CR S-74-3 'Finite element analyses of transverse cracking in low-embankment dams' · 2017. 12....

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~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

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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)

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.

1

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

2

Page No.

1

4

5

6

7

9

9

11

11

14

14

19

26

29

29

33

33

34

38

Conclusions

Literature Cited

Appendix A - Additional Results of Finite Element Analyses

3

Page-No.

39

42

45

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

4

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

5

Page No.

21

22

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

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

7

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

9

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.

10

- "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

11

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

12

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

13

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

14

Rock vaney wans

:f ransverse Sect\OO

c1ay Filling at eattom of Va\\eY

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

... .....

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

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.

18

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 •

19

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

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

21

! 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

I

*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.

22

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

,

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

24

., :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

(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


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



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



1.35 ft of Totol Settlement

Fig. 13 CONTOURS OF cr3 IN EMBANKMENTS WITH LOW TENSILE STRENGTH

Hioh Tensile Strenoth - Stiff Moteriol Properties


....._--0.4 t/ftZ-----

....._ __ OB~-----. 1----1.2----


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 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



1.42 ft of Total Settlement

Low Tensile Strength - Stiff Material PropertitJ

0. 36 ft of Settlement Ourin; 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

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,


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.


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


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


0.4 t/ft2 ----0.8 ----1. 2.


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

/


- -\

- - / - / / / / /

I

I I


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 -----


--·0.2

---0.6


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


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


. Stiff Foundation. 0.34 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


-----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


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

/


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 ----------


t--- 0.2 ------

....-.-- 0.3

Stiff Foundation. 0.37 ft of Settlement During Construction. ,

--- 0.2ft

0.4 --------

i---- 0. 8 ------

1---1.2


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


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 ---


Stiff Foundation. 0 .36 ·ft of Settlement During Construction.

11---- 0.4 t/ft 2

1--- 0.8 .___ 1.2


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


-- / 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---


0.1 ft

---0.2

0.3

Stiff Foundation. 0.36 t"t of Settlement During Construction.

0.8

1.2


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.


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

\ \


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= 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


Settlem-ent = 0.86 ft

Settlement • I.II 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 \ \



·~ / 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 • 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 • O. 86 ft

Settlement • I.I I 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

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