THE UNIVERSITY OF ALBERTA ARCHING THEORY APPLIED TO THE CORES OF ...

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THE UNIVERSITY OF ALBERTA
ARCHING THEORY
APPLIED TO THE
CORES OF EMBANKMENT DAMS
by
G.W. Stevenson
A REPORT
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
I N PARTIAL FULLFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF ENGINEERING
DEPARTMENT OF CIVIL ENGINEERING
EDMONTON, ALBERTA
AUGUST, 1984
THE UNIVERSITY OF ALBERTA
FACULTY OF GRADUATE STUDIES AND RESEARCH
The undersigned certify that they have read, and recommend to
the Faculty o f Graduate Studies and Research for acceptance, a report
entitled "Arching Theory Applied to the Cores o f Embankment Dams"
submitted by G.W. Stevenson i n partial fulfillment of the require-
ments for the degree of Master o f Engineering.
Supervisor
Dr. Z. Eisenstein
4,
Dr. Thomson &L
19-1 ~87
Date:
G. W. Stevenson
Box 3262
Nipawin, Saskatchewan
SOE 1EO
28 August 1984
Professor Z. Eisenstein
Department o f Civil Engineering
University o f A1 berta
Edmonton, A1 herta
T6G 2G7
Dear Professor Eisenstein:
I enclose the report Arching Theory Applied to the Cores o f Embankment
Dams, for the completion o f illy Nonthesis Project for Master o f
Engineering.
I have revised the report i n line with the comments by Dr. Thon~son
and you. I have also added an additional reference since you reviewed
the draft, to the LG4 main dam (Par5 et al, Canadian Geotechnical
Journal, vol 21, no. 2, May 1984).
Thank you for the opportunity to pursue a topic o f my own choice.
The research and report preparation were interesting and rewarding.
I trust that this report meets the requirements for Nonthesis Project.
Yours very truly,
G. W. Stevenson
A simple arching theory i s used to calculate vertical stresses within
the cores o f embankment danrs. The calculated stresses are compared
with published finite element analyses (FEA) and earth pressure
nleasureinents.
The cocilparison with nonlinear FEA shows good agreement for a wide
range of soil strengths and hyperbolic parameters i n the core and
shells. The apparent accuracy o f the arching theory, when compared
the linear FEA, i s poor. Con~putational details o f the TEA do not,
i n general, influence the results.
Vertical core stresses from the arching theory, compared to earth
pressure measurements, exhibit a wide range i n the apparent accuracy.
However, the agreement i s good where design or construction details
do not unduly influence the dain behaviour.
The agreement between the arching theory and TEA, particularly nonlinear
FEA, or earth pressure measurenlents, i s good for a wide range o f
core inclinations, thicknesses and material properties.
INTRODUCTION
BEHAVIOUR OF ENBANKMENT DAMS
THEORY OF ARCHING
ARCHING THEORY APPLIED TO CORES OF DAMS
COMPARISON OF ARCHING THEORY WITH FINITE ELEMENT ANALYSES
General
Linear Elastic TEA
Nonlinear FEA
or
COMPARISON ARCHING THEORY WITH EARTH PRESSURE MEASUREMENTS
SUMMARY
REFERENCES
lABLES
FIGURES
TABLES
1. Summary of data from linear elastic finite element analyses
2. Summary of data from nonlinear finite element analyses
Deformation o f Llyn Brianne darn during construction (after
Carlyle, 1973).
Predicted deformations o f Talbingo dam a t end o f construction
(after Adikari and Parkin, 1982).
Strength mobilized i n Oroville dam (after Kulhawy and Duncan,
1972). Calculated by nonlinear FEA.
Geometry and stresses for soil column sliding between two
vertical surfaces (after Terzaghi, 1943).
Vertical stresses i n the core calculated from arching theory
for at-rest and active stresses on core boundaries.
Geo~iietrci ter~iisu sed i n study.
Cci-e stresses (after Maksimovic, 1973). Linear elastic FEA.
Major principal stress near the base o f a dam (after Eisenstein.
and Law, 1975). Linear elastic FEA.
Core stresses i n zoned darns (after Lee and Idriss, 1975).
Core stresses a t end o f construction (after Cavounidis and
Hoeg, 1977).
Core stresses i n Madin dani (after Flores and Auvinet, 1977).
Core stresses i n Llyn Brianne dam
Core stresses i n Chicoasen dam (after Alberro and Moreno,
1902).
Core stresses as influenced by post-yield behaviour (after
Cavounidis and Vaziri , 1982). Linear elastic FEA. Yield
defined by von Mises criterion, Y=0.7?iH.
Coniparison o f arching theory with linear elastic FEA.
Analysis o f homogeneous embankment (after Clough and Woodward,
1967). Linear elastic FEA.
Analysis of hoinogeneous en~banknrent (after Poulos et a\, 1972).
Linear elastic FEA.
Analysis o f honiogeneous embankment (after Lee and Idriss,
1975). Linear elastic FEA.
Core stresses i n Oroville dam (after Kulhawy and Duncan,
1972). Nonlinear FEA.
Core stresses i n E l Infiernillo dam. Nonlinear FEA.
Core stresses i n Mica dam. Nonlinear Fea.
Core stresses i n Lower Van Norman dani (after Valera and Chen,
1974). Ncnlinear FEA.
Core stresses fro111 parametric study (after Kulhawy and
Gurtowski, 1976). Nonlinear FEA.
Core stresses i n Teton dalr~ (after U.S. Department of the
Interior, 1976). Nonlinear TEA.
Core stresses i n Tehri dam (after Sharma e t al, 1979).
Nonlinear FEA.
Core stresses i n Dartniouth dam. Nonlinear TEA.
Core stresses i n Talbinyo dam (after Adikari and Parkin,
1982). Nonlinear TEA.
Core stresses i n LG4 main dam (after Pare' e t a1 , 1984).
Nonl inear FEA.
Comparison o f arching theory with nonlinear FEA.
Core stresses i n Balderhead dam (after Kennard e t al, 1967).
Core stresses i n Gepatsch dam (after Schober, 1967).
Core stresses i n Hyttejuvet danl (after Kjaernsli and Torblaa,
1960).
Core stresses i n Scaniiiionden dam (after Penn~ana nd Mithchell,
1970).
Core stresses i n High Aswan dam (after Kinawy and Shenouda,
1973).
Core stresses i n Mautthaus dam (after Lorenz, 1973).
Core stresses i n Takase dam (after Takai e t al, 1977).
1. INTRODUCTION
The phenoa~enono f arching within earth and rockfill dams, whereby
stresses are transferred fro111 a relatively compressible core t o
s t i f f e r shells, has long been recognized. Several theories have
been advanced to perinit tire calculation o f core stresses (Lofquist,
1951; Reinius, 1954; Sainsioe, 1955; Trollope, 1957) ; a l l involve
a number o f siniplifying assuiiiptions which may l i m i t the application
o f the theories. The develop~iiento f the f i n i t e element method has
perirri tted a inore rigoroiis analysis o f ewbankiiient stresses than i s possible
with simple theories which yield formulas intended for manual calculation.
Several dams have been successfully instrumented with earth pressure
cells which provide a direct measurecnent o f total stresses (Schober,
1967; Penman and Mitchell, 1970; Adikari and Parkin, 1982). The
measurenients provide a basis for assessing the accuracy o f various
arching theories.
This study w i l l coinpare the theory o f arching as presented by Terzaghi
(1943) with the results o f several f i n i t e element analyses (FEA)
o f and earth pressure nieasureciients within embankment dams. The FCA
include both paranietric studies, where ranges o f parameters are input
t o determine their influence on eiribankriient bchaviour, and studies
o f existing dans utilizing parameters determined from laboratory
testing. I t w i l l be shown tirat i n many cases the arching theory,
assuriiing the active liinit state has been fully niobilized a t the core
boundaries, provides a reasonable estimate o f the vertical total stresses
within tlie core. The liir~itationso f the theory w i l l also be demonstrated.
The stresses within the core a t the end o f construction w i l l be
assessed i n this study, that is, before nonsymetrical loading due t o
reservoir f i l l i n g i s in~posedo n the embankment.
2. BEHAVIOUK OF EMBANKMENT- D-A MS
The data fron~s everal well-instrua~entedd anis demonstrate that movements
within their central portions typically result i n a lateral transverse
spreadinq o f tlie cores. FFA also indicate similar tensile straining
o f the core i n the horizontal direction.
Figs. 1 and 2 present moven~ent data from two embankments. Fig. 1
shows measured deforli~ationsw ithin Llyn Rrianne dam at the end of
construction (Carlyle,1973). Fig. 2 presents calculated deformations
o f Talbingo dam (Adikari and Parkin,1982). For both the central core
o f Llyn Brianne and the inclined core o f Talbingo, the horizontal
strains within the core are tensile.
Several FEA have demonstrated that a high proportion o f the strength
o f the core material i s in~obilizeda t the core boundaries. As an
example, Fig. 3 illustrates the strength mobilization calculated for
Oroville dam (Kulhawy and Duncan, 1972).
The above observations and predictions suggest that an arching theory
which assumes the active strength o f the core to be mobilized a t i t s
boundaries might provide a reasonable estimate of stresses within
the core. It i s recognized that the movements within a dan~a re more
complex than the case o f rigid shells moving away from the core, that
is, the familiar active case for a retaining structure. Despite this
simplification, it w i l l be shown that such an approach provides
reasonable estin~ateso f vertical stresses i n many cases.