 thorough consideration and study than has been given to any existing dam, and 
 I, therefore, urge their acceptance with confidence. 
 
 Figure (4). Sheet A will illustrate some static principles relating to gravity 
 dams, wherein A B D is the form of a theoretical dam, calculated to exactly sustain 
 the overturning pressure of water against it. 
 
 There being no factor of safety against overturning, the resistance of the dam 
 and the pressure of the water are in exact equilibrium. 
 
 With these conditions, the resultant of pressure strikes at the end of a 
 horizontal joint, and the dam takes the shape of a triangle, however high the dam 
 may be. This, under the supposition that no arbitrary limit of pressures be fixed 
 for the outer and inner toes, and that the tendency to crush is ignored. 
 
 Let us now introduce a factor of safety of (2), against overturning, by adding 
 to the breadth of the dam to increase the length of the joints. 
 
 This correspondingly increases the bulk and weight of the masonry to a 
 degree that will require exactly twice the water pressure (to produce overturning) 
 that a full reservoir can ever exert. 
 
 With these conditions, and ignoring excessive pressures, the dam again takes 
 the form of a triangle, as shown on Figure (4) by the lines A B, A C, C B. 
 
 But if (with masonry weighing 156.25 pounds to the cubic foot) we limit the 
 pressures at the toes of the dam to 16 tons per square foot, that pressure will 
 obtain at the line a a, 205 feet from the surface of high water. 
 
 Below that point, the limiting of pressure to 16 tons per square foot will cause 
 the straight lines of the triangular form to bend into the curves a b E and a c F 
 maintaining uniform pressure below that point, lengthening the joints beyond the 
 ratio of the triangle which produces curves. 
 
 We will next consider the reasons for departing from the last described 
 theoretical section A F E, to that of the section under consideration, shown by the 
 outer dark lines of Fig. (4). 
 
 In the theoretical section the resultant forces strike exactly at the end of the 
 middle third. Any additional strain of ice, or wave and wind action would, 
 therefore, produce tensile strains on the inner face as above stated. 
 
12 
 
 To prevent such strains, the section must be broadened lengthwise with the 
 joints, to distribute the increased weight. 
 
 Again, as the maximum pressure will be on the reservoir side, or inner toe, 
 during construction, before sufficient age has given the mortar time to thoroughly 
 harden, we must make a second increase of section to obtain smaller pressures 
 than will exist at the outer toe with a full reservoir. 
 
 The maximum strain with a full reservoir will not come upon the outer toe 
 for months after the structure is completed and the mortar is well hardened. 
 
 The weight of the gravel and water resting on both toes of the dam up to the 
 river bed at g h i and g', h', i' (not considered in the theoretical section) calls for a 
 third increase. 
 
 To maintain the limitations of pressures fixed upon, the back pressure below 
 the river-bed against the outside of the dam (not considered in the theoretical sec- 
 tion) demands a fourth variation, which slightly diminishes the section. 
 
 The fifth variation, increasing the area of the section, is required to thicken 
 and strengthen the outer toe. 
 
 We now com'e to the last cause of change from the theoretical section, at the 
 top of the dam. This sixth increase of section and weight on the diagram (shown 
 at A k t) is required to resist ice, wind and wave action. 
 
 The addition of this weight enable us to encroach upon the theoretical section 
 at t,-t',-t"- without reducing the several factors of safety below the limit fixed; while 
 it adds to the required breadth of section throughout the lower portion of the dam. 
 
 The strain sheet, and its tables, exhibit how evenly all the factors of safety are 
 maintained in the final section, under consideration, providing for all the above- 
 mentioned disturbing conditions. 
 
 As no demonstration could be found of Sazilly's trapezoid of pressure for great 
 dams, I have developed one and obtained a formulated and graphic method of 
 calculating the pressures on the outer and inner toes of joints of high masonry 
 dams, and used them to re-calculate the pressures on the strain sheet obtained by 
 the formula of moments, as a check on those results. 
 
 By this method, as in all others, we must neglect the factor of elasticity 
 in masonry, which affects the results but slightly, and introduces a factor of safety. 
 The demonstration is as follows : (See Fig, 5). 
 
 When the resultant of horizontal and vertical pressures cuts the joint or base 
 A, B, in the middle, all the vertical components must equal each other, and each 
 will equal the total weight of masonry (W) divided by the length (1) measured by 
 the lines A, D, g h and B S. Then the trapezoid of pressures becomes a rectangle 
 and the resultant will cut the base at the same point g, where a vertical line 
 passing through the centre of gravity of the rectangle meets the base. 
 
13 
 
 When the resultant cuts the base, A B, at the end of its middle third (k), then 
 the aggregation of all the vertical components will form a right-angle triangle I A 
 B, measuring the total weight of masonry, and consequently equal in area to the 
 rectangle A B S D. The resultant will also cut its base at the same point k, at 
 which a vertical line passing through its centre of gravity will cut the base. This 
 
 triangle must have a height B I, equal to twice g h, and equal to — -. — and will 
 
 equal the pressure (p) at B, the outer toe of the dam, while the pressure on the 
 inner toe A, becomes zero. 
 
 If the resultant should cut the base outside of the middle third, the pressure 
 at A would become a minus quantity producing undesirable tensile strains. This 
 illustrates the reason for confining the intersection of the resultant within the 
 middle' third of the base. When the resultant cuts the base within and at any 
 point other than at the middle, or at the end of the middle third, a trapezoid will 
 be formed which must be equal in area to the rectangle or the triangle. A vertical 
 line dropped through the centre of gravity of this trapezoid and also the resultant 
 must cut the base at the same point. 
 
 In the rectangle of pressures when the resultant cuts the centre of the base 
 
 W 
 both p and p'= -j-- 
 
 In the triangle, when the resultant cuts the end of the middle third p^ — — — 
 
 and p'=o. 
 
 To find the pressures p and p' when the resultant cuts the base at some other 
 point (m); produce g h the vertical component of the rectangle at the middle of 
 the base, upward through Z and perpendicular to D S. At the point k, where the 
 resultant of the triangular area of pressures cuts the end of the middle third of the 
 base, project a line perpendicular to A I until it meets g h produced at Z. From 
 m draw the straight line m Z, and through the intersecting point h (common to the 
 upper sides of all possible trapezoids of pressure) draw the line o t, perpendicular 
 to m Z. Then will o B equal p, and t A equal p' the pressures sought. 
 
 The sides of the triangles k Z g, are perpendicular to the sides of I S h. 
 These triangles are therefore similar. For the same reason, the triangles m Z g 
 and o h, S, are similar. 
 
 Representing the lines Z g by (a), k g by (b), S h by (c), I S by (d), m g by 
 (e), and o S by (n). 
 
14 
 
 Then 
 a : b : : c : d 
 and 
 a : e : : c : n 
 Therefore by alternation 
 b : d : : e : n 
 and 
 de 
 
 The triangles o S h, and t D h being similar and equal; and the line B, S 
 being equal to S I or d ; when the dam resists water-pressure against it. 
 
 and 
 
 With no water-pressure against the dam 
 
 (3) P=d-T 
 
 and 
 
 (4) P'-^ + T 
 
 In the above formulae b = -r-, d = — e = the distance of the centre of / 
 
 o / 
 
 from the point where the resultant cuts it. 
 
15 
 
 GRAPHIC METHOD. 
 
 Having fixed the point Z, by the method above described at the intersection 
 of g Z and k S, from the point m where the resultant cuts any part of the base / 
 connect the points m and Z by a straight line. Through the point h draw a 
 straight line perpendicular to m Z, cutting B S and A D (or these lines producad) 
 at o and t, then will 
 
 p=Bo 
 p'=A t. 
 
 W . , r r 
 
 By making one-sixth of the base measure -j- m tons to the square toot (u 
 
 being the end of the middle third) then the triangles Z g K and h S I, also Z g m 
 
 and h S o, are not only similar but equal, and p^u m and p' K m, measured 
 
 directly from the strain sheet, when a scale one-sixth of the base measures and 
 
 , . w 
 
 equals m tons —p- 
 
 The same data being required for both the formula and graphic method, 
 makes it convenient to check one by the other. 
 
 As Consulting Engineer, A. Fteley could best give time to arrange, collate, 
 and present to you the information we have obtained respecting existing dams, 
 called for in your resolution. I have requested him to embody those matters in 
 his report, together with any further detailed technical presentations that might 
 suggest themselves to him. 
 
 The details for the tightest mode of bonding, by breaking joints vertically as 
 well as horizontally, the systems of masonry in construction, and a method of 
 securing tightness on the interior, face, I have prepared for contract and working 
 drawings to be made, when the Commission has settled on the main features of 
 the plans now under consideration. 
 
i6 
 
 Table. 
 
 Section of Quaker Bridge Dam, Acting as an Arch 900 Feet Radius, Cal- 
 
 WR 
 
 i 
 
 
 
 \^\j ±jn. 1 sijXJ £> X J. \Jl\i\ 
 
 i U JjJ\ JJ „ 
 
 
 
 Depth 
 
 Span 
 
 
 
 Total pressure on a voussoir 
 
 Depth of 
 
 Pressure per 
 
 below 
 
 or 
 
 Radius. 
 
 Pressure on lo foot Span. 
 
 joint 10 feet long on ex- 
 
 sq. ft. on vous- 
 
 Surface. 
 
 Cord. 
 
 
 
 trados. 
 
 voussoir joints. 
 
 soir joints. 
 
 
 C 
 
 r 
 
 w 
 
 P 
 
 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Tons. 
 
 Tons. 
 
 Feet. 
 
 Tons. 
 
 
 
 10 
 
 900 
 
 0.000 
 
 000,00 
 
 
 0.00 
 
 10 
 
 10 
 
 900 
 
 3-125 
 
 281.25 
 
 19.7 
 
 14-73 
 
 20 
 
 i( 
 
 li 
 
 6.250 
 
 562.50 
 
 21.0 
 
 26.74 
 
 30 
 
 " 
 
 tt 
 
 9-375 
 
 843-75 
 
 23-1 
 
 36-52 
 
 40 
 
 a 
 
 It 
 
 12.500 
 
 1,125.00 
 
 27-5 
 
 40.99 
 
 50 
 
 " 
 
 ti 
 
 15-625 
 
 1,406.25 
 
 31-6 
 
 44.18 
 
 60 
 
 it 
 
 ti 
 
 18.750 
 
 1,687.50 
 
 36.0 
 
 46.87 
 
 70 
 
 10 
 
 900 
 
 21.875 
 
 1,968.75 
 
 44.0 
 
 44-51 
 
 80 
 
 (( 
 
 a 
 
 25.000 
 
 2,250.00 
 
 51-5 
 
 43-68 
 
 90 
 
 it 
 
 ti 
 
 28.125 
 
 2,531-25 
 
 59-5 
 
 42.55 
 
 100 
 
 4 1 
 
 ti 
 
 31-250 
 
 2,812.50 
 
 67.1 
 
 41-91 
 
 no 
 
 11 
 
 a 
 
 34-375 
 
 3,093-75 
 
 77-6 
 
 39-91 
 
 120 
 
 iC 
 
 ti 
 
 37-500 
 
 3,37500 
 
 88.4 
 
 38-17 
 
 130 
 
 10 
 
 900 
 
 40.625 
 
 3-656.25 
 
 98-5 
 
 37-11 
 
 140 
 
 ii 
 
 it 
 
 43-750 
 
 3,937-5° 
 
 109,4 
 
 35-99 
 
 150 
 
 £C 
 
 it 
 
 46.875 
 
 4,218.75 
 
 120.5 
 
 35-01 
 
 160 
 
 CC 
 
 it 
 
 50.000 
 
 4,500.00 
 
 131-3 
 
 34-28 
 
 170 
 
 10 
 
 900 
 
 51-125 
 
 4,781.25 
 
 141-5 
 
 32.60 
 
 180 
 
 10 
 
 900 
 
 51-256 
 
 4,613.04 
 
 152.7 
 
 30.21 
 
 190 
 
 a 
 
 ti 
 
 51-256 
 
 4,613.04 
 
 164.0 
 
 28.13 
 
 200 
 
 u 
 
 it 
 
 51-256 
 
 4,613-04 
 
 174-0 
 
 26.51 
 
 210 
 
 a 
 
 it 
 
 51-256 
 
 4,613.04 
 
 185.0 
 
 24.93 
 
 220 
 
 10 
 
 900 
 
 51-256 
 
 4,613.04 
 
 195-5 
 
 2359 
 
 230 
 
 ti 
 
 ££ 
 
 51-256 
 
 4,613.04 
 
 204.S 
 
 22.55 
 
 240 
 
 (< 
 
 ti 
 
 51-256 
 
 4,613.04 
 
 212.0 
 
 21-75 
 
 250 
 
 ti ' 
 
 it 
 
 51-256 
 
 4,613.04 
 
 216.0 
 
 21-35 
 
 260 
 
 (( 
 
 it 
 
 51-256 
 
 4,613,04 
 
 216.0 
 
 21-35 
 
 The results of the above table are graphically exhibited in sheets (B) and (C). 
 
 Very respectfully, 
 
 B. S. CHURCH, 
 
 Chief Engineer. 
 
REPORT 
 
 OF 
 
 A. FTKLKY, 
 
 Consulting Engineer. 
 
New York, July 25th, 1887. 
 
 B. S. Church, 
 
 Chief Engineer, Aqueduct Commissioners. 
 
 Sir : 
 
 The following is a brief synopsis of the research on the question of high 
 masonry dams, which you requested me to make for the ultimate purpose of 
 determining the forms, dimensions, materials and mode of construction of the 
 proposed Quaker Bridge Dam. 
 
 It is of such importance for the welfare of the future water supply of New 
 York that this subject should be exhaustively studied, and the amount of money 
 involved is so large, that the necessity of acquiring a full knowledge of the 
 practice followed by other engineers in similar instances, became at once evident ; 
 their methods were carefully considered and weighed, and the best practice was 
 followed, as much, as practicable. Owing, however, to the unprecedented 
 magnitude of the proposed dam, which gives rise to some important problems 
 heretofore unsolved, it became necessary, in some instances, to leave the beaten 
 path and to resort to a basis of operations different from that established by 
 others, 
 
 It should be said here that the subject, when submitted to us, was not entirely 
 new, and that we had the advantage of having before us the result of the joint- 
 work of Messrs. Isaac Newton, Chief Engineer, and E. S. Chesbrough and J. W. 
 Adams, Consulting Engineers, of the Department of Public Works, formulated in 
 the official plan of Quaker Bridge Dam, submitted by the Department of Public 
 Works to the Aqueduct Commissioners. 
 
 It is not within the scope of this report to consider the advisability of the 
 construction of Quaker Bridge Dam as an essential part of the new system of 
 water supply for New York ; the opinion of high engineering authorities should 
 place beyond a reasonable doubt the necessity and feasibility of the structure, but 
 additional confidence in its ultimate success must be obviously increased by a 
 consideration of the high masonry dams now in successful operation, although of 
 less magnitude. The most important ones have been represented in section and 
 
20 
 
 in plan on sheets Nos. i and 2, which accompany this report. Table I. gives 
 statistical data in regard to the greatest number of them, and does not require any 
 explanation ; in many cases, data which appeared of interest for the purpose 
 of comparison, were obtained by calculation from plans and other sources of 
 information at hand, but they are in every case designated by proper references. 
 
 A glance at sheet No. i shows a great variety in the shape of the transverse 
 sections of the various dams. The older Spanish Dams, Puentes, Alicante, Val 
 del Inferno, etc., are conspicuous by their heavy sections ; it is plain that their 
 constructors did not design them in accordance with the best principles, and 
 that they have, by accumulating masonry, uselessly increased the pressures on the 
 lower part of the dams. From these increased pressures, however, which in 
 the Almanza Dam attain fourteen tons per square foot, we may derive the proof 
 that the low limits of pressures, recommended by the more modern authorities, can 
 be safely exceeded, as the old Spanish Dams (with the exception of the Puentes 
 which failed from a different cause) have been in long and successful operation. 
 
 The modern French type is represented on sheet No. i by the following 
 dams : Furens, Villar, Ban, Habra, Komotau, Ternay, Hamiz, Gran Cheurfas, etc ; 
 it is almost needless to add that this form, first indicated by Mr. Sazilly, is due to 
 a better understanding of the magnitude and direction of the forces acting on 
 a dam at various stages of the water in the adjacent basin, and that it is from 
 the construction of these dams, and from the indications of their designers, that the 
 most useful information can be procured. 
 
 Other modern dams, the Gileppe, the Vyrnwy, the Zola, present special 
 features which shall be considered in time. 
 
 Before entering into the consideration of these various structures, however, it 
 is proper, in order to comply with the request of the Aqueduct Commissioners, 
 that I should refer, as succinctly as possible, to the authorities which have been 
 consulted on the subject, and to the views advanced by them. 
 
 We kno)v little or nothing of the methods used by the engineers who built the 
 old Spanish Dams to determine their proportions. The design of the more 
 modern dams, built later in France, for the water supply of canals, " show 
 (says Mr. Krantz) a clearer conception of the forces to be overcome, and 
 greater care in regard to economy. In a word, they show a real advance in the 
 art of building. Still they are not irreproachable. It is obvious that they cannot 
 be taken for models." 
 
 Mr. Sazilly was the first * to consider the subject in all its bearings. " With 
 rare insight,** he was able to discern the nature, amount, and direction of the various 
 
 * Annales des Fonts & Chaussees, 1853. 
 ** Krantz, p. 21. 
 
21 
 
 forces which act on reservoir walls at the different periods of filling the basins. 
 From them he deduces rational forms to be given to constructions of this sort." 
 
 His deductions led him to a profile of a stepped section, which he advocates 
 for several theoretical and constructive reasons ; he recommends a limit of 
 pressure on the masonry of about six tons per square foot, and shows his profiles 
 to a height of i6o fget. His method of calculation is intricate and requires, as 
 usual in such cases, a series of approximations ; he assumes that the pressures are 
 distributed in accordance with formula (i and 2) page 25, which seems to have 
 been universally adopted to express the distribution of pressures on any horizontal 
 joint of a dam, and which will be mentioned again in the course of these remarks. 
 
 Mr. Delocre* developed a very complicated method for determining the 
 profile of high masonry dams, which he applied to the design of Furens Dam, 
 admits a limit of pressure of about six tons per square foot, and does not confine 
 the point of application of the resultants to the middle third of the joint ; he 
 assumes in his calculations for the masonry a weight of 125 lbs. per cubic foot. 
 
 Mr. Graeff,t who had charge of the construction of the Furens dam, must 
 be mentioned as the author of a description of that structure. ' 
 
 Mt. KrantzJ gives an interesting and comprehensive review of ' the subject 
 of high masonry dams, and suggests a full series of profiles for dams of various 
 heights, on which the ultimate pressures are about 6.1 tons per square foot. He 
 does not develop the methods which led him to the determination of his profiles. 
 
 His exposition of the comparative sections of high masonry dams is very 
 complete. 
 
 § Professor Rankine, taking occasion of his being called upon to report on the 
 construction of a proposed dam in India, gives his views on the subject of high 
 masonry dams. He calls attention for the first time to the necessity of using a 
 lower limit of pressure on the front than on the back face, for the reason that the 
 pressure upon a curved face of masonry, at any point, is tangent to the curve at 
 that point. 
 
 He also argues on the advisability of keeping the resultants within the middle 
 third of any joint, in order to avoid tension, which, he claims, would otherwise 
 exist at some points of the faces. 
 
 Finding also that, for dams not exceeding 150 feet in height, logarithmic 
 curves give a close approximation to a correct profile of the faces and furnish a 
 rapid method for determining the outline of a Dam section; he recommends their use. 
 
 * Annales des Pontes & Cliaussees, Oct., 1866. 
 
 f Annales des Ponts & Chaussees, Sept. 1866. 
 
 if Study of Reservoir Walls, by J. B. Krantz, translated by F. A. Mahan, 1883. 
 
 § Miscellaneous Scientific Papers, 1881. 
 
22 
 
 * Mr. Bouvier, in an article on the Ternay Dam, claims that fomula (i and 2) 
 p. 25, used to compute the distribution of pressure on the base of dams, should be 
 so modified as to make the resulting pressure depend upon the oblique resultant, 
 in the case of a full reservoir, thus increasing the pressures as otherwise 
 calculated. 
 
 This method accomplishes the suggestion of Prof. Rankine to adopt a lower 
 limit of pressure for the front face. Mr. Bouvier departs from the practice of his 
 predecessors, and admits, on the strength of the crushing resistance of rubble 
 masonry and of hydraulic lime mortar, as shown by Mr. Vicat, that the pressure on 
 masonry can be safely increased to 14 1-3 tons per square foot. 
 
 f Mr. Pochet gives a description of the Habra Dam in Algeria, refers to 
 the poor quality of the materials used and, after giving a list of pressures which 
 obtain in various cases, adds that the limit of pressure of six tons per square foot, 
 generally admitted by engineers, must not be taken as absolute, and that, in his 
 belief, experience will lead to a much bolder practice within the limits of safety. 
 
 X Mr. Pelletreau, after a purely theoretical discussion upon the designing of 
 high masonry Dams, submits a mathematical method no simpler than that advanced 
 by Mr. Delocre. 
 
 § Mr. de Beauve has devised a graphic method for determining the profile 
 of high dams ; his method considers only the limiting condition of pressure, and it 
 requires considerable modification to introduce the condition of confining the 
 point of application of the resultants to the middle third of the base. The deter- 
 mination of a profile by this method is very laborious, but exact. 
 
 Mr. Guillemain, Professor of the School of Ponts and Chaussees, Paris, in an 
 unpublished lecture delivered at that school, reviews the whole subject of design- 
 ing high masonry dams ; he considers that the points of application of the result- 
 ants should be confined within the centre third of the base, and he takes the same 
 views of the computation of pressures distributed on the base of a dam, as for- 
 mulated by Mr. Bouvier, and suggested by Professor Rankine. 
 
 II Mr. McMaster gives some mathematical equations for the determination 
 of a profile ; he also devotes considerable space to certain practical considerations 
 in regard to the building of masonry dams. 
 
 **Mr. Aymard, having access to the early public records concerning the older 
 Spanish dams, has made use of that information, in connection with his examina- 
 
 * Annales des Ponts & Chaussees, Aug., 1875. 
 
 ■)• Annales des Ponts & Chaussees, April, 1875. 
 
 t Annales des Ponts & Chaussees, Oct., '76, Aug., '77, Mar., '79. 
 
 § Manuel de I'Ingenieur des Ponts & Chaussees, translated by E. Sherman Gould, C. E., 1881. 
 
 II " High Masonry Dams "; Van Nostrand's Science Series, No. 22. 
 
 ** Irrigation du Midi de I'Espagne. 
 
23 
 
 tion of the structures, to give a complete account of them ; interesting facts con- 
 nected with the construction and use of the dams are found in the work. 
 
 * Mr. Crugnola, in his exhaustive treatise on retaining walls, devotes a con- 
 siderable space to masonry dams ; he shows the sections of a number of dams, 
 and gives a graphic method for determining the lines of resistance in any assumed 
 profile. 
 
 The author recommends typical sections for various heights up to 164 feet. 
 
 The following documents, bearing on the subject, have also been consulted, 
 viz. : 
 
 The manuscript report of Mr. Bideau to the Minister of Public Works of 
 Belgium, on the plan of the Gileppe Dam. A memoir on the same structure by 
 Messrs. Detienne and Leclerk. 
 
 Miscellaneous notes on the same dam [Proc. Inst. C. E., Engineering News, 
 etc.] 
 
 An article on high masonry dams by Major Tulloch [Professional Papers on 
 Indian Engineering]. 
 
 Proc. Inst. C. E. Vol, 56, p. loi, on the description of a dam built of concrete 
 in Australia for the Geelong Water Supply. 
 
 Proc. Inst. C. E. Vol. 71, p. 379, giving a short description of the Villar Dam. 
 
 Scientific American, May 28th, 1887. A historical and descriptive review of 
 earth and masonry dams, with plans, by David Gravell. 
 
 A report by Mr. Geo. F. Deacon, C. E., as to the Vyrnwy Dam for the 
 water supply of Liverpool, with full account of the methods used for the deter- 
 mination of the profile and for the construction. 
 
 A paper by W. B. Coventry, Proc. Inst., C. E., Vol, 85, Paper No, 2 no. 
 
 Annales des Ponts & Chaussees, June, 1872. A detailed and illustrated 
 description by Mr. Pamairesse of the Barrage de Cheliff. 
 
 Annales des Ponts & Chaussees, Vol. XL, 1886. A theoretical discussion by 
 Mr. Hetier upon the designing of the profile of masonry dams. 
 
 Giornale del Genio Civile, 1885; also, Bacini di alimentazione per cura di 
 G. Torricelli, C. E. 
 
 Annales des Ponts & Chaussees, June, 1872. A detailed description of the 
 Masonry Dam on the " Canal du Verdon," in France, by Mr. de Tournadre, with 
 note describing the Barrage de Zola, 124 feet high. 
 
 Torricelli. — Relazione presentate al Ministero di Agricoltura. 
 
 Lagrene. — Cours de Navigation — II. 
 
 * Muri di Sostegno. G. Crugnola. 
 
24 
 
 Die Thalsperre der Gileppe bei Verviers (F. Kuhn, Dresden). 
 
 Der Civilingenieur for 1879. 
 
 In addition to these special references, it is obvious that other classical and 
 well known authorities have been consulted. 
 
 When considering the exceptional magnitude of the proposed Quaker Bridge 
 Dam, it becomes at once apparent that it is necessary to depart in its design, to a 
 considerable extent, from the practice hitherto followed. The accumulation of 
 ponderous solid masonry with the great and ill defined strains to which it must be 
 submitted is at best, although the only advisable one under the circumstances, a 
 rude and expensive way of solving the problem, and some attempt was made to see 
 whether, in this case, a structural building could not be erected, with its various 
 parts so designed as to resist well known strains, and to render it comparatively 
 easy to locate and remedy defects, if any were found, after construction. 
 
 This study led to the form of an inclined plane, built of masonry of sufficient 
 quality and thickness to resist the percolation of water, and supported on groin 
 arches and stone pillars ; the junction of the structure with the sides and bottom 
 being" effected by means of heavy masonry walls penetrating the rock to suitable 
 depths. 
 
 Whatever may be the objections to such a structure, it niay be seen that all its 
 parts would be subject to well known strains, and would be left open to inspec- 
 tion ; this research, however, was not extended beyond its preliminary stages, 
 because it soon became evident that the masonry pillars and other parts support- 
 ing the structure, should be made of such cut stone masonry as could support the 
 heavy weight reposing on them, and that the total cost of the dam would be 
 unreasonbly high. 
 
 An iron structure built on the same principle would be feasible and econom- 
 ical, but would not present such guarantees of permanence as must obtain for a 
 dam which is to be the main reliance of the future water supply of New York. 
 
 An earth dam, with a core of masonry, was also considered. In such struc- 
 tures, the thrusts exerted by the earth against the centre wall, during construction 
 and at the different stages of the water surface, when filling or emptying the 
 adjacent basin, are unknown or, at the best, very uncertain ; if the wall became 
 fractured under their action, or allowed the water, in places, to pass through ; 
 the leaks, under such a considerable and unusual pressure, would endanger the 
 stability of the earth embankment. Moreover, the authorities agree that this kind 
 of structure is not safe to adopt beyond a certain limit of height, and it was 
 thought unwise to attempt an experiment which, owing to the importance of the 
 interests involved, was not justified by the saving in expense which might have 
 been effected by its adoption. 
 
25 
 
 In this case, where the welfare of New York is concerned, and where the 
 consequences of a possible disaster with 30,000,000,000 gallons of water behind 
 the dam, may well be imagined, we must deal with certainties ; we have before 
 us many successful instances of masonry dams, although of less magnitude, and 
 the proposed structure can be so proportioned and constructed in masonry 
 as to stand effectually the great pressure to which it is to be subjected. 
 
 After this preliminary consideration of the subject, it was consequently 
 decided, in conformity with the opinion expressed by the Engineers of the Depart- 
 ment of Public Works, to build the dam of solid masonry with such differences 
 from previous engineering practice as would be necessitated by the special 
 features of the undertaking. 
 
 In designing the profile of the dam, three well known main conditions are 
 to be observed. 
 
 1st. The point of application of the resultant of the forces acting on the 
 dam, whether or not it be under water pressure, must not be beyond 
 the centre third of the base. 
 
 2d. The pressures on the masonry at either face, and at any point, must 
 not exceed a certain safe limit. 
 
 3d. The sections of the dam, at any point, must be such that no sliding 
 can take place. 
 
 The means used by the various authorities, analytically or graphicall)'-, for the 
 determination of profiles fulfilling wholly or partly these conditions are somewhat 
 different, but the greater number having based the computation of the distribution 
 of strains on the lower joint of the dam or on any horizontal joint, on the method 
 reproduced by Mr. De Beauve* in his " Manuel de 1' Ingenieur," it is proper that 
 attention should be called to it. 
 
 The pressure at each end of the base or joint " is given by one or the other 
 of the two formulae 
 
 (i) p=2 (2—''^) -r 
 
 . . 2 W 
 
 (2) p= 
 
 3 u 
 
 according as u is greater or less than -." 
 
 * Manuel de 1' Ingenieur des Fonts & Chaussees. Translated by E. Sherman Gould, C. E., 1881. 
 
26 
 
 /== length of base or joint. 
 
 p= pressure per unit of surface at one end of base or joint. 
 
 u^ distance from the point of application of the resultant to same end of 
 base or joint. 
 
 W^ total pressure on base or joint. 
 
 This method is based on the hypothesis that the masonry forming the dam is 
 absolutely rigid and leads to the conclusion that the maximum pressures, on any 
 base, take place at one end of it when the reservoir is full and at the other end 
 when the reservoir is empty. But the structure is not rigid, and there is 
 obviously some uncertainty in regard to the distribution of the strains through 
 the mass of the masonry. This view of the subject is illustrated in the following 
 extract of a report of Mr. J. B. Francis to the Chief Engineer of the Department 
 of Public Works. 
 
 "The main part of the dam, I am informed, is intended to be of rubble 
 masonry laid in Portland cement. 
 
 "Although the work may be done in the best manner possible, it will yield a 
 little to the pressure, and the amount of the compression in different parts of the 
 dam will be unequal and nearly proportional to the pressure and depth of the 
 mass of masonry at its different parts. The amount of the compression at 
 different points may be too small to be observed, but I am of the opinion that it will 
 be sufficient to modify to a material extent the result of calculations based on the 
 hypothesis of an incompressible mass, and the effect, I think, must be to cause a 
 distribution of pressure very different from that indicated by the calculations, and 
 to relieve to a great extent, if not entirely, the outer toe of a high dam designed 
 strictly according to the De Beauve method, from the pressure due to the weight 
 of the high part, combined with the horizontal pressure of the water against the 
 up-stream face of the dam. The entire weight must, of course, be supported on 
 the base, but I think a much larger proportion of it will be upon its central parts, 
 than is indicated by the calculation, and that the pressure at the toe, instead of 
 being a maximum, will be a minimum." 
 
 As an additional illustration of the uncertainty of the distribution of pres- 
 sures on the base of dams, the following extract from Rankine's " Miscellaneous 
 Scientific Papers," may be of interest: "The assumption on which this rule is 
 based, of an uniform rate of variation of that component of the pressure which is 
 normal to the pressed surface, is known to be sensibly correct in the case of 
 beams, and is probably very near the truth in walls of uniform, or nearly uniform, 
 thickness. Whether, or to what extent, it deviates from exactness in walls of 
 various thicknesses is uncertain in the present state of our experimental 
 knowledge." 
 
27 
 
 Whatever may be the distribution of the pressure on the base of the dam, it 
 must be admitted that the strains are distributed otherwise than indicated by the 
 formulse ; but as we have no other means of determining these strains with 
 accuracy, and as, on the other hand, the formulae indicate resulting pressures 
 larger than they are in reality, the profiles based on that method show an excess 
 of strength which gives a further guarantee of safety. 
 
 The distribution of strains on the base and horizontal joints of the dam has 
 consequently been computed, in the numerous cases considered, by formula [ij, 
 with the understanding that it indicates, at the ends of the joints, pressures 
 evidently higher than the actual ones, thus adding to the computation a factor of 
 safety of important, although uncertain, value. 
 
 The sections of dams built or proposed by various authorities have been 
 determined by methods involving the consideration of the horizontal and vertical 
 forces acting on the dam, and of the magnitude, direction, and application of 
 their resultant force. Those methods, with the exception of some analytical ones 
 mentioned before, and which are too complicated for practical use, proceed by 
 successive approximations of the profiles, and require considerable time. As it 
 was desirable, in this research, to go thoroughly over the ground and review a 
 number of different profiles before coming to final conclusions, a more expeditious 
 method was sought and used for a large portion of the preliminary studies. 
 This method, although proceeding by successive approximations, was found of 
 great service for simplifying the computations. It is based upon the principle of 
 moments. 
 
 For convenience and accuracy, the profile is divided into horizontal layers of 
 a given thickness. The calculation is begun at the top of the dam, each layer 
 being figured separately. A layer being given, and the profile of the dam above 
 it being known, certain dimensions are assumed for the lower joint of the given 
 layer ; and the position of the two resultants (in case the reservoir is full or 
 empty) are determined by taking moments about- assumed axes. If the first 
 profile does not give results in accordance with the assumed limiting conditions, 
 another is attempted, and a third attempt is very rarely needed. 
 
 To simplify the computations the weight of the cubic foot of masonry is 
 taken as the unit of weight throughout the calculations ; consequently, when con- 
 sidering a vertical section of the dam one foot thick, the area of the section in 
 square feet will give the weight in cubic feet of masonry ; hence laborious reduc- 
 tions are avoided. 
 
 A practical example of the method will illustrate it. 
 
 The upper part of a dam m, n, a, b, Fig. 5, Sheet No. 5, being already known, 
 
28 
 
 it is desired to determine an additional section 20 feet high. The depth of water 
 above the base of the new part is 150 feet. 
 
 The weight of masonry is assumed at 156,25 lbs., per cubic foot. (This 
 weight is within less than a pound that of a block of masonry built for experi- 
 mental purposes with stone quarried in the neighborhood of Quaker Bridge Dam, 
 and has the- advantage of being a single multiple (2.5) of the weight of a cubic 
 foot of water.) The limiting pressure for the back face is supposed to be 
 20,625 lbs. per square foot (10 kilos per square centimetre) = 132 units, expressed 
 in cubic feet of masonry ; the limiting pressure on the front face being 105 cubic 
 feet of masonry. 
 
 We want to find first the point of application of the resultant when the 
 reservoir is empty. The resultant W for the part above joint a b is known in 
 magnitude and position == 5,689.5 cubic feet masonry. The axis of moments is 
 192.5 feet from point b. 
 
 From the previous form of the profile, let us assume that on the front face we 
 will add d k = 2 1 feet to the base a, b, and on the back face c, 1, = 4 feet. 
 
 Divide the trapezoid a, b, c, d, into one rectangle a, k, b, 1, and two triangles 
 b, c, 1 and a, d, k. 
 
 Taking the moments about the assumed axis 
 
 Resultant W 
 
 Rectangle 93 x 20 
 Triangle 21 x i°- • 
 Triangle 4 x 10 . . . 
 
 Totals . 
 
 Weights in cubic 
 feet of masonry. 
 
 5,689.5 
 1,860 
 210 
 40 
 
 Lever Arms. 
 
 224.1 
 
 239- 
 292.5 
 191. 2 
 
 Moments. 
 
 1,275,388 
 
 444,540 
 
 61,425 
 
 7,648 
 
 7,799-5 
 
 1,789,001 
 
 1,7 9-QP' _^ distance of the resultant from the axis of moments = 229.4 ft- 
 7,799-5 
 
 Distance of the point of application of the resistance from point c = 229.4 — 
 [192.5—4] = 40.9 ft. 
 
 In the case when the reservoir is full, the pressure of water will throw the 
 resultant toward the front edge. 
 
 Calling h the depth of water above c d, the moment of the water pressure 
 
 around point d. = x-x — = 225.000, -— being the ratio of the weight of 
 
 23 2.5 
 water to weight of masonry. 
 
 2-5 
 
29 
 ^, , . 1 1 t r 1 • 1 £ 225,000 
 
 Then taking- moments about the resultant found m the hrst case, =• 
 
 ^ 7.799-5 
 
 28.9, which is the distance between the points of application of the two resultants. 
 
 Applying now formula (i) it will be found that the pressures at d and c are 
 101.6 and 126.7 cubic feet of masonry, respectively, inside of the assumed limits 
 of pressure. If greater accuracy is needed a new trial may be had with slightly 
 lower values for d, k and 1, c. 
 
 The results thus obtained have been frequently checked by graphic methods. 
 
 In the various computations of profiles, which will be here mentioned, the 
 vertical pressure of water on the back face of the dam is omitted ; its omission 
 has only a slight influence on the results, which it affects on the side of safety, 
 and simplifies the calculations. 
 
 It may be noticed that in the course of' these remarks, the height of Quaker 
 Bridge Dam has always been computed, from the bed rock, many feet below the 
 river bed, to the top of the structure. It is obvious that the position of its lower 
 part in a deep bed of gravel, and the counter-pressure due to the earth and to the 
 water on the front face, modify to a certain extent the conditions of stability and 
 the intensity of the strains, but no additional strength is given to the dam by the 
 fact of its being imbedded in a great depth of earth, and with due regard to the 
 modifications which may be introduced on account of the presence of a counter- 
 pressure, the dam must be treated as one structure of a uniform character 
 throughout its whole extent. 
 
 At the beginning of this research, a trial profile attempted under conditions 
 of assumed pressures within the limits used by the best authorities, showed con- 
 clusively that the height of Quaker Bridge Dam would compel us to depart 
 from the practice of others, as, in order to remain within the prescribed limits, it 
 would be necessary to spread the lower parts in an impracticable manner and to 
 incline the slopes to an extent incompatible with strength. Fig. i, Sheet No. 5, 
 illustrates this fact. 
 
 The same result would follow the use of the Rankine method and of the 
 types advocated by Messrs. Krantz, Crugnola and others (see sheet No. 3). 
 
 It was then thought that it might be advisable to change the quality of the 
 masonry at the points a, b. Fig. 2, Sheet No. 5, where the application of the 
 pressures recommended became impracticable, and to adopt beyond these points 
 a cut stone masonry capable of supporting greater strains. Further consideration 
 of the case, however, developed the fact that this modification would be very 
 costly owing to the size of the dam ; it is also preferable not to destroy, if possi- 
 ble, the homogeneity of the mass of masonry. 
 
 The only alternative left was to assume higher limits of pressure. Is it safe 
 
30 
 
 to do so? In answer to that question, we may refer again to the opinion of 
 Messrs. Bouvier & Pochet (see page 6), who admit that bolder practice can be 
 resorted to within safety. It must be said also that, in fixing their low limits of 
 pressure, the French engineers have kept in view the fact that the dams may be 
 put under full pressure when their comparatively slow setting mortars have not 
 gained their full strength, while in our case the cements used, with the possible 
 exception of the uppermost part of the dam, will have time to harden satisfactorily 
 before the whole force of the water pressure is brought to act on the masonry. 
 Moreover, it is well known that there are in existence many structures, the 
 foundations of which have to support weights superior to any that may be 
 sustained by the lower parts of Quaker Bridge Dam. 
 
 A computation made of the maximum pressure at the outer toe of some 
 existing dams shows that they attain in several cases from eleven to fourteen tons 
 per square foot. 
 
 It is well known that the ultimate crushing strength of the materials to be 
 used in Quaker Bridge Dam is much above the pressure which will obtain in that 
 structure, and it must not be forgotten that the limits of strength deduced from 
 experiments are obtained with samples of a small bulk, presenting much less 
 resistance to crushing than large masses of masonry laterally supported. 
 
 Adding to these considerations the fact already mentioned, that the pressure 
 on the faces of the dam are undoubtedly below the figures calculated by the 
 general method followed by us, it may be asserted that the pressures calculated 
 for the lower part of the proposed structure can be safely adopted. 
 
 The question may then be fairly asked whether these high limits of pressure, 
 inasmuch as they are considered safe, should not be adopted for the upper part of 
 the profile of the dam, as well as for the lower part. They could, in our opinion, 
 be adopted, but an insignificant saving only would thus be effected and some 
 objectionable features would be produced. The upper part of the dam, which has 
 to resist the additional strains due to the shock of waves and ice and to the action 
 of frost, possibly at a time when the mortar is not fully set ; and which has to 
 carry a roadway, must be designed much wider than it would be if it was subjected 
 only to the combined pressure of masonry and of quiescent water ; such being 
 the case, the thicknesses of masonry corresponding to the higher pressure assumed 
 for the base, could not be adopted near the top without distorting the profile ; 
 if adopted lower down, their effect would be to cause the lower outer slope of the 
 profile to make with the horizontal a sharper angle. Considerable importance is 
 attached to this point ; the downward regular transmission of strains due to 
 superincumbent weight in a pyramidal mass of masonry can be relied on within 
 certain limits only, and it is obvious that it would not take place if the slopes were 
 
31 
 
 too much inclined on the horizon ; the safe limit of acceptable slope is uncertain 
 and depends on the character of the materials and of the workmanship which enter 
 into the structure. 
 
 It may be added also that it is better, where practicable, to follow the practice 
 which has been proved by experience to be successful in dams already built, and 
 to depart from it in the parts only to which it is not applicable, and in which 
 further safety is obtained by the greater extent of the bulk of masonry (with its 
 consequent additional resistance to crushing due to increased lateral support, and 
 its additional strength due to the increased surfaces of cement joints). 
 
 The lowest layers of the masonry, at the time that the dam will be put under 
 pressure, will also have the advantage of the harder set of the mortar due to the 
 time necessary for the building operations. 
 
 The acceptance of this basis of operation disposes of one of the essential 
 conditions previously mentioned for the proper determination of the profile, i. e., 
 that the point of application of the resultants on the base of the dam must be 
 within the centre third of the said base, as, owing to the spreading of the latter to 
 correspond to the assumed limiting pressures, this condition obtains in all cases. 
 Let it be added now that the third condition, i. e., the resistance to sliding, need 
 not require any subsequent attention ; in all cases the horizontal water pressure 
 tending to make the dam slide on its joints is much inferior to the weight of the 
 masonry, and, when taking in consideration the adhesive power of the cement 
 mortar and the roughness of the surfaces in contact, it becomes evident that no 
 sliding motion can take place. 
 
 The weight of the masonry is an important factor in the establishment of a 
 profile, and it can be seen that the weights [actual or assumed] entering into the 
 calculations of the various authorities vary considerably. 
 
 Several weights of the cubic feet of masonry have been used in this research ; 
 156.25 lbs. has been used for the proposed profile of Quaker Bridge Dam, having 
 been determined, as mentioned before, by actual experiment. 
 
 The change of weight, however, has much less influence on the profile than 
 might be supposed, as is seen from an inspection of fig. 3, Sheet No. 5, in which 
 the comparative profiles have been designed under the following conditions : 
 
 Profile a, 
 " b. 
 " c. 
 
 Weight of one cubic foot of Masonry. 
 
 125 lbs. 
 
 145.8 " 
 156.25 " 
 
 Limit of Pressure per square centimeter. 
 
 8 and 10 kilos. 
 7.6 " 9.8 " 
 
32 
 
 The weight of the masonry being for the present an uncertain factor, it was 
 useful to see to what extent the condition of stability would be changed, in case a 
 dam, calculated for a given weight of masonry, were afterwards constructed with 
 materials of a greater or lesser weight. A profile was consequently designed 
 using 156.25 lbs., as the assumed weight of the cubic foot of masonry, and a sub- 
 sequent computation of the pressures made on the supposition that the actual 
 weight of the masonry was 125 lbs. 
 
 The same operation was repeated, 125 lbs. being the calculated weight, and 
 156.25 lbs. the actual weight. 
 
 In the first case the pressures were found as follows for the front face : 
 
 Depths from top. 
 
 Calculated Pressures. 
 Pounds per square foot. 
 
 Actual Pressures. 
 Pounds per square foot. 
 
 30 feet. 
 
 11 .981 
 
 10. 75° 
 
 5° 
 
 13. 260 
 
 13.000 
 
 70 
 
 14.882 
 
 15-750 
 
 90 
 
 15.678 
 
 16.625 
 
 no 
 
 16. ij6 
 
 16.500 
 
 130 
 
 16.224 
 
 16.125 
 
 150 
 
 15-850 
 
 15-675 
 
 171 
 
 16. 146 
 
 15-994 , 
 
 288 
 
 38.376 
 
 35-400 
 
 In the second case, the pressures were found as follows, also for the front 
 
 face : 
 
 Depths from top. 
 
 Calculated Pressures. 
 
 Actual Pressures. 
 
 Pounds per square foot. 
 
 Pounds per square foot. 
 
 30 feet. 
 
 8.888 
 
 9.984 
 
 50 
 
 10.625 
 
 10.000 
 
 70 
 
 11-338 
 
 II. 177 
 
 90 
 
 12 . 250 
 
 12.383 
 
 no 
 
 13.875 
 
 13-803 
 
 130 
 
 15.827 
 
 15.912 
 
 150 
 
 16.250 
 
 16.068 
 
 171 
 
 16.500 
 
 16.378 
 
 288 
 
 33-460 
 
 35-724 
 
 These results, obtained with weights so far apart, show that a small error in 
 the expected weight of the masonry forming the dam would not seriously affect 
 the reliability of the profile. 
 
33 
 
 While on the subject of the weight of the masonry, it is proper to consider 
 whether the fact that a portion of the dam, from the river bed to the bed rock 
 below, is to be submerged in water, is to affect the weight of the structure. 
 
 It would obviously be so, to a certain extent, if the masonry was porous 
 enough to admit water under ordinary hydrostatic conditions, but the dam, at the 
 lower part, is to be so thick and the masonry is to be of such quality that it can 
 be reasonably supposed that the water penetrating it will be mostly, if not wholly, 
 in a capillary condition, and that the whole dam may be considered, for purpose of 
 calculation, as an impervious monolithic mass rigidly and imperviously connected 
 with the rock bottom, and, consequently, not losing weight by the fact of its being 
 in water. It must be added, however, that even if admitting, as it has been by 
 others, that the water would exert an upward pressure on the dam, thus diminish- 
 ing its actual weight on the bottom, the result would not be such as to disturb, to 
 any objectionable extent, the conditions of stability otherwise established. 
 
 This subject leads naturally to the consideration of the advisability of building 
 drains in the mass of the dam, as recommended by others, in order to relieve it 
 from the pressure of water penetrating the masonry. In accordance with the 
 preceding remarks, and with some authorities, their presence is not thought neces- 
 sary, and it is obvious that, unless their construction is superintended with the 
 greatest care, they may become injurious by introducing water into the masonry 
 under conditions which would then become unfavorable. At any rate, we know 
 by the experience of existing dams that they have been built and work successfully 
 without drains, and we fail to find any sufficient reason to discard that practice. 
 
 In the preceding remarks, the conditions of stability referred to have been 
 considered in connection with the base of the dam or with its horizontal joints 
 only, but the tendency of the parts of the dam to rotate about the foot of diagonal 
 joints assumed at various angles, through tlie mass of masonry, has also been 
 examined, and, in all cases, the moment of the masonry around the lower point of 
 the given diagonal joint has been found more than double of the moment of water 
 pressure around the same point. 
 
 The conclusions herein formulated in regard to the pressures that it is thought 
 advisable to allow on the base of the profile, and in regard to the slope of the 
 front face, indicate obviously that, in order to determine the profile of the lower 
 part of Quaker Bridge Dam, the approximate length of the base and the maximum 
 pressures at the toes, must be arbitrarily fixed within the limits which have been 
 shown here to be safe. 
 
 The result of successive approximations demonstrates that by adopting for 
 maximum calculated pressure at the end of the base fifteen tons per square foot 
 (a value which, in view of the opinions previously expressed in regard to the distri- 
 
34 
 
 bution of pressures on the base, is considered safe), the length of the base of the 
 theoretical profile will be about 230 feet, a length which allows of a front slope 
 likely favorable to the transmission of the strains acting upon the structure from 
 its various points to its base. 
 
 In consequence of these views and of the considerations already developed in 
 regard to the limiting pressures adopted for the upper part of the profile, and in 
 view of the comparatively large proportions of the extreme top, it follows that 
 the calculated pressures at the ends of the successive horizontal joints will show 
 progressive values from the top to the base. 
 
 The few sloping lines forming the outline of the profile, which were adopted 
 to facilitate construction, follow closely the many sided polygonal figure which 
 would be indicated by the successive calculations of a number of horizontal slices 
 of the section. 
 
 In the course of these studies Mr. Ed. Wegmann, Jr., Special Assistant Engi- 
 neer, who was intrusted with the mathematical computations connected with the 
 subject, devised a simple and exact analytical method for determining directly the 
 profile of a masonry Dam. 
 
 That method is based primarily on the fundamental formulae for distribution 
 of pressure already mentioned [p. 25], and on the limiting conditions, viz.: that 
 the resultant when the reservoir is full or empty, shall lie within the centre third 
 of the base of the profile ; and that at no point of the faces shall the elementary 
 pressures exceed certain fixed limits. 
 
 For the purpose of calculation, the section of the Dam is supposed to be 
 divided in horizontal slices of a given height, to which the method is applied in 
 succession. 
 
 The vertical component of the water pressure on the slopes of the up-stream 
 face is neglected. 
 
 Reference to the units of weight, etc., employed in the calculations for the 
 Quaker Bridge Dam will be made hereafter. 
 
 The symbols employed are as follows : 
 
 W = Weight of masonry above the layer under consideration. 
 
 W = W plus weight of layer under consideration. 
 
 m = Length of upper joint, already determined. 
 
 /= " " lower " to be 
 
 2h = Depth of layer. 
 
 d = Distance of point of application of W from back end of joint m. [Reser- 
 voir empty.] 
 
 u '= Distance of point of application of W from front end of joint /. [Reser- 
 voir full.J 
 
.35 
 
 u' = Distance of point of application of W from back end of joint /. [Reser- 
 voir empty.] 
 
 p = Elemementary pressure at front end of joint /. [Reservoir full.] 
 
 p' == Elementary pressure at back end of joint /. [Reservoir empty.] 
 
 M = moment of water pressure about the horizontal plane through joint /. 
 
 a = Vertical distance of flow line below top of profile. 
 
 d = Ratio of unit weight of masonry to unit weight of water. 
 
 The method as applied to a general profile consists of two initial equations. 
 
 First initial equation (a). — ^The first initial equation [a] applies to that portion 
 of the profile in which the back face is vertical and covers the case in which 
 the limiting pressure obtains on the front face. It gives the length /of the joint. 
 
 . ^ ^ ,, , 2W7 6dW'+2hm= + 6M 
 
 Equation a. / H = • 
 
 ^ p p 
 
 If the resultant [reservoir full] falls at the extremity of the middle third of 
 the joint, equation [a] becomes equation [b]. 
 
 • ri 1 7. , 7 r2 W', -, 3 d W , . , 3 M 
 Equation [b.] /' + / [— r— + m] — ^-^- — + m + ^. 
 
 Equation [b] again transformed, becomes equation [cj, which gives the depth 
 at which the front face ceases to be vertical [assuming a certain top width for the 
 profile]; z. e., the section being a rectangle of given base, it gives the depth at 
 which the resultant [Reservoir full] will intersect the extremity of the centre third 
 of the joint. 
 
 P , ' ,, Shr Sal" 
 
 Equation [c^.] h = — — . 
 
 4 o 
 
 Equation [cj assumes that the top of the profile is adove the level of the flow- 
 line ; if, on the contrary, the top of the profile coincides with the flow-line, Equation 
 [cJ becomes Equation [c^]. 
 
 O. 72 
 
 Equation [c'.] h" = 
 
 4 
 
 Second initial Equation (d). — The second initial equation [d] applies to that 
 
 portion of the profile in which both faces have a batter, and covers the case in 
 
 which the limiting pressure exists on both faces of the profile. 
 
 Equation [d.] /= [p + p' - 2 h] — 2/[W' + h m] = 6 M. 
 
 If the resultant, when the reservoir is empty, falls at the extremity of the 
 middle third of the joint, then equation [d] becomes equation [e]. 
 
36 
 
 T^ • r 1 , 6M 
 
 hquation [e.J r = . 
 
 If both resultants [Reservoir full and empty] fall at the extremities of the 
 middle third of the joint, then equation [e] becomes equation [f]. 
 
 Equation [f.] -^ + ^ [-jt + H = V-- 
 
 It is obvious that since equations [d], [e] and [f] apply to that portion of the 
 profile in which both faces have a batter, the length of the joint [/] derived from 
 them does not fix the batters of the layer in hand. This renders necessary the 
 supplementary equation [g] by which the offset {x) on the back face is determined.^ 
 
 Equation [g.J ;t: [3 W + 2 h m + h /] =W' [2 /-3d] + hm [/-m]+ /t^-- ]• 
 
 If the resultant [Reservoir empty] falls at the extremity of the middle third of 
 the joint, equation [g] may be simplified to the form of equation [h]. 
 
 Equation [h.] x [3 W + 2 h m + h /] = W [/-3d]-hm^ 
 
 The above equations apply to a general profile. In the Quaker Bridge Dam, 
 for reasons which will be explained hereafter, very long, straight slopes have been 
 adopted for the lower portion of the profile ; and the calculations for a theoretical 
 profile were complicated by the fact that some 87 feet of the structure is below the 
 river-bed, and consequently subjected to additional strains due to the weight of the 
 overlying gravel, and by a counter-water pressure. This special case has been 
 submitted to analysis and the following equations have been deduced. 
 
 The depth of the gravel overlying the base is represented by 2 g. 
 
 Total depth of layer = 2h. 
 
 Ratio % = 9 
 h 
 
 Ratio of unit weight of gravel to unit weight of masonry = /?. 
 
 The limiting conditions being that certain pressures shall obtain on the up- 
 stream and down-stream faces at bed rock, equation [k] gives the length of the 
 base at bed rock. 
 
 Equation [k.] /^[[p'+ p]-2 h [i + 0^/?]] + 2 /[h m [S^^-iJ-W] = 6 m. 
 Equation [1] gives the offset \_x'\ on the back face. 
 
 Equation [1.] ^ [h / [i -f 2 0^ ^^-3 0= /?] + h m [2-2 ©^ /?] -f 3 W] = 
 
 h I' [i-0=y5-f 03^]-hm^[i-03/?] + h/m [1-2 03 y?+ 0=/?]— 
 
 3W'd + 2W'/— ^-^'. 
 
i1 
 
 With the exception of formula [cj, a simple equation of the third degree, it may 
 be noticed that all the others are of the second degree only. In regard to the last 
 two, which may appear too long for practical purposes, it can be seen that they are 
 of easy solution, and that they cover the special case when the lowest calculated 
 section is partly built in gravel overlaying the bed rock, with a counter pressure of 
 water. 
 
 The following table shows the application of the above formulae to the theo- 
 retical profile for Quaker Bridge Dam : 
 
 Elevations of 
 
 Limiting Conditions. 
 
 Equations 
 Employed. 
 
 Values Found. 
 
 Joint. 
 
 Front Face. 
 
 Back Face. 
 
 For / 
 
 For X. 
 
 171. 3 
 
 / 
 
 
 [b ] 
 [b ] ■ 
 [f]&[h] 
 [ e ] & [ h J 
 Ck]&[/] 
 
 /=20 
 
 (2h = 34.7) 
 26.2 
 
 37-4 
 
 53-4 
 
 71.2 
 
 231.8 
 
 
 156. 
 
 3 
 
 / 
 u ^ - 
 
 
 
 136. 
 
 3 
 
 
 
 116. 
 96. 
 
 —52- 
 
 3 
 
 / 
 '^'~3 
 
 p == 8.2 tons. .. 
 per sq. ft. 
 
 p = 15, tons. . . 
 per sq. ft. 
 
 / 
 U'= - . 
 
 3 
 
 , / 
 
 ~3 
 
 p = 15 tons 
 
 per sq. ft. 
 
 2-3 
 2.0 
 
 25-4 
 
 It is by this method that the theoretical profile of Quaker Bridge Dam, 
 shown (Fig. 4) Sheet No. 5, has been computed ; the results have been afterwards 
 confirmed by means of graphic and other methods. The elements of the calcu- 
 lation are as follows : 
 
 The limit of pressure assumed at the down-stream face of the profile is, for 
 a depth of water of no feet (elevation +96) and less, 8.2 tons of 2,000 lbs. per 
 square foot. 
 
 At the back or up-stream face, the condition that the resultant should fall on 
 the end of the centre third of the base led to a pressure, at the end. of the hori- 
 zontal joint, at elevation +96, of 8.7 tons per square foot. 
 
 From no feet depth (elevation +96) to the base of the dam (elevation — 52) 
 the assumed pressures increase steadily until they attain the maximum value of 
 15 tons (30,000 lbs,) already mentioned. 
 
38 
 
 For the sake of simplification, the vertical weight of the water on the inclined 
 portion of the up-stream face is neglected, this slight error being on the side of 
 safety. 
 
 The vertical weight of the saturated gravel resting upon the slopes of the 
 dam below the river bed is taken into account. 
 
 The gravel on the down-stream side of the dam being saturated with water, 
 the resulting counter-pressure of water enters into the computation. 
 
 The weight of a cubic foot of water is taken at 62.5 lbs. 
 
 The weight of a, cubic foot of masonry, for reasons already given, is taken at 
 156.25 lbs. 
 
 The weight of a cubic foot of saturated gravel is taken at 145.875 lbs., 
 equivalent to 0.94 of the weight of masonry [the dry gravel being assumed at 
 125 lbs., with voids equal to one-third of the bulk filled with water]. 
 
 The unit of weight used throughout is the weight of one cubic foot of 
 masonry. It has been already stated that this choice of unit simplifies the calcu- 
 lations greatly. 
 
 The effect of wind pressure on the dam has been neglected. If it blows down 
 the valley when the Reservoir is empty, its tendency is to increase the stability ; if 
 it blows in the other direction the result is the same with a full reservoir, and with 
 an empty or partially empty basin the margin of safety is more than sufficient to 
 counteract the comparatively insignificant effect of the wind pressure. 
 
 The result of the calculation is shown on Fig. 4 (Sheet No. 5), which gives 
 the theoretical profile of the dam, and on Table II., which explains itself: 
 
 The theoretical profile of the dam being determined, certain modifications 
 were advisable to meet some practical requirements of adaptability and of con- 
 struction. 
 
 The width of the top had to be adapted to the requirements of a roadway. 
 A slight addition to the thickness of masonry down to Elevation 170 {i.e., the 
 part covered by the fluctuations of the water surface in the Reservoir) presents 
 the double advantage of increasing the strength of the structure at a point where 
 it may have to sustain shocks from the action of the waves and ice, and of adding 
 to the symmetry of the profile. 
 
 It is also advisable for the purpose of facilitating construction to so regulate 
 the various inclinations of the faces as to give them a simple ratio easy to follow 
 during the building operations. 
 
 Last, as no dependence can be placed on the strength of the sharp triangle 
 of masonry forming the extreme toe of the down-stream face, it is advisable to 
 dispense with it, and to round it off in the form of steps, as shown on Sheet No. 6. 
 
39 
 
 This disposition presents the additional advantage of lessening the. width of the 
 expensive excavation to be made in the bed of the river.' 
 
 These modifications having caused some changes in the distribution of the 
 materials, obviously rendered necessary a new computation of the distribution of 
 pressures throughout the mass of masonry. 
 
 To this end the proposed profile was divided into horizontal sections or slices 
 1 1 feet high. The centres of gravity were found by the usual system of moments 
 for each joint; the overturning moments, etc., were ascertained, and the pressures 
 computed as before in accordance with the formula (i), p. 25, the various units and 
 elements of calculation being the same as those used for the computation of the 
 theoretical profile. 
 
 Table III. gives a synopsis of the results obtained, and shows that : 
 
 The total width of the base is 216 feet. 
 
 The maximum pressure at toe of up-stream face is 15.4 tons per square foot 
 [13.8 tons of 2240 Ibs.J. 
 
 The maximum pressure at toe of down-stream face is 16.6 tons per square 
 foot [14.8 tons of 2240 Ibs.J. 
 
 Average pressure on base, per square foot, 10.49 tons. 
 
 In accordance with the views already discussed in this report, these results 
 are acceptable, and the profile, shown on Sheet No. 6, is recommended for the 
 acceptance of the Aqueduct Commissioners. 
 
 Before closing these remarks on the profile of high masonry dams it is proper 
 that we should refer to several modern structures which, owing to their magnitude 
 and to the known skill of the engineers who designed them, were duly considered 
 by us, namely : the Gilleppe Dam in Belgium and the Vyrnwy Dam near Liver- 
 pool, England, (See Sheets No. i and 2). 
 
 The evidently excessive section of the Gileppe Dam was due, as its desicrner 
 admits, to local reasons of expediency independent from technical considerations. 
 
 The Vyrnwy Dam is intended to be used as a weir, and its shape is such as to 
 lead the water properly in its fall and to support a heavy apron on the down- 
 stream side. 
 
 The special conditions under which these dams were designed do not obtain 
 in the case of Quaker Bridge Dam, and there was no valid reason to follow their 
 peculiar profile. 
 
 A dam has been recently begun near San Mateo, for the Spring Valley Water 
 Company of San Francisco (California), which will be almost as high as the Furens 
 Dam, its height being 170 feet (See Sheets Nos. i and 2). It is to be 20 feet 
 wide at top with straight batters. It is to be built of concrete blocks formed in 
 
40 
 
 place with a mortar of Portland cement. The description of this structure, now 
 at hand, does not mention whether the engineer has more confidence in concrete 
 than in stone masonry, or whether his choice was determined by economical or 
 other reasons foreign to the constructive value of these materials.* 
 
 After determining the profile of Quaker Bridge Dam, the next question in 
 importance is to decide on the plan of the dam, whether it should be straight or 
 curved. 
 
 Referring to the list of dams now in operation, it will be seen that both plans 
 have been followed with successful results. If we consult the various authorities 
 on the subject, we find the almost unanimous opinion that if a curve be adopted 
 for the plan of a dam, it is advisable, notwithstanding, to so proportion the profile 
 of the section as to make it able to stand, by its own gravity, the pressure of 
 the water ; the curved form, in other words, is considered as a sort of additional 
 co-efificient of safety. 
 
 We fail, however, to see how a mass of masonry, proportioned to stand water 
 pressure by its own gravity, can at the same time act as an arch ; if the profile 
 is suflficient, the mass will not yield under pressure, and if it does not yield, no- 
 pressure can be transmitted to the sides through the curve ; the two conditions 
 are incompatible. 
 
 If, on the contrary, the section of masonry is not sufficient to support the 
 water pressure, then the mass will yield to a certain extent under the strain, and 
 some pressure will be transmitted to the abutments of the curve, in the upper por- 
 tion, of the structure ; we say, in the upper portion because it is evident that, if 
 there is, through the adhesive power of the mortar, rigid connection between the 
 dam and the foundation rock, the adjacent parts of the masonry cannot, at the 
 same time, act as an arch. 
 
 Among the curved dams recorded herein we find that all, with one exception, 
 have sections sufificient to resist the water pressures brought to bear upon them, 
 and that they do not act as arches. The exception is the Zola Dam [in France] ; 
 see Sheets Nos. i and 2 and Table I. 
 
 The thickness of the masonry is so small that the resultant falls outside of the 
 front toe and that (unless the excellence of its mortar, and, generally, of its 
 masonry be exceptionally great), its stability is due to the fact that it is built in the 
 form of an arch, the water pressure being transmitted to the abutments. More- 
 over, the form of its section shows that the intention of its designer was that it 
 should act so. 
 
 As, however, the rigid connection of the dam with the rock of the foundation 
 
 * See N. Y. Daily Tribune, October 2d, 1887. 
 
41 
 
 precludes, at that point, the idea of an elastic motion in the masonry and of a 
 consequent lateral transmission of the strains to the abutments, it is impossible to 
 state at what height above the foundation the dam begins to act as an arch. 
 
 Owing to the small width of the valley (a few feet at the bottom and about 
 200 feet at the top) the strains thus produced are evidently such as can be sustained 
 by the masonry, but it is probable that the failure of one part of this dam would 
 cause its total ruin, while, with a self-supporting section, a dam may fail at one 
 point, leaving the balance whole. Such was the case at the dam of Gran Cheurfas 
 (Algeria). 
 
 If we leave this special instance to return to general cases, we must call atten- 
 tion to the important fact that the admissibility of the arch form in the plan 
 of a dam must depend primarily on the intensity of the lateral or horizontal strains 
 that would be transmitted through the structure. 
 
 In the case of curved dams thrown across narrow valleys, it may be found 
 that the lateral strains (admitting that any should be developed), would be such as 
 the masonry could safely support, and, if it is expected that the upper part of the 
 structure might be put under pressure when the mortar, not being wholly hardened, 
 is in a comparatively yielding state, we conceive that a certain amount of motion 
 of the masonry, however small, may be expected, causing the portion affected to 
 act as an arch with the tendency of closing the joints under pressure. 
 
 This advantage can hardly be claimed, however, for structures which are not 
 made of voussoirs, but composed of an irregular mass of stones and mortar, which 
 cannot be relied on for arch work, unless the whole is sufficiently hardened to 
 present an homogeneous and monolithic character. 
 
 When, on the contrary, the width of the valley is such that the strains trans- 
 mitted by an arch would become excessive, that form must be avoided. 
 
 Let us look at the case in hand. 
 
 Great care has been taken in designing the profile that no strains superior to 
 fifteen tons should be produced by the combined action of the water pressure, and 
 of gravity ; other strains will be developed by variations of temperature ; addi- 
 tional local strains will occur, owing to unavoidable irregularity in the quality of 
 the workmanship. Would it be prudent to complicate matters by knowingly 
 submitting the masonry to additional horizontal strains which would be very high, 
 attaining a maximum of over forty tons per square foot ; as far as we can calculate 
 such values, for " in the present state of science, the calculations of stability, 
 treating the dam as a horizontal arch, are so uncertain as to be of doubtful 
 utility." The best information we have in regard to the stability of stone arches 
 comes from experimental data, and we have none bearing on arches of such a great 
 span. 
 
42 
 
 In accordance with these views it is concluded: 
 
 That a dam of such a length as Quaker Bridge Dam, if acting as an arch, 
 would be subjected to excessive strains. 
 
 That, with the profile recommended, it can successfully resist in all its parts, 
 the pressures applied to it, without any additional support. 
 
 That, if built on a curve, it would not act as an arch, and would be more 
 expensive. 
 
 That it is advisable that the dam should be built in a straight line. 
 
 Let us consider, now, other features of importance, second only to the profile 
 and plan of the dam, i. e., the height of the crest of the dam above the water line 
 and the capacity of the weir over which the surplus water is to flow. 
 
 Existing dams furnish good data in regard to the height to be given to the 
 structure, and in accordance with precedents and with the recommendations of 
 reliable authorities, the top of the parapet has been placed at an elevation of 13 
 feet above the ordinary water mark, equivalent to 7 feet above the extreme high 
 water mark, the surface of the roadway being 3 feet below the top of the parapet. 
 This height is amply sufficient to cope successfully with the highest waves which 
 may be expected from the unusual depth and considerable extent of the reservoir. 
 
 As to the capacity of the overflow, it is necessary to depart from precedents 
 on account of the extent of the water-shed and the comparatively heavy rainfalls 
 that occasionally occur in the Croton Basin. 
 
 Judging from the possibilities of rain or thaw in this and neighboring water- 
 sheds, the flowing capacity of the overflow should not be less than equivalent 
 to the flow, in twenty-four hours, of a volume of water represented by a uniform 
 thickness of six inches over the whole water-shed. 
 
 It is true that no such flow is on record, and the actual flow may never, it is 
 hoped, come to that figure; but a combination of adverse circumstances, such as 
 an exceptionally heavy rainfall, occurring at a time when the reservoir is already 
 full, and when the ground is covered with snow, can bring about such a condition 
 of things, and it is wise to be prepared for it. It can be so much more readily 
 done, that an increase in the length of the overflow can be obtained at a compara- 
 tively small cost. . 
 
 The writer, having had occasion to design the overflow of several dams on 
 an equivalent basis, may be allowed to state that, on the occurrence of a freshet 
 which produced a flow somewhat less than one-half of the quantity just mentioned, 
 he could not but feel, in accordance with the sentiment of the people living lower 
 down in the valley, that the channels of discharge were none too large. 
 
 The length of overflow corresponding to these conditions is about 1,300 feet. 
 
43 
 
 It may be mentioned here, that the gate house proposed to be built in con- 
 nection with the dam, is to contain, besides the gates leading to the two aqueducts, 
 some ample channels for the emptying of the reservoirs. These discharging 
 channels, although placed a distance above the river bottom, are so arranged as to 
 allow of the drawing of the bottom water, when necessary to do so. 
 
 In regard to the kind of masonry to be used, the majority of existing struc- 
 tures appear to be built of rubble; they generally give satisfaction, and there is no 
 reason to depart from that practice. Concrete cannot be depended upon as being 
 impervious enough to prevent percolation of water under great pressures and cut 
 stone masonry, in connection with the great bulk of the dam, is obviously excluded 
 on account of its cost. To all probabilities, stone suitable for the work can be 
 found in abundance in the neighborhood, gneiss or granite being predominant ; 
 but in any case, the stone used must be one that will not disintegrate under the 
 influence of time or of the weather. A proper selection of stone is of such 
 moment, and the distance from the work to the quarry or quarries is so important 
 an element of cost (considering especially the quantities to be transported) that 
 the territory in the vicinity of the dam should be examined by excavations, and, 
 if necessary, by boring, in order to determine, before letting the work, the loca- 
 lities from which the stone is likely to come. Such an expenditure would be 
 judicious, and would remove, to a great extent, the uncertainty under which the 
 contractors would labor in making their bids, and the necessity under which they 
 would find themselves to provide in their bids a large margin to meet possible 
 contingencies of excessive cost in transportation. 
 
 The whole masonry of the dam, from bed rock to the top, should be homo- 
 geneous with the exception of the parts which, from requirements of ornamentation 
 and maintenance, may be made of finer masonry. 
 
 Mr. Krantz says that "the joints should be irregular on the faces and in all 
 the sections ; the courses should be thoroughly interlocked, or better still, there 
 should be no courses, and by means of good work this result must be obtained, 
 so that the whole body of the wall shall be a real monolith." 
 
 Mr. E. S. Chesbrough, in a report on the subject to the Department of Public 
 Works, states that: 
 
 " The superstructure should be composed throughout of uncoursed, broken 
 range rubble masonry, built of quarry stone of irregular sizes, laid with full beds 
 and joints. The use of cut stone should be confined to such appropriate orna- 
 ment as may be desired, none being used in the body of the work, not only on 
 account of expense, but also to avoid the introduction of two different classes of 
 masonry. 
 
 " While, as above stated, coursing should be avoided, it would be proper to 
 
44 
 
 keep the work roughly levelled up over its entire length, say every five feet in 
 height, so as to secure an even settlement as the structure goes up." 
 
 To these remarks, which appear to resume the practice generally followed, it 
 may be added that, for the purpose of keeping the faces in good order, and to 
 preserve them from the action of the weather, it is advisable to make the joint 
 closer on the faces or even to use range rubble with a close joint near the surface 
 only, thus lessening the future work of keeping the outer joints well pointed, 
 without disturbing the uniform settlement of the whole mass. In some of the old 
 Spanish dams the faces are even lined with cut stones which are not reported to 
 have caused any trouble. 
 
 As it is of vital importance that all spaces between the stones be filled com- 
 pletely with mortar, they must be of such size as can be easily handled, enabling 
 the masons to secure, beyond doubt, a good bedding, and each stone, with the 
 exception of the smaller ones used for filling up and leveling up cavities, should 
 be so selected or shaped as to present a good bed which will form a solid joint 
 with the level surface prepared to receive it ; all projections presenting too irregu- 
 lar outlines should also be hammered off. These conditions do not admit of large 
 sizes for the stones used, but their limits of size cannot be absolutely determined 
 in advance, and they may vary with the quality of the stone used. 
 
 Large stones, as generally prepared for rubble work, cannot be properly 
 bedded, and better and more expeditious work will be secured by the fise 
 of smaller ones. With few exceptions, the largest stones should not exceed 
 two tons and the largest proportion should be much smaller. The face on the 
 water side should be made as water-tight as possible, either by a careful pointing 
 of Portland cement or by the introduction of a special impervious facing. 
 
 Especial care will be necessary in designing the masonry of the Gate House, 
 which must not present large masses of masonry different in character from that 
 used in the body of the Dam, without forgetting that most of its parts will sup- 
 port heavier pressures. 
 
 The Gate House, however, is at a point on the side of the valley where the 
 risks of unequal settlement are very much diminished by the reduced height of 
 the structure. 
 
 The same precaution must be used on the other side, where an opening must 
 be provided for the flow of the river during construction. 
 
 No special mention of the cut stone masonry to be used for the cornice and 
 parapet work, for the gate house, for the overflow, &c., is necessary here. 
 
 This report would not be complete without a few words in connection with 
 the part of the work which will precede the building of the masonry. 
 
 Existing dams furnish no precedents of the deep excavation necessary 
 
45 
 
 here to reach the bed rock, and we find but few references to the manner of pre- 
 paring the latter to receive the masonry. 
 
 How to make successfully that deep excavation and to take care of the river 
 during the excavating operations, and during the first part of the construction, is 
 the problem presented. 
 
 One plan originally suggested consisted in building across the valley, in 
 heavily timbered trenches, and, from the rock bottom to the river bed, two walls 
 of considerable thickness, forming the up-stream and down-stream faces of the 
 dam respectively; under the protection of those walls, the earth could be removed 
 between them and the wall completed. 
 
 Against that plan several important objections are found : 
 
 In view of the depth of the excavation, which is, at the lowest point of the 
 valley, more than eighty feet deep, and in view of the inclination of the outer 
 faces of the dam, these walls should be very thick, and the trenches containing 
 them correspondingly wide. The excavation of such wide trenches, and their pro- 
 tection by timber, would be very costly, and would especially take a very long 
 time. 
 
 The pressures at the bottom of the trench would be such as to require 
 very heavy timbers placed very close together, thus forming an obstacle to 
 the proper inspection, and to the expeditious and satisfactory laying of the masonry 
 between them. Moreover, the rock bottom, under those difficulties, could not be 
 properly examined and prepared. It is obvious, also, that the Dam would then be 
 erected in its lower part in three parallel and disconnected vertical slices, instead 
 of progressing regularly upward as it should be to secure the gradual settlement of 
 the- mass. 
 
 Notwithstanding the great depth of the excavation, and the evident difficulties 
 accompanying such an operation, the most advisable manner to proceed is 
 to open it without side protection, and to maintain it by means of long slopes on 
 each side. The free access thus procured to every part of the work will allow of 
 the use of powerful mechanical means for removing the earth, and the cost of the 
 excess of excavation, due to the formation of slopes, will be more than compensated 
 by the rapidity and simplicity of the operations, which will obviously lower the 
 cost of the cubic yard excavated, and shorten very much the time necessary to 
 complete the work. 
 
 Another advantage of as great value will result from the unobstructed con- 
 dition of the bottom of the trench which will permit a perfect inspection and 
 preparation of the bed rock and a thorough treatment of the seams and fissures 
 which will, most probably, be found. The foot of the slopes, if necessary, can be 
 locally removed, for a considerable distance, to uncover and fill up important 
 
46 
 
 seams, which it would be found advisable to follow outside of the actual base of 
 the dam. The numerous borings made in the valley show that the materials 
 would be, on the whole, favorable for such an excavation, provided the trench is 
 well drained. 
 
 In order to drain thoroughly the trench, it would be well (in addition to the 
 means provided to take care of the river water) to sink in the bed of the river, a 
 short distance from the upper edge of the excavation, several wells provided with 
 pumping appliances, for the purpose of keeping the slopes dry. 
 
 It is well understood that the unusual depth of the proposed trench, and the 
 constant presence above it of a body of water which, at times, may be very large, 
 constitute difficulties of no mean magnitude, and that great care and foresight will 
 be necessary to achieve success ; but this mode of treating the question appears to 
 be the most rational under the circumstances. 
 
 Closely connected with this subject is that of the conveyance of the river 
 water over the work while the excavating and building operations take place 
 below the level of the river bed. 
 
 It is proposed to build two temporary wooden dams of little height, one above 
 and one below the location of the dam, and to connect them by a water-tight 
 timber flume, the distance of these dams from the edge of the trench to be deter- 
 mined later from a close examination of the grounds, to be not less in each case 
 than, say, 200 feet. 
 
 The dams should be of such height as to correspond to the highest water 
 mark of the flume. 
 
 What should be the flowing capacity of the flume ? 
 
 The records show an instance where the maximum flow of 'Croton River was 
 about 8,000 million gallons in 24 hours. 
 
 The construction and maintenance of a wooden flume (not less than 200 feet 
 wide), as formerly proposed, capable of safely containing such a stream, would be 
 very expensive. It would require (supposing it to be practicable) great vigilance 
 to keep it water-tight, owing to the constantly increasing depth of the excavations 
 and to the consequently frequent change of supports. It would be, at best, a 
 constant obstruction to the rest of the work, and should not be attempted. 
 
 In building operations of this character it is unavoidable that the builder 
 should take some risks; but they must be reduced to a minimum within the limits 
 of a reasonable outlay, and the writer thinks that the following manner of con- 
 trolling the water, which is much less expensive, would afford more chance of 
 protection from the water, although, in some contingencies, it may involve the 
 temporary flooding of the work. 
 
 Instead of maintaining the protecting flume over the work it is proposed to 
 
47 
 
 place it at one side, wholly or partially on a shelf of rock preiDared, where neces- 
 sary, for the purpose. The borings show that the north side would admit of such 
 a treatment. 
 
 As to its flowing capacity, it would be sufficient to make it equal to the 
 volume of the average spring freshet of the Croton River, corresponding to a 
 width of about 60 feet ; but the flume must be so designed that if the river rises 
 beyond its capacity, ample channels, prepared for that purpose on the rocky 
 hillside, must be opened to safely fill up the trench, and allow the freshet to pass 
 over the work without causing more than repairable damage. 
 
 Time and money would then be required to restore the excavation to working 
 order, but this risk is preferable to the constant maintenance of the larger channel 
 during several years. 
 
 As the work of masonry comes up above the level of the river bed, an arched 
 opening can be left for the passage of the flume, to be filled afterwards when the 
 dam is nearly completed. 
 
 After the earth is removed from the proposed foundation on the bottom and 
 sides, all loose or doubtful ledge must be removed until sound rock is found, or 
 until such depth is reached as will be judged sufficient for securing a water-tight 
 connection between the dam and the rock. For the purpose of insuring imper- 
 viousness, and of increasing the resistance of the structure to sliding, the surface 
 of the rock must present numerous projections which need not be regular. In 
 case the rock comes out with smooth surfaces, it would be well to excavate one or 
 more wide longitudinal trenches. It is obvious that any seams that may be 
 encountered must be carefully followed and obliterated by such means as may be 
 suggested by local conditions. If seams and fissures extend to such distance as 
 may require a more thorough treatment, it may be necessary, at places, if not on 
 the whole extent of the work, to penetrate the rock deeply on the bottom and 
 sides with a central trench to be filled afterwards with masonry. 
 
 It need not be said that the cements to be used in the construction must be 
 well selected. It would be well, in order to secure perfect work at the connection 
 of the structure with the rock, to use imported Portland cement at all places 
 wherever such connection is to take place, and in their vicinity, the mortar being 
 in the proportion of one of cement to two of sand. 
 
 The same mortar would also be preferable for the work to be done in the last 
 season on the upper part of the dam and elsewhere, on account of the well-known 
 property of the Portland cement to acquire hardness in shorter time than the 
 domestic brands, thus securing greater power of resistance for the masonry, if 
 it happens to be subjected to full pressures immediately after the dam is put 
 into service. 
 
48 
 
 Portland cement mortar should also be used for the pointing of the outer 
 joints. 
 
 For the bulk of the dam, a mortar made of the same proportions of good 
 domestic cement or a mortar of Portland cement in the proportion of three to one 
 would be sufficient. 
 
 All the statements advanced, the conclusions reached, and the recommenda- 
 tions made in this report are presented on the supposition that every part of the 
 work is to be executed with care, under intelligent and able superintendence ; on 
 that condition will depend the suceess of the undertaking. 
 
 The extensive borings made preparatory to the designing of the plan, 
 especially the two diagonal borings made parallel with the sides of the valley 
 under its whole width, seem to indicate the presence of good compact rock ; the 
 surface indications are also favorable, and although some difficulties are anticipated 
 in preparing the foundations, it is confidently expected that they can be over- 
 come. 
 
 Under the pressures to which the dam will be subjected, some leakage may 
 be expected ; such has been the case for several of the high masonry dams now in 
 existence. If the leakage takes place through the masonry, experience shows that 
 it diminishes gradually, and in regard to the grounds adjoining the dam, if the 
 earth which covers them is not sufficient to prevent water from percolating through 
 fissures that may exist in the rock, it is reasonable to expect that those percola- 
 tions can be located and stopped. 
 
 In order to do full justice to this important subject, and to the investigation 
 made of it, it would have been necessary to enter into more details in regard to 
 the numerous questions which have been examined ; but a complete record of 
 them would have entailed many technical references hardly compatible with the 
 scope and intent of this report. 
 
 Before concluding, I desire to record my indebtedness to Mr. Edward 
 Wegmann, Jr., Division Engineer, whose work in connection with the mathematical 
 part of this research I have already mentioned, and to Mr. Ira A. Shaler, Assist- 
 ant Engineer, for their valuable assistance. 
 
 Respectfully submitted, 
 
 A. FTELEY, 
 
 Consulting Engineer. 
 
Name of Dam. 
 
 Furens . 
 ViUar. . . 
 Gileppe , 
 
 Ban 
 
 Vyrnwy. 
 
 Zola. 
 
 Habra . . . 
 Komatau . 
 
 Ternay. 
 
 Hamiz 
 
 Grancheurfas . 
 
 Tlelat (to be raised higher) .... 
 Djidionia (to be raised higher). . . . 
 
 Boyd's Corners 
 
 Geelong 
 
 St. Etienne, France ■] 
 
 Lozoya, Spain 
 
 Verviers, Belgium . . -j 
 
 France 
 
 Vyrnwy River, Wales.. 
 
 Near Aix, Provence, 
 France 
 
 Provence of Oran, Al- 
 giers 
 
 Assibach, Bohemia . . . 
 
 Annonay, France 
 
 Algeria 
 
 Puentes . 
 Alicante . 
 
 Val del Infierno. 
 
 Lozoya 
 
 Nijar 
 
 Elche 
 
 Almanza. 
 
 Putnam Co., N. Y. ... 
 Victoria, Australia. . . . 
 
 Province of Sorca, 
 Spain 
 
 Watei 
 Watei 
 
 i8 
 
 e- 
 
 Water 
 
 Pov|d, 125 lbs. . . 
 
 Watedi43 lbs 
 
 Water 
 
 Powd, 143.5 lbs. 
 
 160.8 lbs... 
 
 d, 137. 1 lbs. 
 Irriga d, 152 lbs. . . 
 
 Province of Alicante, 
 Spain 
 
 Province of Sorca, 
 Spain 
 
 Madrid, Spain.. 
 
 Province of Almeria, 
 Spain 
 
 Near San Mateo, recently begun , 
 
 Province of Alicante, 
 Spain 
 
 Province of Valencia, 
 Spain 
 
 California, U. S. A. -j 
 
 Powe 
 
 Irrigi 
 
 Wate 
 Irri 
 
 Wate 
 Wate 
 
 Irriga 
 
 Irriga 
 
 Irriga 
 Wate: 
 
 Irriga 
 
 Irriga 
 
 Irriga 
 
 Watei 
 Fra 
 
 d, 167 lbs. 
 
 143 lbs. 
 
 19 
 
 g.i 
 
 15 4 
 
 154 
 
 54 
 
 50 
 327 
 
 4-7 
 
 24 (takes surplus 
 water from large 
 additional area). 
 
 I>II5 
 
 7,950 
 
 675 
 
 279 
 26 
 
 1,800 
 
 £.2 
 
 bo 
 
 ft.S 
 
 U 
 
 340 
 4,400 
 
 3.230 
 
 660 
 
 358 
 
 3,430 
 4,224 
 
 145 
 
 528 
 
 2,723 
 
 142 
 
 980 
 
 3.9&O 
 
 32,000 
 
 Roadway. , . 
 
 Overflow . . . 
 
 Foot-path . . 
 Roadway . . . 
 
 Overflow . 
 
 23 
 
 197 
 (2) 82 each. . 
 
 410 
 
 197 
 
 30 • 
 
 27-5 
 
 39 
 
 24 
 
 _ <U jJ 
 
 8.3 
 
 6.5 
 
 5-2 
 
 5-3 
 
 6.6 
 
Missing Page 
 
TABLE II.. 
 
 SYNOPSIS OF DATA— THEORETICAL PROFILE— QUAKER BRIDGE DAM. 
 
 a 
 
 u 
 
 Ft. 
 
 171-3 
 
 156 
 
 ti6 
 96 
 76 
 
 5° 
 35 
 15 
 -5 
 -25 
 -52 
 
 .a 
 S, 
 
 V 
 
 Q 
 
 Ft. 
 
 34.7 
 
 50 
 
 136 70 
 
 90 
 
 130 
 
 150 
 
 171 
 
 191 
 
 40 
 211 
 
 60 
 231 
 
 87 
 258 
 
 
 O 
 
 Ft. 
 
 o 12.4 
 
 2-3 
 
 3-4 
 3-4 
 3-6 
 3-4 
 3-4 
 3-4 
 4.6 
 
 .S.e.g 
 
 o t« o 
 
 <L> rt 
 
 H 1- h 
 
 m (U v 
 
 i; c 
 -1 X 
 
 3 O 
 
 § ^ bo 
 
 4-> O lU 
 
 (uO 
 
 Ft. 
 
 lo.o 
 
 ro.5 
 
 17.8 
 23-7 
 31-7 
 
 40.1 
 
 49-1 
 .58.8 
 69.9 
 81.6 
 97-7 
 
 4-> 4-> 
 
 .9-5 Q 
 ••-^53 .0, 
 
 a 
 
 nl o 
 
 i3 l-i c! 
 
 in qj .S 
 
 O -t^ wi 
 
 T3 O tn 
 
 S ^ Ph 
 
 <u C g 
 
 *-» o G 
 
 (u) 
 
 Ft. 
 
 6.7 
 
 12.5 
 
 17.8 
 
 25.2 
 
 45-3 
 56.1 
 65-9 
 75-4 
 84.8 
 
 97-7 
 
 •3 o 
 
 V o 
 
 (c) 
 
 Ft. 
 
 7.0 
 
 12.5 
 
 17.8 
 
 .^ a 
 
 (/) 
 
 Ft. 
 
 3-3 20 
 
 26.2 
 
 S3-4 
 
 22.3 
 
 71.2 
 
 26.1 
 
 92.9 
 
 29.2 
 
 1 14.6 
 
 32.2 
 
 137.4 
 
 34.4 
 
 I59-I 
 
 35-5 
 
 180.8 
 
 36.1 
 
 202.5 
 
 36.4 
 
 231.8 
 
 o-S 
 
 o 
 
 (W) 
 
 Sq. ft. 
 ■ Cu. ft. 
 Masonry. 
 
 9 
 
 10 
 
 
 
 a 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 a 
 
 
 
 0. 
 
 
 .a 
 
 ' • 
 
 C8 
 
 
 
 tH 
 
 T3 
 
 
 
 
 V 
 
 ^ 
 ^ 
 
 B 
 SI 
 
 
 
 
 
 3 
 
 
 ^ 
 
 CU 
 
 3 
 
 
 
 cd 
 
 
 
 
 
 
 
 
 
 
 P 
 
 K 
 
 Ph 
 
 
 (pO 
 
 Cu. ft. 
 
 Ibs.per 
 
 834 
 
 1,187 
 
 Masonry sq. ft. 
 
 241 
 
 500 
 
 (P) 
 
 Ibs.per 
 sq. ft. 
 
 6,516 
 
 ^3^°Z^ 
 
 37.4 1,823 980 15,234 
 
 2,731 
 
 3-977 
 
 S,6i8 
 
 7,698 
 
 10,339 
 
 13.304 
 13,508 
 
 16,703 
 
 ^7,519 
 
 20,536 
 22,372 
 
 26,399 
 30,260 
 
 1,620 
 
 2,420 
 
 3,380 
 
 4,S°o 
 
 5,848 
 
 7,216 
 
 8,584 
 
 9>952 
 
 ii,799 
 
 15,234 
 
 15,984 
 
 17,453 
 
 18,462 
 
 19,930 
 
 23,641 
 
 25,466 
 
 27,313 
 
 30,000 
 
 16,391 
 
 16,384 
 
 17,078 
 
 18,219 
 
 20,084 
 
 22,680 
 
 !5,69i 
 
 30,000 
 
 
 12 
 
 
 
 
 , 
 
 
 
 ■a 
 
 
 1-. 
 
 
 
 
 
 
 ■*-> 
 
 
 
 ^ 
 
 B 
 
 3 
 
 
 <+H 
 
 n 
 
 
 
 
 
 
 j_, 
 
 m 
 
 
 
 3 
 
 
 
 
 
 , 
 
 fr 
 
 00 
 
 a 
 
 3 
 
 n 
 
 c 
 
 
 j§ 
 
 H 
 
 ■^ 
 
 H 
 
 
 
 
 
 
 ja 
 
 
 
 !>> 
 
 I*- 
 
 , , 
 
 .Q 
 
 
 "S 
 
 
 
 (1) 
 
 Tl 
 
 1 
 
 & 
 
 > 
 
 13 
 
 ho 
 
 a 
 
 a 
 
 "rt 
 
 .29 
 
 11,328 14,156 .42 
 
 •54 
 
 15,984 -59 
 
 .61 
 
 .60 
 
 ■57 
 
 ■56 
 
 •53 
 
 •49 
 
 •44 
 
 •39 
 
 3.00 
 
 2.24 
 
 2,00 
 
 2.13 
 
 2.34 
 
 2-55 
 
 2.74 
 
 2.92 
 
 3^13 
 
 3-35 
 
 3-68 
 
 Note. — Small figures in column 2 show depth of water on down-stream side of dam. 
 
 Small figures in column 8 represent weight of masonry (equals area masonry) exclusive of gravel on slopes. 
 Large figures in Column 8 below elev. 35 represent total weight of Masonry plus gravel; but in area they represent 
 the area of the masonry plus 0.94 of the area of the gravel. 
 
HIGHEST FLOW LINE E.laA 
 
 COMMISSION 
 :ams 
 
 :tical types 
 
 SHEET N03 
 
 TO ACCOMPANY REPORT OF CONSULTING ENG" 
 
 Lia79 
 149 g 
 RESULTANT DIRECT 
 ^«»IEft-Pn€SSiMfe' 
 EOSOItS LBS. i? , 
 
Missing Page