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(e) Coefficient of frictional re-




0.25*1 0.25*






* Resistance (to horizontal movement ) on part of the original unreinforced cut-off wall
and the original toe probably inconsiderable and treated as forming part of the frictional
resistance of the foundation "soil at the base of the footings.

Note. — No tail-water pressure in any case.

Referring to Table 3, it should be noted that, in connection with
the question of frictional resistance, no attempt has been made in the
case of the original structure to determine the additional resistance of
the original cut-off wall and toe. Inasmuch as the cut-off wall was
unreinforced throughout, and was not tied into the body of the dam
except at a few places, it is believed that the resistance of the cut-off


wall to horizontal movement was not a reliable factor, and that, even
when present, it was inconsiderable in amount. Likewise, the resist-
ance of the original toe was probably negligible, because the toe was
relatively shallow.

The assumed conditions of Table 3, in so far as pressure is con-
cerned, are entirely arbitrary. In view of the fact that, both at the
sections of maximum height and at the typical section of Plate XII,
the strengthened structure has an adequate cut-off, it is certain, of
course, that the uplift pressure actually does not decrease uniformly
from heel to toe, as has been assumed. However, everything con-
sidered, and especially in the absence of definite knowledge regarding
the presence and character of the uplift pressure, it appears reasonable
to base stability analyses on assumed "equivalent" conditions of uplift
pressure (see Table 3, factor id)-2). Manifestly, uplift pressure could
not be exerted over the entire area of the base without causing flota-
tion, which is impossible.

I. — Under ''Normal Maximum Load". — Applying now the assumed
"normal maximum load" conditions of Column (2), Table 3, to the
maximum height sections of the original structure, and stating all
quantities for one bay 15 ft. wide, the results are as follows :

Weight of concrete 1 044 900 lb.

Weight of water on deck 1 194 500 lb.

Sum of loads 2 239 400 lb.

Total resistance to sliding, 2 239 400 lb. X 0.33 = 746 500 lb., ap-

Forces resisting sliding 746 500 lb.

Forces tending to cause sliding 1 218 200 lb.

Or, vice versa, in order that this ratio may become equal to
unity, the coeiBcient of frictional resistance must equal

-— - = 0.54.

II. — Under "Most Severe Conditions Within Limits of Reason". —
Referring to the assumed conditions of Column (4), Table 3, the
spillway crest (Elevation 136) has been adopted as the highest eleva-
tion at which ice pressure could be present, because flash-boards could


hardly have been used with safety on the original spillway. Uplift
pressure has been assumed as acting along the entire width of the
base of the original structure (though over only 50% of the area),
because in severely cold weather the weep-holes through the footings
were frozen up solidly and hence were ineffective. With all quantities
stated, as before, in terms of a 15-ft. bay, the results are as follows:

Weight of concrete 1 044 900 lb.

Water load on deck 985 500 lb.

Total downward pressure 2 030 400 lb.

Deduct uplift pressure 675 000 lb.

Net load 1 355 400 lb.

Total resistance to sliding = 1 355 400 lb. X 0.25 = 338.850 lb.

Horizontal water pressure 1 219 200 lb.

Ice pressure .:3ij; .;;.ri icui. .... 300 000 lb.

Total forces tending to cause sliding. . . 1 519 200 lb.
Hence the ratio of safety is

338 850 1b. ^
1519 200 1b.

Or, in order that the ratio of safety against sliding may become
equal to unity, the coefficient of frictional resistance must equal 0.25
divided by 0.223, viz., 1.12. Evidently, therefore, the Stony River Dam
as originally constructed could not be considered as having a reasonable
margin of safety against sliding.

It would be interesting, of course, to know what coefficient of
gross resistance to sliding obtained prior to failure. In order to derive
the minimum value of such coefficient, the following assumptions are
made, conforming to the conditions which actually existed, viz. :

(a) Head-water level at elevation of spillway crest, viz., at
Elevation 136;
■ (h) No ice pressure;

(c) Horizontal water pressure equivalent to full hydrostatic pres-
sure of 46.5 ft., viz., down to Elevation 89.5;

(d) Uplift pressure negligible;

(e) No tail-water pressure;


(/) Any resistance to horizontal movement furnished by the unre-

inforced cut-off wall or the toe-wall is treated as forming

part of the gross resistance to sliding on the part of the

foundation soil.

Under these conditions, the ratio of the force tending to cause

sliding to the load above the base of the footings, for a 15-ft. bay, was

1 013 600 lb.

2 030 400 lb.

= 0.50.

In other words, the coefficient of gross resistance to sliding, under
the foregoing conditions, was at least 0.50; for, necessarily, the ratio
of safety was at least unity.

Probably the resistance to horizontal movement, as expressed by
such ratio or coefficient, was due in part to cohesion or resistance to
direct shear within the foundation soil itself. That is, it is likely
that failure would occur, not at the relatively rough surface of con-
tact between the footing concrete and the foundation soil, but along
an approximately horizontal plane in the body of the soil just below
the base of the footings. Such resistance to shear will be discussed
further in connection with the expedient adopted to increase the
resistance to sliding in that portion of the dam which was not dis-
turbed by the failure.

It should be noted that in the 65 days prior to the failure, diiring
which period the dam withstood the pressure of the full reservoir,
relatively cold weather obtained, and the ground-water was practi-
cally at its lowest level. In other words, it is likely that the frictional
resistance would have decreased as the foundation soil became more
saturated by leakage and ground-water during the following spring.
Whether the dam would have stood, or how near it was to failure by
sliding, no man can tell.

Mearis to Increase Resistance to Sliding. — Various expedients
were considered for increasing the margin of safety of the original
structure against failure by sliding. The method finally selected
involved the construction of anchoring walls at the heel and toe of
the original structure, essentially as shown on Plate XII, which shows
typical sections of the dam, though not those of maximum height.
In order to explain more clearly the reasons for adopting this method


of increasing resistance to sliding, the alternatives considered will
be briefly described and their advantages and disadvantages stated.
1. — Referring first to the principal feature of the adopted means,
the essential advantages of the anchoring wall at the heel (the action
and construction of which are discussed in more detail later herein)
are as follows (Plate XII) :

(a) It utilizes the foundation soil under the dam, and in effect
also a considerable quantity of the foundation soil immedi-
ately down stream from the dam, to increase the total weight
which must be moved down stream in case the dam is to
fail by sliding.
(h) The construction of such an anchoring wall at the heel seals
the construction joint at the top of the original cut-off wall,
this joint having in some places opened up sufficiently to
allow appreciable, if not indeed serious, leakage.

(c) With such an anchoring wall, any down-stream movement
on the part of the dam will tend to compact the underlying
foundation soil, and, therefore, to make it less pervious.

(d) This was found to be the most economical method of obtain-
ing the desired margin of safety against failure by sliding.

The only disadvantage of constructing an anchoring wall at the
heel alone lay in the resulting high unit pressure against the clay
immediately down stream from such "heel" — as the new anchoring
wall at the heel of the dam has for convenience been styled.

2. — With especial reference to that portion of the original struc-
ture which remained intact, there was, of course, no opportunity to
flatten the slope of the deck, and thus obtain a greater water load.

3. — The loading of the footings of the hollow structure, by using
concrete, rock, or earth, was considered, and was rejected because:
(a) Such additional material would increase the load on the

already too heavily loaded foundation soil;
(fe) The original footings would have required even more
strengthening than was considered necessary with the means
finally adopted;

(c) Such loading would have required special provision for in-
spection of the drainage system; and

(d) The expedient was limited in extent, and, taken by itself,
w^as not considered to be sufficient.


4. — Various structural additions at the toe of the dam were con- .
sidered; among them an L-shaped anchoring wall such as that shown
on Plate XII. This method of obtaining additional resistance to slid-
ing was not open to the objections to the proposed loading of the
original footings. However, if adopted to furnish the entire required
increase in resistance to sliding, it would have been subject to certain
different objections, viz. :

(a) For the same depth below original ground surface, gener-
ally speaking, less increase in resistance to sliding results
than in the case of an anchoring wall at the heel alone; for
the toe-wall does not utilize the foundation material under
the body of the dam.

(&) In the case of this particular clayey soil, the toe-wall, like
the "heel", is limited in efficacy by the safe bearing value
of the soil in compression.

(c) In case of any yielding at the toe of the dam, either down-
ward or down stream, the effect might be to cause either crack-
ing in the original cut-off wall or, at the very least, the
opening of the construction joint at the top of the old cut-
off (Plate XII). Thus, water under reservoir pressure might
immediately be admitted under the base of the dam.

On the other hand, the anchoring wall at the toe has certain advan-
tages not possessed by the "heel", viz. :

(d) By means of its vertical member, the toe-wall confines the
foundation soil under the original footings of the dam, thus
increasing the safe load to which that soil may be subjected.

(e) The horizontal member of the toe- wall in effect increases
the width of the base of the dam, thus decreasing the unit
vertical load on the foundation soil, as will be shown later
in more detail imder the heading "Footings".

It is clear, however, that in cases where it is necessary similarly to
increase the margin of safety of a dam against failure by sliding,
but where there is no opportunity to construct an anchoring wall at
the heel, an anchoring wall at the toe can be made to answer the pur-
pose. Generally speaking, it is merely a matter of proportioning
such a toe-wall properly.


5. — Investigation was made of the desirability of constructing
reinforced concrete columns at the toe of the dam, inclining down-
ward and approximately parallel to the line of action of the resultant
load on the dam. This proposal was rejected, partly because the
result would be equivalent to placing the dam on relatively unyield-
ing supports — stilts, as it were — thus changing the character of the
stresses in the original footings.

6. — The construction of a heavy block of concrete, approximately
square in cross-section and extending along the entire length of the
toe of the dam, was considered and rejected because the L-shaped toe- wall
transmits vertical and horizontal loads into the foundation material to
the same extent, but with much less concrete and excavation.

In view of the foregoing considerations, it was concluded to use
anchoring walls at both heel and toe; for, by means of the toe- wall, it
was possible to reduce to a safe value the otherwise excessive horizontal
load on the foundation soil at the heel. The reconstructed dam acts
essentially as a monolith ; hence down-stream deflection or yielding must
be equal at heel and toe. Inasmuch, then, as the load on the foundation
soil is proportional to the deflection, the unit horizontal loads at heel
and toe are approximately equal.

Likewise, at the new spillway of the dam, an anchoring wall at the
heel was used. Here advantage was taken of the opportunity of com-
bining the cut-off and the anchoring device in a single wall, as shown
on Plate X. As the foundation of the new spillway consists of shale,
the problem of keeping within the safe load against the material at the
heel was not difiicult, and hence no anchoring wall was required at the toe.

Analysis of Anchoring Walls. — The principle on which the design
of the anchoring walls is based applies both in the case of the strength-
ening of the original structure and in that of the construction of
the new spillway. The detailed explanation, however, will be made with
reference to the typical bulkhead section at Bay 35, as shown on
Plate XII.

The use of such anchoring walls, to furnish specific and reliable
resistance to sliding, by utilizing the weight of the foundation material
underlying, and immediately down stream from, a dam, is believed to
be new. The writer first applied it in the case of the State Line Dam
of the Hydro-Electric Company of West Virginia, on Cheat River in
West Virginia.


Referring now to Plate XII, the anchoring wall at the heel is tied
into the dam by twisted, square, steel bars extending through openings
broken through the base of the original deck of the dam. The heel itself
consists essentially of two cantilever members of reinforced concrete,
extending, respectively, above and below the steel which ties the heel
to the original structure. A relatively long cantilever member extends
downward immediately adjacent to the up-stream face of the original
cut-off, and a relatively short cantilever member extends upward im-
mediately adjacent to the base of the original deck. Both cantilevers
are suitably reinforced against stresses due to bending moment and shear.

Although some of the horizontal water pressure is exerted directly
against the anchoring wall or heel, the greater portion is exerted
against the deck, and by the deck is transmitted into the buttresses.
The tie-steel previously referred to is embedded in the reinforced con-
crete footing strengthening, which in turn is thoroughly tied into the
base of each adjacent buttress, as shown on Plate XII. Thus the tie-steel
receives from the buttresses and the footings that portion of the hori-
zontal water pressure which is not exerted directly against the heel, or
has not been taken up by the frictional resistance of the foundation soil
immediately in contact with the footings.

The lower cantilever member of the anchoring wall in turn trans-
mits such surplus load into the foundation soil down stream from the
heel. The fact that the stress is transmitted through the medium of
the original cut-off wall is immaterial, except to the extent that the
cut-off wall serves to transmit some of the load into the foundation soil
below, and down stream from, the bottom of the heel. The reaction
at the top of the lower cantilever, of course, is taken up by the upper
and shorter cantilever and transmitted through the deck, in part directly
into the buttresses and in part into the approximately triangular fillet
of new concrete placed in the angle between the deck and the footings
(Plate XII). Ordinarily, this fillet acts as an arch to transmit the
reaction back into the buttresses and footings. In certain cases, how-
ever, where steps occur in the footings at the centers of bays, it was
necessary to reinforce the triangular fillets to act as cantilever beams
supported at the buttresses and extending outward to the centers of the
adjacent bays.

The effect of the anchoring wall at the heel is essentially to lower
the main "plane of least resistance" to sliding from its original posi-


tion, at or immediately under the base of the footings of the dam, to a
position approximately at the elevation of the bottom of the new anchor-
ing wall at the heel. By "plane of least resistance" to sliding is meant
the surface or surfaces, approximating a plane or planes extending
through the foundation material, along which the total resistance to
horizontal movement (sliding) is less than along any other surfaces or
approximate planes.

In so far as resistance to sliding is concerned, the result of such
lowering of the main "plane of least resistance" is to cause the weight
of the foundation material in advance of the anchoring wall to be
utilized at least as effectively as the weight of the body of the dam
itself. This utilization of the weight of the foundation material occurs
in two ways, as will be apparent by reference to Plate XII. Let it be
assumed that, for the conditions existing in the typical section there
illustrated, the "planes of least resistance" are represented by the lines,
A'B and B-E, respectively. Then

1.— The foundation material lying above A-B and to the left of
B-C must, in case of failure, slide along the plane, A-B.
This is also true of the concrete structure (including the
anchoring wall) and the superimposed water load. The resist-
ance to sliding of these several elements is represented by the
product of their weight multiplied by the coefficient of fric-
tional resistance.

2. — The foundation material lying between B-C and B-E must, in
case of the failure of the dam by sliding, move simultaneously
down stream and upward along the plane, B-E. Such move-
ment of this material, therefore, is opposed, not merely by
frictional resistance, but also by the force of gravity. The
resistance of this particular portion of the foundation material
is analyzed subsequently in more detail.

The location of the "planes of least resistance" is dependent on the
conditions existing in any particular case. For the conditions shown
on Plate XII, a general statement may be made, as follows :

It is evident that, assuming proper design and construction of the
anchoring wall at the heel of the dam, the main "plane of least resist-
ance" cannot begin above A. Neglecting for the moment the existence
of the original cut-off, it is further evident that the main "plane of


least resistance" could not extend downward in a direction such as
A-G. In other words, the resistance along any plane dipping below
the horizontal is necessarily greater than the resistance along the plane,
A-B. Whether the "plane of least resistance" extends horizontally or
in an upward direction from A is a matter for determination by trial
computation. In this particular case, of course, the old cut-ofF wall is
a factor, even though its effect may be indefinite. For instance, were
the break in it to be in an upward direction, such as A-F, its effect on
the location of the main "plane of least resistance" would be nil, or at
least negligible. On the other hand, a break in a downward direction,
such as A-H, might, owing to the strength of the concrete cantilevering
below the elevation of A^ cause the initial point of the main "plane of
least resistance" to be at a lower elevation, for example, at H instead

To the left of the vertical plane represented by the line, B-C, pass-
ing through the down-stream edge of the new toe-wall of the dam, the
foundation material is confined by the weight of the structure shifted,
as it were, toward the down-stream side of the footings by the horizontal
thrust of the water load. In effect, this weight is greatest per square
foot at the very down-stream edge of the toe-wall, which is practically
monolithic with the original structure. The line or plane of failure
could not turn upward (from the main "plane of least resistance") on
the left side of B-C unless the foundation material underlying the dam,
and above such new and increased slope, were to fail in compression,
or were to "flow".

Moreover, at the toe there is a concentration or transfer of horizontal
thrust into the foundation material. In the present instance this
transfer of thrust is accomplished partly through frictional resistance
between the soil and the toe- wall (especially the horizontal leg thereof),
and partly through direct bearing of the toe-wall (especially the
vertical leg thereof) against the soil.

It is probable, therefore, that the main "plane of resistance" would
end approximately below the down-stream edge of the toe-wall, as at B.

If, then, the main "plane of least resistance" is represented by
A-B, it follows that unless (1) the foundation material fails in com-
pression, as along B-C, or (2) the coefficient of frictional resistance is
too great, the "plane of least resistance" will turn upward at B. Gen-
erally speaking, the slope of this plane must be determined by trial,


although, under certain conditions, the slope may be determined by
direct computation.

Theory of Resistance at Toe. — The resistance of the foundation
material at the toe of the dam, by which, on Plate XII, for instance, is
meant the material to the right of B-G, is a factor sufficiently important
to warrant more detailed explanation. Practically, on account of the
character of the material in question, the results of theoretical analysis
represent the actual conditions only approximately. The refinement
of such analysis, however, is worth while, because it aids in obtaining
a thorough understanding of the case.

The problem is essentially one of "passive thrust". The analysis
adopted as applying to the general case is based on the assumptions
that :

(a) The foundation material, viz., earth, is homogeneous and

granular ;
(6) The material is without cohesion;
(c) The coefficient of frictional resistance (being the same as the

coefficient of internal friction) = /;
{d) In case of sliding, failure of the foundation material at the

toe will occur along a plane, such as B-E;
(e) The resistance of the foundation material to compression (as
in the vertical plane, B-C) is so great as not to be the limiting
factor in toe resistance;
(/) The load on the foundation material in a vertical plane (such
as B-C) increases in intensity regularly from zero at C to a
maximum at B',
(g) It is necessary to the stability of a granular mass that the
direction of the pressure of the portions into which it is divided
by any plane should not at any point make with the normal to
that plane an angle exceeding the angle of repose, viz., /.*

Under the foregoing assumptions, it would appear that, in case
of failure of the dam by sliding, a wedge-like section of the foundation
material would be forced upward approximately between and along
B-C and B-E. The toe resistance — in other words the resistance to
movement on the part of such wedge-like section — depends on whether
there is frictional resistance along the vertical plane, B-C^, such as

♦ Rankine's "A Manual of Applied Mechanics", ITth Ed., p. 213, Theorem I.



there is along the inclined plane, B-E. There appears to be no valid
objection to the assumption that the resistance along the vertical plane
is equal to that along the inclined plane. However, the results will
be stated on each basis, the more conservative assumption being that
there is no f rictional resistance in the vertical plane, B-C :

Condition I. — Without friction in the vertical plane, B-C. (See
Fig. 20.)

Resultant' ^^ /

Normal to BE ^\.

Resultant '

Normal to BE
Fig. 21.



Fig. 20.
If i? = horizontal pressure in the plane, B-C, against the
wedge of earth, C-B-E, sufficient to cause movement
of the wedge;
= weight of material (per unit length of dam) included be-
tween j5-C and iJ-^";
a = angle of friction (viz., the angle the tangent of which is /) ;
= angle between "plane of least resistance", B-E, and the
vertical (plane B-C).

Then H = G cot. (9 — a), since the friction along the plane, B-E,

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