THE STABILITY OF EARTH DAMS A Thesis Submitted by Alan W. Bishop, MA(Cantab.)

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THE STABILITY OF EARTH DAMS
A Thesis Submitted by
Alan W. Bishop, M.A.(Cantab.)
, A.M.I..C.E.
For the Dogma of Doctor of Philosophy
in the University of London
Imperial College
May, 1952
The Stsbility of r3rth Dams
A Thesis sulzmit;;ed by
Alan 1.7. Bishop, TI.A.(0antab.),
For the Decree of 'Occtor of Philosophy
in the UniversIty of London.
The central problem in earth dam design Is that of shear
failure, either in the dam alone, or including the foundation
strata. A clear understandinc, of the factors involved is made
possible by do principle of efreetiye stress, and advances in
laboratory technique now enable shear strength rmrametcrs
measured in terms of effective stress to be used-as the basis
of design. The principle uncertainty in large dam design lies
in predicting the pore-pressure at each stage of its construction
and use.
Both elastic end limit elet;ign. methods of analysis are
discussed. A Relaxation solution is given for the elastic stress
distribution in a symmetrical triangular dam. Two classes of
problem for which limit design is used are distinguished, those
in which the pore-pressure is a function of the state of streams
in the coil ( i.e. excess pore-pressures set up durini; construction,
and during draw-down in fills which are not free d-eaining), o.nd
those in which thepore-preseuro is determined by the per:Ilcability
and boundary conditions of the various zones of the fill (i.e.
0 t c a Ely seepage9 and draw-down la' free-draining materials).
Particular attention is given to the design of dar;as having
a pad ilea clay core9 and new methods are developed for
the lateral thrust of the clay core, and for estimating the gain
in strength of a sort foundation layer with -partial consoT'idation.
CONTENTS
Chapter Page
1. Introduction 1
2. Types of stability Analysis 6
16
3. Elastic Methods of Stability Analysis
4. Limit Design Methods of Stability Analysis 38
5. The Mechanics of the Circular Arc Analysis 43
6. Application to Specitic Design Problems:
(a) Stability of a Dhm in which Excess Pore-
pressures are set up during Construction 60)
7. (b) Stability of a Dam in which Excess Pore-
pressures are set up due to Steady Seepage 88
8. cl Stability of. a Dam in which Excess Pore-
pressures are set up due to Rapid Draw-down 94
9 . Stability Problems associated with Puddled
119
Clay Cores
10 . Resistance to Failure in a Thin Soft Layer
at the Base of the Dam 146.
it. Conclusion 160
Acknowledgements 163,
Appendix 1 164
Bibliography .168
CHAPTER I
Introduction
Earth embankments for retaining water may be classed
among the earliest large scale civil engineering works. Yet
.superficially they would appear to have undergone the least
development of any type of structure. Earth dams about
.60 feet in height were successfully constructed in India over
hundred years ago, and, though safe height is not the
:.,only criterion of development, it is interesting to note that
i)A4.'ghest earth dam constructed in this country during
the 19th century was the Yarrow dam, of 103 feet. The
tallest earth dam at present under construction in Britain is
130 feet in height (Daer Valley) , while in the United States
the Anderson Ranch dam, constructed over the period 1941-47/
has a maximum height of about 350 feet above ground level.
•Th ere are probably few dams, however, for which stability
has been tie only factor controlling the height chosen.
Economic factors, the size of catchment area, or biological
actors controlling the maximum permissible depth of water
are of primary.importance; and though they will not be
considered in detail in this thesis it is of interest to
note that on a site underlain by a thick clay stratum the
volume of, bank fill required per unit length will be roughly
3
proportional to the (height) , which places a severe
limitation on the economic height.
In most branches of engineering advances have depended
on two main factors: the development of design methods and
the improvement of the mdchanical properties of the materials
available or the introdubtion of new materials. In the case
of earth dams, the principal construction materials are of
nocessityAhose which lid within a reasonable haulage distance
of the site. The possible improvement of their mechanical
properties by compaction has been affected by the technical
developments of the industrial revolution to an important,
but rather limited extent. The modification of their mecha-
nical properties by the upe of chemical or bitumenous stabi-
lisers or cement is almost unknown in present earth dam
practice(x). Concrete and steel sheet-piling have been
used to a limited extent in the construction of cut-offs and
.core-walls„ but have not led to any major change in design.
On the other hand, important developments have occurred
in our understanding of the mechanical properties of the
traditional, materials and in our ability to measure them
quantitatively. Those have led to methods of analyols and
design which form the principal advance in this branch of
civil engineering. Though superficially no dramatic change
(x)
The injection of cement grout is sometimes used as a
remedial measure in cases of leakage (see for example the
discussion by J. Noel Wood on the paper by Bishop, 1946).
Experiments have also been made on the admixture of bentonite
to a sandy fill to decrease its permeability and increase the
plasticity (Wetter 1948).
in profile has resulted, a rational basis is now available
for ensuring the most economical disposition of the construct-
ion materials and for calculating the factor of safety of
the structure with some 6onfidence.
Those methods must, however,-be considered to supplement
rattier than supersede the experience and judgement of the
practising engineer, The variability of some foundation
strata and the difficulty of predicting the effect of variable
weather conditions on the compaction and excess pore-pressures
in cohesive fills loave considerable scope for experience
and judgement, especially if based on well-conceived field
measurements.
Much, in fact, could be gained from a more explicit and
active cooperation between the engineer and the scientist.
Confirmation of the validity of design methods in the labora-
tory is generally impossible in the case of problems where
body forces due to gravity predominate. The price the engi-
neer must pay for design methods in which he can have confi-
dence is a much greater willingness to take the necessary
field measurements of shear strength, pore-water pressure,
settlement etc., even on structures about whose stability
there is little doubt; Eind the price will generally prove
tote small compared witki the cost of the structure. The
research worker, on the ether hand, must give greater thought
to suggesting tests, design methods and specifications which
are practicable in terms of the soils and climatic conditions
met with by the engineert
If the. need for work in this field is not at once
obvious, it should be noted that at least three major earth
dam failures have occurred in this country in the past twenty
(x)
years and at least six in the , involving expenses
running into many millions of pounds.
Vrom the data presented by Justin and others, it will
be seen that many of the earlier failures of earth dams were
not primarily due to shear failure, but followed over-top-
'ping due to inadequate spillway capacity. The importance
of this danger is now sufficiently realised, and as it is
outside the field of soil mechanics it will not be discussed
here.
Similarly, a number of the earlier failures were due to
ocalised piping or internal erosion caused by seepage paths
()riming at the junction of the fill with the outlet conduit
.or with bed rock. The importance of eliminating any such
is now fully recognised, and the outlet conduit is
now generally either constructed with collars or baffles
whore:. it passes through the impervious core, or driven in
tunnel through the impervious foundation stratum beneath the
darn
(x)Thoso are tabulated by Justin, Creager and Hinds (1945).
The typo of failure which has, however, persisted even
in recent years, and must therefore bo considered the hardest
to design against, is shear failure, either in the foundation
strata 'or in the bank fill itself, generally taking place
during construction. Recent examples in this country are
Muirhoad Reservoir, whore the shear failure occurred in tho
bank fill (Banks, 1948); and Chingforcl No. 2 Reservoir,
where the weakness of the soft underlying stratum was .the
primary cause of failure (Cooling and Golder, 1942).
Justin, Creager and Hinds (1945) quote five failures of
this type in the U.S.A. within the last twenty years,
including both hydraulic fill and rolled earth core dams,
..ranging from 52 to 225 feet in height. It is interesting
note that only one of these was caused by rapid drawdovm,
:Eilthoiigh in conventional design it is against this condition
that bank is usually found to have its lowest factor of
(x)
safety .
It is with a consideration of the problem of shear
failure that the subsequent chapters will be mainly concerned.
A brief history of design methods will be included, but no
attempt will be made to ()over the whole history of earth
dam construction, which is a subject in itself.
(x) Mayer reported in 1936 a number of clrawdovm failures
which had occurred in France in the preceding fifty
years, in dams constructed before quantitative design
methods were in use.
CHAPTER 2
TYPES OP STABILITY ANALYSIS
The stability of an earth dam, as of any structure
in soil mechanics and, in fact, in civil engineering in
general, may be examined by methods of analysis falling
under two main headings. Both types of analysis must be
considered necessary to a full understanding of the problem,
though this is overlooked in much contemporary literature.
The first type is based on the principle of calculating
the stress distribution under the various conditions of
loading to which the dam will be subjected, and comparing
the stresses with the allowable strength of the soil. It
is thus in line with the classical procedure in structures,
though for practical reasons which will be discussed later,
its use is not very general in soil mechanics. As elastic
theory is usually used to cal culate the stresses, the methods
are loosely termed elastic methods though in principle the
assumptions of a linear stress strain relationship and of
reversibility are unnecessary, and aro made only to avoid
difficulties in computation.
The second type is based on the principle of limit design.
If the load on a structure is gradually increased, or, in
the case of a dam, when the stresses are mainly duo to gravity
body forces, the strength is imagined to be progressively