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of the time interval (elapsing between the occurrence of maximum and
minimum temperatures) as regards lessening the formation of tem-
perature cracks.

Mr. Edward Weoiann,* M. Am. Soc. C. E. — Although the multiple-arch

dam has only lately come into prominence, this type was adopted for
the Meer Alimi Dam, in India, more than a century ago. This dam,

* New York City.



Wegmann



DISCUSSION ON MULTIPLE-ARCH DAMS 891

which is about i mile long, is built in plan on a curve, convex up stream, Mr.
and consists of twenty-one smaller arches, having spans of from 70 ^^^'^*""
to 147 ft. The dam is 39 ft. high and has vertical faces on both sides,
except near its crest, where the down-stream face is stepped up stream,
in order to reduce the top width.

The Belubula Dam, in New South Wales, was built about 1898.
It is 431 ft. long, and has a maximum height of about 60 ft. The
lower part consists of a mass of concrete from 1 to 23 ft. deep. The
upper part is of brickwork, and has a height of 36 ft. 9 in. In the
central part of this brickwork there are six buttresses, 28 ft. from
center to center. Between these buttresses there are five vertical,
elliptical arches, inclined down stream at an angle of 60 degrees. The
spandrels between the arches are filled with concrete which covers
the crown of the arches to a depth of 12 in., and joins the side-walls
of the dam, which are of concrete. As far as the speaker knows, these
two multiple-arch dams are the only ones of this type which were
built until recent years.

In 1897, Henry Goldmark, M. Am. Soc. O. E., proposed to build
a multiple-arch dam of concrete at Ogden, Utah.* This dam was to
be 369 ft. long and 105 ft. high above the foundation at the center of
the valley. According to Mr. Goldmark's plan, the dam was to consist
of a number of piers, 16 ft. wide and 32 ft. apart in the clear. Alter-
nate bids obtained for building the dam in the manner described, or,
as an ordinary "gravity dam", showed a saving of from 12 to 15%
in favor of the former plan. Mr. Goldmark proposed to make the
thin vertical arches of the multiple-arch dam water-tight by placing
a lining of sheet steel on their up-stream side.

About 1900, the speaker was retained to design a multiple-arch
dam, 160 ft. high, which was to be built in Virginia, near Washington,
D. C. According to the preliminary estimates, this type was found
to be about 15% cheaper than a gravity section. Water-tightness was
to be insured by coating the up-stream side of the dam with asphalt.
Owing to the practical difficulties which might have been involved
in building a multiple-arch dam 160 ft. high — a type which, at that
time, had only been used for two low dams — the speaker advised his
clients to construct a gravity dam. As the promoters of the project
could not secure the required financial means, the dam was not built
at that time.

George L. Dillman, M. Am. Soc. C. E., has demonstrated, mathe-
matically, the saving that can be effected by building a dam of the
multiple-arch type.f He proposed to give the arches between the
piers a parabolic section, so as to avoid all re-entrant angles.

* Transactions, Am. Soc. C. E., VoL XXXVIII, pp. 291, 302 (December, 1897).
f Transactions, Am. Soc. C. E., VoL XLIX, p. 94 (December, 1902).



892 DISCUSSION ON MULTIPLE-ARCH DAMS

Mr. It is only of late years that a number of multiple-arch dams have

Wegmann. ^^^^ ^^.^^^

In 1908 John S. Eastwood, M. Am. Soc. C. E., of Eresno, Cal.,
built the Hume Lake Dam, in the Sierra Nevada Mountains, as a
multiple-arch dam of concrete. The dam is 677 ft. long and about
60 ft. high, and consists of twelve vertical circular arches which are
supported by thirteen buttresses. At each end of the dam, a wall,
like a core-wall, is built into the side of the valley. In 1910 and
1911, Mr, Eastwood built a similar dam about 200 ft. down stream
from the Bear Yalley Dam, in California. It has a length of 350 ft.
and a maximum height of 91.5 ft. above the foundation. In this case,
bids were obtained for building a rock-fill dam having a reinforced-
concrete curtain, and, also, for an arched gravity dam of concrete. The
multiple-arch dam proposed by Mr. Eastwood was found to be the
cheapest and was adopted.

A few more muitiple-arch dams have been built. Two of these —
the Gem Lake Dam, 700 ft. long with a maximum height of 112 ft.
above the foundation, and the Agnew Lake Dam, 30 ft. high and
280 ft. long, were designed by the author. Mr. Jorgensen, however,
has not only given an interesting account of how these dams were
constructed, but, also, a very complete analysis of the stresses in
multiple-arch dams. The speaker compliments him on his excellent
paper which will be of value to all engineers who have to design
such dams.

Mr. Walter J. Douglas,* M. Am. Soc. C. E. — About 7 years ago the

Douglas, speaker's firm designed and built, in the Adirondacks, the Garoga Dam,
a nmltiple-arch structure having a 200-ft. spillway of the gravity
type. The concrete arches are 60 ft. high, and their thickness at the
top is 2 ft., increasing to 4 ft. at the bottom. There was no difficulty in
taking care of the thrust, the foundation being of good slate, strong
enough to take the concentrated load transmitted by the buttresses.
The economy of the multiple arch was found to be small when its cost
was compared with that of the gravity section used for the spillway.
The speaker thinks that in most cases where the cost of skilled labor
is high and material is cheap, the ordinary gravity type is about as
cheap as the multiple arch. The difficulties of constructing thin arches,
such as those shown in the paper, often more than offset the saving in
material.

The speaker's firm has made a great many designs of dams since
the Garoga Dam was built, but has only constructed one other of the
multiple-arch type. This was the Peck's Lake Dam, built near the
same locality as the Garoga Dam. The height of the arches, above
the surface of the ground, varies from 25 to 45 ft. As far as the

• New York City.



DISCUSSION ON MULTIPLE-AKCH DAMS 893

speaker knows, this is the only multiple-arch dam which has not been Mr.
built on a rock foimdation. The foundations were of slightly indurated ^°"^^^«-
sand and gravel, but not hardpan. The pressure is distributed by rein-
forced concrete slabs at the toe of the buttresses. As a security against
horizontal movements, the arches penetrate about 10 ft. into the
ground, where they are loaded uniformly by the reaction of the soil,
and, therefore, they are catenary in tension. This part of the arches
is heavily reinforced with steel rods, which are well bonded into the
buttresses. This arrangement worked out very satisfactorily.

The dams described by the author are very intei'esting, but, the
speaker believes, they are not conservatively designed. All engineers
who are interested in the development of reinforced concrete, as applied
to structures other than buildings and bridges, know that every once
in a while something "gets by." Tanks have been built in recent
years, which are 4 in. thick at the top, 8 in. at the bottom, and more
than 100 ft. high, but the speaker thinks that is no justification for
building similar ones. He believes that both the arches and the but-
tresses of the dams shown in the paper are unnecessarily thin.

The speaker cannot see how the triangular girder, mentioned on
page 866, will take up the unbalanced thrust of the arches if one of
them should fail, and would ask for more detailed information on
this point.

The most serious objection which can be raised against multiple-
arch dams is the fact that failure of one unit will destroy the stability
of the whole structure. The speaker believes that an occasional abut-
ment buttress, similar in purpose to the abutment piers of arch bridges,
consisting of a series of spans should be introduced in the design of
multiple-arch dams having a large number of arches.

On page 865, the author says:

"The total vertical load on the section shown in Fig. 6 is seen to
be 6 332 tons, and the horizontal water pressure, 5 062 tons, both
on a 40-ft. span. If the coefficient of friction is taken at 0.75, it
is seen that the actual shear along the base amounts to only
5 062 — 6 332 X O-'^'S = 313 tons. There is considerable steel in
the section to help take up this shear, and, therefore, it was not deemed
necessary to eliminate the shear entirely."

This statement, the speaker believes, is incorrect. The shearing
resistance of an elastic solid is an elastic attribute of the material.
The deformation caused by shearing forces, if within proper limits,
will disappear after the actuating forces have been discontinued. The
frictional resistance is of an entirely different nature, and can act
only after the section has failed under shear. The resisting friction
can be developed only by minute, but measurable, movements of ad-
jacent planes. This movement is progressive, that is, the dislocation
caused by the forces resisted by friction will not disappear when the



89.1: DISCUSSION ON" MULTIPLE-AECH DAMS

Mr. structure is relieved of load, and a second application will necessitate
oug as. ^ further movement. In designing one should rely on shear or on fric-
tion, and not on both.

As regards the determination of the direct stresses, the speaker
would state that the stress computed by the author on page 866,
acting on planes at right angles to the resultant, is not necessarily the
maximum compressive stress, and that methods are now available for
computing the principal stresses in a buttress quite accurately.*

The speaker has made the foregoing criticism because, as the
author correctly states on page 851, "the stresses and dimensions can
be calculated with great accuracy", in multiple-arch dams, although
such calculations are almost impossible in earth or rock-fill dams. The
determination of the stresses is subject to many uncertainties, even
in gravity dams. The design of this latter type, however, is being
developed along scientific lines with very satisfactory progress, and the
gravity dam has the advantage of a great number of precedents over
the multiple-arch dam.

In the case of solid impervious rock foundation, the speaker de-
cidedly prefers the gravity dam, and doubts whether material saving,
if any, can be obtained by the use of the multiple arch, even if this
latter would have a considerably smaller volume. The unit price of
masonry for the multiple-arch dam is out of all proportion to that of
the gravity dam, as illustrated by the price of $22 per cu. yd., given
by the author.

If the foundation is fissured rock or other good but pervious
material, the multiple-arch dam, generally, should be the more eco-
nomical type, because the voliime of the gravity dam must be increased,
in order to meet the uplifting action of the water.
Mr. Edwin Duryea,! M. Am. Soc. C. E. — The speaker's home and most

Duryea. ^£ -^[q professional practice are in California, and he is familiar with
the general climatic and hydrographic conditions throughout the State
and in the Sierra Nevada Mountains, though not with those of Mono
County, in which are built the two dams forming the subject of this
paper. However, hydrographic conditions are known to be quite uni-
form throughout the high Sierras of California, and presumably in
Mono County they do not differ materially from those of the parts with
which the speaker is familiar.

A previous speaker has expressed doubts as to the adequacy of the
spillway arrangements of these two dams to pass safely such intense
floods as might be expected to occur at long intervals from such a small
drainage area as 22J sq. miles. In most parts of the United States,
such apprehensions would be justified, but not in the high Sierras of
California.

* See the papers of Levy, Unwin, Hill, Ottley, and Brightmore.
t San Francisco, Cal.



DISCUSSION ON MULTIPLE-AKCH DAMS 895

Throughout that State practically all the year's precipitation occurs Mr.
during the winter, from about October to about March, inclusive, with "'"^^*-
hardly any (and none such as will cause floods) during the warmer
months of April to September. Hence, in the high Sierras, the year's
precipitation is practically all in the form of snow, which accumulates
throughout the winter to depths of even 20 ft., or more, settles and
packs until melted gradually by the increasing temperatures of the
spring and summer, and passes off as stream flow in the form of slowly
rising floods, which usually begin in April, culminate in June, and
terminate about the middle of July. It is this condition of winter
rains in the valleys, which soak the ground and start the growth of the
crops, in conjunction with the snow stored in the high Sierras, which
by its gradual melting furnishes water for irrigation throughout the
growing season of April to September, that causes the very great suc-
cess of irrigated agriculture in the Great Valley of California.

On the drainage area above these two dams (at elevations of from
9 000 to 12 000 ft. above sea level), and even at much lower elevations,
this condition of stream flow from the slow melting of the snow must
be marked and invariable; and on that area there can be no direct
connection between excessive storm intensities and excessive flood
intensities.

The speaker has examined many dams in the high Sierras of Cali-
fornia and, at first, was strongly impressed by the apparently very
inadequate provisions for spillway capacity and "free-board" of those
dams, as judged by necessities elsewhere. Soon, however, he realized
that provisions which would have been very inadequate and unsafe in
most other regions are quite safe in the high Sierras.

A previous speaker has mentioned the small number of arch dams
as yet built in the world, placing the number at only about 15. The
speaker has built an arch dam which may not be included in that num-
ber. It is the Goodwin Dam, on the Stanislaus Kiver, not far from
Stockton, Cal., and serves to raise and divert the waters of that river
for the irrigation of the South San Joaquin and Oakdale Irrigation
Districts, which together comprise about 144 000 acres. The dam con-
sists of two arches with a buttress between them; there is also a small
buttress at the south end of the dam to replace a rock abutment which
was badly shattered by the blasting of a canal. The south arch is
299.4 ft. in crest length, with a maximum height of 78 ft.; the north
arch is 159.8 ft. in crest length, with a maximum height of 42 ft. The
buttress between them is on a ridge of rock (slate) near the middle of
the river, and has a maximum height of masonry of only 22 ft.

The two arches have radii (of their vertical up-stream sides) of
135 ft., and are proportioned for "pure arch action" by the ordinary
arch formula and for maximum arch stresses of 300 lb. per sq. in.
(43 200 lb., or 21.6 tons per sq. ft.). Except that the minimum arch



896 DISCUSSION ON MULTIPLE-ARCH DAMS

Mr. thickness (in the upper parts. of the arches) was fixed arbitrarily at

Durvcft

8 ft., the arches were thickened 4 ft. arbitrarily at the rock surface
(this thickening decreasing to zero 8 ft. above), as a safeguard against
possible erosion by the very turbulent waters of the pool just below the
dam. The crest was made of a somewhat unusual shape to permit
larger flows over it without reducing its strength, and the arches were
reinforced against temperature stresses by steel bars, near their crests
and for 6 ft. below, near their up-stream and down-stream sides. The
thickness of the south arch, 59.8 ft. below its crest (just above the
thickened base), is 12.2 ft.; that of the north arch, at the corresponding
point, 24.5 ft. below its crest, is 8.0 ft.

The arches are proportioned (aside from the exceptions noted) for
300 lb. per sq. in. and for the maximum arch thrusts caused by floods
up to 25 ft. in depth over the crest, making allowance, however, for
the relief of the arch pressure by the variable "back-water" against
the down-stream sides of the arches. Two measured floods are known
(in 1907 and 1911) which would have caused depths on the crest of
the dam (had it then been built) of about 15 ft. The dam was com-
pleted in 1912, and since then several floods of about 6 ft. in depth
have passed over it. The drainage area above the Goodwin Dam com-
prises about 928 sq. miles of mixed low and high Sierras, from an ele-
vation of 350 ft. above sea level (the crest of the dam) to an extreme
height of more than 10 000 ft.

The first requirement in any dam should be certain safety, but the
next should be economy; and the usual reason for designing an "arch"
dam is that thus considerable saving below the cost of a "gravity" dam
often may be effected, without (at least in the judgment of the designer)
any sacrifice in safety. The Goodwin Dam is a good example of such
a saving in cost. Six other dam sites were surveyed, three up stream
and three down stream from the Goodwin site. Estimates of cost were
made for "gravity" dams on all seven sites, and for three other plans
of arch dams on the Goodwin site. By the choice of the Goodwin site
and the two-span arch dam adopted and built, the saving effected was
more than half that of the most obvious procedure — the raising of an
existing gravity dam If miles up stream, already the property of the
two Irrigation Districts, the enlarging of the intervening If miles of
their existing canal on the north side of the river, and the building of
the same length of new canal on the south side.

In 1903, the speaker designed two other arch dams for California
streams, neither of which, however, has been built.* The larger one
was to have been 138 ft. in maximum height, and made up of eight
semicircular arches, supported on intervening buttresses 50 ft. from
center to center. The backs or up-stream sides of the arches were to

* Transactions, Am. Soc. C. B., Vol. LIII (December, 1904), pp. 172-175.



DISCUSSION ON MULTIPLE-ARCH DAMS 897

have been vertical, with radii of 26.5 ft. The smaller dam was to have Mr.
been 30 ft. in maximum height, with eight spans of 19^ ft. from center ^"''y^*-
to center of buttresses. The "deck" or up-stream side of the dam was
to have been a plane with an inclination of 0.64 vertical to 1.00 hori-
zontal, in order to distribute the foundation pressures more evenly over
a rather weak rock foundation. The crown thickness of the deck was
to have been 2 ft., and the radii of the inclined semicircular arches
forming the under side of the deck were to have been 8^^ ft.

Mention is made in the paper, and by a previous speaker, of the
freedom of multiple-arch dams (or other thin dams) from "uplift"
forces. Such forces are quite certain to exist in greater or less degree
under all thick masonry dams. The speaker recently had an opportunity
to measvire the uplift forces existing under parts of the base of a high
masonry dam (the La Boquilla Dam, in the State of Chihuahua,
Mexico, of 244 ft. maximum height). The measurements extended over
a period of 22 months, and for depths of water behind the dam (above
the foundation level) of from 140.3 to 213.6 ft. ; and comprised measure-
ments in thirty-nine holes, aggregating sixty-three or more hole
measurements of the uplift. He hopes soon to present these measure-
ments in full to the Society; and will only say now that, although
the foundation of that dam, in its natural condition, was a very good
limestone, with but few and minor defects (which were all repaired
with great care and cost by cement pressure grouting) , still the measure-
ments of the pressures show the existence of "uplifts'* which, in gen-
eral, lie on straight lines decreasing from (at the "heel" of the dam)
one-third of the depth of water in the reservoir above the foundation
plane, to zero at the "toe" of the dam. Incidentally, the dam had been
designed to withstand uplifts varying from two-thirds of the depth
of the water at the heel to zero at the toe.

Regarding the use and safety of arch dams, one general thought is
worthy of serious consideration : Several (only a small proportion,
however) "gravity" masonry dams have failed. It is true that these
failures were probably always from faults perceived afterward to be
due to recognized poor design or construction, and that they would not
have occurred had the design and the construction of the profiles and
the foundations been in accordance with recognized good practice.

On the other hand (even though most arch dams are much thinner
than gravity dams, and though there should be no reason to suppose
their profiles and foundations to have been in general designed and
constructed more carefully), the speaker does not recall, among the few
arch dams as yet constructed, even a single failure.

It is realized that such reasoning is not conclusive, but, neverthe-
less, it appears to the speaker at least probable that the "arch" dam
possesses greater reserves of strength and safety than the "gravity" dam.



898 DISCUSSION ON MULTIPLE-ARCH DAMS

Mr. L. H. NisHKiAN* Assoc. M. Am. Soc. C. E. (by letter). — The

author has rendered to the Engineering Profession a much needed
service by opening up for discussion the subject of multiple-arch dams.

There is no question that, in the future, dams of this type will pre-
vail over other types in many locations, and, therefore, a detailed dis-
cussion of methods of design and construction is timely and profitable.

At first glance the structural design of a multiple-arch dam seems
to be quite simple, requiring the design of a concrete arch under
definite forces, of a buttress to uphold the arch, and of a foundation to
hold the buttress in place.

On closer study, many problems arise. The upper and lower ends
of the arch barrel are difficult of even roughly approximate analysis,
and the designer has to depend largely on his judgment. The weight
of the arch between the buttresses is carried partly on the latter and
partly on the lower end of the arch. In designing the arch, the author
has considered its weight component normal to the buttresses as being
carried by arch action to the buttresses, and, presumably, the component
parallel to the buttresses as being carried by direct column action down
to the footings at the lower end of the arch barrel. In the design of
the buttress and foundation, however, it has been assumed that the
entire weight of the arch is acting, through its center of gravity, on
the buttress.

The writer agrees with Mr. Jorgensen in regard to the method of
designing the arch ring, but cannot agree with him in throwing the
entire weight of the arch on the buttresses. It appears to the writer
that only the weight component normal to the buttress should be con-
sidered as acting on it. These two assumptions are widely at variance,
and result in a large difference, both in the point of application and in
the line of action of the resultant force on the buttress.

The author finds an upper and a lower limit i'or the direct com-
pression stresses in the buttress. It will be found, however, that the
stress produced by the normal component of the arch thrust on the
buttress is equal to, or greater than, the maximum stress given
in the paper. In this case, the arch thrust, due to water pressure
at a depth of 80 ft., is approximately 80 X 62.5 X 23.08 = 115 000 lb.,
and the thrust, due to dead weight of arch ring, is approximately
150 X 3.7 X cos. 50° X 23.1 = 8 000 lb., or a total arch thrust of
123 000 lb. This will result in a force of 123 000 X 2 X sin.

119° 57'

— — — = 21H 000 lb. per lin. ft. on tlie buttress. The Imttress

is here 4.25 ft. thick; therefore, we have a stress of -t-zt- ^ = 348



San Francipco, Cal.



DISCUSSION ON MULTIPLE-AECH DAMS 899

lb. per sq. in. Although in no sense dangerous, this is in excess of Mr.
the stress of 317 lb. per sq. in., given by the author as the maximum
existing in the buttress. One must be careful in using average values
of stresses where the average is for a large area.

The author has made the section of the arch normal to the up-stream
edge of the buttress, circular. As is pointed out in the paper, the
pressures are not uniform on the arch ring, with the result that, near
the top, it is necessary to move the arch out 5 in. at certain points, in
order to make its center line coincide with the line of pressure. To
avoid this difficulty and maintain a constant shape from top to bottom,
it is only necessary to make a horizontal section of the arch circular in
shape. A normal section will now be an ellipse, and it will be found



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