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This experiment demonstrates that the loss of head due to the ver-
tical diaphragms is proportionally less in the rear than in the fore sheet-
piling, and that, in neither case, is this neutralization in agreement
with the so-termed "creep" theory. The author attributes the great
difference in the effectiveness of the two lines of sheet-piling to the
much greater depth of fore piling as well as to its location half way
down the base of the dam, the assumption being that the obstruction
of the deep curtain in the center of the base acts as a throttle valve
to the percolating subcurrent at a position where the latter is well
imder way, thus causing a sudden loss of head. This view the writer
deems to be correct, but applicable only to the quite abnormal con-
ditions present in the experimental model. The depths given to the
sheet-piling are far in excess of actual practice. That of the central
line reaches to 125 ft. below the base of the dam, that is, to half the
depth of the porous stratum; half the waterway is thus cut off, which
must cause congestion. It is quite possible that this throttle-valve
action may exercise a retroactive effect on the rear diaphragm, reducing
its efiiciency. However this may be, it is evident that the abnormal
conditions existing in the model render the results obtained from the
experiment of small practical value, and that the actual neutralizing
effect of vertical curtain-walls remains still to be decided by further
experiments made under normal conditions.

Mr. Colman, in the interesting discussion on his valuable paper
previously mentioned, states that, in his opinion, sheet-piling is of no
value in the reduction of head because it is not absolutely water-tight.
This view is also held by irrigation engineers in India. In that
country curtain- walls are made of oblong masonry under-sunk blocks,
the narrow spaces between which are closed as well as practicable with
concrete. Reliance, however, is not placed on these massive curtains
with regard to their capability in the neutralization of uplift. In
Egypt, cast-iron piles were used in the Assiut Barrage, and each joint
was provided with a hollow space which was filled with cement grout.



DISCUSSION ON DESIGNING AN EABTH DAM '37

It is believed, however, that the vertical length was omitted from Mr.
consideration, o-wing to the lack of reliable data regarding their '^
action. From these remarks, it will be evident that experimental data
of a positive and exhaustive nature regarding this important subject
would be a great boon to the Profession all over the world. Until such
data are obtainable, it is thought that the theory of "creep", which
even Philip a M. Parker,* M. Am. Soc. C. E., has termed "fascinating",
should hold good as a fairly accurate and safe guide in design.

Some new developments have recently been made by the writer and
published in a small work entitled, "Dams and Weirs", a copy of which
has been presented to the Library of the Society.

In this the term "piezometric line" is used for the stepped line
which forms the upper boiuidary of the area of uplift, thus distinguish-
ing it from the hydraulic gradient, which latter is the ratio, H : L, L
denoting the total length of travel, or creep, vertical as well as hori-
zontal. Whatever value is assigned to vertical obstruction, it is clear
that wherever it occurs a step down must result in the piezometric line
and, further, as will now be shown, the latter will not necessarily be
always parallel to the hydraulic gradient. Where there is no vertical
curtain and no part of the superstructure is porous, the hydraulic
gradient and piezometric lines will naturally coincide. A further de-
velopment consists in the introduction of a filter bed of porous mate-
rial, or the insertion of holes in the solid impervious floor or apron,
which have the effect of stopping the uplift behind it by allowing
the free exit of water. If solid material is prevented from passing
out with the escaping water, all deleterious piping action is nullified;
consequently, this porous length can be considered as effective as part
of the line of travel of the percolating undercurrent. Thus, the direc-
tion of the piezometric line will be still further divorced from the

TT

sloping line, -~, termed the hydraulic gradient. The introduction

of a filter bed in the fore apron of the Hindia Barrage on the Euphrates
was the first instance of this kind on a large scale. Another point of
importance which may well be mentioned is the formation of a rear
apron, impervious to water, behind a high dam, by the promotion of
silt deposit by the river itself. This process can be facilitated by con-
structing the dam in stages, thus allowing time for the gradual de-
posit during several freshets. Many dams owe their safety to this
complaisant action of natural forces, which otherwise, due to insuffi-
cient provision of enforced travel of the percolating undercurrent,
would have failed. One further matter remains to be mentioned
while there is opportunity for bringing it to notice: What is the
effect, if any, of the imposition of weight on a porous foundation,

* "The Control of Water."



28 DISCUSSION ON DESIGNING AN EARTH DAM

Mr. subject to a head of water, in preventing or delaying its disintegra-

'^ ■ tion by piping?

The writer has checked the estimation of the loss of head due

to vertical obstructions, according to the "creep" theory, and the

results show the author's statements to be erroneous.

In Fig. 8, the length of travel is: horizontal, 745 ft., vertical

(2 X 65 4- 2 X 85) = 300 ft. The total value of L, then, is 745 +

300 = 1045 ft. The hydraulic gradient will then be 1 in 10.45.

The neutralization of head effected in the rear diaphragm would then

2 X 65 2 X iS.5

be — —— — = 12.4 ft.; and that in the fore piliuo; will be '- =. 16.2

10.45 '■ ^ 10.45

ft., as compared with the actual results, 5 and 21 ft., respectively,
the discrepancy in the totals being only 2 ft. With regard to Fig. 9,
the vertical component is 2 X 125 = 250 ft.; adding this to the hori-
zontal, which is the same as before, that is, 745 ft., L = 995 ft., say,
1 000 ft., and the hydraulic gradient is 1 in 10. The loss of head

2 X 125

due to the vertical diaphrasrm will then be = 25 ft. In

^ ° 10

Fig. 11, the loss of head appears to be about 20 ft. If the piezometric

line, due to the theory of creep, were plotted over the experimental

one, the differences would be apparent to the eye. This places the

theory in a much better position than was previously apparent, and

also somewhat discounts the special pleading in its favor made under

a partial misapprehension of the facts. However, the experiment being

made under abnormal conditions, the results cannot be accepted as

convincing.

Mr. J. C. Oakes,* M. Am. Soc. C. E. (by letter). — The application of

the term "hardpan" to an uncemented material is unfortunate, as the
meaning of the word in engineering literature is limited to materials
hard to excavate, and more or less cemented by clay, carbonate of
lime, oxide of iron, or other binding material.

In the last paragraph of "General Conditions" the stratum of so-
called hardpan is referred to as "the impervious stratum." Later, in
the experiments to determine the hydraulic gradient of the com-
bined material, it is proved that this material is not impervious,
but that it is readily saturated; for the porosity of the combined
material is determined by that of the finer material, and, referring
to the experiment to determine the gradient of the combined material,
the author states:

"In the morning of the second day, fully 80% of the water was
still on the surface, and at the end of 47 hours both tubes were filled
with water, although the valve at the base had been closed for the
entire period."

* Major, Corps of Engrs., U. S. A., Philadelphia, Pa.



Oakes.



DISCUSSION ON DESIGNING AN EAETH DAM 39

It is apparent, therefore, that even though the valve at the bottom Mr.
remained closed, the water drove out the air and fully saturated the
material in the tank, as there existed no difference in head in the
two tubes at the end of the test period.

The author states that it was found impossible to determine the
exact hydraulic gradient of this combined materia], because in another
test "no water appeared in either of the tubes shortly after the valve
was opened." It is evident that a sufficient length of time was not
allowed to elapse, else the water would have appeared in the tubes,
as proved by the saturation of this material just mentioned. He then
assumes that the hydraulic gradient of the combined material "was
not greater than 1:1, although it was evidently much steeper."

The writer supposes the author to mean that the slope of the
gradient was not less than 1 : 1, although the tests apparently proved
nothing. The slope of the hydraulic gradient in earthen dams is not
generally as steep as 1:1, and in fact is seldom steeper than 35 : 100.
It would seem, therefore, that careful and thorough tests should have
been made before assuming 1 : 1 as the proper slope of the gradient
for the material in question.

Furthermore, the assumption is made that, by using the combined
materials in the up-stream section to secure water-tightness, and avoid
transmission of water pressure through that section in any great
amount, the hydraulic gradient can be made to begin at or near the
up-stream toe of the dam. This is a dangerous assumption, as the
material will become saturated, and some seepage will take place. Even
if the fine material had been found, experimentally, to be practically
impervious, it was not safe to assume that the coarse and fine materials
could be mixed on a large scale in such manner that there would be,
throughout the whole length of the dam, no points where the mixture
would be imperfect, and where water might not seep through the
combined material with greater or less facility.

Those who have had experience with filter beds, or have studied
their action, know that care must be taken in placing the filter bed
materials so that a uniform density will result. Whenever variation
occurs, the water readily finds the paths of least resistance, and soon
forms small channels through which it escapes. These channels
gradually become larger, until the efficiency of the filter is destroyed.
Lack of uniformity of the mixture of the materials under discussion
will undoubtedly cause similar action, and, with material as fine as
that described, a small quantity of seepage may cause piping, or
the carrying away of the material, and the destruction of a portion
of the up-stream section of the dam. Again, in Table 1, showing
mechanical and chemical analyses, it is stated that 52% of the fine
material is insoluble. If then, 48% of this earth is soluble, seepage



30. DISCUSSION ON DESIGNING AN EARTH DAM

Mr. through it may be assisted very materially by the dissolving of the
Oakes. soluble parts.

With reference to the upper line of sheeting used under the first
model dam, the author states: "* * * the loss of head is very
small and not in proportion to the length of the sheet-piling." He
does not explain why this upper row of sheeting did not accomplish
as much in proportion to its length as the lower row, but, relying on
what seems to be insiifficient data obtained from a very small model,
he abandons the upper row of piles and evolves a theory, which he
claims explains the results obtained, but which, the writer thinks, does
not explain those results satisfactorily. This theory is:

"* * * the sheet -piling cut-off was greatly similar in its effect
to a partly closed valve, wherein the water is retarded and shows a
higher pressure head just above the cut-off and a lower one just below."

He states that this theory wholly explains the ineffectiveness of
the upper row of sheet-piling as a cut-off, but the writer does not see
why, if the theory is correct, the upper sheeting should not also have acted
as a partly closed valve. In other words, why does not the theory
apply to one line of sheeting as well as to the other? It is a generally
accepted principle of design that, where the apron is water-tight, the
row of sheeting to be most effective must be at the up-stream edge.
If the up-stream section of the dam, composed of the mixed materials,
had been impervious, and the sheeting water-tight, it seems to the
writer that the greatest effect, in proportion to length, would have
been obtained by the upper row of sheeting. The author appears to
recognize this faintly, for, on page 22, he states :

"In any dam, the correct place for a cut-off wall, under conditions
such as these, namely, a pervious foundation, is at, or near the
up-stream toe."

This statement is certainly correct when the dam is impervious,
but it is not correct in case of a pervious dam or apron. It seems
to the writer that the inefficiency of the upper row of sheeting can
be readily explained, either by its lack of water-tightness, or by
seepage through the material of the dam, between the pool and some
point or points of the foundation down stream from the line of sheeting.
Owing to the short period of time during which the experiment
was carried on, the material above the second line of sheeting,
being much thicker, did not become thoroughly saturated, seepage
did not proceed directly from the pool through the material of the
dam to a point down stream from the second row of piling, and con-
sequently this row of piling did accomplish what was to be expected
of it.

Although nothing is said about the length of time to which the model
was subjected to the various heads of water, it is noted that, on each



DISCUSSION ON DESIGNING AN EARTH DAM 31

of the days that the work was carried on, from four to eight experi- Mr.
ments were made. In one case five experiments were made in the
afternoon, so that it is very evident that a very short period of time
was allowed for each experiment. With the material as fine as that
described, complete saturation near the core-wall could not have been
expected in such short time, but if, in each experiment, the head
had been maintaned for a niimber of days, complete saturation would
have taken place, and it would then have been fovmd that the lower
line of sheeting was also inefficient.

Nothing is stated in the paper as to the percentage of voids in the
coarser material, but the impression is given that water passed through
this material very freely. If, then, after a time, the material in the
upper section of the dam becomes thoroughly saturated, the writer
does not see what is to prevent the carrying away of the fine material
of the dam section through the coarser material of the foundation,
thereby causing ultimate failure of the dam. He can see no advan-
tage whatever in placing the line of sheeting as shown in Fig. 9. If
the material forming the upper section of the dam is impervious, then
the line of sheeting should be near the up-stream edge. If the material
is not impervious, then it should be under the core-wall and connected
therewith to form an impervious sheeting from crest of dam to foot
of piles.

Fig. 8 indicates that the proposed dam is to withstand a depth
of water of 100 ft., and Fig. 9 shows the design with a base approxi-
mately TOO ft. wide. For 100 ft. of this width the dam section is
from 10 to 15 ft. thick. As the core-wall and sheet-piling do not
necessarily increase the line of percolation, the percolation factor, or
ratio of length of line of percolation to head, is approximately 7, which
is much too small, if the writer understands the nature of the materials
of foundation and dam section. Furthermore, it may be possible for
seepage to take place along lines at 45° with the vertical and meeting
at the foot of the core-wall, in which case this factor becomes about
2i. This possibility is increased because the core-wall will tend to
concentrate the seepage at its foot, and such seepage will escape
under the wall and upward through the down-stream section, probably
at an angle of approximately 45 degrees.

According to the best authorities, these factors are too low. Among
these authorities may be cited Mr. W. G. Bligh, whose experience and
theories are dismissed by the author with the statement :

"This theory gives structures of ample dimensions, as has been
shown by practice, but was found to be incorrect, after due experi-
menting, as will be noted later."

If the author means that the experiments that he describes in
this paper prove the falsity of Mr. Bligh's theory, the writer must dis-



33 DISCUSSION ON DESIGNING AN EARTH DAM

Mr. agree with him, as, in his opinion, the model was too small, the experi-
Oakes. j^gj^^g ^qq fg^^ and too little time was devoted to each experiment to
warrant any siich broad statement. It seems to the writer that errone-
ous conclusions, or at least tmwarranted conclusions, were drawn by
the author. It seems very doubtful whether results obtained with
such a small model may be considered to hold for heads 120 times
as great as those used in the experiments. In writing about the failure
of a dam on sand foundations, and giving his opinion on the values
of required percolation factors, Mr. Bligh has sounded a warning which
exactly covers this case, as follows :

"The proper value of this factor is found, not by artificial experi-
ments on a small scale, but by undisputable statistics which bear on
the capacity of the various pervious materials which may compose a
river bed to resist the undermining influence of the pressure of the
water upheld."

A remarkable statement occurs on page 15, as follows:

"The long up-stream slope was given in order to allow the down-
ward pressure of the water over the up-stream section to have a bal-
ancing effect on the upward pressure beneath the dam, as blow-outs
would be improbable in this portion of the dam."

If the writer understands this sentence correctly, the author seems
to feel that, although improbable, blow-outs may occur in the bottom
of the reservoir, and he extends the dam up stream to prevent this by
providing something for the down-stream pressure of the water to
act on.

Although the author, under "Conclusions", has mentioned the prin-
cipal caiises of failure of earthen dams, he makes a number of state-
ments in the last two paragraphs that do not seem to follow neces-
sarily from the experiments described in this paper. Although pos-
sibly true, he has certainly not proved that :

"Where the sand or gravel foundation is of very great depth, a
short cut-off would not be as efficient as in a shallower founda-
tion, * * *."

Nor has he proved by his design that:

"* * * where models are constructed, results can be obtained
which enable the engineer to make correct designs better than by any
other method of study."

It appears to the writer that the use of a very small model, and
the lack of certain precautions, such as allowing sufficient time in
each experiment for the material to be thoroughly saturated, and the
assumption that the material is impervious, or practically so, where
it is very evidently not so, has led the author to arrive at erroneous
conclusions, and to design a dam, which, if constructed as designed,
is likely to fail.



DISCUSSION ON DESIGNING AN EARTH DA.M 33

The writer has had occasion to be deeply interested in the subject Mr.
of dams on sand foundations, and has found no example of a dam
on a pervious foundation constructed with, a cross-section approaching
in boldness that designed by the author. It will be very interesting,
indeed, to know whether the dam has been constructed as designed,
and, if so, to learn at a later date how it fulfills its purpose.

There is a statement at the end of the paper to which the writer
is willing to subscribe in its entirety, as follows :

"Each design is a problem in itself, and the experiments described
herein should not be misinterpreted, or applied too broadly."

C. E. Grunsky,* M. Am. See. G. E. (by letter). — The question of Mr.
the effect of water-tight sheet-piling which does not extend entirely
through a layer of pervious material, on the hydraulic gradient in
that layer, is one of vital importance in many cases where either a
dam must be built on a pervious foundation or not built at all. Every
contribution toward the solution of this problem should be welcomed
by the Profession. The wi-iter suggests one which should be tried out :

Let D represent the depth of the gravel bed, in feet.

Let d represent the depth of the sheet-piling, in feet.

Let s represent the fall, in unity, of the hydraulic grade line for
those portions of the gravel bed not affected by the sheet-piling. This
is the gradient that will cause a flow in the gravel equal in quantity
to the leakage under the dam.

Let S represent the fall in unity required to create the velocity
with which the water flows imder the sheeting through a section of
gravel from B to C, Fig. 12, being a layer with a thickness oi D — d
feet in which the water is assumed to flow horizontally.

Let k represent the reduction of hydrostatic pressure due to the
sheet-piling, expressed in feet.

The velocity of the water in the gravel is proportional to the
hydraulic gradient. Therefore,

' = 1^' (')

The velocity at which water moves through the gravel toward the
gravel-filled space, 0-B, under the sheet-piling, Fig. 12, decreases
with the distance from 0-B. Uniformity of velocity at uniform dis-
tance from 0-B may be assumed. Up stream from the sheet-piling,
therefore, the hydraulic gradient should be practically constant at
each point of each of the full concentric lines shown in the diagram,
and there should be a gradual increase of the gradient from s at
the outermost line passing through A, C, and D, to the gradient, 8,
at all points on the line, 0-B. Down stream from the sheet-piling,

* San Francisco, Cal.



34



DISCUSSION ON DESIGNING AN EAETH DAM



Mr. on the other hand, there should be a gradual decrease of the hydraulic
Grunsky. g^g^^jg^^ from S at the line, 0-B, to s at the outermost of the con-
centric lines passing through A, C , and D'.

The change in the gradient from s to 8, up stream from the line
of sheeting, and from 8 to s, down stream from the same line, is
practically proportional to the distance from 0-B, because the increase
of the area of the gravel through which the water must pass is pro-
portional or nearly so to this distance, and velocity and therefore
velocity head in a gravel bed are inversely proportional to cross-
sectional areas.




y^my-w/zw/y^w/MiyW'^^'^^'^d



Fig. 12.



It follows that the total fall of the hydraulic grade line throughout
the distance, C-C, will be

8 + s



2



X {C'C).



But C-C = -2 {A-0) = 2 a.

The total fall of the hydraulic grade line in the distance, C-C =
D-D', is, therefore,

8 + s ^ ^ , /8 + s\

J (2d),ovd (^ ^ y

The fall of the grade line in the same distance, if there were no
sheeting, would be 2 d s.

Consequently :

h=d (8 + s) — 2 d s (2)

h = d (8 — s) (3)



Substituting the value of 8 from Equation (1),



h =



d'' s
D—d



(4)
(-5)



DISCUSSION ON DESIGNING AN EAETH DAM 35

7 " - ..\ Mr.

or, /l = — (b) Gninsky.




When there is no sheeting, d = and h = 0. When the sheeting
extends to bed-rock, then s = 0, d = D, and h is indeterminate; the
flow is completely checked. This also appears from Equation (1),
which makes S =: co. The fall in unity at the sheeting is infinity,
and the hydraulic gradient comes to a full stop at the line of the
sheeting.

Equation (5), applied to the F. C. Horn model, for the particular
case when s = 1: 9, indicates the following for 85-ft. sheeting:

For D = 240 ft.
and d = 85
and 5^1:9

85 X S5 1 .
/.==-^^^X^^=o.2ft.



For 40-ft. sheeting d = 40,



and , = !i2ii»x 1=0.9 ft.

200 9

For 125-ft. sheeting, the loss of head would be 15 ft.

These results, it is believed, are fairly dependable. The hypothesis
on which they are based is certainly more reasonable than the "creep
theory" for which the writer has found no theoretical justification.

It will be noted that the examples here given apply only to the
particular cases in which s = 1 : 9, that is, s = 0.11. To make com-
parisons with the experimental results obtained with the model, the
first determination should be of the value of s, which will vary for
each length of sheeting. The effect of the sheeting expressed by the
total drop of the gradient is proportional to s, which is a variable.

The slope of the hydraulic gradient, or value of s, to be used in



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