A Rapid Method of Construction Control for Embankments

8/2/2019 A Rapid Method of Construction Control for Embankments

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E N G I N E E R I N G M O N O G R A P H S N o . 26

U n i t e d S t a t e s D e p a r t m e n t o f t h e I n t e r i o rB U R E A U O F R E C L A M A T I O N

A Rapid Method of ConstructionControl For Embanlsrrnentsof Cohes ive Soi lby J a c k W . H i l f


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United St ates Department of the Inte riorFRED A. SEATON, SECRETARY

Bureau of ReclamationFLOYD E. DOMINY, Commissioner

GRANT BLOODGOOD, As sis tan t Com mission er and Chief Engi neer

Engineering MonographsNo. 26

A R A PID METHOD OF C ON STR U C TION C ON TR OL

FOR EMBANKMENTS OF COHESIVE SOIL

by Jack W . Hilf

Division of DesignCom miss ione r's Office, Denver, Colorado

Th is monograph is an amplification of a pap er presented at the Confer-ence on Soils for Engineering Purposes, sponsored by Committee D- 18on Soils for Engineering Purposeso f the American Society for Testin gMat eria ls and the Sociedad Mexicana de Mecanica de Suelos, held a tMexico City, Mexico, Dec ember 9-14, 1957. The paper was subse-quently published by the ASTM a s Special Technical Publication, ST P


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ENGINEERING MONOGRAPHS are publishedin limited editions for the technical staff of theBureau of Reclamation and interested technicalcircles in government and private agencies.Their purpose is to record developments, inno-vations, and progress in the engineering andsci entific techniques and practices that are em-ployed in the plan ning, design, construct ion, and


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CONTENTS

Preface. . . . . . . . . . . . . . . . . . . . . . . .

Introduction. . . . . . . . . . . . . . . . . . .

Density Control

Moisture Control. . . . . . . . . . . . .

. . . . . . . 0 . . . . . .

. . . . . . . . . .

Examples. . . . . . . . . . . . . . . . . . . . . . .

Procedure for Rapid Compaction Control Method. . . . . . . . . . .C om pl et ion o f Te st f or R eco rd Pu rp ose s . . . . . . . . . . .Example 1. . . . . . . . . . . . . . . . . . . . . . . . .Example 2. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Use of Rapid Method by Bureau of Reclamation. . . . . . . . . . . . .Summary. . . . . . . . . . . . . . . . . . . . . . . . . .

Acknowledgments. . . . . . . . . . . . . . . . . . . .Appendix AuAlternative Methods of Obtaining the

V al ue 7d (1 + '\If)' . . . . . . . . . . . . . . . . . . . . . . .mGeneral. . . . . . . . . . . . . . . . . . . . . . .Original Development. . . . . . . . . . . . .Method Using Percentage of Wet Weight as Abscissa. . . . . . . . .

. . . .

Appendix B--Derivation of Correction Curves for MoistureControl. . . . . . . . . . . . . . . . . . . . . . .

Appendix C - - Pa ra bol a M et ho d . . . . . . . . . . . . . .Analytical solution. . . . . . . . . . . . . . . . . . . . . . . .Graphical solution. . . . . . . . . . . . . . . . . . . . . . . .Tabulated values. . . . . . . . . . . . . . . . . . . . . .

Appendix DuAlternative Method to Eliminate DryingRequirement for Soils Close to Optimum Water Content. . . . . . . .

F or ms 7 -1 62 4 a nd 7 -1 62 4A . . . . . . . . . . . . . . . . . . . . .List of References. . . . . . . . . . . . . . . . . . . . . . . . .

Pa~e13471111121213131515

16161618

1919192020

22*27


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Number

LIST OF FIGURES

1 Comparison of compaction curves--Proctor and rapidmethod. . . . . . . . . . . . . . . . . .2 W et density versus optimum water content . . . . . . . .3 Example in which fill water content is less than optimum. .4 Example in which fill water content is greater thanoptimum.. . . . . . . . . . . . . . . . . . . . . .5 Mechanical mixer and paddles used in the laboratory.6 Theory of rapid construction control method . . . . . . .78

Graphical solution for peak point of parabola . . . .Tabulation of coordinates of peak point of parabola . . . .

9 Alternative procedure to elim inate requirement for dryingsoils that are close to optimum water content. . . . . .10 Example of elim ination of drying requirement for a soilwetofoptimum. . . . . . . . . . . . . . . . .11 Tabulation of coordinates of peak point of parabola foralternativemethod.. . . . . . . . . . . . . . .

*Flgures 8 and 11 are folded sheets in pocket inside back cover.

Page

589

10141721*2324

*


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PREFACE

This monograph presents a method of evaluating quickly and accu-rately the compaction of cohesive soils used in construction of earthembankments. In contrast to the time-consuming methods previouslyused, the technique presented in this monograph makes it possible todetermine the essential values of moisture and density within an hourafter the field measurements are made on an embankment. W ith thismethod, effective compaction control can be carried out expeditiouslya nd e co nom ic al ly .

In brief, by use of the rapid method, the degree of compaction ofthe fill is precisely determined by comparing the density of the embank-ment with a laboratory standard. This is done by a simple mathematicaldevice. A lso, by this method, moisture control to a satisfactory degreeof precision is achieved.

The theory of the rapid method is descrloed in this monograph aswell as step-by-step procedures and results of experiences to date withthe method. Appendixes to the text contain supplementary informationand m athem atical derivations.


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INTRODUCTIONEffective construction control of cohe-

sive soils requires more than merely meas-uring the dry density and the water content ofa sample of compacted embankment. Thesevalues must be compared with the laboratorymaximum dry density and the optimum watercontent, which are obtained under standardtest procedures. The comparison is made bycompacting specimens of the soil, obtainedfrom the fill for the density test, at the watercontent of the fill and at several other watercontents to determine the laboratory mois-ture-density curve for that soil.

A ll operations in this comparative pro-cedure, except the determ ination of watercontents needed to convert wet densities todry densities, require about one hour, de-pending on whether the sample requiresscreening to remQve particles larger thanthe maximum size used in the laboratorytests. Determination of the water contentof a sample by drying to constant weight at110 C may require up to 24 hours for clayeysoil. Because of the advantages of earlyknowledge of the field comparison results,many methods have been proposed to obtainresults rapidly.

The Proctor needle has been used to ob-tain the approximate difference between opti-mum water content and fill water content. 1 *Rapid methods of determining water con-tent values include: The alcohol-burningmethod; 2 the Bouyoucos alcohol methodu sin g a h yd rometer; 3 and a moisture metermethod using calcium carbide to generateacetylene in a closed container connected toa pressure gage. 4 All of these rapid mois-ture methods are either approximate or theygive correct values of water content only forcertain kinds of soils. Hence, the standardoven method must be used in addition, or atleast as a periodic check.

If a particular laboratory dry density-water content curve is assumed to be appli-cable to the soil being tested, an approximatedry density of the fill can be obtained from agraph, by comparing the in-place wet densityw ith the wet density of the soil compacted inthe laboratory cylinder at fill water con-tent. ,~* Another method uses the wet densityat fill water content and the Proctor needlereading of the soil in the cylinder to chooseone of a set of typical curves from which theapproximate maximum dry density and opti-mum water content can be found. ~ ,** Approx-imate methods developed on Bureau of Rec-lamation jobs to facilitate acceptance ofrolled fill are typified by the one used duringconstruction of the Bureau of Reclamation'sTrenton Dam in Nebraska, involving an esti-mation of the fill water content. In thismethod a complete compaction test was madeby starting with the field sample and adding adefinite amount of moisture or drying to re-move a definite amount of moisture. Thefield moisture was given an assumed valueand the other compaction test moistures werecomputed from it. A dry density curve wasplotted, and the field test was evaluated.

In a study concerned with the propertiesof compacted cohesive soils,6 these methodsof control were reviewed. It became appar-ent that exact information on the ratio of drydensity of fill to laboratory dry density at fillmoisture was readily available w ithout know-ing the water content. In addition, it wasfound that by compacting various specimensin the compaction test procedure and record-ing the amount of water added to or takenfrom the soil as a percentage of fill wetweight, a wet density curve could be obtained.This curve could then be converted to wetdensity on a fill water content basis, fromwhich the exact percentage of fill ~ densityto laboratory maximum dry density can be


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DENSITY CONTROLIn the Proctor compaction test, samples

of soil containing different amounts of mois-ture are compacted in a container of knownvolume by a specified type and amount ofcornpactive effort. For each sample the re-sulting weight of the soil mass divided by thevolume of the container is the wet density.The dry density is defined as the weight ofdry solids in the compacted, moist soil massdivided by the volume of the container. Thisimplies that the water is contained within thevoids of the soil mass and contributes to theweight but not to the overall volume of themass.

The water content of the soil is ex-pressed as a percentage or ratio of the dryweight of the soil which makes it independ-ent of the state of compactness of the soilmass. The wet weight of compacted soil inthe container consists of the weight of drysoil and the weight of water. In terms ofunit weight or density,

"Iv ="Id +wrd = "Id(l +v)

where 1 v = wet density of the soil mass"I d = dry density of the soH massv = water content

Curves of wet density versus water contentand dry density versus water content areshown in Figure 1 (a). The maximum ordinateof the dry density versus water content curveis called the Proctor maximum dry density orlaboratory maximum dry density, "I d , andmthe abscissa where it occurs is called theoptimum water content, v o' The value of thewet density at that point is "Id (1 + v ).m 0

Consider a field density test made in soilcontaining no graveL (The procedure in soilscontaining gravel is similar, except for thescreening required and the computations nec-

The ratio of fill wet density, 'l vf ' (w et w ei~ htof soil extracted from the hole divided by thevolume of the hole) to "cylinder" wet densityis identical with the ratio of their dry den-sities, since both wet densities are at thesame water content:1 "I d (1 + vf) "df r fr;; = 1d (1 + Vr) = r;- = C Equation (1)e e e

where "I dr and"I de are fill dry density and

"cylinder" dry density, respectively. Thevalue of the ratio, C , indicates the relationbetween the compactive effort used on the filland the laboratory compactive effort.

The ratio, D, of fill dry density to labo-ratory maximum dry density, which is thebasis of density control, could be obtainedfrom wet densities in a similar manner if thevalue "I d (1 + v f) could be found, where "I dm mis the laboratory maximum dry density. Thevalue D would be obtained by dividing the fillwet density by this quantity:

D = "Id (1 + v f) "Idf =- !"Id (1 + v f) "Idm mEquation (2).

The rapid method is a procedure for obtain-ing the value "Id (1 + v ).m fConsider a sample of soil that was taken

from a fill with a wjiter content, vr ' some-what less than optimum, and compacted in acylinder in a specified manner. If we desig-nate its resulting "cylinder" dry density as"I d , then its "cylinder" wet density would be:e"I d (1 + vf) .This "cylinder" density at fillcwater content is shown in Figure l(a).


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~~~~~....S: .&0'i

Ii.....rn0I:!0.....(')

t11 i')('to...,"g(')

~CDm.I'"d6(')('to0Ii[

~l-(/)Zw0

-- -Y. ( 1+ Wol___-dm

(0)PR OCT OR C OM PA CTIO N C UR VE

Wet dens itY ') d ( 1+ W) ,VS W- -- ,

~>-I-({)ZWC

)de ( I + W f)

I-00LLU~ - -- )dm ( I+Wo)- -- -- -- -- -- -- --uQ:wQ.(/)0Z::J0Q. -)d e (1 + W f)------

Dry density v vs w ,'d,//,,- -idmu - - - --- IIII1~I+-1~I+-151011",I+-10,~IEI

::>1EI.- 1"'0.101

)d m (1 + W o)I+wo =)dm

III1~I I+-1~I+-1gl01 1""bl~I-I~I0 W A T E R C O N T E N T , w , IN P E R C E N T A G E O F D R Y W E IG H T

I-00LLUID::JUQ:wQ.(/)0Z::J0Q.~

(b )R AP ID METHOD COMPACTION CURVES

Wet densi ty ,v ( 1 + w ) , v s Z - - ,'d I

0 A D D E D " W A T E R , Z , IN P E R C E N T A G E O F F IL L W E T W E IG H T

w - w fZ :~

)d m ( 1 + w o )= )d m ( I + w f)1 + Z m


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(1 ) 7d (1 + wf)'c7d(1+w)

(2 ) 2 2(1 + z )2

soil in percentage of fill wet weight. ** Thischange in origin is equivalent to consideringthe moi st soil removed from the fill to be"dry;" that is, the water associated with thesoil at fill water content is treated as solidmaterial. Values of z are in percentage of"dry" weight by this concept.

By adding water to samples of the moistsoil (all samples are at fill water content tostart with), and by mixing and compactingthem in the usual manner, a wet density ver-sus z curve--the upper curve in Figure l(b)--is obtained. The values of ordinates of thiscurve are the same as the wet density curvein Figure 1 (a). However, the abscissas arevalues of z rather than of w. The analogybetween Figures l(a) and l(b) can be com-pleted by drawing the converted wet densitycurve in Figure 1(b). This is done by divid-ing each ordinate of the upper curve by(1 + z). The resulting curve is sim ilar inshape to the Proctor dry density curve. Thevalues of the ordinates of the converted wetdensity curve are not dry density, however,but are dry density multiplied by the expres-sion(l + wf)' 'This can be proved as follows:

The ordinates of the converted wet den-sity curve were obtained by dividing the wetdensities, "Yd(l + 'II), by(l + z). The valuez is defined as added water in percentage offill wet weight. Therefore

W Ws - wf Ws - w - wfZ = Ws(l + wf) - 1 + w f Equation (3)where W is dry weight of soil.s

W - W1 + Z = 1 + --1. = . ! : t. ..L1 + wf 1 + wf Equation (4)Hence7d(1 + w) - 7d(1 + w)1 + z - = 7d (1 + 'IIf)

The m axim um ordinate of the convertedwet density curve must be 7d (1 + wf) ' be -mcause the only variable in the ordinate of thecurve is 7 dJ the expression (1 + wf) is con-stant for any given density test.

It should be noted that the Proctor curves,show n in Figure 1(a), cannot be d rawn u nle ssthe values of water content are determined,whereas the curves shown in Figure 1 (b) canbe drawn without knowing values of water con-tent. The values of z used in Figure 1 (b) aremerely the ratios of pounds of water added topounds of moist soil removed from the fill andare known.

Hence, the value7d(1+Wf) 7d

D- f =-.f-7d(1+wf) 7dm mEquation (2)

can be obtained precisely from wet densi-ties alone by finding the peak point of the7d (1 + wf)curve. That curve is obtained byplotting the points:

(3 )7d(1+w)

3 31 + z 3

W - wfetc. It should be noted that z =- can be+'11negative as well as positive. fThe determination of the maximum ordi-

nate of the7 d(l + wf)versus z c urv e p re se ntsthe same problem one encounters in findingthe maximum dry density in a dry densityversus water content curve. In general, the


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to be a parabola rhose axis is parallel to theld(l + wf) coordinate axis. The parabolamethod of locating the maximum ordinate isgiven in Appendix C. Its use is not essentialto the rapid method, but it has been found ad-vantageous in reducing the number of pointsrequired and it provides a unique value forthe peak point without sketching the curve.

In a further effort to simplify the proce-dure to obtain D, the coordinate sheet onwhich the curve is plotted is provided with aseries of diagonal lines which enables the di-vision of wet density by the quantity(l + z) tobe done graphically, so that points of coordi-

nates [z, 1d (1 + Wf)] can be plotted w ithoutusing a slide rule or calculating machine.Once the maximum ordinate, 1d (1 + wf> isobtained, either by the parabola &ethod or bysketching the curve, the value

ld (1 + W f) ldD - f = --K- 1 d (1 + W f) 1 dm m

Equation (2)

can also be obtained graphically by using thediagonal lines as explained later under thesection, E xam ples.

MOISTU RE C ON TR OLThe location of the peak point of the1 d(l + W f> versus z curve shows whether the

the soil is at optimum water content (Wo)' oris less than or greater than optimum. How-ever, the exact magnitude of the differencebetween optimum water content and fill watercontent is unknown. From Equation (3), itfollows that:

Wo - wf = zm(l + wf) Equation (6)where zm is the abscissa of the peak point ofthe curve. Forzm = 0, Wo - wf = 0 for anyvalue ofwf' For values of zm other than 0,the magnitude of wf is needed to obtainWo - wf'

From Equation (5), it follows that:l+w 01 + w f = 1+Z m Equation (7).

Hence, another expression for the differencebetween optimum and fill water contents isobtained by combining Equations (6) and (7):

Zm

estimating Wo is reduced to ~:~ (0.05) =0.00098 for Wo - wf; this small error is ac-ceptable for control purposes.

To avoid the necessity of estimating wfor Wo for each density test, a set of curveswas prepared which automatically estimatesWofor the coordinates of the peak point of theconverted wet density curve. Figure l(b)shows the relation between the peak point ofthat curve and the wet density at optimumwater content. The approximate relation be-tween the latter value and the optimum watercontent was determined for 1,300 soils com-pacted by the Bureau of Reclamation's stand-ard of com paction, * and is shown in Fig-ure 2. *~, The relationships of Figure s 1 (b)and 2 were combined to obtain the curvedlines shown in Figures 3 and 4.

*The Bureau of Reclamation's standard usesa 1/20-cubic-foot cylinder, 3 layers, 25blows per layer of a 5. 5-pound hammerdropped 18 inches. Compactive effort is12,375 foot-pounds per cubic foot.


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\

""" ",'...-.. '. WET DENSITY VS, OPTIMUM WATER CONTENT

0": FO R 1300 SAMPLES&.1:'

: ::;":....." , ",l"" '':0 ~.::~.ow "0"'..''''M:'1:.;0 .i -. ' : ' ~ : : ~ .: r : : 1{ ' " t i" -, "::, , ' : ,; '~,:,, ' : I. . ""." , .1 0' '" "" ",,/, '" 'I"'". ,.o;...." ~'. -.?"o.. ' ~', '; r ..' .. .'"0 0 . "-r"; .. .. . . - 0". .. eo" ".r.- ,,-. "0". . ' : . . :, :, ."0. o~:".

. "::: "::. .:. . :":0:-..:

',:.~.,

.. ,"~::\\~ ' ' ,,

" ~ ' :"",.. ,0 "-' 0' r\""" :, , . ".'" 0.'

.:.\ .. "." \..",. :" .\

150

,,~

"5

140

'"..I-o......II>......II-Z...I-Z8 130III:...i:IE::>:IE;::...0I- 12 5C..l-e; ;Z...0I-....

120


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O'zj~I;i~.~ ....~8 13 7.... W"iitzj ~135J ffi 134Q.I;'

I-'-13 ~~(j\I-'-)::rCO ....,1-" ~..... .. . 1 27!(1)

'1() ( )8 123.4-c+(1)~> -

1-" t 121rn !III-' ~120(1) 0rnrnc+

ORIEO % DRIED %.WEIGHT WEIGHT7.49 -0./ 7.32 -2.47.48 -0.3 7.3/ - 2 . 57.47 -0.4 7.30 -2.77.46 -0.5 7.29 -2.87.45 -0.7 7.28 -2.97.44 -0.8 7.27 -3./7.43 -0.9 7.26 -3.27.42 -1./ 7.25 -3.37.4/ -/.2 7.24 -3.57.40 -/.3 7.23 -3.67.39 -/.5 7.22 -3.77.38 -/.6 7.2/ -3.97.37 -/.7 7.20 -4.07.36 -/.9 7./9 -4./7.35 -2.0 7./8 -4.37.34 -2./ 7.17 -4.47.33 -23 7./6 -4.5

RAPID COMPACTION CONTROL MTHODFOR 7.~O LSS. OF' M OIST SOIL

FEA 1 URE m _ ~ ~ _ q ! ! ! P " ! ~ DATE h_':-:::::-::-_n-- TEST NQ - -~- -- -

D,__!~!~Q_.- %C'--~~~:~~-_, %" 0- " f- --~!~8 %

F i ll " o te r c o nt e nt , "f' ___n!~,J!_h_-- %F i ll d r y d e n si ty o f - NO.4' -_U_Q,~ "lnJLab.max.dry densit;, -- h_H?"!!,'- ___"lftJCy l inderd ry densi ty' !Q!~_3._- "1ft)Op timum "o te r c o nt e nt , "0' - _!~, ~ - - -- %

-) -2 -I 0 ., +2 .) +4 +5 '67-1624(2-59 )Bureau of Reclamotion ALSO ADDED WATER IN PERCENT O F F ILL W ET W EIGH TWo- Wf (% ) FOR PEAK POINT OF CURVE WHEN CORRECTED AS SHOWN BY CURVED LINES


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f-8 137"-&~!i ~134Q.'d&-1="~.to,1 IJ I~;;

~..,.I:S...,.nt:T......0 H"...j: :!CD>-j()g&

~..,.en0tI>-jm&CD>-j

DRIED % D R I E D %W E I G H T "EIGHT7.49 -0./ 7.32 -2.47.48 -0.3 7.3/ -2.57.47 -0.4 7.30 '2.77.46 -0.5 7.29 -2.87.45 -0.7 7.28 -2.97.44 -0.8 7.27 -3./7.43 -0.9 7.26 -3.27.42 -/./ 7.25 -3.37.4/ -/.2 7.24 -3.57.40 '/.3 7.23 '3.67.39 '/.5 7.22 -3.77.38 '/.6 7.2/ -3.97,37 -/.7 7.20 -4.07.36 -/.9 7./9 -4./7.35 -2.0 7./8 -4.37.34 '2./ 7./7 -4.47.33 -2.3 7./6 -4.5

145 RAPID COMPACTION CONTROL METHODFOR 7,~O LS5. OF MOIST SOILFEA TURf -h ue . ~ -~ "! ?- ~~ -- - u--- DA Tf u-- ---::=: --_u TEST NQ u ': ": ': '" - - -

D'--~,~:~.u" %L ,- '! !. :. o. -u , %wo - w f - _~_~"'''m %

F i ll wa te r c o nt en t. w { '. , u -- ~!~p--- ,-- - %Fill dry density a{'No.4 'u '_o.!C!Uh#/ft.JLob.mox.dry density' . - - - !t:J!"~_. #/rtJC ylin der d ry den sity,u_ --~ o.!"! If/fl.JOp t imum wa ter con ten t , wo ' --'_7.,-2 %

'>-I- 121in:5 120aI- 119UJ:s J Ia

111116115114113112III

+67. i624(2' 59)Bureau o f Rec lama ti on ADDED WATER IN PERCENT OF FILL WET WEIGHTALSO Wo- W f (%) FOR PEAK POINT OF CURVE WHEN CORRECTED AS SHOWN BY CURVED LINES

', -


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These lines show the correction value tobe added to Zm to give Wo - wf" The correc-tion value shown by the curved lines (to thenearest 0.1) closest to the peak point of theconverted wet density curve [Coordinates

Z , "/ (1 + W )] is added algebraically tom d fmZm to give a value for Wo - wf that is suffi-ciently accurate for control purposes.

EXAMPLESFigures 3 and 4 are examples of the

rapid compaction control method, using theforms designed for the Bureau of Reclama-tion's laboratory compaction standard withthe 1 /20-cubic-foot cylinder. By changingthe weights of soil sample and of water addedin proportion to the size of cylinder used,these forms are suitable for density controlfor any compaction standard. In addition,there are indications that the correctioncurves for moisture control which were pre-pared for the Bureau of Reclamation's com -paction standard may be satisfactory forother com paction standards of approxim atelythe same compactive effort. For example,the correction curves in Figures 3 and 4 arebelieved to be applicable to the compactionstandard used in Mexico 7 and to the stand-ards of the American Society for TestingM a-terials and American Association of StateH ig hw ay O fficia ls.8 9

In Figures 3 and 4 all lines are black.However, in the forms used by the Bureau ofReclamation the lines are in color. Theseforms, Forms 7-1624 and 7-1624A, areshown in this monograph following AppendixD . The diagonal lines are black, and thecorrection curves are light red lines. Thefirst form includes the normal density rangeused in Figures 3 and 4. The second form isused for low density soils. The followingstep-by-step procedure explains the use ofthe form s.Procedure for Rapid Compaction Control

Obtain fill wet density of minus No.4

To obtain Point (1). Compact soil at fillwater content into a standard cylinder. Plotthe resulting wet density on the 0 percentvertical line on Figure 3 or Figure 4.

To obtain Point (2). To 7.50 pounds ofsoil at fill water content add 68 cubic centi-meters (2 percent) water, m ix, and compactinto a cylinder to determine wet density.Find the point on the + 2 percent diagonalline corresponding to the wet density; pro-ject vertically to the 0 percent diagonal line,thence horizontally to plot Point (2) on the+ 2 percent vertical line. The ordinate of theplotted point is the wet density divided by1.02 .

To obtain Point (3). If Point (2) isgreater in ordinate than Point (1): To 7.50pounds of soil at fill water content add 136cubic centimeters (4 percent) water, m ix,and compact into a cylinder. Find the pointon the + 4 percent diagonal line correspond-ing to the wet density; project vertically tothe 0 percent diagonal line, thence horizon-tally to plot Point (3) on the + 4 percent ver-tical line. The ordinate of the plotted pointis the wet density divided by 1.04.

If Point (2) is smaller in ordinate thanPoint (1): Permit 7.50 pounds of soil at fillwater content to dry without loss of soil;then w eigh. * The table on the right-handportion of Figure 3 or Figure 4 gives thepercentage of water loss corresponding tothe dried weight. Compact the dried soilinto a cylinder. Find the point on the diag-onalline (interpolate if necessary) corre-


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density divided by 1 plus the negative per-centage: [1 + (- 0.(2) = 0.98].Three plotted points are sufficient if both

the left and right points are lower in ordinatethan the center point; if not, a fourth point isnecessary. Find the point of maximum ordi-nate of the curve by the parabola method,Appendix C, or by sketching the curve if thenumber and locations of the points permit ac-curacy without use of the parabola method.

Plot the fill wet density of minus No.4fraction on the 0 percent vertical line .

To obtain D : Project the maximum ordi-nate horizontally to the 0 percent diagonalline, thence vertically to the value of the fillwet density. D = 100 percent plus the inter-polated percentage given by the diagonallines, taking minus signs into account. D isfill wet density divided by the maximum ordi-nate of the curve.

To obtain C: Project Point (1) hOrizon-tally to the 0 percent diagonal line, thencevertically to the value of the fill wet density.C = 100 percent plus the interpolated percent-age given by the diagonal lines, taking minussigns into account. C is fill wet density di-vided by the ordinate of Point (1).

To obtain Wo - wf: This value is the ab-scissa of the point of maximum ordinate cor-rected by adding the value shown in red (thecurved lines) on the chart nearest to the peakpoint, interpolating where necessary, andtaking minus signs into account.Completion of Test for Record Purposes

Dry a sample of minus No.4 fraction toconstant weight in an oven at 1100 C to ob-tain fill water content, w f' Then:Fill dry density of -

No.4 = Fill wet density of -No.4 + (1 + wf)

Example 1Figure 3 is an example in which the fill

water content is less than optimum. The testdata are:Fill w et density = 127.5 pounds per cubic foot

We t d en si tyi n p ound sper cubic

Point foot

Convertedw et d en sityin p ou nd sper cubic

foot:i\

in p erc en t

(1 )(2 )(~ )

12~.4128.6124.6

024

12~.4126.1119.8

By the parabola method0 1.6 126.~

thenD - ~ - 1 01.0 p ercen t126.~ -C = ~~:, = 10 ~.~ p ercen t

Wo - wf = + 1.6 + 0.2 = + 1.8 percent (dryo f o ptimum)These values are sufficient to accept or re-ject the compacted fill according to criteriaestablished for the work.

After the fill water content has been de-termined by drying a sample to constantweight at 110. C, the field density test iscompleted for record purposes as follows:Wf = 1 5.0 p erc en t


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Example 2Figure 4 is an example in which the fill

water content is greater than optimum. Thetest data are:Fill w et density :: 125.8 pounds per cubic foot

W et d ensityin p ou nd sper cubic

Point foot

Convertedw et d en sityin p ou nd sper cubic

foot:i3

in p erc en t(1 )(2 )(3 )

128.4121.8126.6

128.4124.2123.7

0+2- 2.3

By the parabola method0 - 0.7 128.9then

D = 125.8 - 97 6 Percent128.9 - .

c = ~~:~ = 98.0 percent- Wo - wf = - 0.7 - 0.1 = - 0.8-

percent (w et).

These values are sufficient to accept or re-ject the com pacted fill according to criteriaestablished for the work.After the fill water content has been de-

termined by drying a sample to constantweight at 110 C, the field density test iscompleted for record purposes as follows:Wf = 18.0 percent7 d f ' = ;:iB8 = 106.6 pounds per cubic foot

7 d = ~ : i B 9 = 109.2 pounds per cubic footm128.4 - loB 8 Pounds P er cubic foot7d = 1.18 - .C W = 0.18 + (1.18)(- 0.007) =0 0.172 or 17.2

percent.

USE OF RAPID METHOD BY BUREAU OF RECLAMATION

The rapid method of control described inthis monograph has been used satisfactorilyon about a dozen earth dams since May 1957,and has been adopted as a designation in theEarth M anual 1 for control of all compactedcohesive soils on Bureau of Reclamationprojects. Prior to initiating the procedure inthe field, it was tested in the Bureau's EarthLaboratory at Denver, Colorado.

It was found that a mechanical method ofmixing the water with the soil was desirableto assure uniformity of the resulting water

Although the relative humidity of the at-mosphere in the Denver laboratory was low (2to 20 percent), at temperatures of 65 F to75 F, loss of moisture during the mixing ofsoil and water was only about 0.1 percent ofdry weight of soil. This small value pre-cluded the necessity of correcting for loss ofmoisture during the te st. Additional time andheat are required to reduce the water contentto obtain a point on the converted wet densitycurve that is less than fill water content. Onone of the field projects, a stream of heatedair is passed over the bowl during the mixing


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Bowl Capacity : 3 gallonsMotor: 113 HP, 60 cycles, 115 volts, single phase, 3 speed maximum,l , 7 25 rpm.Mixing head speeds; 47 rpm, 90 rpm , and 160 rpm .Pad dle No. 1: Blades made from 112- by 112-inch angle iro n sharpenedand shaped.Pad dle No. 2: Modified pas try beat er- -Blades have been develed and


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weighing of the final m ixture will determinethe magnitude of correction to be applied.In most cases, loss by evaporation can becompensated for by adjusting the amount ofwater added. As yet, no such adjustment hasbeen found necessary on the Bureau projects.The fan-type scale of 25-pound capacity,reading directly to 0.01 pound, has beenfound satisfactory for weighing the soil be-fore and after mixing.

The parabola method, described in Ap-pendix C, has been found to be desirable, butit is not an essential part of the rapid method.Cases have occurred where the peak point of

The primary purpose of the controlmethod described in this monograph is toprovide a correct and sound basis for accept-ance or rejection of compacted fill in theshortest possible time. As explained, this isdone without requiring the determination ofthe values of dry density or of water content.There appears to be little justification for re-lying on assumed compaction curves to com-pare w ith the fill density when the rapidmethod, giving an exact ratio of fill dry den-sity to laboratory maximum dry density, isavailable.

M oisture control is considered essentialin the construction of high earth dams, and itis the key to effective use of compactionequipment in all earth embankments. Therapid method provides moisture control in-formation in terms of the difference betweenoptimum water content and fill water content.A lthough the value is not precise, it is con-sidered to be close enough for control pur-poses. There is no advantage in using the

the converted wet density curve was found tocoincide with one of the compaction points byvirtue of symmetry. In that connection, itw ill be found desirable to modify the step-by-step procedure given under the section, Ex-amples, when Points (1) and (2) are of thesame converted wet density. Instead of add-ing 4 percent of water to obtain Point (3) andthen using the parabola method to obtain thepeak point, it is evidently better to add 1 per-cent of water (34 cubic centimeters) to 7.5pounds of moist soil. This w ill determine thepeak point directly, since the axis of the pa-rabola is located at z = +0.01.

SDDIARY

ratio of fill water content to optimum watercontent for moisture control in lieu of the dif-ference between these values, since both theratio and the difference depend on the magni-tudes of fill water content and of optimumwater content, which are unknown.

An additional advantage of the rapidmethod over the approximate methods is thatthe data obtained for control purposes in therapid method can later be used to obtain thecorrect values of dry density and water con-tent for record purposes. This is accom-plished by obtaining only one water content--the fill water contentnby drying a sample inthe oven.

In addition to its use in the constructionof earth dams, the method described in thismonograph is believed to be particularly ap-plicable for control of compaction of highwaysand canal embankments, where the compac-tion characteristics of the soils are likely tovary along their routes.


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A P P E N D I X AAlternative Methods of Obtaining the Value

rd (1 + wf>mGeneral

For density control the value

rd (1 + w f> rdD - f = --!-rd(l+wf> rdm m Equation (2)

can be obtained from wet densities, providedr d (1 + wf> is found. Under the section,mDensity Control, of this monograph, a methodof obtaining this value is given in which theabscissa of the wet density curve and the con-verted wet density curve is z. There are twoother possible abscissas that can be used toobtain the same result. These are includedhere to make the derivation of r d (1 + wf>complete. m

O rig in al D ev elo pm en t*The wet density corresponding to the max-

imum laboratory dry density is r (1 + W >dm 0 'where Wo is optimum water content. Thiscan be w ritten r (1 + W - W + W > =0 r fmrd (1 + w f> + rd Wo - rd wr"m m m

The value of r d Wo is the total weight ofwater per cubic f~t in the soil mass at max-imum dry density, and 7d Wf is that portionmof the foregoing weight of water which is at-tributable to fill water content. Then theexpression 7d Wo - 7d wf is the weightm mof water per cubic foot that must be added

manner: A measured quantity of water isadded to a known weight of loose soil at fillwater content and mixed. The mixture iscompacted in a laboratory cylinder by thestandard procedure. The ratio of the wetweight of soil in the compacted cylinder tothe wet weight of the loose soil mixture,multiplied by the weight of water added tothe loose soil, gives the required incrementof weight of water.

The wet density point corre sponding tomaximum dry density can be obtained by us-ing "cylinder" wet density (at fill water con-tent) as a reference point (0,0) in a plot asshown in Figure 6. The increment of water(times 20 for a 1/20 -cubic-foot cylinder)and corresponding increment of wet densityis plotted as a point (X l' y 1) on the solidcurve. Other points to determ ine this curveare obtained in a similar manner by increas-ing the amount of water added to specimensat fill water content. The equation of thesolid curve is y = r(x). If each ordinate ofthis curve is reduced by its correspondingabscissa, the dashed curve Y =f(x)-x is ob-tained, wmse ordinate represents the amountof additional soil at fill water content abovethe amount represented by "cylinder" wetdensity that was compacted in the cylinder asthe result of adding more water. The maxi-mum point (xm ' Ym) of this curve must cor-re spond to the maximum amount of dry sol-ids, since the only variable in the equationfor Y is 7 d. When Y is a maximum,

d[f(x) - x] - 0dx -,d[f(X)]- 1 - 0dx - , d[f(x)] - 1dx - "

Hence, the point on the y = f(x> curve cor-responding to maximum dry density is theone where its slope equals unity. Then7w


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>-I- -(/ )ZW0I- -W~a::WI--00Zo...JU-towm>::J0ma::Wa. .>-I--(/)-0U>zZ::JWo00..I--zw-3:U-0I- -ZW~wa::

y = Yd(1 + w> - Yd (1 + wf>cX = Yd(w - wf>Y = Y - X = Yd(1 + wf> - Ydc(1 + wf>

,/,,I, I I

" 1A J,/ I,--- -- --- 7,"

Y3

f(x)m IIIIIIIIIIII1X : /Y=f(x)-xm I ,Y \ , '3 '-1 i - - - - -- - -- - ; ;..-4- -iY2- ~'-f":::- ::- :-:-~ - - - r -- -~--.r /' I I II IYI- ,Yr' // :,- -. Ir, I/: I/ I II I

V : :I I'v. I IIW e = 0 0 XI X2 Xm X3

,Y2 /'

/


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where R = the ratio of cylinder dry densityat fill w ater content to laboratory maxim umYd

dry density, but :y1- = C [Equation (1)deYdf Ydhence, CR = :;-- . -. - D, de Ydm - .

If, for the first specim en, Y1 = Y1 - X l isless than 0, then a decrement of water is usedon the next specimen (the soil is m ixed toallow drying to a weight corresponding toabout a 2-percent decrease in weight). Thisprocedure is continued as necessary to de-termine a maximum point on the Y curve or aslope of unity on the y curve.Method Using Percentage of Wet Weight asAbscissa

A converted wet density curve of ordi-n.ltes Yd (l + wr) can be obtained from a wetdensity curve by plotting these curves with anabscissa t, where t = (1 x ) . This ab-Yd + Wscissa is added water in percentage oftotal wetweight of the mixture of moist soil and water,

wr d - wfl d W - Wt - - ---1..Yd (1 + w) - 1 + W Equation (10)

W - wf 1 + wr1 - t = 1 - - - - Equation (11).l+w- l+wHence,

(1 + Wf)Yd{l + w){l - t) = Yd(l + w)(l + w)Yd (l + Wr) Equation (12)

and the. peak pO{int of the Ydel + W r) versustcurve IS Yd 1 + W r)'m

Points for the Ydel + wf) curve can beobtained by adding specific amounts of waterto 7.50 pounds of moist soil at fill water con-tent, m ixing and compacting. For example:

0.15~1 - -7.50 + 0.1531 - 0.02 - tan d

0.3125 - -7.50 + 0.3125 - 0.04 - tThe resulting wet densities are multiplied by{] - t)to obtain points on they del + w f)curve.


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APPENDIX B

Derivation of Correction Curvesfor Moisture ControlThe curved lines shown in Figures 3

and 4 are loci of equal magnitudes of a cor-rection value, 6, which when added to zgives Wo - wf. Let m

6 + zm = Wo - wf Equation (13)then 6 = Wo - wf - zm ' Substituting forWo - wf from Equation (8) results inz6 = ~ (w - Z ) Equation (14).+ zm 0 mLet the relation represented by the curve inFigure 2 be written:

Wo = f[7d (1 + W )].m

0Since

.7 d (1 + W ) = 7d (1 + W )(1 + Z )mOm f mWo = f[7d (1 + W f)(l + z )].m m

Substituting for W in Equation (14), weobtain z

06 = - m (f[7 d (1 + Wf )(l + z )] - z )+z m mm m Equation (15).

Usually the function f[7d (1 + wfH1 + zm)]mis not known analytically, hence, theform z6 = -.!!L- (w - z )l+z 0 mmEquation (14) is used. By assuming values ofcoordinates zm and 7d (1 + wf) the valuem7d (1 + Wo)= 7d (1 + wfH1 + z ) is obtained,m m mwhich from Figure 2 provides an approximatevalue of wO' Thus every coordinate point onthe graph can be assigned a correction value6 to be applied when the peak point of a con-verted wet density curve occurs at that coor-dinate.

Correction curves sim ilar to those shownin Figures 3 and 4 can be prepared for anylaboratory standard of compaction by first ob-taining an approximate relation between7d (1 + W )and Wo for that compactive effortm 0similar to the relation shown in Figure 2 andproceeding as in the foregoing. Unusual soilswith very low or very high specific gravitiesmay require construction of different correc-tion curves. However, if the 7d (1 + W ).m 0versus Wo plots are w ithin the range shown bythe points in Figure 2, the correction curvesshown in Figures 3 and 4 can be used.

APPENDIX C

Parabola Method where y = 7 d(l + Wf) - 7 d (1 + W rand 2pc fis the latus rectum. For z = Zl = 0 and


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-z 2ymYm = Z(Z - 2z )mEquation (18).

By substituting, first, Z2' Y2 and then Z3' Y3for z,y in Equation (17) and then equating,zm is found to be: y

l(z - z ) 2-

1 3 2 Z2Z = -[z + Equation (19).m 2 2 Y Y2-_2

Z2 Z3

Graphical solution. Figure 7 describesthe graphical solution for zm and Ym.

Tabulated values. Figure 8 (in pocketinside back cover) gives coordinates of thepeak point of the parabola when Points (1),(2), and (3) are equally spaced horizontallyin 2 percent increments. It was obtainedfrom Equations (18) and (19).


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. ~ O } - - - B/" J~ ~,// K~0

v ..., H0A '~I L , - A X I S \' \ G

Parabola M e t h o dG ra p h ic a l s o lu t i o n fo r v e r te x l 0 1 o f a p a r a b o la w h o s e a x is is v e r t i c a l , g i v e n th r e e p o in t s

A , a , a n d C . I f m o r e t h a n th r e e p o in t s a r e a v a i la b le l u s e t h e t h r e e c lo s e s t to o p t im u m .

H0A,-2 -I 0 +1 +2 +3 +4

I. D r a w h o r i z o n t a l b a s e l i n e th r o u g h th e le f t p o in t , A , a n d d r a w v e r t i c a l l in e s th r o u g hp o in ts B o n d C .D r a w l in e DE p a r a l le l t o A B ,p o in t E l i e s o n th e v e r t ic a l l i n e th r o u g h p o in t C iP r o je c tE h o r iz o n t a l ly to e s t a b l is h p o in t F o n th e v e r t ic a l l i n e th r o u g h B .D ra w lin e DG p a r a l le l t o A C , p o in t G l ie s o n th e v e r t ic a l l in e th r o u g h p o in t C .L in e F G in te r s e c ts th e b a s e l in e a t H . A x is o f p a r a b o la b is e c ts A H ; d r a w th e a x is .I n te r s e c t i o n o f l in e A B w ith th e a x is is a t J j p r o je c t J h o r i z o n ta l ly to K I w h ic h l i e s o n

t h e v e r t ic a l l i n e th r o u g h p o in t B .L i n e KH i n t e r s e c t s t h e a x is a t 0 , t h e v e r t e x .

2 .3 .4 .5 .6 .

NOTE; I f p o in t s A I B , a n d C a r e e q u a l ly s p a c e d h o r i z o n t a l ly ( th is is t r u e w h e n 2p o in ts a r e o b ta in e d b y a d d in g w a t e r o r w h e n s o i l i s d r ie d e x a c t ly 2 p e r c e n t ) s te p s 2 a n d 3a b o v e a r e e l im in a te d . P o in t F c o in c id e s w i th p o in t B a n d p o in t G is h a l fw a y b e tw e e n th e b a s el i n e a n d p o in t C . H e n c e , p o in t H is o b t a in e d b y d r a w in g B G a n d p o in t 0 is o b ta in e d b y s te p s 5a n d 6 a s u s u a l . S e e g r a p h b e lo w .


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APPENDIX DAlternative Method to Eliminate DryingRequirement for Soils Close to OptimumWater Content

Points (1) an d (2) of the converted wetdensity curve are obtained in the usual man-ner as given in the section, Examples.

To obtain Point (3) when Point (2) iss ma ll er i n o rd in ate th an Po int (1 ) but within3 pounds per cubic foot of that point: In lieuof drying 7.50 pounds of soil at fillwatercontent as required in the procedure givenunder the section, Examples, for the rapidcompaction control method, add 34 cubiccentimeters (1 percent) of water to thisquantity of soil, mix, and compact into a cy 1 -inder. Find the point on the +1 percent diag-onalline corresponding to the wet density,project vertically to the 0 percent diagonalline, thence horizontally to plot Point (3) onthe +1 percent vertical line. The ordinate ofthe plotted point is the wet density divided by1.01.

I f P oi nt (3) thus obtained is greater inordinate than Point (0, the peak point of theconverted wet density curve can be obtainedgraphically by the parabola method. If Point(3 ) is smaller in ordinate than Point (0, th~graphical procedure for obtaining the peakp oi nt r eq ui re s e xt ra po la ti on w hi ch r ed uc esits accuracy. For this case, calculateY /Y , where Y l is the difference in ordi-3; 2

nates of Points (1) and (3), and Y2 is the dif-ference in ordinates of Points (1) and (2).Figure 9 gives the location of the axis of theparabola (distance zm from the origin) forr ati os Y /Y 2 . This figure is an enlargementof a portion of Form 7-1624A which followst hi s a pp en di x.

For example, ifPoint (1) = 117.6 pounds per cubic footPoint (2) = 115.1 pounds per cubic footPoint (3) = 116.8 pounds per cubic footYl= 117.6 - 116.8 = 0. 8Y2= 117.6 - 115.1 = 2.5

Y/Y2 = 0.8/2.5 = 0.32, from Figure 9,zm = -0.4 percent.

With the axis of the parabola determined,the mirror images of Points (0, (2), and (3)can be plotted as shown by Points ( 11 ), ( 2' ),and (3') in Figure 10. The peak point of theparabola, Point (0), i s o bt ai ne d b y d es ig na ti ngPoint (3 ') as A, Point (1 ') as B, and Point (3)as H and proceeding with the parabola methodconstruction. The coordinates of the peakpoint of the converted wet density curve are:(-0.4, 117.7).

Tabulated values. Figure 11 (in pocketinside back cover) gives coordinates of thepeak point of the parabola for this alternativemethod. These values can be used in lieu ofthe procedure shown in Figures 9 and 10.


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.46.44.42

S~ .40~.~ .38tII\.O .360f-'olI-' .34:~ .32g'C'i)

~~.30I ~~~..281)0bid .26tII~(1)n(1)

11..24t\:> 8'~w 0 (1) Y2.22'd ~8 ' .20~(1)~I .18.16'i ~(1)0 .14g '1~(1)

(1)~ .12j .~'1 ~.10

~.08~'1 .06

.04

.02

R AP ID M ET H OD OF COMPACTIONCONTROLALTERNATIVE PROCEDURE TO ELIMINATE REQUIREMENT FORDRYING SOILS THAT ARE CLOSE TO OPTIMUM WATER CONTENT

I,l--~ml.I,

I

KE Y

0 -4.0 -3.8 -3.6 -3.4 -3.2 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2-.mO"E1JWAITfMN-P&RCf:NLOFF IL L W ET W EIG HT F OR P EA K P OIN T (Z m)

Point!!)- -.....Point (3) ..... ..... " "oint(2 )

~2,,

0Y, -Y2 -

+1Z~- (Zm+ 112z K, - (Z m+ 21 2

+2

0 +0.2 +0.4 +0.6 +0.8 +1.0


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32/35


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R APID METH O D O F C OMPACTIO N C O N T R O LTABUL ATION OF COORDINATES OF PEAK POINT OF PARABOLA F ~GURE - Tabulation of coordinates of peak point of parabola.


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T a b u l at e d v a lu e s a r e c oo r d i n a t e s ( u p p e r v a l ue x l o w e r va l u e Y )of t he peak po in t o f a parabo la whose ax is is ver t ica l , g iventhree points A,B, and C spaced 2% apar t hor izon t a l ly . Theo r i g i n o f c o o r d i n a te s i s a t p o i n t A, t h e e x t r e m e l e f t p o i n t .Y2 i s t he o rd ina t e o f po in t B m inus o rd ina t e o f po in t A .Yq i s t he o rd ina t e o f po in t C m inus ord in a t e o f po in t A, Y4 may be negat ive.

V A L U E S OF Y 4 GPO 840080

RAPID MET HOD OF COMPACTION CONTROLT A B U L A T I O N O F - C O O R D I N A T E S O F P E A K P ~ N T F P A R A B O L A( A L T E R N A T I V E M E T H O D T O E L I M I N A T E D R Y I N G R E Q U I R E M E N T F O R S O I L S C L O S E T O O P T I M U M W A T E R C O N T E N T )M A R C H 1960

V A L U E O F Y I


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E X A M P L EYI = 117.5 - 1 1 6 . 6 = 0. 9yP = 117.5 - 115 . 0 = 2. 5F r o m t a b l e , Z m =-0.8

Y, = 0. 2

Henc e c oord ina t es o f peak po in t o fpa rabo la , p o in t 0 , a re : ( - 0. 8 , 117 . 7 )

~ a b u j a t e d a l ue s a r e c o o rd i n at e s( u p p e r v a l u e Z m , l o w e r v a l u e Y m )o f t h e p e a k p o i n t o f a p a r a b o l aw h o s e a x i s i s vertical, g i v e nt h - w e p o i n t s ( 1 ) , ( 2 ), a n d (3 ) s pac eda t Z = O ; Z =+ 2 % , an d Z = + I %r e s p e c t i v e l y . T h e o r i g i n o f c o o r d i n a t e si s a t p o i n t (11, t h e e x t r e m e l e f t p o i n t .T h e d i s t b n c e YI i s t h e o r d ~ n o t e f p o i n t (I)m i n u s o r d i n a t e of p o i n t ( 3 ) ; Y , may bep o s i t i v e , o r n e g a t i v e w h e n o r d i n a t e o fp b i n t (3); s gr e a t e r t h a n o r d i n a t e o f p o i n t ( l )T h e d i s t a n c e Y i s th e o r d i n a t e o f p o i n t ( I )m i n u s o r d i n a t e o f p o i n t ( 2 ) ; Yp i s a lway sp o s i t i v e .

FIGURE 11 - Tabulation of coordinates of peak point of parabola for alternative method. GPO 837638

A Rapid Method of Construction Control for Embankments

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