cr s-74-3 'finite element analyses of transverse cracking in low-embankment dams' · 2017. 12....
TRANSCRIPT
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Unclassified SEC RITY CLASSIFICATION OF TH15-PAG£Jll'!uUl n.t.._Fn!e~ed) u -
REPORT DOCUMENTATION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM '· REPORT NUMBER 12. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER
~ont.'l"nrt. 'R"mrwt. ~-7h- ~ 4. TITLE (Md Subllt/e) S. TYPE OF REPORT & PERIOD COVERED
FINITE ELEMENT ANALYSIS OF TRANSVERSE CRACKING Fi nnl ~. IN LOW-EMBANKMENT DAMS 6. PERFORMING ORG, REPORT NUMBER
7. AUTHOR(•) 8. CONTRACT OR GRANT NUMBER(•)
Guy Lefebvre J. Michael Duncan
DACW39-68-C-0078 9. PERFORMING ORGANIZATION NAME ANO ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK
AREA & WORK UNIT NUMBERS College of Engineering Office of Research Services University of California, Berkeley, Calif. 94720
II, CONTROLLING OFFICE NAME ANO ADDRESS 12. REPORT DATE
Office, Chief of Engineers, U. s. Army October 1974 Washington, D. c. 20314 13. NUMBER OF PAGES
100 14. MONITORING AGENCY NAME & AOORESS(ll dllferent from Conttolllnl Office) 15. SECURITY CLASS. (of Ihle report)
Soils and Pavements Laboratory Unclassified U. s. A:rmy Engineer Waterways Experiment Station
15•. OECL ASSI Fl CATION/ DOWN GRADING P. o. Box 631, Vicksburg, Miss. 39180 SCHEDULE 16. DISTRIBUTION STATEMENT (of Ihle Report)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT (of /he ab•tract entered In Block 20, If dllferen/ from Report)
18. SUPPLEMENTARY NOTES
19. KEY WORDS (Conllnue on reverae a/do II n~c•H•I')!' and Identity by block number)
Earth dams Embankment cracking Finite element method Settlement (Structural)
20. ABSTRACT (Continue en,.,,., •• •tde II necH•MY and Identify by block number) The objective of this research was to study some of the factors leading to
transverse cracking in low-embankment dams using finite element analyses. The factors studied were: (1) the analysis procedure, gravity turn-on or construe-tion sequence, (2) the magnitude and time of occurrence of the settlement of the dam, (3) the stress-strain characteristics of the dam material, and ( 4) the shapi of the abutment profile. The study showed that the zones of tension calculated using gravity turn-on analyses can in some cases be significantly different from those calculated using construction sequence analyses and that it is ~refer&ble
DD FORM I JAN 73 1473 EDITION OF I NOV 65 IS OBSOLETE · Unclassified SECURITY CLASSIFICATION Of' THIS PAGE (ll'hen D•t• Entered)
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Ilpclas""ified SECURITY CLASSIFICATION OF THIS PAGE(Wh.,, Data l!nlet9d)
20. ABSTRACT (Continued) to use construction sequence procedures for anal~ses !Jr tension in dams. The analyses indicated -that -the sizes of the zones cf tension increase with the magnitudes of the differential settlements and that settlement after construc-tion results in more tension than does settlement during construction. Reducing the stiffness of the dam material has the effect of reducing the size of the calculated tension zone, but reducing the tensile strength of the material to a very low value has only a small effect on the size of the tension zone.
Unclassified SltCUIUTY CLASSIFICATION OF THIS PAGE(ll'!len Data f!nlered)
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FOREWORD
The work described in this report was performed under Contract No,
DACW39-68-C-0078, "Behavior of Zoned Embankments and Embankments on Soft
Foundations," between the u. s. ·Army Engineer Waterways Experiment Station and the University of California. This is the fifth report on investiga-
tions performed under this contract. The first report, "Finite Element
Analyses of Stresses and Movements in Embankments During Construction,"
by F. H. Kulhawy, J. M. Duncan, and H. Bolton Seed, was published in
November, 1969. The second report, "Three-Dimensional Finite Element
Analyses of Dams," by Guy Lefebvre and J, M, Duncan, was published in
May, 1971. The third report, "Effect of Reservoir Filling on Stresses
and Movements in Earth and Rockfill Dams," by E. S, Nobari and J. M.
Duncan, was published in January, 1972. The fourth report, "Hydraulic
Fracturing in Zoned Earth and Rockfill Dams," by E. S, Nahari, K. L. Lee
and J. M. Duncan, was published in January, 1973. The research was
sponsored by The Office, Chief of Engineers, under the Civil Works Program
CWIS No, 00169, "Finite Elements (University of California) •11
The general objective of this i;esearch, .which was begun in June,
1968, is to develop methods for analysis of stresses and movements in
embankments. Work on this project is conducted under the supervision of
J. M. Duncan and H. Bolton Seed, Professors of Civil Enginering. The pro-
ject is administered by the Office of Research Services of the College of
Engineering. The phase of the investigation described in this report was
conducted, and the report was prepared by Guy Lefebvre and J, M. Duncan.
The contract was monitored by Mr. ·c. L. McAnear, Chief, Soil Mechanics Division, under the general supervi~ion of Mr.·J. P. Sale, Chief,
Soils and Pavements Laboratory. Contracting Officer was BG E. D. Peixotto,
CE, Director of the U. s. Army Engineer Waterways Experiment Station.
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TABLE OF CONTENTS
Foreword
List of Figures
List of Tables
List of Symbols
Conversion Factors, U. S. Customary to Metric (SI) Units
Introduction
Field Experience - Many Dams are Damaged by Traverse Cracks
Differential Settlements are an Important Cause of Cracking
Stress is a Better Criterion for Cracking than is Strain
Finite Element Analysis Procedures
Conditions Analyzed
Material Properties
Tension Zones Calculated by Gravity Turn-on and Construction Sequence Analyses Are Not the Same
Tension Zones Calculated in Gravity Turn-on Analyses Depend Primarily on the Ratio of Moduli in Dam and Foundation
Settlements After Construction Are More Likely to Produce Cracking than 1s Settlement During Construction
Large Zones of Tension Are More Likely When the Dam Material is Stiff
The Size of the Tension Zone is About the Same for High and Low Tensile Strength
Some Types of Abutment Irregularities Have Little Effect . on Tension Zones
Hydraulic Fracturing Can Increase the Size of the Zone of Potential Cracking
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Page No.
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4
5
6
7
9
9
11
11
14
14
19
26
29
29
33
33
34
38
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Conclusions
Literature Cited
Appendix A - Additional Results of Finite Element Analyses
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Page-No.
39
42
45
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Fig. No.
1
2
3
4
5
6
7
8
9
LIST OF FIGURES
Titl.e
Stresses and Strains During Construction and After Settlement
Three-Dimensional View of Dam on Clay Foundation
Finite Element Mesh for the Longitudinal Section
Finite Element Mesh for the Longitudinal Section of.a Dam with an Irregular Abutment
Settlement Profile for End-of-Construction and Long-Term Condition
Compaction Characteristics for Pittsburg Sandy Clay
Stress-Strain Curves for Pittsburg Sandy Clay at Two Compaction Conditions
Modulus Variations for High-Tensile-Strength and Low-Tensile-St rength Assumptions
Comparison of Minor Principal Stresses Calculated by Three Different Methods of Analysis. Stiff Material -High Tensile Strength
10 Contours of Minor Principal Stress Calculated by Linear Gravity Turn-on Analyses Using Different Modulus Values but the Same Ratio of the Dam Modulus to the Foundation Modulus
11 Contours of Minor Principal Stress Calculated by Gravity Turn~n Linear Analyses Using Different Ratios of the
Page No.
13
15
16
17
20
23
24
25
27
30
Dam Modulus to the Foundation Modulus 31
12 Contours of cr3 in Embankments with High Tensile Strength 32
13 Contours of cr 3 in Embankments with Low Tensile Strength 35
14 Contours of cr3 in Embankments with High Tensile Strength -Effect of Irregular Abutment 36
15 Contours of cr3 in Embankments with Low Tensile Strength -Effect of Irregular Abutment 37
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Table 1
Table 2
LIST OF TABLES
Stress-Strain and Strength Characteristics of Embank-ment Fill Material
Stress-Strain and Strength Characteristics of Foundation Soils
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Page No.
21
22
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LIST OF SYMBOLS
a - normal stress
£ - normal strain
a, - major -princ-ipal stress -...
cr3 - minor principal stress
x - horizontal direction
y - vertical direction
Ei - initial tangent modulus
Et - tangent modulus
c - cohesion intercept
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CONVERSION FACTORS, U. S. CUSTOMARY TO METRIC (SI)
UNITS OF MEASUREMENT
U. S. customary units of measurement used in this report can be converted
to metric (SI) units as follows:
Multi~l:z: B:z: To Obtain
feet 0.3048 meters
pounds 4.448222 newtons
pounds per cubic foot 16.018489 kilograms per cubic meter
atmospheres 101.325 kilonewtons per square meter
tons per square foot 95.760567 kilonewtons per square meter
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Introduction
When transverse cracks develop in a dam, they can constitute a sig~
nificant hazard to safety, and there is thus a need for reliable methods
of anticipating the locations and extent of transverse cracking, The
finite element method has considerable potential for analysis of tension
and cracking in dams, and the method has already been used quite widely
for that purpose, notably by Covarrubias (1969), Casagrande and Covarrubias
(1970), Covarrubias (1971), Lee and Shen (1969), Strohm and Johnson (1971),
and Eisenstein, et al (1972). The study described in this report involved a review of the analysis
procedures employed in previous investigations and a parametric study to
determine the effects of a number of factors on the size of the calcu-
lated tension zone and the magnitude of the calculated tensile stress.
These factors were: (1) The analysis procedure--gravity turn-on and con-
struction- sequence analyses, (2) the modulus of the embankment soil,
(3) the tensile strength of the embankment soil, and (4) the shape of
the abutment profile.
A previous report under this research project was concerned with
hydraulic fracturing on horizontal planes (Nobari, Lee and Duncan, 1973),
and a subsequent report will consider longitudinal cracks and their effect
on embankment stability.
Field Experience - Many Dams ara Damaged by Transverse Cracks
Casagrande (1950) described two cases where differential settlements
resulted in development of transverse cracks across dams of such a
severe nature that major piping ensued and the reservoirs had to be emptied.
The details of the two cases. differ, but it is evident that the transverse
cracking was in both cases caused ~y differential settlements, the dams
being unable to conform with these movements without cracking.
Peterson and Iverson (1953) described the failures of two low earth
dams in western· Canada, In both cases the fill was compacted in a very
dry condition to low density. The settlements which caused the cracking
are believed to have r~sulted from compression of the fill in the lower
part of the embankment as it became wet during reservoir filling, The fill
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above was unable to acconnnodate the resulting differential movements, and
cracked. Water flowing through these cracks eroded the soil quickly with
the result that eventually very wide channels were washed through the dam, and the reservoirs were completely emptied.
A similar occurrence caused the failure ~f Wi£t~r Dam during the
-first -filling of the reservoir (U. S. Army Engineer WES, 1959; Bertram,
1967; Sherard, 1973). Large flows through cracks in the dam and evident
piping developed when the reservoir rose rapidly during a storm. The
path of leakage appeared to follow the course of the former stream channel
and probably resulted from differential settlements in the closure section.
Bird (1961) described the case of a 200-ft-high* dam with a narrow
central core. A transverse crack across the core developed above a break
in the abutment profile where there had been a haul road during construction.
Internal drains and filters controlled the erosion, but the cloudy
appearance of the water emerging from the drains indicated that there was
some amount of internal erosion.
Marsal and Ramirez (1967) described in detail the movements observed
in El Infiernillo Dam, including the development of transverse cracks near
both abutments during the first filling of the reservoir. The foundation
of the dam was rock and not very compressible, and the cracks probably
resulted from differential settlement within the dam itself due to
compression of the rockfill when wetted·by the reservoir water. The abut-
ments were steep, and the measured settlements varied along the axis of
the. dam from zero at the abutments to a maximum near the center of the
valley. There were zones of extensional strain at the top of the dam near
both abutments, and the cracking occurred in these zones.
Gordon and Duguid (1970) described the cracking at Duncan Dam in
British Columbia, which underwent extremely large .settlements during con-
struction. Because large foundation settlements (about 14 ft) were
expected, the cracking which developed was anticipated, and great effort
was devoted to minimizing the cracking and to repairing the cracks which
did develop in order to assure the integrity and safety of the dam,
Sherard (1973) has summarized a number of experiences with various
types of cracking in dams. The following important points are quoted
from his summary:
* A table of factors for converting U. s. customary units of measurement to metric (SI) units is presented on~page 7.
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- "Differential settlement cracks have been common in all types
of embankment dams with earth cores. In the great majority of
. cases no leaks have developed, the cracks have been repaired
by simple means, and the dam has subsequently performed
satisfactorily."
- "In a· small number of dams, concentrated leaks in cracks have
caused serious piping damage or complete failure."
- "In many cases, severe cracking in modem, well-constructed
dams has been caused by compression of soil foundations."
Differential Settlements are an Important Cause of Cracking
The frequent association of settlements and cracking in dams leaves
little doubt that differential settlements are an important cause of
cracking in dams. Because of the requirements of compatibility of
deformations', some parts of a dam must unde~go extensional strain as it
settles differentially, and as a result differential settlements frequently
cause cracking. Leonards and Narain (1963), Lee and Shen (1959), and
Lowe (1970) have discussed the mechanism by which settlement can produce
cracking and the importance of various factors controlling the locations
and the severity of settlement cracks.
Sherard (1973) has found that transverse cracks in dams may also
be caused by shrinkage when the surface of the embankment is permitted to
dry out after compaction. He says that it is sometimes not possible to
differentiate between these two types of cracks ·and that shrinkage due to
drying may accelerate the development of cracks due to settlement and
increase the widths of settlement cracks.
Stress is a Better Criterion for Cracking than is Strain
Early studies of the tensile behavior of soils and of cracking in
dams were concerned with the tensile strain at failure and the magnitudes
of ·tensile strains in dams and used the magnitudes of these tensile strains
as the criterion for crack formation (Leonards and Narain, 1963). For
purposes of .interpreting finite element analyses, however, it is preferable
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to use stress as a criterion for crack formation, because it is possible
to have extensional strains in zones of compressive stress, as shown in
Fig. 1.
The stresses and strains in an element of soil in an embankment
dam are shown in Fig. 1. The conditions when the top of fill was at
the level of the element are denoted by A. At this stage both the
stresses and the strains in the element were equal to zero. The conditions
of the element at the time when the dam had been completed are denoted by
B. The magnitudes of both the vertical stress (o ) and the horizontal y stress (o ) increase as fill is placed on top of the element, and the x eleme~t compresses under the weight of this fill. Fig. 1 shows the
conditions for one-dimensional compression under the weight of this fill,
so that after completion of the dam the horizontal strain £ is zero and x the vertical strain e is greater than zero (compressive).· The conditions
y of the element after some settlement are also shown in Fig. 1. Depending
' on the amount o~ settlement, the strains and stresses in the element
could produce the conditions shown by either C or c'. At both points C and c' the strains are extensional, and if strain was used as a criterion of cracking, it would be considered that the strains at condition c would indicate some possibility of cracking. However, for condition C the
stresses are still compressive and there is· thus no possibility of tensile
cracking at condition c. It is thus clear that strain is not a good criterion for cracking.
When the initial stresses are not zero, strains are only indicative of
changes in stress and not the actual stresses. The stresses can remain
compressive even though the' strains are extensional. Depending on the
magnitude of the initial stress, some amount of extensional strain will
be required to induce tensile stress, as at C1 in Fig. 1. The greater the
magnitude of the initial compressive stress, the greater the amount of
extensional strain required to induce tensile stress.
At the top of the dam, where the initial stress is zero, both strain
and stress would be equally good criteria for cracking. Since there is no
stress initially, any amount of extensional strain must induce tensile
stress. Because it is relatively easy to measure movements on the crest
of a dam, it may be considerably more convenient to use strain as a
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Top of DomJ
Soil Element/
O"y (Compression}
A - ofter compaction
----------~ ... ax B- after completion Tension A Compressio~ of dam
Stresses C and c'- ofter settlement
€y (Compression)
c' c e-----a--•B
-------fllt---------lillll"£ Compressionx Extension. A
Strains
of dam
Fi Q. I STRESSES AND STRAINS DURING CONSTRUCTION AND AFTER SETTLEMENT
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criterion of surface cracking, and it has no shortcomings for this
purpose.
For cracking beneath the surface, however, strain is not a good
criterion. Stress is a better criterion for cracking at depth because
_it-takes -into-account the effects of the initial stresses,
Finite Element Analysis Procedures
Finite element analyses of tension and cracking in dams have been
performed by Covarrubias (1969,1971), Casagrande and Covarrubias (1970),
Lee and Shen (1969), Strohm and Johnson (1971), and Eisenstein, et al,
(1972), Some of these studies employed "gravity turn-on" analysis
procedures and others used analyses which simulated the actual sequence
of events involved in construction of the dam. Some of the studies were
performed assuming that the stress-strain behavior of the soil was linear,
and others were performed using ~onlinear'and stress-dependent stress-
strain behavior. The results of these different procedures were compared
during this investigation to determine the conditions for which they may
be useful.
A. Conditions Analyzed. The analyses performed during this
investigation were concerned with the behavior of a 40-ft~high embankment
dam on a 30-ft-thick compressible foundation, as shown in Fig, 2. The
conditions in the longitudinal section were analyzed assuming plane strain
conditions, which have been shown by previous studies to provide a satis-
factory degree of accuracy (Lefebvre and Duncan, 1971; Lefebvre, Duncan
and Wilson, 1973).
The finite element meshes used in the analyses are shown in Figs. 3
and 4. These meshes are essentially the same except for the profile of
the abutment rock, which is irregular for the section shown in Fig, 4.
The finite element analyses were performed using four different
procedures:
(1) Gravity turn-on analyses for dams on compressible foundations.
Forces representing the weight of the entire dam were applied
at one time. The analyses were performed in one step, and
_linear material properties were employed. The modulus values
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Rock vaney wans
:f ransverse Sect\OO
c1ay Filling at eattom of Va\\eY
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t
r 40ft
I L. ' i-... ,.. .... I r- v: ... ,...
V·ffil' .... ... '/~ ...
r- IV·~-... ... 1.#(' ...
[/~~I r "' r /~ 1.5
- L. ... .1"' 30ft
t: /~'1" &..
1 r- /dt' ~
/:.~ ... r /·~ .Jm. ~ ~~ ~ 1'_ ~- 60ft. 105ft - I
Fig. 3 FINITE ELEMENT MESH FOR THE LONGITUDINAL SECTJON
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... .....
T 40ft
30ft
1
~
I ·-p;.. '.? ,_ • r /.~ ·-• /"til' r I i- v.~ '-
r ~ I/·~ _J1 ,_ I ~tiff ~~/~ 15 L r ~~ 'L ·-• /~ 1.5 r • /·'1" r '-r ~~ i- /~_JI ~ /r# 1.5 ·-i- /t?P '-• r /fc
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for these analyses were calculated using the formulas for
tangent modulus and tangent Poisson's ratio used by Kulhawy,
Duncan and Seed _(1962)_, ass_uming _at--rest pI"es-sur-e condi-tion-s
in each element for the purpose of calculating the modulus.
This procedure gave modulus values of about the same magnitudes
as those used in the incrementally nonlinear construction
sequence analyses,
(2) Construction sequence analyses for embankments on rigid founda-
tions. The nodal points at the bottom of the dam were assumed
fixed so that there was no foundation settlement. Construction
of the embankment was simulated in eight increments, each
involving placement of a 5-ft layer of fill. The values of
Young's modulus and Poisson's ratio for each element were
reevaluated at each step of the analysis, using the formulas
for tangent modulus and tangent Poisson's ratio used by Kulhawy,
Duncan, and Seed (1969), Each step was analyzed twice, the
first time using modulus and Poisson's ratio values correspond-
ing to the stresses in each element at the beginning of the
increment, and the second time using modulus and Poisson's
ratio values corresponding to the average stresses during the
increment.
(3) Construction sequence analyses for embankments on compressible
foundations. The analysis procedures were the same as for
embankments on rigid foundations. The properties of the
foundation soil were varied to achieve various amounts of
settlement during construction.
(4) Analyses to simulate settlement after construction, Starting
from the ~nd-of-construction condition with a relatively small
amount of settlement, displacements were imposed at the base
of the embankment to simulate settlement after construction.
The shape of the final settlement profile was the same as that
calculated in the construction sequence analyses with compres-
sible foundations. These varied slightly depending on the
embankment properties, which had a small effect on the settlements.
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The shape of a typical final settlement profile is shown in Fig. 5. The settlement at the base of the embankment was in-creased gradually, in four equal steps, from the end-of-
construction profile to the long-term settlement profile.
B •. Material Properties. Two sets of dam material properties were used in the analyses. As shown in Fig. 6, these corresponded to the properties of Pittsburg sandy clay compacted to two different water contents. The relatively soft properties were selected for a compaction condition wet of optimum water content, and the relatively stiff properties were selected for a condition of higher dry density at optimum water content. Stress-strain curves for these conditions are shown in Fig. 7, and the values of the stress-strain parameters used in the analyses are listed in Table 1. These data are taken from the report by Kulhawy, et al. (1969).
The foundation properties used in the analyses were selected to be representative of the properties of undisturbed clays. The values of the stress-strain_parameters for the foundation were varied to achieve various amounts of settlement in the foundation, as shown in Table 2.
A review of data relating to the tensile strength of soils showed that some soils have v_ery high tensile strength in laboratory tests, while others have essentially no tensile strength. In view of the difficulty of generalizing.these divergent results it was decided to perform analyses using two extreme assumptions concerning the tensile strength of the compacted embankment material. These were:
(1) That the tensile strength was high, and that the embankment material was capable of withstanding any tensile stress, provided only that the resulting state of stress did not exceed that corresponding to the limiting values defined by the strength parameters c and ~ and the confining pressure, a3 • The same procedures as described by Kulhawy, Duncan and Seed (1969) were used in calculating the values of tangent modulus (Et) except · that the values of initial tangent modulus (Ei) for values of cr3 less than one atmosphere were assumed to vary with cr3 as shown in Fig. 8. These values of Ei are proportional to the strength of the material, (cr1-a3)f' calculated using the values of c, ~, and cr3 •
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N 0
..-------------------------------------------------------~' ,7 Longitudinal Section of the Dom
End-·of-Construction Settlement Profile -- o----------------1 -- c g .o.5 -E Imposed Displacement '5 3 1.0 >~ L----...!.--~----.,, 1.5
0 Long..:rerm Settlement Profile
Fig. 5 SETTLEMENT PROFILE FOR EN[}-()F-CONSTRUCTION AND LONG-TERM CONDITION
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Table 1. Stress-Strain and Strength Characteristics of Embankment Fill Material
Condition (See Fig. 6) Soil Parameter
Stiff Soft
Unit Weight, y (ton/ft 3) 0.0645 0.0645
Cohesion Intercept, c (ton/ft 2 ) 1. 72 1.40
Friction Angle, cf> (degrees) 12 4
Modulus Number, K 720 200
Modulus Exponent, n 0.25 0.50
Failure Ratio, Rf 0.93 0,93
Poisson's Ratio Parameter, G 0.4 0.4
Poisson's Ratio Parameter, F 0 0
Poisson's Ratio Parameter, d 0 0
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! I
!
I
I
I
Table 2. Stress-Strain and Strength Characteristics of Foundation Soils
Settlement, End of Construction*-ft Soil Parameter
-0.3 -0.4 -1.3 . -1.4.
Unit Weight, y (ton/ft 3 ) 0.058 o·.058 0.058 0.058
Cohesion Intercept, c (ton/ft2 ) 0.75 0.75 o. 75 0.75
Friction Angle, cj> (degrees) 0 0 1 0
Coeff. of Lat. Earth Pressure at Rest, K 0
0.6 0.6 0.6 0.6
Modulus Number, K 150 160 125 110 I
Modulus Exponent, n 1.0 1.0 i 1.0 1.0
Failure Ratio, Rf 0.8 0.8 ! 0.8 I 0.8 i
I Poisson 1 s Ratio Parameter, G 0.45 0.45 I o. 36 o. 36
Poisson's Ratio Parameter, F 0 0 ! 0 0 I !
Poisson's Ratio Parameter, d 0 i 0 ; 0 0 I
I
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*At the bottom of the embankment at the centerline. The magnitudes of the settlements also varied slightly from case to case depending on the properties of the embankment fill material.
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125
Harvard Miniature Compaction
' 7 Layers, 15 Tamps/ Loyer \ ' ' ' \ ' ' 0 12.5-lb Tamps 120 \ ' ' \ ' l:l. 25..fb Tamps \ ' \ ' 0 50-lb Temps \ ' .., \ ' Mod. AASHO \ ' • - \ ' Mox. Density ~ ' ::2 ' 115 ' ' "" ' - ' ·- ' ., ' c • ' 0 ' ' "" 110 ' ' d ' ' ' ' ' \ ' ',~ \ ' ' .... \ ' ' l'a 105
\ \I' ' ',~% \ .... ~ ',IS\ \ ~ 'cs;, ..:-.... ' ' \* ,c90 ' ',.g. '
100 8 10 12 14 16 18 20 22 24
Water Content - %
Fig. 6 OOMPACTION CHARACTERISTICS FOR PITTSBURG SANDY CLAY
23
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N -' .,, c 2 -rt) b I
0 -
Stiff 5
0"3: 1.0 t /f t2
CT3= 0 4
er 3 = -1.0 t/ft2
cr3 s1.0 t/ft2 _ O 3 0'3- 0'3 = -1.0 t/f t2
2
O'--------"------------------------..._----~ 0 4 8 12 16 20 Axial Strain - 0/o
Fig. 7 STRESS-STRAIN CURVES FOR PITTSBURG SANDY CLAY
AT TWO COMPACTION CONDITIONS
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., :J :J
"O OC\a :! -' .. ., c fS Q) -g' I 0 ·-t- ll.J -0 ·-:t: c ....
1200
1000
800
600
400
200
0
I Hi9h Tensile Strength I High Modufus in Tension
Ten... I ~comp.
-3 -2 -I 0 I 2 3
., ::J
1200
:; 1000 "O
~~ 800 -.... _ ...... ; ~ 600 O' .2 C I
{:. w 400 0 +:
. ·- 200
Minor Principal Stress - cr3 - tons/ft2
l Low Tensile Stren9th f
- Modulus~ 0 in Tension
Ten . .,..__-+-•
c - 0--------------------------------3 -2 -I 0 I 2
Minor Princi pol Stress - cr3 - tons/ft2
Fig. 8 MODULUS VARIATIONS FOR HIGH-TENSILE-STRENGTH AND LOW-TENSILE-STRENGTH ASSUMPTIONS
2.5
3
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(2) That the tensile strength of the embankment material was
essentially zero. The modulus values were calculated using the
procedures described by Kulhawy, Duncan, and Seed (1969). As
shown in Fig. 8, ~th_e values __of -init-ial tan-gent modulus defineil
by the equations used in this procedure decrease to zero as the
value of cr3 decreases to zero. For calculated values of cr3 less
than zero, the value of Ei was taken equal to a very small value,
for practical purposes zero.
These two assumptions correspond to the extreme conditions of very
high tensile strength and essentially no tensile strength, and comparison
of the results of analyses performed using these assumptions provided a
basis for judging the effect of tensile strength on the locations and the
sizes of zones of tensile stress in embankments.
Tension Zones Calculated by Gravity Turn-On and Construction Sequence Analyses Are Not the Same
Contours of cr3 calculated in three finite element analyses of the
longitudinal section are shown in Fig. 9. The procedures used in these
analyses were as follows:
(1) The gravity turn-on analysis shown at the top of Fig. 9 was
performed by applying loads representing the weight of the
embankment to the mesh representing the embankment and foundation,
as if the embankment had been constructed in a gravity-free
environment and then gravity had been turned on. These loads
produced a settlement of 1.46 ft at the base of the dam at the
centerline. Loads were not applied to represent the weight of
the foundation.
(2) The construction sequence analysis shown in the center of Fig. 9
was performed in increments, building up the embankment layer by
layer on a foundation which was sufficiently compressible so that
the end-of-construction settlement at the base of the dam at the
centerline was 1.42 ft,
(3) The construction sequence analysis shown at the bottom of Fig. 9
was also performed in increments, building up the embankment
26
-
0.4 t/ft2
a.--0.8
Gravity Turn-on Analysis. 1.46 ft of Settlement at Bose of Dom ot Center Line
0.4 t/ft 2
...... -0.8
.,__ 1.2 ------
Construction .. Sequence Analysis. 1.42 ft of Settlement During Construction
0.4 t/ft2 0.8 1.2 ---
, Construction Sequence Analysis. 0.34 ft of Settlement During Construction 1 1.08 ft of Settlement After Construction, Total Settlement 1.42 ft
·Fig. 9 COMPARISON OF MINOR PRINCIPAL STRESSES CALCULATED BY THREE DIFFERENT METHODS OF ANALYSIS. STIFF MATERIAL - HIGH TENSILE STRENGTH
27
-
layer by layer on a foundation of sufficient compressibility so that the end-of-construction settlement at the base of the dam was 0.34 ft. Subsequently, in additional steps, displace-ments were imposed along the base of the dam to simulate settlement after construction, conforming to the shape of the settlement profile shown in Fig. 5. The final settlement at the base of the dam at the centerline was 1.42 ft.
The contours of a3 in Fig. 9 indicate that the construction sequence analysis with all settlements occurring during construction produced.the least extensive zone of tension and the smallest tensile stresses. The gravity turn-on analysis and the construction sequence analysis with most of the settlement after construction produced much larger zones of tension and much higher tensile stresses.
The size of the tensile zone for the construction sequence analysis with settlement after construction is somewhat greater than for the gravity turn-on analysis. This aifference is not considered to be significant, however, because the material properties used in the two analyses corres-pond only approximately. The gravity turn-on analyses were necessarily linear, and there is thus an inevitable difference between these analyses and construction sequence analyses, which used nonlinear properties. The modulus values used in the gravity turn~on analysis were calculated using the same values of the stress-strain parameters as used in the construction sequence analyses, for assumed at-rest pressures in each element. The modulus values used in the two types of analyses thus correspond approxi-mately, but not so closely that the difference between the results of the grav~ty turn-on and construction sequence analysis with settlement ·after construction can be considered significant.
It can be seen that in the cases of the gravity turn-on analysis and the sequence analysis with settlement after construction, the largest tensile stress is at the top of the embankment over the sloping abutment. This appears to be a result of the fact that, as the already-completed embankment settles, it behaves somewhat like a beam which is fixed at the end and the maximum tensile stress develops in the extreme fiber. This behavior is modified somewhat in the case of the sequence analysis with all
28
-
settlement during construction, because only a portion of the embankment
exists when the settlement occurs. As a result the tensile zone is much ,
smaller, the tensile stress is much lower, and the location of the maximum
tensile stress is below the surface of the embankment.
Tension Zones Calculated in Gravity Turn-on Analyses Depend Primarily on the Ratio of Moduli in Dam and Foundation
Contours of a3 calculated for two gravity turn-on analyses are shown
in Fig, 10. In both cases.the modulus values were constant throughout the
dam and throughout the foundation, and the ratios of dam modulus to founda-
tion modulus were 5. It may be seen that even though the modulus values
used for the analysis at the top were 20 times as large as those used for
the analysis at the bottom, the results are exactly the same.
The reason is that the other factors (Poisson's ratio and unit weight)
were the same for the two analyses. Under these conditions the settlement
depends only on: the modulus values. ·As the foundation modulus decreases,
the settlement increases, and the strains in the dam increase corresponding-
ly. If the dam modulus decreases in pro~ortion with the foundation modulus,
the changes in the magnitudes of strains and modulus in the dam compensate
each other perfectly, and the stresses remain exactly the same. Thus, in
gravity turn-on analyses, the absolute magnitudes of the moduli of the dam
and foundation are of no importance for the magnitude of the tensile
stresses, Only their ratio affects the results.
The results in Fig, 11 show that as the embankment becomes successively
stiffer than the foundation, the size of the tensile zone and the magnitude
of the tensile stresses increase,
Settlements After Construction Are More Likely to Produce Cracking than is Settlement During Construction
Contours of cr3 for three different conditions are shown in Fig. 12:
(1) Those shown at the top were calculated using construction sequence
analyses, for conditions of a stiff foundation. The end-of-construction·
settlements at the base of the embankment at the centerline were between
0,3 ft and 0,4 ft. (2) Those shown in the center were calculated using con-
struction sequence analyses with a more compressible foundation, The
29
-
---OA-t/tt2-__ _
--o.a---
0.4 t/ft 2---0. 8 ---
Ed = 1000 =S Et 200
Fig. 10 CONTOURS OF MINOR PRINCIPAL STRESS
C~LCULATED BY LINEAR GRAVITY TURN-ON ANALYSES
USING DIFFERENT MODULUS VALUES BUT THE SAME
RATIO OF THE DAM MODULUS TO THE FOUNDATION
MODULUS
30
-
1------ 0.4 t/ft 2 ---t----- 0.8 --t-------1.2 ---
.6
t---0.4 t/ft2_~ t----0.8
t----0.8 1.2
1.2 Ed .1Q=I Et 40
Ed 380 - =-=IO Et 38
Fig. 11 CONTOURS OF MINOR PRINCIPAL STRESS CALCULATED
BY GRAVITY TURN -ON LI NEAR ANALYSES USING
DIFFERENT RATIOS OF THE DAM MODULUS TO THE FOUNDATION MODULUS
31
-
w N
Hioh. Tensile Strength - Stiff Material Properties
0.8
t-----1.2 -~
1.6
0.34 ft of Settlement Ourino Construction
L------0.4 t/ft----1-----0.a----l,------1.2---
1.42 ft of Settlement Durino Construction
0.34 ft of Settlement Durino Construction 1.08 ft of Settlement After Construction I. 42 ft of Toto I Settlement
Hioh Tensile Strength - Soft Material ProPerties
0.4t/ft1·----------',~' J.----0.8 ----------~ 7 1-----1.2 --------~ 1---~l.6
0.37 ft of Settlement Ourino Construction
1---- 0.4 t/ft2-----
l2
t----1.6
1.35 ft of Settlement Durino Construction
i-----0.4 t/ft2·----t----0.8----t----1.2
i-----1.6
0.37 ft of Settlement Ourino Construction 0.98 ft of Settlement After Construction I .35 ft of Total Settlement
Fig. 12 CONTOURS OF ~ IN EMBANKMENTS WITH HIGH TENSILE STRENGTH
-
end-of-construction settlements were about 1. 4 ft. (3) Those shown at the
bottom were calculated using construction sequence analyses with some
settlement during constructicP~ and addition-al settlement- after- construc-
tion. The end-of-construction settlements were the same as at the top of
the figure, and the final settlements were the same as in the center of the
figure.
The tensile stresses calculated for the cases where most of the
settlement occurs after construction are considerably larger than for the
cases where all of the settlement occurs during construction. Thus, while
there is a tendency for larger settlements to produce larger zones of
tension and larger tensile stresses, the time of occurrence of the settle-
ment is more important than the magnitude of the settlement.
Large Zones of Tension Are More Likely When the Dam Material is Stiff
The results shown on the left side of Fig. 12 were calculated using
stiff material properties in the dam and those on the right side were
calculated using soft material properties. It can be seen that the zones
of tension and the magnitudes of the tensile stresses are smaller for the
soft dam. In the case where all settlement occurs during construction,
there is an appreciable zone of tension in the stiff dam but none in the
soft darn. In the case where most of the settlement occurs af~er construction,
the tensile zone is considerably larger and the maximum tensile stress is
about twice as high for the stiff dam as for the soft darn.
The Size of the Tension Zone is About the Same for High and Low Tensile Strength
All of the results shown in Fig. 12 were calculated assuming that the
tensile strength of the dam material was high, and the calculated tensile
stresses were quite large for some cases. To investigate the effect of the
assumed tensile strength, similar analyses were performed assuming that
the tensile strength of the material was essentially zero. As soon as
tension developed within an element, it was assigned a very small modulus
value, thus simulating practically complete loss of resistance to further
33
-
deformation. The results of these analyses are shown in Fig. 13. The
contours of cr3 at the top were calculated for relatively small.settlements -during construc~ion, ana those at the bottom were calculated for the same
amounts of settlement during construction followed by considerably more
settlement after construction.
Comparing the results in Figs. 12 and 13, it can be seen that the
magnitudes of the tensile stresses are much smaller when the tensile
strength is assumed to be negligibly small, but the sizes of the tensile
zones are not much different. It may be concluded, therefore, that the
locations and size of tensile zones can be predicted fairly reliably even
though the tensile strength of the dam material may be difficult to measure
or estimate accurately.
This result seems curious in one respect: It would be anticipated
that a material with negligible tensile strength would crack at the first
tendency for tension to develop and that the cracking would relieve the
tensile stresses. There may thus be a difference between the results shown
in Fig. 13 and the results which would be achieved if it was possible to
simulate actual cracking and crack propagation. Such an analysis might
show one or more open cracks surrounded by intact material-under no tensile
stress.
Even though they are based on simplifying assumptions regarding
tensile strength· and the mechanism of tension failure, the results shown
in Figs. 12 and 13 are probably sufficiently accurate for most practical
purposes. It would be anticipated that tension cracks might develop anywhere
within the shaded tension zones shown in these figures. Because the
locations and sizes of these zones are about the same for extreme assumptions
regarding tensile strength, these analyses appear to provlde a fairly reliable
indication of the region within the embankment within which cracking might
occur.
Some Types of Abutment Irregularities Have Little Effect on Tension Zones
·The results in Figs. 14 and 15 compare the contours ~f o3 for cases
where the abutment profile is irregular with the results of the previous
cases, where the abutment profile was smooth. When these cases were analyzed,
34
-
Low Tensile Strenoth - Stiff Moterior Properties
-----1.2
1.6
0.34 ft of Settlement Ourino Construction
0.34 ft of Settlement Ourino Construction
1.08 ft of Settlement After Construction
1.42 ft of Totol Settlement
Low Tensile Stren9th - Soft ~oteriol Properties
----0.4 t/ft2-----------
----0.8 ---------
1-----1.2 --------~---1.6 -----
0.37 ft of Settlement Ourin9 C.onstruction
._ __ 0.4 t/tt2----
._ __ 0.8 -----1---- I. 2----
i---- 1.6
0.37 ft of Settlement Ourino Construction
0.98 ft of Settlement After Construction
1.35 ft of Totol Settlement
Fig. 13 CONTOURS OF cr3 IN EMBANKMENTS WITH LOW TENSILE STRENGTH
-
Hioh Tensile Strenoth - Stiff Moteriol Properties
0.34 ft of Settlement Ourino Construction
....._--0.4 t/ftZ-----
....._ __ OB~-----. 1----1.2----
1.42 ft of Settlement Ourino Construction
0.4 t/ft2----o.e----1.2---
0.34 ft of Settlement During Construction 1.08 ft of Settlement After Construction 1.42 ft of Total Settlement
Hioh Tensile Strength - Stiff Material Properties
0.36 ft of Settlement Ourino Construction
1.34 ft of Settlement Ourino Construction
0.36 ft of Settlement During Construction 0.98 ft of Settlement After Construction · I. 34 ft of Total Settlement
Fig. 14 CONTOURS OF a-3 IN EMBANKMENTS WITH HGH TENSILE STRENGTH - EFFECT OF IRREGULAR ABUTMENT
-
Low Tensile Stre"9th - Stiff Material Properties
a-----0.4 t/ftl 1-----0.a---~ ----1.2 ___ _
1.6
0.34 ft of Settlement Ouri09 Construction
0.34 ft of Settlement Ourino Construction
1.08 ft of Settlement After Construction
1.42 ft of Total Settlement
Low Tensile Strength - Stiff Material PropertitJ
0. 36 ft of Settlement Ourin; Construction
0.36 ft of Settlement Ourino Construction
0.98 ft of Settlement After Construction
1.34 ft of Total Settlement
7
Fio. 15 CONTOURS OF CT3 IN EMBANKMENTS WITH LOW TENSILE STRENGTH - EFFECT OF IRREGULAR ABUT~ENT
-
it was expected that they would_provide examples -demonstrating a great
effect of irregularities in abutment profile. In fact, however, the
results show just the opposite. They show that in some cases there is not
a great effect of abutment shape.
The reason for this somewhat surprising effect is that nearly all of
the settlement occurred within the foundation, and very little was due to
compression of the embankment. Therefore, the amount of differential
settlement due to the irregularity of the abutment was minor and was not
large enough to change the extent and location of the tension zone.
If there had been a greater amount of settlement due to the compres-
sibility of the dam material, the abutment irregularity would have had a
larger influence on the tension zone. It is significant that settlements
due to time-dependent compression of the dam material have not been
considered in these analyses, In cases where settlements due to, compres-
sion of the dam material are appreciable, abutment irregularities as severe
as those shown on the right-hand sides of Figs, 14 and 15 would have a
significant effect on the magnitude of the tensile stresses and the size
of the tensile zones.
Whether or not an irregularity in the abutment profile will signifi-
cantly affect the zones of tension within an embankment thus appears to
depend on its effect on the settlement of the dam, If the irregularity
causes significant differential settlement in the embankment, due to
compression of either the foundation or the dam material, it will increase
the size of the tensile zones and the magnitudes of the tensile stresses,
In cases like those shown in Figs, 14 and 15 on the othe;r hand, the abutment
irregularity do~s not result in appreciable differential settlements, or in
any significant effects on the tension zones.
Hydraulic Fracturing Can Increase the Size of the Zone of Potential Cracking
The analyses discussed in the previous pages have all represented
the longitudinal section using plane strain conditions, and all are total
stress analyses, The susceptibility of soil to tension cracking is governed
by effective stresses, however, as discussed by Kjaernsli and Torblaa (1968),
Vaughan (1970), and Nobari et al (1973), Cracking is possible under conditions
38
-
where the total stress is still compressive, but is smaller than the
water pressure. For the 40- ft-high embankment:_ considered- in- this~ report,
the water pressure at the bottom of the embankment would be on the order
of 1.0 tons/ft2 if the reservoir level was 5 ft to 10 ft below the crest.
Thus, at the bottom of the dam, the water pressures could exceed the
total stresses wherever the value of cr3 is less than about 1 ton/ft2 • The magnitude of the compressive total stress required to prevent hydrau-
lic fracturing would decrease linearly ·from about 1 ton/ft 2 at the base
of the dam to zero at the reservoir water level. Examination of the
contours of a3 in Figs. 9 through 15 show that the zone subject to crack-ing by hydraulic fracturing could be appreciably larger than the zone of
tension. Accurate evaluation of the likelihood of hydraulic fracturing
on transverse planes would require three-dimensional analyses, including
the effects of the water loads on the stresses in the dam. Although the
three-dimensional effects and the changes in stress within the dam due
to the water loads are not included, the simplified analyses described in
this report can provide at least an approximate guide as to the areas of
the dam where transverse hydraulic fracturing would be expected.
Conclusions
This study illustrates the effects·of several factors which in-
fluence the likelihood of transverse cracking in dams. From these
studies the following conclusions may be drawn:
(1) The tension zones calculated by gravity turn-on and construc-
tion sequence finite element analyses are not the same.
This same conclusion was reached previously by Strohm and
Johnson ( 1971) who also performed comparative studies. The
results of gravity turn-on analyses appear to be most rep.re-
sentative of cases where a large part of the settlement occurs
after construction.
(2) The principal factor controlling the results of gravity
turn-on analyses is the ratio of the modulus of the dam to
the modulus of the foundation. For cases where the unit
weights and Poisson's ratio values are the same, the calculated
39
-
stresses depend only on the ratio of these modulus values.
(3) The values of the stress-strain parameters used in construction
sequence analyses can be determined rationally from the results
of laboratory tests. In cpntrast, it is difficult to select
suitable modulus values for gravity turn-on analyses because the
soil behavior is assumed to be linear, and it is very difficult
to determ~ne a single modulus value which can represent the
behavior of the soil in all parts of a dam with a high degree
of accuracy.
(4) Differential settlements can lead to development of extensive
zones of tension and quite high values of tensile stress with-
in dams. Settlements which occur after construction lead to
much larger zones of tension and much higher tensile stresses
than do settlements which occur during construction.
(5) The stiffer is the material of the dam, the larger will be the
zone of tension and the greater will be the tensile stresses
resulting from the same amount of differential settlement. The
finite element analyses indicated that compacting the dam
material on the wet side of optimum can reduce the stiffness
sufficiently to greatly reduce the tensile stresses 'in embank-
ments and to eliminate tensile stresses completely in some
cases.
(6) The finite element analyses also showed that the tensile
strength of the soil does not have a large effect on the size
of the .zones of tension caused by differential settlements.
Analyses performed using extreme assumptions regarding the
tensile strength of the dam material resulted in zones of
tension which were of nearly equal size.
(7) The analyses showed that some types of abutment irregularities
do not result in significantly larger zones of tension. It
may be inferred from these studies that abutment irregularities
will have a large effect on the zones of tension only when the
irregularities give rise to differential settlements of signifi-
cant magnitude.
40
-
(8) Cracking or hydraulic fracturing may occur in areas where the
total stresses are compressive but are smaller in magnitude-
than the water pressures. The plane strain analyses performed
in this study provide a basis for an approximate assessment of
the danger of hydraulic fracturing, and indicate that the size
of the zone where hydraulic fracturing can occur may be
appreciably larger than the zone of tension.
(9) The methods and techniques employed in these finite element
analyses could be used _to make detailed evaluations of crack-
ing for complex conditions in actual dams where the conditions
may be different from those considered in this report,
41
-
LTTERATURE -CITED
Bertram, G. E. (1967) "Experience with Seepage Control Measures in Earth and Rockfill Dams," Transactions of the 9th International Congress on Large Dams, Istanbul, Vol. 3, p. 91.
Bird, John M. (1961) "Uncertainties in Earth Dam Design, 11 Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 87, No. SM3, June, PP• 33-68.
Casagrande, A. (1950) "Notes on the Design of Earth Dams," Journal of the Boston Society of Civil Engineers, October.
Casagrande, A. and Covarrubias, S. W. (1970) "Cracking of Earth· and Rock-fill Dams," Contract Report No. S-70-7, U. S. Army Engineers Waterways Experiment Station, Vicksburg, Mississippi.
Covarrubias, S. W. (l9p9) "Cracking of Earth and Rockfill Dams, 11 Harvard Soil Mechanics Series No. 82.
Covarrubias, s. W. (1971) "Cracking of Earth and Rockfill Dams. Comparison of Observed and Theoretical Tensile Strains in the Crests of Two Earth and Rockfill Dams," Contract Report s...:71-11, U. S, Army Engineers Waterways Experiment Station, Vicksburg, Mississippi, April. ·
Eisenstein, z., Krishnayya, A. v. G. and Morgenstern, N, R. (1972) "An Analysis of Cracking in Earth Dams," Proceedings of the Symposium on Applications of the Finite Element Method in Geotechnical Engineering, U. s. Army Engineer Waterways Experiment Station.
Gordon, J. L. and Duguid, D. R, (1970) "Experiences with Cracking at Duncan Dam," Transactions of the 10th Congress on Large Dams, Vol. 1, pp. 469-486,
Kj aernsli, B, and Torblaa, I. (1968) "Leakage through Horizontal Cracks in the Core of Hyttejuvet Dam," Norwegian Geotechnical Institute, Publication No. 80.
Kulhawy, F, H., Duncan, J.M. and Seed, H.B. (1969) "Finite Element Analysis of Stresses and Movements in Embankments During Construction, 11 Report No. TE 69-4, Office of Research Services, University of California, Berkeley,
Le~, K. L. and Shen, C. K. (1969) "Horizontal Movements Related to Subsi-dence," Journal of the Soil Mechanics and Foundations Division, ASCE, Vol, 95, No. SMl, January, p. 139.
Lefebvre, G, and Duncan, J. M. (1971) "Three-Dimensional Finite Element Analyses of Dams," Report No. TE 71-5, College of Engineering Office of Research Services, University of California, Berkeley, May,
42
-
Lefebvre, G., Duncan, J. M. and Wilson. E. L. (1973) "Three-Dimensional Finite Element Analyses of Dams," Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 99, No. SM7, July.
Leonarda. G. A. and Narain,. J. (1963) "Flexibility of Clay and Cracking of Earth Dams, 11 Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 89, No. SM2, March, PP• 47-98.
Lowe, J., III (1970) "Recent Developments in the Design and Construction of Earth and Rockfill Dams," Transactions of the 10th Congress on Large Dams, Vol. 5, pp. 1-60.
Mars al, R. J. and Ramirez, L. (196 7) "Performance of El Infiernillo Dam, 1963-66, 11 Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 93, No. SM4, July, pp. 265-298.
Nobari, E. s., Lee, K. L. and Duncan, J. M. (1973) "Hydraulic Fracturing in Zoned Earth and Rockfill Dams," Department of Civil Engineering, University of California, Berkeley, Report No. TE-73-1.
Peterson, R. and Iverson, N. L. (1953) "Study of Several Low Earth Dam Failures," Proceedings of the 3rd Int. Conf. on Soil Mech. and Found. Eng., Vol. 2, pp. 273-276.
Sherard, James L. (1973) "Embankment Dam Cracking, 11 published in Embankment-Dam Engineering - The Casagrande Volume, Edited by R. C. Hirschfeld and s. J. Poulos, John Wiley and Sons.
Strohm, W. E. and Johnson, s. J. (1971) "The Influence of Construction Step Sequence and Nonlinear Material Behavior on Cracking of Earth and Rockfill Dams," U. S. Army Engineers Waterways Experiment Station, Miscellaneous Paper S-71-10, May.
U. s. Army Corps of Engineers, Waterways Experiment Station (1959) "Review of Soils Design, Construction and Performance Observations, Wister Dam, Oklahoma," WES Tech. Report No. 3-505.
Vaughan, P. R. (1970) "Cracking of Clay Cores of Dams," Proceedings of the British Geotechnical Society, January.
43
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APPENDIX A
Additional Results of Finite Element Analyses
This report is concerned with the development of transverse cracks
in embankment dams, and the best way of assessing the likelihood of
cracking in dams is by examining the calculated values of minor principal
stress. Therefore, in the figures of the report, only the contours of
minor principal stress have been presented and discussed. For other purposes
it may sometimes be useful to have the complete stresses and displace-
ments within the dam available, and for this reason contours of the cal-
culated stresses and displacements have been prepared and are included in
this appendix. These results include the minor principal stresses, the
major principal stress orientations, the vertical displacements, and the
horizontal displacements, Contours of major principal stress and maximum
shear stress are included for some cases.
The figures are arranged as follows:
-Figs. A-1 through A-6 compare the results for a gravity turn-on
analysis, a construction sequence analysis with 1.4 ft of settle-
ment during construction, and a construction sequence analysis
with 0.3 ft of settlement during construction and 1.1 ft of
settlement after construction.
-Figs. A-7 through A-12 compare the results for gravity turn-on
analyses conducted using different modulus values but the same
ratio of dam modulus to foundation modulus.
-Figs, A-13 through A-18 compare the results for gravity turn-on
analyses conducted using three different ratios of dam modulus to
foundation modulus,
-Figs. A-19 through A-22 compare the results of construction
sequence analyses for a stiff embankment with high tensile
strength on three different foundation conditions.
-Figs, A-23 through A-26 compare the results of construction
sequence analyses for a soft embankment with high tensile strength on three different foundation conditions.
45
-
-Figs. A-27 through A-30 compare the results for a stiff embankment
with high tensile strength, for various amounts of settlement after
construction, beginning from a settlement of 0.34 ft at the end of
construction,
-Figs. A-31 through A-34 compare the results for a stiff embankment
with low tensile strength, for various amounts of settlement after I
construction, beginning from a settlement of 0.34 ft at· the end of
construction,
-Figs. A-35 through A-38 compare the results for a soft embankment
with high tensile strength, for various amounts of settlement
after construction, beginning from a settlement of 0.37 ft at the
end of construction.
-Figs. A-39 through A-42 compare the results for a soft embankment
with low tensile strength, for various amounts of settlement after
construction, beginning from a settlement of/0.37 ft at the end of
construction.
-Figs. A-43 through A-46 compare the results for a stiff embank-
ment with high tensile strength, on three different foundation
conditions, each with an irregular abutment profile.
-Figs. A-47 through A-50 compare the results for a stiff embank-
ment with high tensile strength, and with an irregular abutment
profile, for various amounts of settlement after construction,
beginning from a settlement of 0.36 ft at the end of construction.
-Figs. A-51 through A-54 compare the results for a stiff embankment
with low tensile strength and with an irregular abutment profile,
for various amounts of settlement after construction, beginning
from a settlement of 0.36 ft at the end of construction.
46
-
1.4 1.2 1.0
Gravity Turn-on Analysis. 1.46 ft of Settlement at · Bose of Dam at Centerline.
-- 0.2ft -----t--- 0.4
.,___ 0.6 ------- 0.8-----
1.0----1.2---. .
Construction Sequ ance Analysis. 1.42 ft of Settlement During Construction.
06 0.4 Q2ft 1.0 0.8 .
1.2
1.4
Construction Sequence Analysis. 0.34 ft of Settlement During Construction. 1.08 ft of Settlement After Construction, · Total Settlement 1.42 fl
Fio~ A-I VERTICAL DISPLACEMENTS CALULATED BY THREE DIFFERENT ANALYSIS PROCEDURES .
47
-
-0.02 --------o.os ------0.1
Gravity Turn-on Analysis. 1.46 ft of Settlement at Base of Dam at Centerline.
Construction Sequence Analysis. 1.42 ft of Settlement During Construction.
0.10
0.02ft
Construction Sequence Analysis. 0.34 ft of Settlement During Construction, 1.08 ft of Settlement After Construction, Total Settlement 1.42 ft.
Fig. A-2 HORIZONTAL DISPLACEMENTS' CALULATED BY THREE DIFFERENT ANALYSIS PROCEDURES
48
-
2.0 t/ft
i..---1.6
Gravity Turn-on Analysis. 1.46 ft of Settlement ot Bose of Dom at Centerline .
.__ ___ 0.4 t/ft2 --------------~ ,,___ ___ 0.8 1.2
1.6 ------~-::::::::::-2. 0 ------2.4
Construction Sequence Analysis. 1.42 ft of Settlement During Construction.
1.6 t/ft2
Construction Sequence Analysis. 0.34 ft of Settlement Durino Construction, 1.08 ft of Settlement After Construction, Total Settlement 1.42 ft.
Fig. A-3 MAJOR PRINCIPAL STRESSES CALULATED BY THREE DIFFERENT ANALYSIS PROCEDURES
' I
49
-
0.4 t/ft 2
1--- 0.8
Gravity Turn-on Analysis. 1.46 ft of Settlement at Bose of Dam at Centerline.
0.4 t/ft2
--o.e --1.2
Construction Sequence Analysis. 1.42 ft of Settlement During Construction.
0.4 t/ft2 ----0.8 ----1. 2.
Construction Sequence Analysis. 0.34 ft of Settlement During Construction, 1.08 ft of Settlement After Construction, Total Settlement 1.42 ft.
Fi9. A-4 MINOR PRINCIPAL STRESSES CALULATED BY THREE DIFFERENT ANALYSIS PROCEDURES
50
-
_.... / I /. / / / I
I I I / / I /
Gravity Turn-on Analysis. 1.46 ft of Settlement at Base of Dom at Centerline.
--\ I /
I
I
/
I
I
I
/
Construction Sequence Analysis. 1.42 ft of Settlement During Construction.
- -\
- - / - / / / / /
I
I I
Construction Sequence Analysis. 0.34 ft of Settlement During Construction, 1.08 ft of Settlement After Construction, Total Settlement 1.42 ft.
Fig. A-5 MAJOR PRINCIPAL STRESS DIRECTIONS CALULATED BY THREE DIFFERENT ANALYSIS PROCEDURES
51
-
..__ __ 0. 8 t/ft2
0.4: / t----0.4
a-----o.a -----
Gravity Turn-on Analysis. 1.46 ft of Settlement at Bose of Dam at Centerline.
11-----0.2 t/ft 2
------ 0.4 -----
Construction Sequence Analysis. 1.42 ft of Settlement During Construction.
--·0.2
---0.6
Construction Sequence Analysis. 0.34 ft of Settlement During Construction, 1.08 ft of Settlement After Construction, Total Settlement 1.42 ft.
Fig. A-6 MAXIMUM SHEAR STRESSES CALULATED BY THREE DIFFERENT ANALYSIS PROCEDURES
52
-
0.8 t/ft 2
1.6 ---Ed = 1000= 5 Et 200
-- 1.6 Ed 50 -=-=5 Ef 10
Fig. A-7 CONTOURS OF MAJOR PRINCIPAL STRESS CALCULATED BY LINEAR GRAVITY TURN-ON ANALYSES USING DIFFERENT MODULUS VALUES BUT THE SAME RATIO OF THE DAM MODULUS TO THE FOUNDATION MODULUS
53
-
0.4t/ft2 __ _
0.8 ---1.2
0.4 t/ft2 ---0.8
1.2
. Ed 50 -•-•5 Ef 10
Fig. A- 8 CONTOURS OF MINOR PRINCIPAL STRESS CALCULATED BY LINEAR GRAVITY TURN-ON ANALYSES USING DIFFERENT MODULUS VALUES BUT THE SAME RATIO OF THE DAM MODULUS TO THE FOUNDATION MODULUS
54
-
- _... ·/ I I - - / / / / I
I I I / / I Ed • 1000115
/ / Ef 200
- / I I - / / / ./ I I I I I I / I
Ed 50 · I . I I I I / -•-•5 Ef 10
Fig. A-9 DIRECTIONS OF MAJOR PRINCIPAL STRESS CALCULATED BY LINEAR GRAVITY TURN-ON ANALYSES USING DIFFERENT MODULUS VALUES BUT THE SAME RATIO OF THE· DAM MODULUS TO THE FOUNDATION MODULUS
55
-
11---0.6 t/ft t----0.4-~
-----0.2
t----0.4 ----0.6
r----0.4 ---r---- 0.6 Ed 50 -•-•5 Ef 10 Fig. A-10 . CONTOURS OF MAXIMUM SHEAR STRESS
CALCULATED BY LINEAR GRAVITY TURN-ON ANALYSES USING DIFFERENT MODULUS VALUES BUT THE SAME RATIO OF THE DAM MODULUS TO THE FOUNDATION MODULUS
56
-
0. :30ft 0.25 0.20 0.15 0.10 0.05
6.0ft
Ed 50 -•-•5 Ef 10
Fig. A-II CONTOURS OF VERTICAL DISPLACEMENT CALCULATED BY LINEAR GRAVITY TURN-ON ANALYSES USING DIFFERENT ,MODULUS VALUES BUT THE ,SAME RATIO OF THE DAM MODULUS TO THE FOUNDATION MODULUS
57
-
l.2ft---0.8
0.4
.Ed 50 -•-=5 Et 10
Fig. A-12 CONTOURS OF HORIZONTAL DISPLACEMENT· CALCULATED BY LINEAR GRAVITY TURN-ON ANALYSES USING DIFFERENT MODULUS VALUES BUT THE SAME RATIO OF THE DAM MODULUS TO THE FOUNDATION MODULUS
58
-
0.8 t/ft2:.__-------------~,,
I. 6
2.4
t-- l.6t/ft2 ---
2.4
1.6
0.8
o.e _______ _
Ed = 200 =5 Et 40
Ed 380 · -= -: 10 Et 38
Ag. A-13 CONTOURS OF MAJOR PRINCIPAL STRESS CALCULATED BY GRAVITY TURN-ON LINEAR ANALYSES USING DIFFERENT RATIOS OF THE DAM MODULUS TO TI4E FOUNDATION MODULUS
59
-
-1------0-.4tfft2 --~ t----- 0.8 --t------1.2 --
1.6
..---0.8
Ed = 200 = 5 Ef 40
t--0.8
t---0.4
Fig. A-14 CONTOURS CF MINOR PRINCIPAL STRESS CALCULATED BY GRAVITY TURN-ON LINEAR ANALYSES USING DIFFERENT RATIOS OF THE DAM MODULUS TO THE FOUNDATION MODULUS
60
-
I I
-
-
\ I \ l
\
-,,,- /
I
I
- ..-' / I I I
__, / I
I I I I I I
I
.,,,,- ./ I
/ / /
/ / /
I I /
I I I · I I I
I I I
/
,,_,, / I I
/ / / I I / / I
Ed 40 -=-•I Ef 40
Ed a:>O -··-=5 Et 40
EcJ 380 -· -·· 10 Et 38
Fig. A-15 DIRECTIONS OF MAJOR ~INCIPAL STRESS CALCULATED BY ~VITY TURN-ON LINEAR ANALYSES USING DIFFERENT RATIOS OF 11-IE DAM MODULUS TO THE FOUNDATION MODULUS
61
-
-----0.4 ----
Ed 40 -·-· Ef 40
Ed roo -•-•5 Et 40
Fig. A-16 CONTOURS OF MAXIMUM SHEAR STRESS CALCULATED BY GRAVITY TURN-ON LINEAR ANALYSES USING DIFFERENT RATIOS OF THE DAM MODULUS TO THE FOUNDATION MODULUS
62
-
,.___ 1.6 ft
1.2 ft 0.8 0.4
1.2 ft 0.8 0.4
Ed 40 -=-· Ef 40
.. Ed 200 -•-=5 Et 40
Ed 380 -· -· 10 Et 38
Fig. A-17 CONTOURS OF VERTICAL DISPLACEMENT CALCULATED BY ~VITY TURN·ON LNEAR ANALYSES USING DIFFERENT RATIOS OF 1llE DAM MODULUS· TO THE FOUNDATION MODULUS
63
-
-0.1
Ed 40 -=-•I Ef 40
Ed 3)() -•-•5 Et 40
Eel 380 -· -• 10 Et 38
Ao. A-18 CONTOURS OF HORIZONTAL DISPLACEMENT . CALCULATED BY
-
t-------0.4 t/ft 2-----------,,; .,_ ____ 0.8 ---------~
1.2 --------
1------- 1.6 Rigid Foundation. No Settlement.
-------0.4 t/ft2
t-:------- 0.8 t-------- 1.2
1.6
Stiff Foundation. O .34 ft of Settlement During Construction.
-- 0.4 t/ft2
-o.e --1.2
Soft Foundation. 1.42 ft of Settlement During Construction.
Fig. A-19 CONTOURS OF MINOR PRINCIPAL STRESS . CALCULATED FOR HIGH TENSILE STRENGTH · BEHAVIOR• USING STIFF MATERIAL PROPERTIES
IN THE DAM AND FOUNDATION PROPERTIES ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS
65
-
Rigid Foundation. No Settlement.
- / 1 I I I I I I .
' I I I I I I I Stiff Foundation. 0.34 ft of Settlement During Construction.
-- ./ \ /
I
I
/
I
I I
Soft Foundation. 1.42 ft of Settlement During Construction.
Fig. A·20 DIRECTIONS OF MAJOR PRINCIPAL STRESS CALCULATED FOR HIGH TENSILE STRENGTH BEHAVIOR, USING STIFF MATERIAL PROPERTIES IN THE DAM AND FOUNDATION PROPE~TIES ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS
66
-
t------0-.0+ ft- -------~
----- 0.02 -------
1------ 0.01 Rigid Foundation. No Settlement.
r------ 0.lft i-----0.2
r---o.3
Stiff Foundation. 0.34 ft of Settlement During Construction.
r--- 0.4ft ____ _
0.8 -----
1.2
Soft Foundation.- 1.42 ft of Settlement During Construction.
Fig. A-21 CONTOURS OF VERTICAL DISPLACEMENT CALCULATED FOR HIGH TENSILE STRENGTH BEHAVIOR• USING STIFF MATERIAL PROPERTIES IN THE DAM AND FOUNDATION PROPERTIES ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS
67
-
Does not exceed 0.003 ft
Rigid Foundation. No Settlement.
. Stiff Foundation. 0.34 ft of Settlement During Construction.
Soft Foundation. 1.42 ft of Settlement During Construction.
Fig. A-22 CONTOURS OF HORIZONTAL DISPLACEMENT CALCULATED· FOR HIGH TENSILE STRENGTH BEHAVIOR, USING STIFF MATERIAL PROPERTIES IN THE DAM AND FOUNDATION PROPERTIES ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS
. 68
-
----0.4t/fti-______________ ./
11---- 0.8 ..._ __ 1.2
1---- 1.6
Rigid Foundation. No Settlement.
-----0.4 t/ft2 ___________ _
1----0.8 ._,_ ___ 1.2
f.6 -----
Stiff Foundation. 0.37 ft of Settlement During Construction.
----- 0.4t/ft2-------
r---- 0. 8
---- 1.2 --------..
r---1.6
Soft Foundation. 1.35 ft of Settlement During Construction.
Fi;. A-23 CONTOURS OF MINOR PRINCIPAL STRESS CALCULATED FOR HIGH TENSILE STRENGTH BEHAVIOR, USING SOFT MATER I AL PROPERTIES IN THE DAM AND FOUNDATION PROPERTIES ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS
69
-
-
I I
Rioid Foundation. No Settlement .
. I
Stiff ·Foundation 0.37 ft of Settlement During Construction.
\ . \
\
\ \
I I
I
I I
I
/
Soft Foundation. 1.35 ft of Settlement During Construction.
Fio. A-24 DIRECTIONS OF MAJOR PRINCIPAL STRESS CALCULATED FOR HIGH TENSILE STRENGTH
. BEHAVIOR, USING SOFT MATERIAL PROPERTIES IN "THE DAM AND FOUNDATION PROPERTIES
· · ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS
70
-
--- 0.04 ft------------
,___ 0.08 ----------
Rigid Foundation. No Settlement.
t--- 0.2 ------
....-.-- 0.3
Stiff Foundation. 0.37 ft of Settlement During Construction. ,
--- 0.2ft
0.4 --------
i---- 0. 8 ------
1---1.2
Soft Foundation. 1.35 ft of Settlement During Construction.
Fig. A-2·5 CONTOURS OF VERTICAL DISPLACEMENT CALCULATED FOR HIGH TENSILE STRENGTH BEHAVIOR, USING SOFT MATERIAL PROPERTIES IN "THE DAM AND FOUNDATION PROPERTIES ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS
71
-
Does not e1tceed 0.01 ft
Rigid Foundation. No Settlement.
0.01 n-----------0.02
0.03
Stiff Foundation. 0.37 ft of Settlement Ourino Construction.
Soft Foondation. 1.35 ft of Settlement During Construction.
Fig. A-26 CONTOURS OF HORIZONTAL DISPLACEMENT CALCULATED FOR HIGH TENSILE STRENGTH BEHAVIOR, USING SOFT MATERIAL PROPERTIES IN 'THE DAM ANO FOUNDATION PROPERTIES ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS
72
-
1------ 0.4 t/f t 2 t-----o.e-t------- 1.2 a.----- 1.6
0. 4 t/ft2 ---0.8
1---1.2
----1.2
-- 0.4t/ft2---1---. 0. 8 . ---
- 1.2 ---
0.4 t/ft2 ----0.8 ----1.2 __ _
Fig. A-27 CONTOURS OF MINOR PRINCIPAL STRESS CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
73
-
-I
I
,
/
I I
I
I
I I
I
I
I
' . J
..- ,,,. / I
I I / / I
- / I - - .,..,... / I
-
I ./ / /
/ /
\ I
- - / \ / /
Fig.A-28 DIRECTIONS OF MAJOR PRINCIPAL STRESS CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
74
-
1------ 0.1 ft 1----0.2
t---- 0.3
0.3 . 0.2 0.1 ft 0.4
0.5
0.4 0.6
0.8
0.8 1.0
0.8 0.6 OA 0.2 0.1 ft 1.0
1.2
1.4
Fig. A-29 CONTOURS OF VERTICAL DISPLACEMENT CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
75
-
Fio.A-30 CONTOURS OF HORIZONTAL DISPLACEMENT CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR ANO STIFF MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
76
-
t----- 0.4 t/ft2 1------ 0.8 1.2
1.6
1---- o. 4 t/ft 2 ---·o.e 1---- 1.2
1.6
0.4 t/ft 2 . 1---0.e __ _ ---1.2 --1.s __
0.4 t/ft2
---0.8 t---- 1.2
Flg.A-31 CONTOURS OF MINOR PRINCIPAL STRESS CALCULATED USING LOW TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES FOR
. DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
77
-
\
\
'
/ I I
I
I
I
I
I
I
I I I I
/ . I
- / / I I I / / I
\
-' I
-
- / I ,,.,. / I
/ / / I
I I I
- / / /
I I I
\
Fig.A-32 DIRECTIONS OF MAJOR PRINCIPAL STRESS CALCULATED USING LOW TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
78
-
0.1 ft
t----- 0.2
"---0.3
0.5
0.6
t---- 0.6
0.8
1.0
1.2
1.4
0.4
0.8 0.6 0.4 0.2 ft
1.0 0.8
Fig. A-33 CONTOURS OF VERTICAL DISPLACEMENT CALCULATED USING LOW TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER. CONSTRUCTION
79
-
0.17 0.14ft
0.10,_ ---
Fig.A-34 CONTOURS OF HORIZONTAL DISPLACEMENT CALCULATED USING LOW TENSILE STRENGTH BEHAVIOR ANO STIFF MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
80
-
r----- o. 4 t/ft 2 0.8
I. 2
I. 6
t---- 0.4 t/tt 2
0.8
1.2
1.6 ----
0. 4 t/ft2
--o.e 1.2
1.6~
a--- 0.4 t/ft2
--- 0.8
1.2
1.6
0.4 t/ft 2
0.8
1.2
t----1.6
Settlement• 0.85 ft
Fig. A-35 CONTOURS OF MINOR PRINCIPAL STRESS CALCULATED USING HGH TENSILE STRENGTH BEHAVIOR ANO SOFT MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
81
-
- -I -I -I I
- - -\
.1
- -
i I·
I
\ I I
I I
- "/ /
I I ., I
I I . I
\ \ /
I \ I I
-\ \ \
I I I
- / / \ _. / /
I I / I I I I
Fig. A-36 DIRECTIONS OF MAJOR PRINCIPAL STRESS CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR AND SOFT MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
82
-
0.2
r--- 0.3
0.4
0.4 0.6
i----o.e S ettlement = O .85 ft
1.0
Fig. A-37 CONTOURS OF VERTICAL DISPLACEMENT CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR AND SOFT MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED- AFTER CONSTRUCTION
83
-
_,,...- O.OI ft / . /0.02
0.03
0.04
S ettlement = 0 .85 ft
Fig. A-38 CONTOURS OF HORIZONTAL DISPLACEMENT CALCULATED USING HIGHTENSILE STRENGTH BEHAVIOR AND SOFT MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
84
-
....._ ___ 0-.4 t/f-t2 ----------~ 1----- 0.8
t.2 ---------
' .6
0.4 t/ft2 ----~ 0.8
1.2
t---1.6
--- 0.4 t/ft 2------o.e -----
1.2 ---
t----t.6 --
1----0.4 t/ft2 --------- 0.8 ---1.2
1.---- 0.4 t/tt2 0.8 I .2
---1.8
Fig. A-39 CONTOURS OF MINOR PRINCIPAL STRESS CALCULATED USING L
-
- , I
\ I
I
\ '
- -\ \ I .
-\ \ \
I l
. - -...... ' I
\
-\
-
/ I
I I
I I I I
,,, I I I I I I I I I
.,...,. I
\ - / I
\ I / I
- _,... / ' / I \ I / I
I
Fio. A-40 DIRECTIONS OF MAJOR PRINCIPAL STRESS CALCULATED USING LOW TENSILE STRENGTH BEHAVIOR ANO SOFT MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
86
-
..__ 0.2
0.3
0.4
0.4 0.6
i---o.e
1.0
1.2 08 0 6 0.4 0.2 ft 1.0 . •
Fig. A-41 CONTOURS OF VERTICAL DISPLACEMENT C'ALCULATED USING LOW TENSILE STRENGTH BEHAVIOR AND SOFT MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
87
-
0.0
0.04
0.08
Fig. A-42 CONTOURS OF HORIZONTAL DISPLACEMENT CALCULATED USING LOW TENSILE STRENGTH BEHAVIOR AND SOFT MATERIAL PROPERTIES FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION
88
-
0.4 t/ft2 ------------~ 0.8
1.2 ------
r---- 1.6 ---
Rigid Foundation. No Settlement.
Stiff Foundation. 0 .36 ·ft of Settlement During Construction.
11---- 0.4 t/ft 2
1--- 0.8 .___ 1.2
Soft Foundation. 1.34 ft of Settlement During Construction.
Fig. A-43 CONTOURS OF MINOR PRINCIPAL STRESS CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES IN THE DAM AND FOUNDATION PROPERTIES ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS. IRREGULAR ABUTMENT.
89
-
' l I
Rigid Foundation. No Settlement.
-- / I I
1
I I I I I I
I I Stiff Foundation. 0.36·ft of Settlement During Construction.
-J I
I
- / I I /
/ / I /
Soft Foundation. 1.34 ft of Settlement ~uring Construction.
Ag. A-44 DIRECTIONS OF MAJOR PRINCIPAL STRESS CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR ANO STIFF MATERIAL PROPERTIES IN THE DAM AND FOUNDATION PROPERTIES ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS. IRREGULAR ABUTMENT.
90
-
t---- 0.01 ft------
---0.02---
Rigid Foundation. No Settlement.
0.1 ft
---0.2
0.3
Stiff Foundation. 0.36 t"t of Settlement During Construction.
0.8
1.2
Soft Foundation. 1.34 ft of Settlement During Construction.
Flg. A-45 CONTOURS OF VERTICAL DISPLACEMENT CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES IN THE DAM AND FOUNDATION PROPERTIES ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS. IRREGULAR ABUTMENT.
91
-
Does not exceed 0.002 ft
Rioid Foundation. No Settlement.
Stiff Foundation. 0.36·ft of Settlement During Construction.
Soft Foundation. 1.34 ft of Settlement During Construction.
Ag. A-46 CONTOURS OF HORIZONTAL DISPLACEMENT CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES IN THE DAM AND FOUNDATION PROPERTIES ADJUSTED TO CAUSE DIFFERENT SETTLEMENTS. IRREGULAR ABUTMENT.
92
-
0.4 t/ft2
1----0.e 1----1.2
1.2
0.4 t/ft2
0.8 1.2
~ End of Construction Settlement = O .3 6 ft
Settlement= 0.61 ft
Settlement • 0.86 ft
Settlement • I.II ft
Fig. A-47 CONTOURS OF MINOR PRINCIPAL STRESS CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES IN THE DAM FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION. IRREGULAR ABUTMENT.
93
-
--I
-I
I
·- I I I / / I I / / / I I
.,,... J
- / I I I / I I
- / I ........ / / I / / / I I / /
..- / I _.. / / I
I / / / / /
- _.. / I -- / / / I / / / I
I
End of Construction Settlement= 0.36 ft
\
Settlement= 0.61 ft
\ \ \
Settlement = 0.86 ft
\ \
Settlement = l.t I ft
\ \
Settlement• 1.34 ft
Fig. A-48 DIRECTIONS· OF MAJOR PRINCIPAL STRESS CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES IN THE DAM FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION. IRREGULAR ABUTMENT.
94
-
0.1 ft
0.2
0.3
0.5
0.8
0.2ft
~ End of Construction Settlement = O .3 6 ft
Settlement= 0.61 ft
Settlement = o. 86 ft
Settlement = I. II ft
Settlement= 1.34 ft
Fig. A-49 CONTOURS OF VERTICAL DISPLACEMENT CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR ANO STIFF MATERIAL PROPERTIES IN THE DAM FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION. IRREGULAR ABUTMENT.
95
-
End of Construction Settlement= 0.3 6 ft
Settlement= 0.61 ft
Settlement = 0.86 ft
Settlement = 1.11 ft
Settlement= 1.34 ft
Fig. A-50 CONTOURS OF HORIZONTAL DISPLACEMENT CALCULATED USING HIGH TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES IN THE DAM FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION. IRREGULAR ABUTMENT.
96
-
0.4 t/ft2
---0.8
1.2
0.8 .
1.2
1.2
"'-/ End of Construction Settlement= 0.36 ft
Settlement• 0.61 ft
Settlem-ent = 0.86 ft
Settlement • I.II ft
Settlement • 1.34 ft
Fig. A-51 CONTOURS OF MINOR PRINCIPAL STRESS CALCULATED USING LOW TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES IN THE DAM FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION. IRREGULAR ABUTMENT.
97
-
- ..-- / 1 J
I
- ...-I / I I
-I /
I I ' / I I I I I I
..- / I / / I / / I I / /
.- / I
/ / ./ / / I
End of Construction Settfement • 0 .3 6 ft
I \ \
Settlement • 0.61 ft
Settlement • 0.86 ft
·~ / I I \
-- / / I l I /
-/ /
/ / I
I
..- / I / I I , ./ I
Settlement • I.I I ft
\ \
Settlement • l.34 ft
Fio. A-52 DIRECTIONS OF MAJOR PRINCIPAL STRESS CALCULATED USING LOW TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES IN THE DAM FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION. IRREGULAR ABUTMENT.
98
-
0.1 ft
0.2
0.3 ~
0.3 0.2 0.1 ft
0.4 0.2ft
b.e
.1.0 0.8 0.6 0.40.2 ft
End of Construction Settlement= 0.3 6 ft
(
Settlement • 0.86 ft
Settlement • I. II ft
Settlement= 1.34 ft
Fig. A-53 CONTOURS OF VERTICAL DISPLACEMENT CALCULATED USING LOW TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES IN THE DAM FOR DISPLACEMENTS IMPOSED. AFTER CONSTRUCTION. IRREGULAR ABUTMENT.
99
-
End of Construction Settlement • O .3 6 ft
Settlement• 0.61 ft
Settlement • O. 86 ft
Settlement • I.I I ft
Settlement• 1.34 ft
Fig. A;...54 CONTOURS OF HORIZONTAL DISPLACEMENT CALCULATED USING LOW TENSILE STRENGTH BEHAVIOR AND STIFF MATERIAL PROPERTIES IN THE DAM FOR DISPLACEMENTS IMPOSED AFTER CONSTRUCTION. IRREGULAR ABUTMENT.
100