531 STUDIES IN THE CONSTRUCTION OF DAMS: EARTHEN AND MASONKY. SECOND EDITION. In Medium Svo. Pp. i-xvi 4- 195. With Frontispiece, 32 Plates and 1 16 Illustrations in the Text. COAST EROSION AND PROTECTION. BY PROF. ERNEST K. MATTHEWS, A.M.LvsT.C.E., F.U.G.S. CONTKNT*. Wave Action. Erosion and Accretion. Types of Sea Walls. Reinforced Concrete Sea Defences. Other Types of Protection by Sea Walls. Action of Sea Water on Cement and Concrete. Groynes. Design of Sea Walls. Erosion v. Accretion. .Materials and Methods of Preservation of Sea Walls INDEX. "A fascinating book . . . no tea coast town can afford to be without it . . . this valuable contribution . . . contains the latest information.'' MunicipalJournal. In Cloth. Pp. i-xiii + 160. With 8 Detailed Drawings and 91 Illustrations in the Text. REFUSE DISPOSAL. BY PROF. E. R. MATTHEWS, A.M.lNST.C.E., F.K.S.E., &c. CONTENTS. Collection of House Refuse. Disposal of Refuse. Conversion to Manure. Destruction by Burning. Types of Destructors. The Mel drum Destructor. Heenan Destructor. Other Destructors. Dawson-Manfleld Destructor. Installations for Villages, Workhouses, Hospitals, Factories, etc. Use for Clinker. Chimney Con- struction. Vacuum Cleaning; and Dust Collecting. INDEX. " Absolutely reliable . . . The value of such a treatise to the Municipal Engineer, to members of Local Authorities, and others interested in the subject cannot well be over-estimated. "Mun icipal Journal. In Medium 8vo. With over 800 Pages and over 1000 Illustrations. Cloth. A MANUAL OF CIVIL ENGINEERING PRACTICE, Specially Arranged for the use of Municipal and County Engineers. BY F. NOEL TAYLOR, CIVIL ENGINEER. CONTENTS. Ordnance Maps. Chain Surveying. Surveying with Angular Instru- ments. Levelling.- Adjustment of Instruments Mensuration of Areas, Volumes, &c. The Mechanics of Engineering, etc. Beams. Pillars, Stanchions and Shafting. Design of Structure. Arches. Graphic Statics. Materials of Construction. Engineering Foundations Brickwork and Masonry. Walls. Constructional Car- pentering. Road Materials. Road Construction. Reinforced Concrete Construction. Masonry Bridges and River ^york. Hydraulics. Land Drainage. Pumping Machinery and Stations. The Use of Water-Power. Main Drainage. Sewage Disposal. Royal Commission on Sewage Disposal. Salford Sewage Works. Sanitation, House Drainage and Disinfection. Refuse Disposal. Waterworks, Preliminary Considerations and Sources of Supply. Construction, Filtration and Purification. Waterworks. Dis- tribution. Chimneys, Brick and Steel. Steel Construction : Stanchions, Rivets and Bolts. Steel Construction ; Beams and Girders. Combined Structures in Iron and Steel. Specification. Electric Tramways. Appendix. INDEX. " A veritable vade tnecitm . . . would prove an acquisition to the library of any Municipal Engineer." Surveyor. TWENTY- FOURTH EDITION. Crown 8vo. Cloth. With Numerous Tables and Illustrations. A MANUAL OF CIVIL ENGINEERING. BY W. J. MACQUORN KANKINE, LL.D., F.R.S. CONTKNTS. Engineering Surveys. Materials and Structures. Earthwork. Founda- tions. Masonry. Carpentry. Metal Work. Underground and Submerged Structures. Combined Structures. Roads. Railways. Collection, Conveyance and Distribution of Water. Canals. Rivers. Tidal and Coast Work. Waterworks. Sea Defences Harbours. INDKX. LONDON : CHARLES GRIFFIN & CO., LTD., EXETER ST., STRAND, W.C. 2. PHILADELPHIA: J. B. LIPP1NCOTT COMPANY. STTJDIE S IN THE CONSTRUCTION OF DAMS EARTHEN AND MASONRY. ARRANGED ON THE PRINCIPLE OF QUESTION AND ANSWER FOR ENGINEERING STUDENTS AND OTHERS. BY PROFESSOR E. K. MATTHEWS, B.Sc.(ENG.), Assoc.M.lNST.C.E., F.R.S.(ED.), M.SOC.INGS.CIVIL(FRANCE). AUTHOR OF "COAST EROSION AND PROTECTION;" " REFUSE DISPOSAL," ETC. WITH THIRTY DIAGRAMS. LONDON: CHARLES GRIFFIN & COMPANY, LIMITED. PHILADELPHIA: J. B. LIPPINCOTT COMPANY. [All Rights Reserved.] ^ PREFACE. THIS little book is intended to be of assistance to Engineering Students who may be preparing for the "Associate Member- ship" Examination of the Institution of Civil Engineers, the Examination of the Institution of Municipal and County Engineers, the B.Sc. (Engineering) of our Universities, or other similar Exams. The text takes the " Question " and " Answer " form, which has been found by experience to be a most useful method of disciplining the mind of the Student to grasp essential teaching and at the same time learn how to express his knowledge. The .matter is dealt with in a manner suited to fundamental principles, and the numerous diagrams form an integral part of the studies. E. R. MATTHEWS. UNIVBRSITY COLLEGE, UNIVERSITY OF LONDON, March, 1919. 43178G SYMBOLS AND ABBREVIATIONS. The following nomenclature is employed throughout this work : r = weight in Ibs. of a cubic foot of water (62-5), or in cwts. (0-557). ?' weight in Ibs. of a cubic foot of mud, 85. AT = weight in Ibs. of a cubic foot of masonry. H = head of water in feet. A T = head of water above the liquid mud level. h. 2 = head of liquid mud.
MASQNRY
QUESTION 1. A masonry dam, 20 feet high, 4 feet
wide at the top, and 12 feet wide at the bottom,
has its faces straight, the water face being vertical.
Draw the line of thrust when the water level is 2 feet
from the top. Take the specific gravity of the masonry
as 2-25. (Inst. C.E. Exam. Question.)
Answer. The dam under consideration is illus-
trated in Fig. 1, which is drawn to a scale of 8 feet
to 1 inch, the force diagram being to a scale of
100 cwts. to 1 inch.
The total water pressure on the wall varies as the
head, and may be represented by the area of the
triangle ABC. In a low^ dam B C may be taken as
being equal to A B, although it really measures less.
The centre of pressure passes through the centre of
^ >... ...... CONSTRUCTION OF DAMS.
CONSTRUCTION OF DAMS. 3
gravity of this triangle, and occurs at E, so that
A E = f A B, and, if we consider a strip of the
wall 1 foot wide, the resultant pressure P will be
as follows :
rH 2
~
where P = the normal pressure ;
r = the weight of a cubic foot of water
= 62-5 Ibs.
= 0-557 cwt.;
H = head in feet,;
b = the constant breadth of the strip = 1 foot.
In the case now being considered
P Q'557 x 1 x 18 2
2
0-557 x 18 2
2
180-468
2
= 90-234 cwts., say 90-2 cwts.*
So that we know the magnitude, point of application,
and direction of P.
Let us now consider the line of thrust. The weight
of the dam must first be ascertained, and we are told
* It is quite unnecessary for the student to use the last two decimals,
seeing that both masonry and water may vary in density, and that
when designing the dam the resultant is kept well within the middle
third of the base.
4 CONSTRUCTION OF DAMS.
that the specific gravity of the masonry of which it
is to be built = 2-25 ; therefore
Weight of wall = 160 x 2-25 x 62-5
(Cub. ft. of (Specfic (Weight of
masonry) gravity of cub. ft. of
masonry) water)
= 22,500 Ibs., or 201 cwts.
The weight of the wall will act through the centre of
gravity of the section. The resultant may be found
graphically as shown in Fig. 7. It will be observed
that R (the line of thrust) is well within the middle
third of the wall, and, therefore, the structure is quite
strong enough.
QUESTION 2. Give a sketch of, and briefly describe,
one or more important high masonry dams.
Answer. Excellent examples of high masonry dams
may be seen in this country, in America, France,
India, Spain, and Australia.
Furen's Dam (France). Fig. 2 illustrates a remark-
able dam in France, known as Furen's Dam. Its
base is 161 feet in width, and the depth of water
impounded is 164 feet. The structure is 18 feet
9 inches in width at the top, and the dam is built
upon a rock foundation. It is some years since this
dam was constructed, and it shows no sign of failure.
The maximum pressure on the dam is 6 tons per
square foot only, which is very low seeing that en-
gineers often reduce the dimensions of the structure
so as to provide for a pressure of 9 tons per square
CONSTRUCTION OF DAMS.
5
foot, while in America a working pressure of 14 tons
per square foot has been allowed.
Fig. 2.
Fig. 3. Vyrnwy Dam, Liverpool Waterworks.
Vyrnwy Dam (England). This is an interesting ex-
ample of dam construction in England (see Fig. 3),
6 CONSTRUCTION OF DAMS.
The structure was erected a few years ago in con-
nection with the Liverpool Waterworks. It is built
upon a rock foundation, is 117 feet 9 inches in width
at the base, and retains a depth of water of 136 feet
on one side, and about 45 feet on the other. The
late Sir Benjamin Baker, M.Inst.C.E. (ex-President,
Inst.C.E.), was the consulting engineer in connection
with this fine piece of engineering work.
Olive Bridge Dam (America). This structure,
which was completed in 1914, represents tjie
latest important masonry dam which has been
built, and is an excellent example of what may be
done in the way of dam construction ; it is one of
the largest dams in the world, and is one of the main
dams in connection with the New Water Supply
Scheme for Greater New York (Fig. 4). Its length
is 4,650 feet, height 220 feet, thickness at base
190 feet, and at top 23 feet. The width of the storage
reservoir, which it retains, varies from 1 to 3 miles,
and the maximum depth is 190 feet ; the depth of the
reservoir averages 50 feet. For the construction of
this dam seven villages were submerged, 32 cemeteries
had to be removed, and 2,800 bodies had to be rein-
terred. Eleven miles of railroad had to be relocated,
64 miles of highways discontinued, and 40 miles of
new highways constructed.
Three million cubic yards of earth and rock had
to be excavated, and over 8 million cubic yards of
embankment to be placed, while the quantity of
CONSTRUCTION OF DAMS. 7
masonry to be placed represented approximately
1 million cubic yards.
3,000 men were employed in the construction of
this dam.
QUESTION 3. (a) What forces operate on a masonry
dam ? (b) How may a dam fail ? (c) How would you
proceed to design a high dam ?
Fig. 4. Olive Bridge Dam, U.S.A.
Answer. (a) Reservoir dams are subject to two
main pressures a vertical pressure due to the weight
of the dam, with its resultant passing through the
centre of gravity of the structure, and a horizontal
pressure, due to the water in the reservoir ; both can
8 CONSTRUCTION OF DAMS.
be calculated. Whe the reservoir is empty, the
only pressure on the dam is that due to its own weight.
In addition to these two main pressures, ice pressure
may occur by the surface of the water becoming
frozen and upward water pressure may occur at the
base of the dam.
(b) There are four ways in which a dam may fail,
they are as follows :
(1) The structure may overturn about the edge
of any joint, due to the resultant passing beyond
the limits of stability.
(2) It may fail by the crushing of the masonry
or foundation because of excessive pressure.
(3) By the sliding or stearing on the foundation
or at any joint owing to the horizontal thrust being
greater than the structure can withstand.
(4) By tension occurring at any joint and causing
rupture at that joint.
(c) In designing a high masonry dam, we take a
trial section, and divide this up into smaller sections,
as shown in Fig. 5. We then proceed to find out
whether the top section of the dam " No. 1 " is suffi-
ciently strong to act as a low dam, holding up the
depth of water shown. We calculate the weight of
this portion of the dam, taking A T = weight in Ibs.
of a cubic foot of masonry, and the water pressure,
and ascertain whether the resultant passes well within
the middle third of the wall ; if it does not do so,
we must increase the width of the base so that R
CONSTRUCTION OF DAMS.
9
will come within the middle third of it. Having done
this, we take Sections 1 and 2, and assume that
these two sections combined form the dam. The
centre of gravity of the two sections must be ascer-
tained, the weight of the structure and the water
pressure must be calculated, the centre of pressure
TT
acting at a point -^ above base, where H = depth of
Water Level
Fig. 5.
water or head. We can in this way divide the dam
up into as many sections as we choose, and ascertain
the strength of each section.
We proceed in the same way with Sections " Nos.
3 and 4," except that we now have, in addition to
the water pressure due to a head of \ (see Fig. 5),
10 CONSTRUCTION OF DAMS.
a mud pressure of h. 2 , and, whereas r = 62'5 Ibs. per
cubic foot in the case of water, with mud r 1 = 80 to
90 Ibs. per cubic foot, say 85 Ibs.
We must also calculate the pressure on the back
of the dam of the earth backfill, or mud, E T , the dam
for this purpose may be treated as a battered-face
retaining wall. While we should know what this
back-pressure is, in designing the dam it is wise to
make no allowance for it.
QUESTION 4. A reservoir wall has been built too
light in section, and it is proposed as a temporary
measure to strengthen it by putting in a tie-rod.
What is the best position for this tie-rod ? And why ?
The reservoir is rectangular in plan.
Answer. Fig. 6. Let the sketch A B C D illus-
trate the reservoir wall, and H the maximum depth
of water. When a rigid plane is pressed upon by
water, there is one point in that plane at which the
resultant of all the pressures acts ; this point is called
the " centre of pressure," so that if a force is applied
at the " centre of pressure " which is equal to the
resultant P, then all the pressures against the wall
will be counterbalanced, and the structure will be
in equilibrium. The position of the " centre of pres-
sure " in a rectangular figure immersed in water is
at a point | H from the base, measured up the
centre line F E, so that it follows that when a tie-rod
is to be put in extending across the tank from wall
CONSTRUCTION OF DAMS.
11
to wall, its position should be where the " centre
of pressure " occurs ; this is shown in sketch as P P x .
QUESTION 5. A reservoir dam is 12 feet in height,
9 feet wide at the base, and triangular in shape, the
water face being vertical ; the weight of the masonry
is 125 Ibs. per cubic foot. When the reservoir is filled
Fig. 6.
to the upper edge of the dam, find the point at which
the resultant line of pressure intersects the base.
Answer. The dam referred to is shown in Fig. 7,
and also the point at which the resultant cuts the base.
This resultant is arrived at as follows : The total
water pressure on the dam is represented by the area
of the triangle A C D, and the resultant pressure
passes through the centre of gravity of this triangle,
CONSTRUCTION OF DAMS.
CONSTRUCTION OF DAMS. 13
and acts at P, so that if we consider a 1-foot length
of the wall
r = the weight per cubic foot of water
= 62-5 Ibs., or 0'557 cwt.
b = a 1 -foot strip of wall,
the volume of the prism will be
A C x C D AC 2 H 2
~ x 1 =
P =
2 2
r&H 2
2
0-557 x 1 x 12 2
2
= 0-557 x 72 = 40-1 cwts.
The weight of the wall is to be taken as 125 Ibs.
per cubic foot.
The cubic contents of one foot of wall being
ACxCB 12 x 9 ,
x 1 = ^ x 1 = 54 cubic leet.
** 2t 2i
Weight of dam 54 x 125 = 6,750 Ibs., or 60-26 cwts.
The resultant R cuts the base within the middle third
of the dam namely, at a point 3 feet 4 inches from
the outer edge of the dam B.
QUESTION 6. How would you ascertain the water
pressure on the face of an embankment ? Illustrate
your answer by a sketch.
Answer. The water pressure on E D, the face of
the embankment (see Fig. 8), for each foot of the
14
CONSTRUCTION OF DAMS.
structure, is represented by the area of the triangle
EDF x 1 foot. This force P will act through the
Fig. 8.
centre of gravity of the triangle at a point Pj. D F
= H. As the area of a triangle is equal to its base
Fig. 9.
multiplied by half its height, and the weight of water
is taken as 62*5 Ibs. per cubic foot, then, if the measure-
CONSTRUCTION OF DAMS. 15
merits are taken in feet, the pressure on the embank-
ment will be
Ej_xDF x 62 . 5 = ED x DF x 31 . 2 51bs.
The resisting weight will be the sectional area of the
embankment, multiplied by its weight per cubic foot.
QUESTION 7. What are the suggestions made by
Molesworth relative to the thickness of high and low
masonry dams ?
Answer. Moles worth's general rule regarding the
thickness of high masonry dams is as follows :
High Masonry Dams (see Fig. 9).
Let H = height of dam in feet.
x = any depth below surface of water in feet.
y = offset from vertical line to outer face of
dam at any depth x in feet.
z = offset from vertical line to inner face in
feet.
b = width of dam at top in feet.
a = width of dam at J H from top in feet.
P = limit of pressure allowed on the masonry
in tons per square foot, say, 9 tons, as
in the case of the La Terrasse dam.
Then _ ...
P + ('03 x)
-09 x
P
b = 0-4 a.
16 CONSTRUCTION OF DAMS.
If y as given by the formula be less than 0*6 x, it must
be increased to 0*6 x.
Low Masonry Dams. Molesworth also gives a
useful general rule for use in the designing of low
masonry dams, and one that it is possible to remember.
It is as follows :
Minimum Thickness.
Let T = minimum thickness of dam at any depth
" d " below the surface of the water.
g --= specific gravity of the masonry.
= for light masonry, 130 Ibs. per square foot
= 2-08.
= for ordinary masonry, 140 Ibs. per square
foot = 2-24.
= for heavy masonry, 150 Ibs. per square
foot = 2-40.
d --= depth below surface of water.
Then T = 1-5 -4=-
v g
Another general guide as to the thickness of a
low masonry dam is as follows :
Width at bottom = height x 0*7.
Width at middle = height x 0'5.
Width at top = height x 0'3.
This is illustrated in Fig. 10.
QUESTION 8. Sketch and describe the construc-
tion of an earthen embankment. Set out in detail
how you would proceed to build the puddle wall.
CONSTRUCTION OF DAMS.
17
Answer. The embankment is illustrated in Fig.
11 ; the method of constructing this is as follows :-
A very careful selection of the site having been made,
Fig. 10. Molesworth's Suggestion.
Top Water Line
[Minimum width
top 6 n
Thickness here fa/n.-
jt/>. depth oF Water.
B
Fig. 11.
A. B. Must go do wn
to Impervious Stratum.
after trial shafts and boreholes have been sunk, the
position for the puddle wall should next be fixed;
2
18 CONSTRUCTION OF DAMS.
this is usually about the middle of the embankment.
It must be carried down to an impervious strata,
compact clay being an ideal foundation for the dam,
and as to its dimensions, it should not be less in thick-
ness at the ground level than one-fifth the depth of
water to be impounded, and should be a thickness
at the top of 6 feet or more. The puddle wall should
be carried up above the highest water level, and before
its construction is commenced the trial shafts should
be plugged with puddled clay. The height that the
dam is required to be will decide its length. No part
of a dam requires more care in constructing than
the puddle wall. The location of this, and its dimen-
sions and height having been fixed, the puddle trench
is excavated. It is usual to taper this, and to batter
the faces of the wall above, as shown in the sketch,
the reason for this tapering being that the clay below
original ground level becomes more compressed than
in the upper part of the puddle wall, and owing to
the narrowing of the wall at the extreme bottom the
clay becomes even more compact. Making the wall
of greater thickness at ground level than at the top
increases the weight on the tapered portion below
ground level.
Should any streams be met with when excavating
the puddle trench, these must be carried by pipes
to the down-stream toe of the embankment.
In longitudinal section the puddle wall should be
constructed in the manner shown in Fig. 12, the clay
CONSTRUCTION OF DAMS.
19
being cut out in steps, and a bye-wash put in near
the top of the embankment.
The clay used should be exposed for some time
after being cut in pieces, and must then be ground
in a pug-mill, from whence it is taken to the trench,
put in in layers not exceeding 6 inches in thickness.
It is worked into a plastic mass by being trodden on
repeatedly by the workmen, and it is cut up by the
men, who use narrow spades for the purpose. The
surface should be kept moist by the addition of water,
too much of which is undesirable. Should the puddle
Max Water Level
Fig. 12.
trench contain water which percolates in from the
sides, this must be pumped out.
When the puddle wall is above ground level, it
must be supported by tipping selected filling in 6-inch
or 9-inch layers on both sides of it ; this filling may be
quarry spoil, or clay, or other selected material, and
should be so placed that its weight will assist in holding
up the wall (see Fig. 13). The filling should be well
watered, and rolled with a heavy roller ; sometimes
a steam roller is used. Before this filling is placed,
20 CONSTRUCTION OF DAMS.
the soil on the original ground for a depth of, say,
8 or 9 inches should be removed ; this will be used
again later to cover the outer slope of the embankment.
This " selected " filling having thus been placed, the
remainder of the filling is then put on in layers and
well rolled.
A batter of 3 to 1 on the water face and 2 or 2|
to 1 on the outer slope would be satisfactory. The
inner slope should be stone-pitched, or paved with
concrete slabs, and a rubble masonry or concrete
Fig. 13.
(6 to 1) toe is advisable. A road is sometimes con-
structed on top of the bank, and the width of the
bank at this point may be anything from 7 to 20 feet ;
it should not generally exceed 16 feet. The height
above the surface of water of the top of the embank-
ment should not be less than, say, 4 feet.
QUESTION 9. Say what you consider to be an
ideal site for a large storage reservoir, and why ?
Illustrate your answer by a sketch.
CONSTRUCTION OF DAMS.
21
Answer. The selection of the site for an impounding
reservoir is a matter of the greatest importance. One
of the best sites it is possible to choose is one in which
there is an impervious stratum, such as compact clay
or close-grained rock free from fissures. A site where
there is no possible likelihood of the water becoming
contaminated, and one where there is a large water-
shed, and where there is a wide and flat valley draining
into a stream, the valley extending for a considerable
Stream
'atural Lake
Figs. 14 and 15. Ideal Site for Storage Reservoir.
distance, and, at its lowest level, ending in a narrow
and deep gorge, where there is a natural lake, and
where a dam can be constructed at a fairly low cost,
and the level of the lake raised to any required height,
would be very suitable. These conditions are shown in
Figs. 14 and 15. It is assumed that the town to be
supplied with water lies at a much lower level than
the site for the storage reservoir shown in the illus-
tration.
22 CONSTRUCTION OF DAMS.
QUESTION 10. What is the amount of storage
necessary to amply provide for a period of excessively
dry weather ? Describe two notable examples of the
use of lakes as storage reservoirs in connection with
the water supply of towns.
Answer. 120 to 250 days' supply should be allowed
for, according to the rainfall of the district ; the first
figure may be taken in a wet district, and the second
if the district is dry.
Two notable examples of the use of existing lakes
as storage reservoirs are Loch Katrine and Thirlmere.
In both instances the water level in the lake was
raised by building a dam across the valley. Loch
Katrine has an area of 3,119 acres, and the water
level was raised 4 feet, and assuming a shrinkage of
3 feet below its original level to allow for an exces-
sively dry period, then the minimum quantity of
water stored is 5,687 million gallons. Glasgow is
thus provided with 50 million gallons per day of
water, and works are now in progress which, when
completed, will double this amount.
This huge storage reservoir is 34 miles from
Glasgow.
Thirlmere supplies Manchester, although it is situ-
ated 100 miles from that city. The service reservoir
is 4 miles outside the city, and there is a fall between
the impounding and service reservoirs of 2 feet per
mile.
CONSTRUCTION OF DAMS.
23
The lake was raised by the construction of a con-
crete dam faced with masonry. The structure is
built on the solid rock, and is carried up to a height
of 57 feet above the former level of the lake.
QUESTION 11. (a) Sketch and describe an earthen
embankment, where, instead of putting in a puddle
wall, a rubble masonry core has been constructed.
(b) What objection is there to this form of construction ?
Fig. 16.
Answer. (a) There are several examples in America
of earthen dams constructed on this principle, but
very few in this country. Fig. 16 illustrates an
American example. This dam was constructed briefly
as follows : The centre line of the dam having been
fixed, a trench was excavated down to the solid rock,
and much of the original ground was also excavated,
as shown in Fig. 16. The rubble masonry wall was
then built upon this rock foundation ; there was
plenty of stone in the district for this wall. This
24 CONSTRUCTION OF DAMS.
core wall was 18 feet in thickness at the base, and
12 feet at the top, and was carried up above maximum
water level. As the building of the wall proceeded,
the filling, in 6-inch layers, was added ; this nearly
kept pace with the wall, and was well watered and
rolled. The dam is 30 feet wide at the top, and the
slopes are steeper than is usual namely, 2 to 1.
The water-face is pitched, and the height of the dam
above original ground level is 120 feet, the depth
of water retained being 95 feet.
(b) Rubble walls have the disadvantage often of
leaking badly, whereas puddle walls do not err in this
respect. They are usually more expensive than puddle
walls. Their use, however, can be recommended
where clay is not to be found in the district where
the dam is to be constructed, but good stone is plenti-
ful, and a rock foundation is available. Under these
circumstances, however, a concrete wall is preferable,
although this is more costly than rubble.
QUESTION 12. What circumstances would guide
you in your decision as to whether a dam should be
of masonry or whether an earthen embankment should
be constructed ?
Answer. Where clay and filling in a district is
scarce (especially the former), but there is a good
rock foundation for the dam, and plenty of available
stone, and the structure is to be 80 feet or upwards
CONSTRUCTION OF DAMS. 25
in height, a masonry dam should be constructed.
If the dam is to be less than 80 feet high, and is to
be built on a clay foundation, an earthen em-
bankment will be found to be cheaper, and quite
as useful.
QUESTION 13. How would you find (a) the centre
of gravity of a triangle, (6) the centre of gravity of
a parallelogram, and (c) co-ordinates of the centre
of gravity in a figure ?
Answer. (a) The centre of gravity in a triangle
is found by bisecting the base B C at D (see Fig. 17),
joining A D, and finding a point E which is one-third
A D. In an equilateral triangle the centre of gravity
is its centre.
(6) The centre of gravity of a parallelogram lies
at the intersection of its diagonals ; this does not
apply to other four-sided figures ; for instance, in
26
/r.
CONSTRUCTION OF DAMS.
Fig. J^ it is clear that the intersection of the
Fig. 18.
diagonals is nowhere near the centre of gravity of
the figure.
Fig. 19.
(c) Co-ordinates of the centre of gravity in a figure
(see Fig. 10) may be found as follows :
/&
X
B-
C /2 A + B
A - B
CONSTRUCTION OF DAMS.
27
QUESTION 14. Sketch and describe a low re-
inforced-concrete dam. How would the strength of
this be calculated ?
Answer. Fig. 20 illustrates such a dam. It con-
sists of a reinforced-coiicrete slab 6 inches in thickness,
A
Water Level
Fig. 20.
supported by R.C. beams, and plain concrete but-
tresses, say, 14 inches in thickness, spaced at 6-foot
centres ; the concrete throughout this structure is
in the proportions of 1 : 2 : 4 namely, 1 of Portland
cement, 2 of sand, and 4 of broken stone, suitable for
28 CONSTRUCTION OF DAMS.
passing through a f-inch ring for the reinforced work,
and through a 1-inch ring for the buttresses. A toe
must be constructed into the rock as shown, to prevent
water getting under the structure. The reinforcement
throughout will consist of steel rods, varying in size
according to the depth of water. The working stresses
of the materials used will be as follows :
Lbs. per Sq. Inch.
Concrete in compression, . 600
Adhesion of concrete to metal, 100
Concrete in shear in beams, 60
Steel in tension, . . 16,000
(Assuming that the steel has a tenacity of not less
than 60,000 Ibs. per square inch.)
The dam is built on the solid rock, and its height
is 16 feet above the rock surface.
In arriving at the strength of this structure it
must be noted that all the buttresses have to do is
to resist a compressive stress ; there is no need for
these to be reinforced. Three things must be known
before we can design these buttresses :
(1) The amount of the resultant thrust due to the
water pressure, the centre of pressure being at P.
The water pressure will vary from zero at A to a maxi-
mum at C.
(2) The weight of the beams and slab resting on
these buttresses.
(3) The weight of the buttresses themselves.
CONSTRUCTION OF DAMS. 29
As to the beams and slab, these can easily be
calculated, for they will be treated as ordinary floor
W I
beams and slabs, except that instead of the B M = -r-,
o
as in the case of a load equally distributed, and the
W
shearing force = -^, the loads on the beams and slab
Zt
will vary in proportion to the depth of water. Their
own weight must also be taken into account, and
the weight of the reinforcement. It is usual to allow
for the weight of concrete -f the weight of reinforce-
ment to weigh 150 Ibs. per cubic foot.
QUESTION 15. In the practical designing of a
masonry dam, the shape arrived at theoretically is
often improved ; give an illustration of this, and
show by a sketch what you mean.
Answer. An instance of this is shown in Fig. 21,
which represents the outline of a triangular-shaped
dam. Theoretically the portion of the dam which
is not hatched represents a structure which is quite
capable of holding up the water H in the reservoir,
but the engineer by using a little more concrete im-
proves on the shape of this dam by the addition of
the portions hatched. The resultant thrust, it will
be observed, passes through the middle third
of the base, which it did before the base was
widened.
30
CONSTRUCTION OF DAMS.
Fig. 21.
Fig. 22.
CONSTRUCTION OF DAMS. 31
QUESTION 16. Give a formula for ascertaining the
total pressure on a dam where the water face is
battered.
Answer. The usual formula is
P = -- sec >.
A