Research Report 163

LABORATORY DETERMINATION OF. DY.NAMIC MODULI

OF FROZEN SOILS AND OF ICE

Chester W. Kapler

January 1969 -

DA TASK 1 T062112A 13001

U.S. ARMY MATERIEL COMMAND

TERRESTRIAL SCIENCES CENTER

COLD REGIONS RESEARCH & ENGINEERING LABORATORY HANOVER, NEW HAMPSHIRE

THIS DOCUMENT HAS BEEN APPROVED FOR PUBLIC RELEASE AND SALE; ITS DISTRIBUTION IS UNLIMITED.

ii

PREFACE

The investigation reported herein is part of a comprehensive investigation and study of methods for description, c_lassification and determination of the strength prop­erties of frozen soils and ice-soil mixtures conducted by the Arctic Construction and Frost Effects Laboratory (ACFEL)* of the U.S. Army Engineer Division, New England, for the U.S. Army Snow, Ice and Permafrost Research Establishment (USA SIPRE)*.

- The data collected in each of the three phases of the comprehensive study have been summarized in ACFEL Technical Reports 40 (SIPRE Report 8), 44 (unpublished), and 48 (unpublished). The complete investigation involved the following major topic areas, of which the present summary report covers one: temporary compressive strength, temporary tensile stre rgth, temporary shear strength, ice crystal structure, plastic de­formation, dynamic moduli, overall evaluation of physical properties, and, _a system for description and classification of frozen soils.

Investigations were in part funded under the continuing Military Construction In­vestigations (MCI) program conducted for the Engineering Division, Directorate of Mili­tary Construction, Office, Chief of Engineers and administered by the Civil Engineering Branch (Mr. T.B. Pringle, Chief). This report was published under DA Task 1TQ62112 A13001, Cold Regions Research - Applied Research and Engineering.

The study was performed under the general direction of Mr. K. A. Linen, Chief, ACFEL (presently Chief, Experimental Engineering Division, CRREL) and Mr. J.F. Haley, Assistant ChieC ACFEL, and the direct supervision of Mr. C. W. Kaplar, Project Engineer (presently Research Civil Engineer, CRREL).

The author wishes to acknowledge the contribution of Dr. Francis Birch, Dep1

art­ment of Geology, Harvard University, who designed and constructed the magnetic vi­brator used in this study. Grateful acknowledgement is also extended to Mr. O.W. Simoni, Soils Engineer (presently Assist::tnt Chief, Alaska Field Station, CRREL) for the preparation and freezing of the test specimens, and to Mr. M. Levey, Geologist, who performed most of the tests.

Lieutenant Colonel John E~ Wagner was the Commanding Officer/Director of the U.S. Army Terrestrial Sciences Center* during the publication of this report, and Mr. W.K. Boyd was Chief Engineer.

USA TSC is a research activity of the Army Materiel Command.

-* ACFEL was merged with SIPRE in 1961 to form the U.S. Army Cold Regions Research and Engineering Lab~ratory (USA CRREL), now an element of the U.S. Army Terrestrial Sciences Center (USA TSC), Hanover, New Hampshire.

CONTENTS

Preface .............................. -........... _ ... -..... -.............. .

Abstract .............. · . · . · · ·- · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · Introduction ........ ~ ................................................. · · ·

Background ............... _· ............. -............. -· .... · · · · · · · · Definitions .................... · . · · . · · · · · · · · · · · · · · · · · -. · · · · · · · · · · · Notation ......................... -............................... .

Investigations ·performed ................................................ . Materials .......................................... _ ...... : ....... . Test equipment ......... · ...................................... -..... .

Preparation· and freezing of specimens ....... ~ .... .- ........................ . Molding of specimens .. , ............................. , ............ . Therrnocouples ........................................ -· ...... ~ ... . Saturation of specimens ........................................... . Placing trays in freezing_ cabinet ................................... . Specimen freezing procedure ...... · ................................. . Preparation of frozen specimens for testing ........................... .

Test procedures ........................................................ . Test results and discussion ........................ - .................... . Conclusions ....................... _ ................................ · .... . Selected bibliography .. ~ .............................. , .................. . Appendix A: Test results ............... : ............................... .

ILLUSTRATIONS Figure

iii

Page

ii iv

1 1. 1 2 3 3 3 9 9 9 9

10 10 10 13 15 23 24

1. Grain size distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2. Electromagnetic three-mode beam vibrator . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3. Apparatus used in tests for dynamic modulus. . . . . . . . . . . . . . . . . . . . . . . . . . 7 4. Specimen of McNamara concrete sand showing permanent bar magne_ts frozen

flush with end of beam ........................... ·-·......... 7 5. Horizontal beam tray .............. ; ..................... -. . . . . . . . . . . 8 6. Vertical beam tray................................................. 8 7. Typical beam of undisturbed Boston blue clay frozen in horizontal position 8 8. Typical beam t>f undisturbed Boston blue clay frozen in vertical position . 8 9. Typical temperature and heave data for each tray of specimens. . . . . . . . . . 11

10. Summary of data presented on Figures Al-A14 ...................... ~ . 16 11. Comparison of dynamic modulus E of ice obtained by- various investigators 18 12. Summary of longitudinal or P~wave velocities in ice measured by various

investigators ..... -.............................. ·. . . . . . . . . . . . - 18 13. Relationship of soil type and dynamic modulus, EL, at 20F............. 22

TABLES

I. Materials 'tested ............................... · .. -.................. . II .. Summary of soil characteristics ........... -............... ~ . . . . . . . . . . 4

:IlL Tabulation of specimen data for dynamic modulus tests . . . . . . . . . . . . . . . . 12 IV. ;Summary of dynamic modulu$. tests .. ~... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 V. Comparison of propagation velocities of dilatational sonic waves in frozen

ground -..... -~ . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 19

ABSTRACT

This report presents a surpmary of results of laboratory investigations of frozen soils and ice to determine the elastic moduli by the dynamic (sonic) method. Th~ elastic moduli were indirectly ·obtained by measuring the fundamental resonant frequencies of flexural, i"ongitudinal, and torsional vibrations i~duced in pr~sma,tic beams by electromagnetic means. Yibration tests were .performed on a total of 56 specimens repre~enting 12 different mate~ials (8 natural soil types, ranging from coarse-grained to fine-grained; 2 blended sqils; a natural peat; laboratory-frozen ice and natural lake ice, at temperatures ra11ging from apP,roximately · +32F to -lOF). Elastic wave velocities (longitudinal and torsional) were computed for each m~terial in the range of test temperatures studied~ Ail so~ls were satur~tedor were close to, saturation. · · · .~ · ·

The dynamic moduli of elasticity of the frozen soils were found to increase with a decrease in temperature, the greatest rate of increase occurring between +32F and +20F. Coarse granular soils gave the highest values and clays the lowest in the ratio· of more than 4 to 1. ·Dynamic Young's modulus; E, computed from flexural vibrations· was usually lower than dynamic E computed from longitudinal vibrations. Average values ofdynamic Pais;;. son's ratio for all soil types computed from average values of E and G (longitudinal vibra­tions) ranged from 0.26 to 0.38. Values of Poisson's ratio for the various soil types did not collrorm to any logical pattern related'to t~mperature or soil type.

The dynamic moduli of elasticity of ice showed only slight depende_nce _on tempera­ture, and test~vaJues were more cons!stent th<:tri thos.e ofthe soiis. Natural lake ice was i~ast temperature dependent and gave thy.~ost c9n_sistent ~e~\llt~. :pymimiqmoduli of ice E (lon~ituqinal:_v~br:~pon) ai1q~_G.,GoHip~re.d cJo~ely ~ftli y~l~e~: reported b~. O,~he.r ~~vesti­gators. Average va1ues of"Poisson''s ratio for ice ~e~~- rea~~)llable but less consistent, ranging froni 0.3? to 0.41.

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Background

LABORATORY DETERMINATION OF THE DYNAMIC MODULI .

OF FROZEN SOILS AND OF ICE

by

Chester W. Kaplar

I. INTRODUCTION

The determinations of the elastic properties of frozen soils and of ice were made as part of studies of strength properties of frozen soils:(AGFEL, 1954; ACFEL, 1952). The elastic properties .. of frozen soils h~we not been extt=msivelv ~tudierl, but several·investigators',(Boyle et al., .193( Ewing et al., 1934b; Kornfeld et al., 1942; Lagutin et 3'1., '1946; Nakaya,' 1959; 'Northwoo~d, 1947; Tsytovieh et al., 1936, l93:i) have measured the elastic properties of ice. In this study tests were conducted on both media, to obtain needed data and facilitate comparison between the two. In these laboratory investigations, dynamic methods were used in non-destructive tests. Vibrations were induced in beams of frozen soil and ice by electromagnetiC' means. That such dynamic . methods are more suitable than static methods for determining elastic properties is supported ,by many investigators (Wilson et al., 1948; Boyle· et al., 1931; Dorsey, 1940; Ewing et al., 1934a). The static method usually involves measurements in the plastic rather than the elastic range of de­form'ation. Ela:::::t.ic deformation takes place over such a small range of load and deformations that extremely -small stresses must be used, and the deformations within the elastic range 'are so small · · that their measurement is difficult and subject to considerable error (Butkovich and Landauer, 196J)."

The dynamic method is an indirect procedure relating sonic resonant frequencies to the elastic properties of the material. By its use, the l~rge aberrations caused by plastic deformation can be avoided. In the field, velocities of elastic waves produced by buried explosive charges may be measured directly. In the laboratory, longitudinal and transverse wave velocitiesmay be computed from the resonant frequencies induced in small beams of frozeri soil and of ice.

It is hoped that the results of these studies will be usefUl in seismic applications in perma­frost regions for possible identification of frozen subsurface strata and in the· design of foundations of critical structures subjected to vibrating or oscillating loads. Data frqm these tests have been useful in the design of radar foundations in permafrost.

Definitions

Elasticity. Elasticity is the property of a strained body by which it retur~s to its initial size and shape after release of load causing the strain. The body is considered to be perfectly elastic if it recovers its original size and shape completely after unloading; it is partially elastic if the · deformation produced by external forces· does not disappear completely after unloading.

Modulus of elasticity (Young's modulus). Young's modulus of elasticity is· the rate of change of unit direct stress with respect to unit direct strain (based on original length) for t~e condition of uniaxial stress within the proportional limit. ·

Modulus of rigidity (modulus of elasticity in shear or in torsion). Modulus of rig.idity is the rate of change of unit stress with respect to unit shear strain, for the condition of pure shear within the proportional limit.

Plastic deformation. Plastic deformation is non-elastic deformation· of the material under load; i.e., it is non-recoverable when the load is removed.

I

2 LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE

Poisson's ratio~ Poisson's ratio is the ratio of lateral unit strain to longitudinal unit strain, under the condition of uniform and uniaxial longitudinal stress within the proportional limit.

Degree of saturation. The ratio, expressed as a percentage, of the volume of water (or of ice) in ~ given soil mass to the total volume 1 of voids.

. Frost heave. The raising of a surface due to the formation of ice in the underlying soil (see Percent heave, below).

Frost-susceptible soil. A soil in which significant ice segregation will occur (usually in the form of lenses) when certain moisture and freezing temperatures are present.

Percent heave. The ratio, expressed as a percentage, of the amount of heave to the depth of frozen soil before freezing.

Ice content. The ratio, expressed by weight or volume, of the amount of ice in a frozen soil to the amount of dry soil. If by weight, the weight of the ice phase compared to the weight of dry soil, preferably expressed as a percentage; thus, if all moisture is frozen, ice content by weight is exactly equal to water content. If by volume, the volume of the ice compared to the volume of soil solids, expressed as a decimal.

lee segregation. The growth of ice as distinct lenses, layers, veins, or masses in soils -commonly, but not always, oriented.normal to the direction of heat loss.

Void ratio. The ratio of the volume of voids to the volume of soil solids in a given soil mass.

Water content. The ratio, expressed as a percentage, of the weight of water in a specimen to the ~eight' of dry soil. In this report, the water content of a frozen soil includes water in the form of ice and any non-frozen water present. ·

Notation

c

G

['f, f'L, f't

g

A factor depending upon the shape and size of the specimen, mode of vibration and Poisson's ratio (Pickett, 1945) -

Young's modulus of elasticity derived from flexural vibrations

Young's modulus derived from longitudinal vibrations

Modulus of rigidity (elastic modulus in torsional vibrations)

Fundamental resonant frequency corrected for mass of magnets

Observed fundamental resonant frequency

Gravitational acceleration (386 in./sec 2)

Number of nodes

k Ratio of radius of gyration of magnet to that of specimen (used in frequency correction formula for torsional vibrations)

L Length of specimen

M Weight of magnets

R A geometrical factor used in torsion theory (Pickett, 1945)

V Velocity of wave propagation

w Unit weight of specimen

W Total weight of specimen

11 Poi-sson's ratio

Subscripts f, L, and t refer to flexural, longitudinal and torsional vibrations, respectively.

LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE ;~

II. INVESTIGATIONS PERFORMED

Materials

Table I lists the materials investigated. the number of specimens of each material tested, and the orientation of the beams dming unidirectional fret~Zing.

Table I. Materials tested.

Number of ::;pecimens tested

Fwzen

________ __ M!~reri!!:_l ----~ -----------~llul ___ ------------~~iz~Itall~---

I'eabody gravelly sand (minus ;~ '4-in. mesh)

NcNamara concrete sand Blend, Me Namara concrete sand

and East Boston till Blend, Manchester fine sand and

East Host011 till E<tst Boston till* New Hampshire silt Fairbanks silt Yukon s i1 r. Boston blue clay (undisturbed) F;argo clay (undisturbed) plaskan peat (undisturbed) lee, labor;uory-frozen Ice, uaturalt

SP 2 SM

SMT 0

SNHT n SEH'l' u SNHS 2 SFS ()

SYS ()

SBC 6 SFFC 5 SAP 1

SI fj

SI-(P) 1

* Fom specimens consisted of materials passing the No. 1 mesh sieve and one speciu1en of material passing the ~3 .. '4-in. sieve.

0 1

5

5 5

G r, 0 0 1 4 0

t Specimen obtained from large beam cnt from na.tmal Llke iee Ltt Portage Lake, Maine, in March 1953.

Specimens of Fargo (North Dakota) clay, Boston (Massachusetts) blue cLly, and· Alaskan (Fair­banks) peat were cut from undisturbed chunks; all specilllens of other soils were remolded in the laboratmy. From two to ten specimens of each material were tested at various temperatures ranging from approximately. +32F to -10F. The grain size distributions of the soils used are shown in Fig­me 1. A complete summary of soil characteristics and sources will be found in Table II.

Test equipment

Dynamic modulus test apparatus. The principal items of equipment used in this investigation are shown in f 1 igures 2 and 3. The complete apparatus consisted of a variable frequency oscillator capable of producing· frequencies from 18 to 220,000 cycles per second, an amplifier, a cathode-ray oscilloscope, a vacuum tube voltmeter, and a magnetically coupled specimen vibrating apparatus and detectm. The magnetically coupled vibratm was designed aud constructed for this study by Dr. FLmcis Birch of Harvard University. Beams having dimensions of approxinmtely 11.1~ x llh x 11 in. were used in the investigation. The vibrator, however, can accomodate beams up to 2 :~ iu. square in cross section.

Permanent bar magnets, 3/ 16 x 3

/ 16 x 2 in., were frozen flush into horizontal ~.::roove~:; prepared in each end of the frozen specimen beams with the ends of the magnet~.; protmding 1

;~ in. on each side lFig. 4). Vibration of the specimens was actuated by two oscillatiug mahnetic fields from a pair of r1ectromagnets mounted in series at one end of the apparatlls. Each dectromagnet consisted of very fine wire wound around a C-shaped laminated core. The air gaps betwf.:en t: he poles of the magnets were ~ in., sufficient to accommodate the :j 16 in. thick bar magnets without t.ouchi ng.

SOIL LEGERD

SP-

SM

SNP.T

SEBT

SJIIRS

SFS

SYS

SBC.

SFFC

SAP

NOTES:

TABLE II

Su:.!MARY OF SOIL CHARACTERISTIC::;

IEPAJmEIIT OF THE AR!ofi' . ·UIU'IED SOIL CLASSIFICATIOR *·

SOURCE

A 'l"l'ERBERG LIMITS

CX>MPACTION CII.AMC'reRISTICS

TYPICAL PROPERTIES OF SPECD!EN;, ,

~=~~C MAX. DRY OPI'IMIJM (before freezing) 1---_:___: ________ -:-rGROUP=-:::=--t--:L:-:I~Q~UID=-t-PLA=-:-;::ST:;:I;:C:;ITI=:-r::.SHilDOCA=-;~:-:;G::;-iE UIHT WT • JlABr DRY UNIT VOID

DESCRIPI'ION SYMBOL LIMIT I!mEX LIMIT (per) I ( perce~~ WT. ( pcf) RATIO

Peabody Gravelly Sand

McNamara Concrete Sand

'!!lend, ~.~c!iB~~M Cc-nc~te

.~r:nd ::nf. East 5ost::m 7ill

Bleitd, :.~r~nchester Fine Sand snd Ee:2t ?~st-,or. ~ill

East Boston Till (-3/4")

New Rampahire Silt

· Fairbanks Silt

Yukon Silt

Boston Blue Clay

Fargo Clay

PeabOdy, Mus •

Needham, !.ass.

s•• Blended with o.5o; r.Jinus 40 r.Jesh C'EBT

SNH 3lended with '5<> mim'2 hO roesh ~E!lT

East Boston, !.ass.

Manchester, N. R.

Fairbanks, Alaska

Bank run gravelly SAJm

SAND, brovn, angular, processed for concrete

Silty ~AND

Silty SAND

Clayey, gravelly SAND (Glacial Till) .

Light gray brovn, inorganic clayey SILT .

Brovn and gray SILT, containing traces of mica and some organic matter

Whitehorse, Gray, well graded, inorganic Yukon Terri tory, clayey s'ILT ·. .. ranad&

No. Calllbri<i8e, Maas. Stiff lean CLAY, relatively. homogeneous and --free of fractures and varves

SP

SP

S1<!

sc

CL-ML

ML-OL

CL-+CL

CL

Fargo, North Dakota Dark gray, friable, highly plastic CH..OR homogeneous fat CLAY, vi th honey-comb structure (organic content ~)

Fairb&nlt.s , Alaaka Dark brown to black PEAT; rtbroua, Pt partially. deCOIIIPOHd ( Or@llolliC content 82 percent)

non-plastic

I non-plastic I . nr;n-p1nstic

I non-plBstic

21

26

28

28

27

68 46

(l) Providence Vibrated Density (Proc. 2nd Int. Conf. on Soil Mech. and Fdn. Engineering, v. 4, p. 243) (2) :.:edified AAO::HO n,;nsi ty (AS~-~ T180-57D) (3) 2tandard Proct~r Density (AS'J:".' T99·57A)

2.72 134 (1)

2.72 123 (1)

1L72 142 (2) 6.8

2.72 128 (2) 9.2

2.76 137 (2) 8.1

2.70 107 (2) 15.6

2.68 ll2 (2) 15.7

2. 73 121 (3) 12.8

22 2.81

15 2.76

1.52

* Technical Memorandum-No. 3-357, WaterwaY.~~ Experiment Station, Vicksburg, Mississippi, vol. 1, Mar. 1953.

12) 0.356

117 0.456

0.262

-1?1

.0· 653

10) 0.590

115 0.479

1.057

LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE 5

100

90

80

0

0

40

30

20

10

100

90

80

~ 70

~ 60

~ so i:

~ 40

i 30

10

100

COBBLES.

~

I '\"' I I \

.I SP-

I

I I I

I I I

I

I' I

li

,. 2" l'lz'' I" 314 ¥ ri

I I I

I I I I

I I I I

I

10

1\ 11--II ~

II ........ i'f', SM \ I ["'\ ~ I i'\. \ I I "\. I '\ I I

4 10

"'\ '\.

" I I I I SMT I I I

1 "e I 20 30 40 70 100 200 Us' Standard s·e s·ze

N 1:1 \ Iii

lif \ I \ I

I \ I \SNH 1 ......

I

'-1 \ \ I

I \ I ..._ SEBT \ ...... ;

\ \ .......... \

N\ \ I ...... "'\~ r---... ~

......::::: 0.01 0.001

SILT or CLAY

20 30 40 10 100 200 U.S. Standard Sieve Sin

........ J \ I

I \ I

I \ \ \

SNHT..o\ \ \

"\. \ I 1\.. \

..........

~ ..... I -...;;::::

~ ....... ...._ 0

1000 100 10 LO 01 0.01 _0.001 Groin Size in Millimeter•

COBBLES GRAVEL SAND

Coors• Fine oar1e Medium

.. 1:. I

; I

1.0 01· G roln Size in Millimeters

GRAVEL SAND Coarae Fine Coarse Medium Fine

Fine SILT or CLAY

; l

SILT or CLAY

I I

0.0001

Figure 1. Grain size distribution. See Table I for soil names.

Circuit switch

A~'uslable brass platform an post lOr supporting specimen at nodal points for flexural vibrations.

Fixed center support posls. /Jross; used wllh longitudinal and torstonal vtbrohons.

Quarter node support posts

Coli. Copp•r wlr• WtiiiiJt/ ti,DIIIIt/ &/Jf. ltJ t"O.D. 1111d S/11" ~i~~.

Electro-M~gnet Holder SCA~E IN INCHES

o-

C1Jrt1. 16 lomintJYt~d pltJit~s Each plat• 1/64• in lhidtttlll

Electro -mognet holder

Adjustable support for eleclro-maqnel holder

SCA~E IN INCHES

Steel guide runner

I"' 0 2" 3"

1-l W I

Jl tl ~ Switch Dir~cl/on

,------"B:::::ID::::,Ck_~'--o\!'-'-f---T=::-=: -- F, L

Yt1/low

Wiring Diagram

Lominoted 'electro-magnets for pickup.

Figure 2 .. Electromagnetic three-mode beam vibrator (for flexural, longitudinal and torsional vibrations).

-("') ~

LABORATORY DETERMINATION OF DYNAMIC.. MODULI OF FROZEN SOILS AND OF ICE 7

Figure 3. Apparatus used in tests for dynamic modulus. Figure 4. Specimen of McNamara concrete sand showing permanent bar magnets frozen flush with end

of beam.

The electromagnets were held in horizontally and vertically adjustable supports and could lie in either a horizontal or a vertical plane. A switching arrangement was provided to eriable correspond­ing poles of each electromagnet to be of the same or of opposite polarity. The arrangement of the two detector magnets on the other end of the apparatus was the same as on the driving end.

Freezing trays. Two wooden molding trays were used in the preparation and freezing of the soil beams used in the investigation. Each was constructed of white oak and treated to resist moisture absorption. One of the trays contained six horizontal compartments, 11h x 4112 x 12 in., for horizontally positioned soil beams (Fig. 5). Since freezing was from top to bottom the ice lenses* in these specimens formed in a direction parallel to the longitudinal axis of the beam (Fig. 7). The specimens molded in this tray are identified by the prefix HB (Horizontal Beam). The other tray (Fig. 6) contained 25 vertical comp;:trtments, 11h x 11h x 12 in., for the preparaFion of beams to be frozen in a vertical position, i.e., beams in which ice lenses formed in planes normal to the longi­tudinal axis of the beam (Fig. 8) . The samples molded in this tray are identified by the prefi.x VB (Vertical Beam) .

Both types of trays were constructed of removable sections to facilitate dismantling andre­moval of frozen specimens. Along the top and bottom edges of each tray there was provided a con­tinuous rubber gasket, ~ in. thick and 11h in. wide, and a series of ~-in. stud bolts for attaching watertight covers made of 11-gage galvanized sheet steel. Top and bottom covers each contained a ~-in. brass nipple 3 in. long in the center, for attaching de-airing and saturating apparatus. When the trays were assembled and filled with test beams, a ~ in. thick filter mat was placed on both top and bottom within the space provided by the thick rubber gasket. These mats were built up from 64 x 64 weave mu'slin (next to specimens), 18 x 14 mesh bronze screen cloth and lh-in. 18-gage galvanized expanded metal. The filter mats and covers were used during the simultaneous evacua­tion and saturation of all the specimens in the tray prior to freezing. The top cover and mat were removed during the freezing of the specimens. Sample preparation and freezing'procedures are des­cribed below.

* Note that the reference here is to ice lenses, not crystal .optic· axes.

8 LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE

Figure 5. Horizontal beam tray. Figure 6. Vertical beam tray.

Figure 7. Typical beam of undisturbed Boston blue clay frozen in horizontal position. Ice lenses oriented horizontally, parallel to longitudinal axis of beam. Note magnets in ends of sample.

* . - -' .... • .. . . . ' . . . . ' -·· -·- •.. · • - ' - ~

~ ~ ~ ~ t.., l t : ~11 4 4 f> ~~i!~t~

~:t~. --~ . _ .. <-:' 11

- ' ·< >:<~ .,4:. · __ : ~:;.~~-.~i~~~;~~-~-1~:!

··Figure 8. Typical beam of undisturbed Boston blue clay frozen in vertical position. Ice lenses oriented perpendicular to

longitudinal axis.

LABORATORY DETERMINATION OF DYNAMIC MODULI OF .FROZEN SOILS AND OF ICE 9

III. PREPARATION AND FREEZING OF SPECIMENS

Molding of spe.ciinens

-With the exception of the undisturbed materials, i.e., Boston blue Clay, Fargo clay, and Alaskan peat, the· test ·soils were molded at optimmri water content*' to densities approximately .95% 'of the . maximum determined by the. Providence Vibrated Den·sity Test (Lane, 1948) for the cohesionless' sbils, i.e., Peabody gravelly sand and McNamara concrete· simr, and the Modified AASHO Tests, ASTM T18G-57D or ASTM T99-57 A for the other soils. ' ,. . · ··. · .

Before the soil was placed in the-freezing trays, the.inside walls of the .wooden molds were lubri­cated with a thin coating of petrolatum an~ lined wi.th traqsparent ~ellulose acetate, 0.007 in. thick. The petrolatum and acetate served to. minimize the side friction of frost-susceptible specimens during the period of heave and facilitated the removal of fro.zen specimens from the molds. With the bottom fUter mat in place between the bottom cover and the mold, the bottom cover was E;ecur~d tightly against the rubber gasket by means of the studs, nuts and washers. The sp~cime11s we,~e the~ either compacted or i_nsert~d into the molds. ·

Generally, two individual soil beams·were obtained from each 4% in. deep compartment of the horizontal beam tray. ·With the filter mat and the bottom cover plate in placey a known quantity of soil was uniformly placed and compacted to a depth slightly over 1% in. Next a %-in. layer of -Ottawa sand was deposited, and over this material another beam of soil was· compacted in place. The %-in~ space remaining between the top layer of soil and the top of the mold' was filled with Ottawa sand. The top filter mat and cover were then put in place and fastened.

For the undisturbed clays and peat, .horizontal be~ms or. segments 1% in. Wide .and 4% in~ deep were cut to size from a large undisturbed chunk sample from a horizontal section, oriented in the. same position as in the field. ,

The preparation of remolded specimens in the vertical beam tray c·onsisted ·of placing the soil in. the vertical-_eompartment in thin layers and compacting. with a 1% in. squar.e wood block. · Except for only. one specimen of Alaskan peat, no vertic~ beams were cut from undisturbed field chunks because of difficulties ·in manipulating suoh slender specimens (1% x 1% x 12)n.). ·

Thermocouples

In at least one specimen in each tray, copper-constantan thermocouples were placed at approxi­mately 2-in. vertical intervals or closer, as an aid in the regulation of the rate of freezing. Other thermocouples were placed at the top and bottom of some specimens for assurance that freezing had taken place in all parts of the tray.

Saturation of specimens

Before freezing, .the specimens in the tray were de-aired and then saturated in a +40F cold room. After de-airing by use of a vacuum at top and bottom via the nipples on the cover plates, water was admitted at the bottom while the (je-airing proce,~s was continued at the top. · The pro­cedure was continued for a minimum of 12 hours for the non-frost-susceptible soils (cohesionless sands and gravels) and 24 hours or longer for all the other .soils, until the discharge of water at the top of the tray was virtually free from air. During the saturation process, the specimens had. cooled to approximately 40F prior to being placed in the freezing cabinets.

* The water content for which maximum density is obtained for a given compactive effort.

10 LABORATORY DETERMifVATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE

Placing trays in freezing cabinet

After saturation was completed the specimen trays were placed in the freezing cabinets within the +40F cold room. The top metal cover and mat were then removed and thin aluminum plates were placed over each specimen to prevent sublimation. A source of de-aired water was connected through a constant-feed water level device to the brass nipple on the bottom cover plate and. the water-control dev.ice was adjusted to maintain the elevation head at the level of the tops of the specimens during freezing. The space between the tray and the walls of the cabinet was insulated with granulated cork to confine heat flow to the vertical direction.

Specimen freezing procedure

Specimens were frozen unidirectionally from top to bottom, with the bottom of the trays exposed to a temperature of approximately +38 to 40F. · Freezing was initiated by lowering the air temperature in the freezing Gabinet to approximately +15F, until crystallization was observed in the uppermost part of the specimen. The cabinet temperature was then raised to +29F by resetting the thermo­regulator .and leaving the cover of the cabinet open for a short period of time, usually 20-30 minutes, to warm up the chamber. Thereafter~ the cabinet air temperature was reduced daily by successively larger decrements as necessary to freeze the specimens uniformly in the time required -· at a rate ranging from approximately lh to %in. per day. Trays containing ice specimens were given one extra day of freezing at the end to ensure that the specimens were completely frozen. Temperatures within the specimens were read daily and temperatures in the cabinets were adjusted accordingly, depend­ing upon the progress of the 32F isotherm within the specimens. The heave of each specimen was measured daily to the nearest half-millimeter. Measurements were obtained by scale readings at the intersection of a meter stick placed vertically on the metal plates on the top of the specimens and a metal bar placed across the cabinet opening. · Figure 9 illustrates typical temperature and heave data obtained during freezing.

Preparation of frozen specimens for testing

Aiter freezing, the specimens were. removed by carefully dismantling the tray. The appearance and a brief description, including size and frequency of ice lenses, were recorded. Each specimen was trimmed to uniform dimensions, measured, weighed, and tempered for a period of at least 16 hours at each test temperature before sonic testing. A tabulation of the pertinent data obtained for each specimen is pre sen ted in Table IlL

E E I

w ~ 1&.1 :r

VI 1&.1 :r 0 z I :r 1-Q.. 1&.1 0

~ N .., • 0 ..J 1&.1 CJI

(/)

cr :;)

0 :r I ....

1&.1 IE C)

"' 0

LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE 11

: .$t :_;:£ Gt-:~ ;+ L~ ~j : (-: ! l ~JHEAV:E. vs TiMEl -- ; i. ·:-r····· _._r;_ lj !-J: i1 1! :.'.:. ; t·! I I I

! i

4 =:-:-- -~ T --· r- ··. It l -! f ; l 1 : • ! l ; I ·~ • ' • - !, ·I I ! 1 I ! j 1'4 t : ' ' . ! ! · ' I ·• · · • /"' ·. ~ ;'·:· I cf' ; 0 15

• f ; • I . ! I -; L '-l+ -l H+r++- +i-T i-t ~-i-~·; : ' =+-: :· _;: r:c i +!.Y' r : ·sNI-tt-foe ~· II .. ; i ll 3

• I : :. . ! . I j I y!. ! . l • . • I . . 1 i • j I ; y ,. I ,. ·-t-;:-,1-iji _;:, ·~, i,·.Ytllli I· !I::;; r; i~l , ·i .·. ___ o.lo

-- 1 , ! , 1 • • , ...., 1 • 1 r 1 1 1 1 ; •

! i i-;

~ :_ __ :~.>~'_·== -Tt,·:-.~r,:r .. · ~~r~~)?: 1 : -":- · +~~~;frJ~?1~~~~- :L~ -~r4~. :=rt -~n -~~~~ :~+ t. ~---;·- 0.05

~~-:.L•-t.- I+' t I/ tt--~ i :_"-t·:i·t-;·;,,,. ·! .·L__·_i: _L-t-.: L :1 . : i tl ~ 0

b>i4'· -++ -+ -t~~=- ·l~l ·--- ·~-- J-i·-~+-l--l-+-- -+-- _.__ :~ -'+ -+ i • + , ·i··•·H--+· 0 3 4 6 8 9 tO 12 13 14 15 16 17 18 19 20

DAYS IN TEST

0 I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 0~~~1l~FFfF~~~~~II~~~CLrJ~~~~±IIl~~~rT~ll~FrrT1° -~ -;.... ': -t-• ~=j:: :.t PENETRATIO-N OF 32°F. TEMPERATURE vs TIMEt=~ . :t't ~tt -~-

2 ~ F'~,_l-h; .. ~ ............. -+ .. . - - ~ r ~ ~t"{--r-+-r-+.t 1.....,c-+.P~l,...- -------+r+-- 'j -Tt~ · -(:-- -·-- -jH +----- + 1 ll~~--· ·

4 t~*'~·~~-:t-~:~-t~---~~~~8f~~,~~·~·~·-~-~-~-~·~~-~~=~-~--f·~-~-:ti~-~-F-f·~:~~t:~{~:~:·F-~t··~~-i-~--~~:f·l-~~·f--+~Jj~---ttJ·~~~-~*~~·-~-~~~J:~~;t~-~-+1:~1~+~.~~~-~~"-~~· ~t+- ::-S~HT 308: -, - .:-., ..;..: - -~-----rr I r· :·.:- =rF

1

.. - - ·::::-:-:-::'-:-·· -+' i. ~· -t r 4

6 j t- ; F-iT ij - :·"'-""7 ::-'~- ;;;.;,'<'::.r-Sf§!_-.JC!S !· .. i ! -~ , \. · ~:_:- ·· • • : \ ; 1.

_:t-:-~::-=f--r- ~Y :t:=l-=1 : 1~_.::f:.:t.:..c=::.:._.:__~~ :_r+~-.;J · _ !.+. J1'·~:: _ -J.) _ ~- . .::b4~ 6

:1 ... ;-:r -+·-·- ·· ---+-;----- __._ ·.;..l. ::""'~+ t . -j·! t·· · ·· 'T. 8 r-•-f-.,-L ~-+---- ··r· .. •·. I!"-. • ~~ f - -- -· •-- .. -·- ...... ,_. 'f .. 8

.Lt -t t J ;_ -L~ ·-"--- + J.L .! ...._ .. ~. ':":Ht··· ---,.;,..,.....Llf'· . _:_... :----. -1·-f--· !- 1

• ' ' - r f I 1 ' 4-; ·· ~iT' - - · ·

tO --i-,- ~l-+·_;: ·-:.1_ r' -~· . ~t~ I ! ; l . l -~. ---~i!- , .. 1 f ~~~ t; j tO ; l

1• !·; r· • it!, , l : i · : .. · t ~\ • , ;

12 ; i · i' ·; i. .L 1 · '··• i I· ; I i 1 1 · ! 1'-1~!

12 0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480

HOURS IN TEST

24 48 72 93 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480

~: -~-f~l::-t-- .:±::fCUMULATIVE DEGREE- HOURS BELOW 32°F. VS TIME f·' ·'- :.::-r= ~tt tt 7000

o ..J.__ - •-r-+-- -i • - ·- · ·· T · ... _!-.. ---·-- +-J ... :. + ... c ~lo f-' -+i-t]:f-H-~~~::-f~ :~·t-·: .. ~ ·V . _J_--- f- ~·ft :<. -·;·.:-- J l ~. i 6ooo

t:i 25 j !r ' _' ~~-t.ht ~ 1-+-f- !'-'"7" _ -j - __ ~-~---;_:: : ; : ~ -~ I- :~:J J 5000

-~ ·--:-- AVERAGE CAlJI,;Eli~M;ER~TU~E-'.!'- --~~ ·-.- - I H--- ---~ ---I -·+ ·:[_ L.'-. ~ 20 n·~~tr:-;_:~ :~~:IT :~I-~~ -_ .1: :::1: I . . . v. --r- H-- ,_ r 4000 ~ 15 + •. ,- .. t T H --· - -I. I -- -- ~. +~ .: ~, .. -__ : i~ ~-c- t~ : _: w +: ;-_:-j---- -r t- c- _,__ t.i L.:t~- - -d--~ ·_\ . -j_- _ L+- 1--'--1---t-~ -fr· SAMPLES FROZEN 3000

~ ;t__,_H-r-- l-1..: 1·-- -~ ("-+-:::to~R.tfJiws~./, ~ =~--~-: _:~:.-~~ ~~:-:- IN TRAY VB-9

- ~ 10 • 1:::t: -' • + ·! -'-- - - ~c--- · - ~ ,...1-..- _..) .. .,. SEBT-305 lhru 308 incl. 2000.

m • I -•-1- - !- r- '-·- - LJ.::~i-1--- . -~- · ·-;--_;__ l !- 1-- : - i- --+: ~"" _ .. F-f _ 1- __ ~f~~,-~ f=::=:r::: SYS- 3 76 lhru 380 incl.

SFS 374 thru 378 incl. 1000 --+- f---:-= ~ · t 1-r-f- - --r ---~--~ --r-t SMT 306thru 310 incl .

·. - :;.- .- C.:. • - ··1..: r=.: ::.1= SNHT -306thru 310 incl. ·o

0 7000

6000

5000

4000

3000

2000

1000

0

. ~-+ f+ -

---++++

.Fisure 9. 'fypical temperature and heave data tor each tray_ of specimens.

"' "' : u ! I : 1-Q..

"' 0

"' cr :l o. : I .... w cr C)

""' 0

12 LABORATORY DET-ERMINATION OF DYNAMIC MODULI OF FROZEN SOILS.AND OF ICE

TABLE III

TABULATION OF SPECIM~N DATA- FOR DYNA~IC MODULUS TESTS

MATERIAL' SPECIMEN NUMBER

Peabod) ·Gravelly Sand SP-300 (-3/4 inch size only) SP-301

McNamara Concrete SM-154 Sand SM-200

Blend, McNamara Con- SMT-306 crete Sand and East SMT-307 Boston Till SMT- 308

SMT-309 SMT-310

Blend, Manchester Fine SNHT-306 Sand and.East Boston SNHT -307 Till SNHT-308

SNHT-309 SNHT-310

East Boston Till

New Hampshire Silt

Fairbanks Silt

Yukon Silt

Booton Blue Clay (Undisturbed)

Fargo Clay (Undisturbed)

Alaskan Peat (Undisturbed)

SEBT-304 * SEBT-305 * SEBT-306 * SEBT-307 * SEBT-308 ** SNHS-150 SNHS-152 SNHS-153

SFS-374 SFS-375 SFS-376 SFS-377 SFS-378

SYS-376 SYS-377 SYS-378 SYS-379 SYS-380

SBC -307 SBC-307A SBC-308 SBC_:309 SBC-309A SBC-310

SFFC-366 SFFC-366A SFFC-367 SFFC:368 SFFC-369

SAP- i48 SAP-150.

Ice, Artificially Frozen SI-670 Tap Water SJ-671

SJ-67Z SJ-673 Sl-674 SJ-675 SJ-664 sr-6'65 SJ-667 SJ-668

Ice, Natural - Portage SI-(P) Lake

TRAY NUMBER

HB-11 HB-11

HB-3 VB-2

VB-9 VB-9 VB-9 VB-9 VB-9

· VB-9 VB-9

VB-9. VB-9 VB-9

VB-9 VB-9 VB-9 VB-9 VB-9

VB-2.

HB-3 HB-3

VB-9 VB-9 VB-9 VB-9 VB-9

VB-9 VB-9 VB-9 VB-9 VB-9

HB-11 HB-11 HB-11 HB-11 HB-11 HB-11

HB-11 HB-11 HB-11 HB-11 HB-11

VB-2 HB-3

HB-10 HB-10 HB-10 HB-10 HB-10 HB-10 VB-4 VB-4 VB-4-VB-4

POSITION APPROX. JN,TRAY RATE OF DURING

FREEZING FREEZING inch/day

0, 50 0~ 50

0. 50 0. 50

0. 75 0, 75 0. 75 0. 75 0, 75

0, 75 0 . .75 0, 75 0, 75 0, 75

0, 75 0, 75 0. 75 0. 75 0, 75

0, 50 0 .. 50

.0- 50

0, 75 0, 75 o. 1s 0, 75 0, 75

0, 75 0, 75.

·.: 0, 75'

0,75 0, 75'

0. 50 0. 50 0, 50 0, 50 0, 50 0, 50

0, 50 o: 50 0, 50 0, 50 0, 50

0:50 0, 50

0, 75 0. 75 0, 75 o. 75 o. 75 O; 75 o. 50 0. 50 o. 50 o. 50

(I)

u L

u

u L

M

u L M u L

M

u L

L

L

u L

u L

u L

Notes: (1) U, M, and L indicate upper, middle, and lower sections, respectively, in freezing tray compartment.·

(2) After trimming. (3) Computed-from measured dimensions and dry weight of

trimmed specimen. (4) Rati:J ::Jf v::>lume :Jf v:Jids fillt•d with ice to total void volume

expressed as a percentage. All water assumed frozen.

(5) All water assumed in frozen state,

All specimens supplied with water during freeziry.g.

WET UNIT DRY UNIT WATER WEIGHT WEIGHT CONTENT DEGREE

OF · SPECIMEN WET AFTER AFTER AFTER OF ICE !LENGTH. lA VERAGE TOTAL

PECIMEN 'AREA WEIGHT FREEZING .FREEZING FREEZING SATURATION in, sq. in. lb. (2) (2) (2)

12.03 -II. 86

I 2; 00 II. 84

II. 00 II. 00 II. 00 II. 00 10.95

. 10.93 II. 03 10.95 10. 93 II. 05

II. 06 II. 05 10.99 10.99 II. 08

II. 52 12,00 12.00

11.00' 11.00 ·II. 00 II. 00 11.00

11.01 II. 03

'.r 1.01 11.09 10.93

2, 52 2. 43

2. 22 2. 26

2. 46 2. 23 2. 28

'2. 28

2. 58

2. 66 2. 45 2. 29 2. 34 2. 71

2. 67 2. 31 2. 32 2. 31

2. 59

2. 21' ·2. 24

2. 27

2. 44 2. 29 2. 32 2. 36 2. 58

2. _44

2,'23 . 2. 2s-

2. 28 2. 62

-2. 267 2. 188

1. 978 2. 067

2. 130 2. 008 2. 077 2. 068 2. 284

. 2. 227

2. 004 I. 962 I. 973 2. 273

2. 337 2. 145 2, I 23 I. 936 2. 388

I. 610 I. 700 I. 760

1. 850 I. 800

. I. 852

I. 856 z:o 17

1. 96i. 1.'847 I. 869 I. 925 2, 081

pcf pcf (2) ( 3)

129 131

128 133

136 141 143 142 140

133 128 135 133 131

137 145 144 132 144

109 109 112

119 123 125 124 123

.126

130, 130 132

_}26

113 116

113 117

118 I 24 127 127 125

r 19 115 118 116 117

125 133 131 127 129

77 . 85

85

94 100 104 102 99

102 t06

. !109 110 105

"!o "lo

14. 5 12,7

13.6 13. 9

15. I 14.2 12. 5 12. 2 12. 1

12. 31 13. I 13:9 13, 2.

14.'1 tt II. 2 7. 0 9. 4 5. 7

12. 2

41, 5 28, 1 31. 4

26, 5 23.0 zo: 5 21. 5 23.7

22,9 22. 3 20, I 19.8 20.'2

I

(4)

85 81

80 91

100. 100 100 100 97

85

94 84 93

89 71 90 48

100

100 84 94

99 100 9s 98

!f_IO

100. 100 100 100 96

10. 77 10.70 10.73 10,63 10.61 10.63

2. 28. 2. 28 2. 26 2. 28 2. 28 2. 26

I. 416 . 100 110

65 80 4R 59 52 76

54, I

37. 2 85.0 60,8 '73. 8 41.6

98 95 98 ~4

95 97

10. 95 '11. 08 II. 03 10.93

.'0, 99

I 1'. 10 11,90

10.47 10.45 10.47 10.42 10. 51

'o.I0,'47

10.49 10. 51 10, 50 10. 50

9. 95

2. 26 2. 15 2. 01 2. 19 2. 18

2.,26.· 2. 12

2. 25 2. 25 2. 22 2. 26 2. 26

··2. n z. 38 2. 34 2. 28 2. 26

2. 24

-I. 546• I. 243 I. 336 1. 265.

I. 492

I. 589 1, 494 1. 402 I. 492 I. 50 I

0 .. 904 I. 030

0. 761 o. 745 0, 752 0, 750 0, 756

o. 76J . 0, 783

o. 787 0, 77Z 0. 765

.0. 7Z5

88 9.5

90 107

II. I

108 . 109

108 108

62 71

56 55 56 55

55 :.55 ..

54 55 56 56

56

83 81 81 80 80

13 19

33. 5 33.4 35, 6 34. 5 35. 3

3'11 280

* Only material passing No.4 mesh sieve,

94 89 95

. 90 .

92

98 100

** Only material pasaing 3/4-inch mesh sieve.

t Computed from measured dimensions a~d dry weight of entire specimen before trimming.

tt Computed from wet weight and dry weight of entire specimen before trimming.

VOID RATIO

0, 503 0, 464

0. 503 0, 452

0, 439 0. 369 0, 337 0, 337 o. 369

0, 427 0,477 0, 439 0, 464 0, 451

0, JiB 0, 295 0, 315 0, 357 0. 336

1. 190 0, 984 0, 984

0. 780 0, 673 0 .. 609 0, 640 0, 690

0, 671 0, 608 0, 563 0, 549 o; 623

I, 698 1, 191 2. 654 1, 973 2, 373 I. 308

1 .. 076'

I. 127 I. 127 I. 154' I. 154

6, 302 3. 996

RATIO:

VOL. ICE VOL, SOIL

(5)

0. 430 0, 377

0, 403 0, 412

0, 448 0, 421 0. 371 0. 362

. 0, 359

0. 365 0. 389 0, 412 0, 392 0, 418

0. 337 0, 2.11

0, 2.83 0, 172 0, 367

1.·222 0, 827 0, 925

0, 775 0, 672 0. 599 0, 628 0, 693

0. 682. 0. 664 0, 598 0, 589

,o. 601

I. 658 I. 140 2. 604 ):863 2. 261 I. 275

1. 008 I. 005 I. 072 I, 038 I. 063

6. 150 4, 641

LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE 13

IV. TEST PROCEDURES

The specimens, with bar magnets frozen-in horizontally across each end, were supported by their sides in a horizontal position in the apparatus between pairs of posts with blunt cone-shaped prongs. For longitudinal and torsional vibrations, the beam was supported midway between the ends. For flexural vibrations the beam was supported at the "quarter nodes," a di-stance .from each end equal to 0.224 times the length of the specimen.

The two driving electromagnets were positioned so that each projecting end of the bar magnet embedded in the test beam lay between the poles of an electromagnet.

Since the poles of the electromagnets change polarity with the frequency of the alternating current in the coils, they alternately attract and repel the permanent bar magnet, causing the speci­mens to vibrate. The position of the two driving electromagnets, the direction of the current in their respective coils, a~d the position of the specimen support(s) determine the type of vibration that is induced.

For flexural and torsional vibrations, the electromagnets were set so that their poles were in the same vertical plane as the bar magnets on the specimen (Fig. 3). To produce flexural vibrations, the alternating current was made to pass through the coils so as to produce polarities of opposite sign in the corresponding poles of the two driving electromagnets. The resulting simultaneous attraction and repulsion of the bar magnet in an up and down direction caused the beam to vibrate in flexure. To incite torsional vibrations, the beam was supported firmly at its midpoint and current passed through the driving magnets to induce the same polarity simultaneously in corresponding poles of both driving magnets. This caused the specimen to vibrate in torsion about its longitudinal axis. Longitudinal vibrations were produced with the poles of the electromagnets placed in a hori­zontal plane, with corresponding poles having opposite polarity, the specimen being supported at the midpoint. The effect was alternately to push ~nd pull on the bar magnet in a horizontal plane, parallel to the longitudiQal axis of the specimen.

The permanent bat ~agnet at the opposite end of the beam was caused to vibrate at th~ same frequency and the fluctuations of the magnetic field induced an electromotive force of varying in­tensity in the receiving or detecting coils. In theory, the peak voltage is induced when the speci­men is vibrating at its natural frequency and the amplitude of the vibrations is then at a maximum. The fundamental resonant Jrequency was detected with a vacuum tube voltmeter and/or a cathode­ray oscilloscope connected to the detecting coils, and read from the dial markings of the calibrated oscillator. ·Peak readings on the voltmeter and oscilloscope were also obtained from overtones or harmonics of the fundament·al frequency. In the torsional and longitudinal modes, the overtones are nearly integral multiples of the respective fundamental frequencies •. In the flexural mode, the fre­quencies of the first two overtones occur at 2. 7 and 5 times the fundamental frequency.

The following equations (Pickett, 1945) were used in the computations:

Flexural vibrations.

Et = CW(lt?.

(A value of %was as_sumed for Poisson's ratio 11 to find C from curves given in Pickett, 1945. The _value of 11. is not critical and the assumption is reasonable.)

Longitudinal vibrations.

14 LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE

and

and

Torsional vibrations.

w(Vt) 2 R G == --­- g

[R is 1.183 for a square prism (Pickett, 1945)].

Correction to observed frequencie~ for mass of magnets (Rayleigh, 1929).

Flexural vibrations: f 1 = t[ (l + 2M)

w

I M Longitudinal vibrations: f L == f L (1 + -)

w

Torsional vibrations: ft = f~ (l + K2

M) w

Poisson's ratio. Poisson's ratio is computed from E and G using the relation:

E 11 = --1·

2G

It should be remembered that these formulas are strictly applicable only to an isotropic elastic solid complying with Hooke's law.

LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE 15

V. TEST RESULTS AND DISCUSSION

The individual test results for all materials and specimens are presented in Appendix A. Sum­maries are presented in Table IV and Figure 10. The individual values of moduli of elasticity and rigidity obtained from the measured resonant frequencies are presented in graphs a and c of Fig­ures A1-+A14, for each test temperature. The test temperatures ranged from approximately +32F to below -10F. The elastic wave velocities at resonant frequencies for the longitudinal and torsional vibrations are plotted versus temperature in graphs b and d.

Theoretically, for an elastic isotropic homogeneous solid the dynamic modulu.s of elasticity de­rived from flexural and longitudinal vibrations should be the same. In most of the present tests the numerical values of E obtained from flexural vibrations were slightiy lower than those obtained from longitudinal vibrations. These differences are not surprising since a frozen soil containing irregu­larly stratified ice lenses cannot truly be considered as isotropic homogeneous material. Only an isotropic material, in which every plane is a plane of symmetry, can be characterized by only two elastic constants such as Young's modulus and Poisson's ratio (Love, 1927).

In graph e of Figures A1-A14 are presented curves of dynamic Poisson's ratio [calculated using the relationship f1 =(E/2G)- 1) vs temperature. Average values of dynamic E and G obtained from curves in graphs a and c of Figures A1-A14 were used in the above formula. Of the two sets of data for Poisson's ratio the values computed using longitudinal vibrations are believed more reliable and reference is made to this set when comparing these data.

The plotteq data and summary curves in Figure 10 show that dynamic moduli and elastic wave , velocities in frozen· soils are temperature dependent - more so at temperatures above +20F and less so at colder temperatures. The propagation velocities in the silts and clay appear to be particularly sensitive to temperature changes in the range from +32F to +20F. Below about +20F the velocities increase linearly and are less dependent on temperature. This behavior is due to the varying per­centages of non-frozen water believed to be present in the soil at temperatures below freezing (Tsytovich, 1957).

A comparison of laboratory-determined dilatational wave velocities with those obtained in permafrost .by seismic refract ion methods shows good agreement for comparable soil types as indi­cated in Table V. ·

The agreement in Table V varies in some instances, principally because no borings were made in the field work and precise knowledge of the overburden was lacking except from general geologic knowledge of the area.

A comparison of the dynamic moduli of ice obtained during this study with the work of other in­vestigators also reveals very close agreement. The moduli of elasticity computed from results of longitudinal vibrations in these tests are shown plotted on Figure 11 along with other data previously summarized in USA SIPRE Report 8 (ACFEL, 1952). ·

On Figure 12 are shown plotted the dilatational wave velocities of both laboratory and field seismic data on ice for comparison with the present results. It will be seen here that the laboratory results are compatible with the results of other investigators. The field velocities in ice sheets and ground ice are higher. This is due to the fact that velocities of longitudinal waves in thin bars or rods, in thin plates ;.and in infinitely extended solids are all different. Available formulas (Ewing, et al., 1934) show that longitp.dinal velocities in a thin ice plate may be 5 to 10% higher than in thin ice rods, and in extended ice masses the velocities may be 20-25% higher depending upon the value of Poisson's ratio f1 used in the formulas. This is borne out by the experimental data pre­sented in Figure 12~

::t. 0

~

"'

16 LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS .AND OF ICE

>:, ->- > ,_

>-u 10

g ,_

~ "' ~ B

! ~

-' C(

-' z C(

~ 6 z 3

0

§ ~

I

I I 30' zo 0 -10 30 zo 10 0 -10 -20

TEMPERATURE· IN DEGREES· FAHRENHEIT TEMPERATURE IN DEGREES FAHRENHEIT

LONGITUDINAL WAVE VELOCITY VS TEMPERATURE 0

TORSIONAL WAVE VELOCITY VS TEMPERATURE b

MODULUS OF ELASTICITY VS T'EMPERATURE c

BASED ON FlEXURAL VIBRATIONS.

- ~-J - . ~ - ~---1------j

~

J >-,_ u.

~-

~ <f) :::> -' :::> 0 0 :I

MODULUS OF ELASTICITY vs TEMPERATURE

d

sy[o ON LOI NGITUDINiL VIBRATIINS

0-~~--+'----~~-.£--, ·-+-1-:-. ,-_-1----l-----

~--~~l'Q I

·~

~

>-1-. 0 a ii ... 0 <f) :::> -' :::> 0 0 :I

--1- -

zo 10 o -10 -zo TEMPERATURE IN DEGREES FAHRENHEIT.

MODULUS OF RIGIDITY VS TEMPERATURE·

e

SP Peabody Grav~illy Sond

SM Me Namaro Concrete Sand

SMT Blend, Me Namara Concrete Sand and EastBoston.TIII ·

SNHT Blend, Manchester Fine Sand and East Boston Till

. ~ 0.3 SEBT East Boston Till

SNHS New Hampshire Siit

0 I

POISSON'S RATIO. VS TEMPERATURE· f

20 10 -10 -20

TEMPERATURE IN DEGREES FAHRENHEIT.

POISSON'S RATIO VS TEMPERATURE g

SFS

~YS

sec SFFC

SAP

Sl

Sl !P)

Fairbanks Silt

Yukon Silt

Boston Blue Cloy

Forgo· Cloy

Alaskan Pe-at

Laboratory FrQun .Ice H • Horizontal , V =·Vertical

Portage Loke Natural Ice

Figure 10, Summary of data presented on Figures Al-Al4. Each curve-represents test results of two to six specimens. Curves of Poisson's ratio vs temperature are based on values taken from

pertinent curves in graphs c, d and e.

TABLE IV

SUMMARY OF DYNAMIC MODULUS TESTS( I)

Numbet of Range of ModUli of Range of Moduli of

6 Range of Velocities, v,

Specimens Elasticity, E, psi x 106 Rigidity, G, psi x 10 ft/ sec x 103 Material Symbol Tested (Flexur~l and Longitudinal) (Longitudinal)

t30°F -10°F +30°F. -10°F t3o° F ~10°F

Peabody Gravelly Sand SP 4. 2 - 5. 2 5. 0 • 6. 2 f. a - 2. 0 2. 3- 2. 4 13.2 - 13. 5 14.7 14.9

McNamara Concrete Sand SM 3. 6 - 4. 3 4. a - 5. 1 1.4-1.7 1. 9 - 2. 0 ll. 4 - ll. 9 13. 2.

Blend; McNamara Concrete Sand SMT 1. a - 2. 6 4. 6 - 5. 4 o. a - o. 9 I. 9 - 2. 1 ~- 9 - 9; 0 12.6 - 13. I a,nd East Boa·ton Till

Blend, Martchester Fine Sand SNHT 2. 7•- 3. 5* 4, 0 - 4. a l. 4•- 1. 6• 1.7- t.a 10, a•- 11. o• 12., 7 - 12. a and East Boston Till

East Boston Till SEB'I' 1. 2*- 2. 2* 3. z - 4. 4 o. 6*- o. a• 1.4- I. a 7.4•-a.o• 11.5-11.9

New Hampshire Silt SNHS z. 4 - z. a . z. 7 - 3, 6 o. 6 - l, 0 l. z - I. 3 10.0 - 10.9 10. 7 - 11. 8

Fairbanks Silt SFS l. 3 - z. 0 3. 0 - 3. 6 0. 5 - 0.1:1 1.3- 1.5 '7. 7 - a. 9 11. 3 - I I. 7

Yukon Silt · SYS I. 3 - Z. 0 2. 9 - 3. 5 0,6-0,7 1.2- 1.3 1. o - a. 4 10. 9 - 11. z

Boston Blue Clay SBC o. 5 - 1. 0 l. a - z. 5 .0. 2- o. 4 o. 7 - 0. 9 5,4-7.4 9.'9 10.4

Fargo Clay SFFC 0, I - 0, 3 o .. a - l.O 0, 1 o. 3 - o. 4 3,0-3.4 6. 2. - 6. 6

Alaskan Peat SAP o. "Z*- 0. 9* I. 0 - 1.4 o. 3 o. 5 6.7*-7,4* a. 6 - 9. 2

Ice, Artificially Frozen SI 1.0- 1.2 1.?- 1.3 0. 4 - o. 5 o. 5 9. 7 - 10.0 10. 1 - 10.4 (Horizontal Beams)

Ice, Artificially Frozen (Vertical Beams)

SI 1.1-l.Z 1.5- 1.7 o. 4 o. 4 - 0. 5 9. 7 - 10. I 10.4 - 10. 6

lee, Natural • Portage Lake, SI-(P) I. 201< I, 3 o. 5• o. 5 - 10. 0* " 10. 3 Maine

(1) The value's shown on this table, with the exception o£ Poisson:s ratio, were obtained from the data presented on Figures Al-A14.

(2) Values of Poisson's ratio taken from curves presented in graphs e, Figures Al-Al4,

* Extrapolated from graphs.

Poisson's Ratio (2)

Range of Velocities, Vt, ft/ sec x 103 (Torsional) Flexural Longitudillal

+30° F -Hi°F +30°F -10°F +30~ -10°F

7.4-7,a a. 3 - a. 5 0.13 o. 16 o. 2.5. o. 31

6.5-7.3 7.5-7.7 0. 2.9 o. 2.7 0.2.0: 0 .. 26

4. 7 - 4. 9 7.3-7.5 0. 1 ~ 0 .. 24 0 •. 40" o. 31

6. o•- 6. 3* 7.4-7.5 0.10 0. 16 0.3~ 0. 2.5 . 4. 5*- 4, 9* 6. 4 - 6. 9 o. 07•:• 0. I 3 O.l6•:• o. 30

4. 8 - 5, a ' 6. 6 - 6. 9 o. 43 o. 3l•:• 0. 35 o. 2.1*

4. 5 - 4. 7 6. 5 - 6. 8 0. 2.1 0. 14 0. 33 o.u

4. 2 - 4, 5 6. 1 - 6. 2 O.l2 O.l4 o. 41 o. 36

2. 9 - 4, 0 5. 5 - 5, 9 o. 14 0. 2.4 0. 4a o. 41

I. 7- 2. 1 3, 4 - 3. 6 o. 17 o. l4 0. 37 0. 39

4, 3*- 4, 5* 5. z o. 32•:• 0. l8 o. 1 o·~ -0. u

5. 4 - 5. 5 5. 7 - 5. a O.l9 o. za o. 39 O.H

5. 3 - 5, 5 5, 7 - 5, 9 o. 36 0. 3l 0. 4l o. 38

5,7* 5. 7 o.za•:• o. 34 o. 3l•:• 0. 36

18 LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE

INVESTIGATORS'

0 . Sovel.'ev ( 1959)

Lotze (1957)

e- Boyle and Sproule ( 1931)

c Trqwbridge and McRae (1885)

• Reich and Stierstodt (1931)

Koch (IB85l

Ewing, Crary and Thorne (1934)

4> r-.tokoyo (1959)

.... e. Frost Effects Laboratory ( 1952 l

MODE OF VIBRATION

Longitudinal

Longitudinal

Longitudinal

Longitudinal.

.Longitudinal

Flexural

Longitudinal

Flexural

Flexural

TYPE OF ICE

Glacier

River

Lake

Artificial

Lake

Artificial

Glacier

Artificial

ANGLE BETWEEN LENGTH OF SPECIMEN AND OPTIC

AXIS OF CRYSTALS

Avg.

0°,_45° ,.90°

90°

goo

2xl06

~-,--.-~--~----,-----,-----,------,-----,-----.----~------r-----r-----~----~----~ 3 1

I 1 1

.I _I I 1

·

1

:

1 1 1 1 ll40xl0 N~

f- ICE] @ @ @ -e----.,..-----e-~-·-1 I 1- -~4>~c-•~-! 62S ~---~!~.3:...=. ---r!>\._VB c!l

[HB . . LPORTAGE LAKE,ME. - 70 ::: I- - w I I _l I :, .

• 30 20 I r'o I 0 I -10 I -io I -310 0 T E M P E ·R AT U R E, F

0

Figure 11 . . Comparison of 9ynamic modulus E of ice .obtained by various investigators.

For Frost Effects Laboratory tests (1951), circled points indicate flexural vibration parallel to direction of freezing. All other points are for flexural tests in which the vibration was transverse to the direction of freezing. ( 4) indicates average of four tests by Boyle and Sproule from longitudinal vibrations of rods of river·ice. Angles between length of specimens and optic axes of crystals were: 90° in two tests, 45o in

VL (m/sec)

0

I

ICE PLATE

21cm .t\. 0 THIN ICE SHEET

32 16

T

one test, and oo in one test.

E M

0

LEGEND

ct WOLCKEN, 1963 ·X ROBIN,GdeQ,-·1953 ~ BROCKAMP et al, 1933

0 ROETHLISBERGER, 1961

-16

P E R A T U R E

+

ll JOE STING, 1954 8 BULL, 1955 A HELLBARDT, 1955 0 EWING et al, 1934a

+ BOYLE 8 SPROUL~ , 1931

,I

13.0 xl0 3

12.0

10.0

9.0

VL (ft/sec)

Figure 12. Summary of longitudinal or P-wave velocities in ice measured by various investigators.

LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE 19

Table V. Comparison of propagation velocities of dilatational sonic waves in fr?zen, ground ( ft/sec) .

Frozen material .

type

Sands and gravel

Muck (Silt with organic)

Glacial till

Barnes, 1928

10.0 - 13.0 X 103 ,

at 25-30°F 1

· · Investigator

Joesting, 1954 Roethlisberger, 1961

13.0 - 15.25 X 103 .

at 25-30°F

4.25 -10.0 X 103

at 25-30°F

14.7 X-~· 103

at 14°F

15.5-·x 103

~t. 13. eF

Present study

13.6 :_ 14.1 X 103

at 25°F

6~6 - 10.6 X 103

at 30°F . 10.2 - 12~4 x 103

at -10°F · ·: ''

7.2- 8.0 ,x 103 ·

at 30°F 10.6 "'"':' 11.9 X 103

at -10°F

In sharp contrast tothe strong temperature dependence of the elastic properties of frozen soils, the elastic properties of ice, whether laboratory frozen or natural, appear·little affected by temperature. The elastic wave 'velocities and elastic moduli for ice, as shown in Figures A12-A14, are only slightly higher at -10F than they are at _+30F.

It may also be noted that the· dynamic Young's moduli, E, as derived from flexural and longi­tudinal vibrations differ only slightly, indicating that ice more closely satisfies the assumption of . isotropism and homogeneity than frozen soils. This is further indicated by the gre\ater consistency of the test data· obtained.·

For the soils tested the individual values of dynamic Poisson's ratio, using Young's modulus E determined from longitudinal vibrations, show a wide scattering, ranging roughly from 0.10 to over 0.50 at the higher temperatures, and from approximately 0.15 to 0.45 at -10F. The greater bulk of values fall between 0.25 ·and 0.40. The silts and clays show greater divergence of values than the soils composed of coarser-grained particles, such as the gravelly sand and the glacial till. The ..... values of Poisson's ratio for ice, although covering a relatively wide range,,show the least- scatter­ing of all the materials tested. ·

Some of the wide scatter may be due to the fact that· the values of E and G used in computing fl were not measured at exactly the same temperature because of unavoidable operating conditions. Test temperatures may have differed in some cases by as much as 1F. ·

The wide variation of fl for different specimens or a given so1i at a given temperature and mode of vibrationalso reflects the sen~itive dependence of Poi~son's ratio upon the values of the modulus of elasticity and rigidity in-the formula fl =(E/2G) ~::1.: A very small percentage change in E and/or G is ampiified greatly in the values of p.. For example, assuming G!E = 0.40 (a good approximation in most cases): if the error in E and G is only 5% (this is more than a reasonable estimate based upon the scatter of·points on the moduli plots), then the maximum error in fl is of the order of 5q%. To restrict the maximum error in fl to 20%, E and G must each be determined to an accuracy of the ·order of 98%, which is very difficult to achieve. In these studies, in view of the many areas of measurement and since E and G are also proportional to the frequency and length squared, it is most probable that the maximum error in any one determination of E and G is unlikely to be less than 5%. For this reason it would appear that any value of Poisson's ratio computed from a single test cannot be considered reliable. Furthermore,· ttie formulae and equations used here are applicable only to homogeneous, isotropic and elastic materials. ·

· 20 LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE

Taken as a whole, the values of dynamic Poisson's ratio indicated by the summary curves in Figure 10f and g, which are gased on the average values of the modulUs of elas6city. derived from flexural and longitudinal Vibrations (the average curves in Figure 10 c and d) and the values of the m9dulus of rigidity (the average curves in Figure 10 e) appear to be of the right magnitude. How­ever, ·as stated previously, the flexural values are believ~d to be somewhat less reliable than the longit_udinal values. This evaluation is based-largely on the fact that curves of Poisson's ratio vs · temperature computed using E from. flexural vibrations (Fig. 10 f) show a greater variability and in­consistency than those in Figure 10 g which were computed using E from longitudinal vibrations. Therefore in subsequent paragraphs, references to and comparison·of values of Poisson's ratio will be made only for data plotted in Figure 10 g.

From the curves shown in Figure 10f .and g it;'is impossible to express the relationship of Poisson's ratio.to temperature in general terms applicable to frozen soils as a whole. Some of the curves are concave in shape, others are convex. For some soils, Poisson's ratio increases with temperature; for others, it decreases.

The greatest variations between p.-values· for the different soils occur at the higher tempera­tures, i.e., above +20F. ·Whereas the other graphs in Figure 10 reveal an ordered relationship be­tween soil types according to soil texture, and a consistent dependence on temperature, no such relationship is evident for the computed values ·of p. for these same soils. For example: values of Poisson's ratio (longitudinal) for two clays, Boston blue clay (SBC) and Fargo clay (SFFC), are sharply inconsistent with each other. The p.-values (longitudinal) for two· of the silts, Fairbanks silt (SFS) and Yukon silt (SYS), show opposite trends at temperatures below +15F but are reason­ably close above that temperature.

The value of Poisson's ratio for ice in the range of -5C _to- 15C was determined by Ewing, Crary and Thorne (1934) to be 0.365 ± ~007 by use of dynamic .methods (longitudinal vibrations); the average curves of Poisson's ratio {longitudinal vibrations) for ice presented in Figures A12 e -A14 e show comparable values. The individual values, however, ranged from 0.28 to 0.4_6 in a 40F , range; with the greatest .~ifferen?es occurring between specimens frozen vertically. Natural lake ice ranged from 0.32 to 0.36 p.. It is evident here that the same limitation to obtaining a reliable and reproducible value of Poisson's ratio hold~ for ice· as for froz~n soils. · .

The scope of these tests did not include a· study of the effect or such factors as crystal . size, structure, or specific crystal axis orientation on the elastic properties of ice. However, ob­servations· of the general effects of crystal orientation were possible by tests performed on vertically frozen and horizontally fro.zen ice beams. Crystallography studies of laboratory-frozen ice speci­mens (Goodby and Kaplar, in prep) reveal that the c-axis is generally oriented parallel to the directio~. of freezing except neai the surface where small crystal~ have been observed to deviate from the vertical.

The average results from the two different types of beams as shown plotted in Figure 12 show that the iongitudinal wave velocities in the vertically frozen beams were slightly higher, the difference. in velocity increasing with decreasing temperature~ At ~20C the difference was about 60 m/sec. Differences of this magnitu~e were also observed by other investigators' (Savel'ev, 1962; .Thiel and Ostenso, 1961).

The variations in water content and density occurring in the frozen soils were incidental, resulting from ·varying degrees of uncontrolled ice segregation which occurred during freezing, and undoubtedly thes~ influenced the elastic behavior. With the limited data available an attempt was made to correlate unit density and water content with the elastic properties but no consistent re- : ·lationship could be found. A fertile field is present in this area for additional research on frozen . soiis. Studies of dynamic properties of unfrozen soils (lida;:1940; lshimoto et al., 1936; Wilson 'etal., 1961) show that the dynamic elastic properties o~ a sand or clay are af~ected by the unit weight, moisture content, and pressure on the specimen. 'It is logical to assume that the dynamic elastic

LABORATORY DETERMINATION OF DYNAMIC MODULI OV FROZEN SOILS AND OF ICE 21

properties of frozen soils would also be dependent upon the unit weight and moisture (ice) content. However, it is1 not certain whether pressure on saturated frozen soils would have the same influence on unfrozen soil. In unfrozen soil the increase in value of dynamic modulus _is believed due to the impr.ovecl contact of grains under pressure as well as pressure within the grains themselves, but in a saturated frozen soil where the grains are most likely separated by ice the applied pwssure may not have the sar1le effect. This is -an area where more experimental work is needed. In 1960 the author initiated the development of a triaxial apparatus which will enabl_e lateral and vertical pres­sures to be applied to a cylindrical soil.specimen, which can then be tested for dynamic elastic properties, modulus of elasticity (longitudin<;!l vibration), and the dynamic modulus of rigidity (tor­sional vibrations) in both the frozen and unfrozen conditions. These two moduli, E and G, will permit the computation of Poisson's ratio, f.l· reliable values of which are needed. A contract feasibility study (Foster-Miller Associates, 1960) also indicated the suitability of such an apparatus and technique for-measurement of damping coefficients.

A recent =increase of interest in the dynamic properties of soils under confining pressures is reflected in the _publication of new studies by other investigators (Brutsaert, 1964; Richart, 1960; Wilson et al., 1961). Laboratory studies have been conducted at USA CRREC-to determine the elastic properties of soils at various lateral confining pressures using greatly refined techniques and improved apparatus (Stevens, 1964, 1966). These studies were coordinated with field studies, using field vibratory equipment, conducted by the U.S~ Army Waterways Experiment Station (Fry, 1963) and the U.S. Army Ohio River Division Laboratory (1964).

A study of graphs a through e on Figu.re iO indicates that the elastic properties, the dynamic moduli of elasticity and rigidity, and propagation wave velocities are prinCipally dependent on the type of soil. The coarser-grained soils show higher wave velocities and greater modulus values. The clays have the lowest values, with ice somewhat intermediate. Figure 13, on which the arbitrarily chosen 50% particle size (by weight) has been plotted vs the modulus EL for 20F, illus­trates this relationship more clearly.

The limited data available are not considered sufficient to draw any conclusions as 'to the effect, if any, of the manner in which the soil specimens were frozen, vertically or horizontally, although one might expect that the orientation of ice lenses in a beam of frozen soil would affect the overall dynamic properties. Additional experimentation. with close control of such parameters as soil density and water content. might shed more light ori the subject. From practical considera­tions, it would be extremely difficult to arbitrarily control the size and spacing of ice lenses in frost-susceptible soils frozen at normal rates with or· without availability of free water.

Suggested further application of dynamic modulus method to study of frozen soil properties. Sonic (dynamic) methods have been used for rpany years in determining the quality of concrete in slabs and monolithic structures. Kesler and Higuchi (1953) claim to have established .a relation­ship between the dynamic modulus of ~lasticity, the damping capacity of concrete, and the com­pressive strength of concrete which enables prediction of the strength of concrete within an error of 5%. Since frozen soils, concrete, and ice are viscoelastic materials, the viscous properties can be evaluated by recording the logarithmic decrement, which is a measure of the 4amping capacity.

Studies by Chang and Kesler (1956) indicate that there may exist a relationship betwee~ the statiG (creep) and dynamic behavior of concrete. Nakaya (1959) used the dynamic method to study the viscous properties of ice •. It would appear that a promising field for further research and study is present to co~relate· the viscoelastic properties of frozen soils with -dynamic properties.

22 LABORATORY DETERMINATION OF.DYNAA11C MODULI OF FROZEN SOILS AND OF ICE

Ql c

~ 0 10

II)

~ Ql

E

·e

Qj v E -~ 0

I.Jj

N

(/')

w _J u 1-0:: <( a..

CLAY ~(SFFC}

Glacial Till ( E B T h-~-<>--4

SILT (SFS} 1--04 . I SILT

~. ~(SNHS} (SYS} ~ ·

NOTE All· fine ,grained soils es.sentially saturated

Coarse grained soils saturat~d> 80 percent

EL , DYNA~IC MODULUS,~ psi

Figure 13. Relationship of soil type and dynamic modulus, E L' at 20F (-6.7C) ..

LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE- 23

VI. CONCLUSIO~S

The following conclusions and observations may be drawn from these and other studies:

1 •. Vib~atory non-destructive techniques can be successfully applied in the laboratory to the study of the dynamic elastic properties of frozen soils and ·or ice.

2. The technique affords a fertile field for investigation of the viscoelastic properties of fro zen soil.

3. The dynamic moduli (E and G) and elastic wave propagation velocities of frozen soils increased with a decrease in temperature: the greatest rate of increase occurred between+20F and +32F. At temperatures lower than +20F the dynamic properties of fine-grained soils (silts and clays) were markedly more temperature-dependent than those of the coarse-grained soils. This de­pendence is believed chiefly due.to the progressive freezing, .with decreasing temperature, of addi­tional pore water, both in the adsorbed layer and in the ~rnaller,pores, and isa function of grain size. The mineralogical composition of the soil grains and the type and quantity of ions present in the pore water may also be significant contributing factors .. Alaskan peat (water content ,......, 300% by weight) and ice showed only a slight increase in modulus and wave transmission velocities with decreasing temperature.

4. In the range of temperatures used and the· degree of saturation achieved in these investigations:

a. The elastic moduli for the coarser..:grained soils were mor_e than four times those for fine-grai~d soils and ice.

b. The wave velocities for coarser-grained soils were more than .twice those for · the fine-grained soils and ice.

5. Values of Poisson;s ratio for frozen soils as .computed from average values of E (longitudinal vibrations) and G _generally range between f-L = 0.26 and 0.38. Within this range aver­age curves of Poisson's ratio vs temperature show_ed a very·irregular, unpredictable pattern unre­lated to soil type, although the coarser soils gave more consisten.t results.

6. The dynamic elastic properties of ice, including elastic wave velocities, as deter­mined by these_ tests were consistent with findings of ~ther investigators. Values of Poisson's ratio for a given ice specimen showed remarkable consistency throughout the temperature test range although the difference between-some specimens was considerable. The average values of Poisson's ratio for the laboratory-frozen ice and natural lake ice, based on results obtained using longitudinal vibrations, ranged from 0.30 to 0.41; but the maximum range of individual values was 0.28 to 0.46.

7. The present limited data are insufficient to draw any conclusions as to the effect, if any, of the manner in which the soil specimens were frozen, i.e., in vertical or horizontal position. However, values of Poisson's ratio computed for individual ice beams frozen vertically show a much greater deviation from the mean than those from horizontally frozen beams, indicating a possible effect of crystal size and structure.

8. All the materials tested were anisotropic and, therefore, high accuracy cannot be expected from the use of _simplified theory, assuming isotropy.

9. Velocities and elastic constants developed by procedures such, as outlined in this report may be useful in seismic explorations in permafrost and for predicting t.he response of frozen foundation. materials to dynamic loading.

10. The results obtained from these studies pertain to frozen s.oils which are saturated or close to being saturated.

24 LABORATORY DETERMINATION OF-DYNAMIC MODULI OF FROZEN SOILS AND OF ICE·

SELECTED BIBLIOGRAPHY

American Society for Testing and Materials ( 1962) Symposium on soil dynamics. 64th Annual Meeting,Atlantic City, N.J., June 26, 1961. ASTM Special Technical Publication 305.

. ~ . .

------·-----~---------'-< 1963) Symposium ·on dynamic behavior of materials, Albuquerque, N .M., Sept. 27-28, 1962. ASTM Spec(al Tchnical P~blica­tion 336.

Barnes, H. T. (1928) Ice engineering. Montreal: Renouf Publishing Company, p~ 48-50.

Behrendt, J;C. ( 1964) Antarctic Penins.ula .traverse. Geophysical results relating to glaciological and geological studies. The University of Wisconsin, Geophysical and Polar Researc~ Center, Research .Report Series No. 64-1.

Bernhard, R.K. ( 1958) A study of soil wave propagation. Highway Research Board Pro­ceedings, vol.. 37, p. 618-646.

______ ( 1963) Bibliography on soil dynamics. u.s.·· Army Cold Regions Research and Engineering Laboratory (USA CRREL) Special Report 89.

Boyle, R. W. and Sproule, D.O. (1931) Velocity of longitudinal vibration in solid -rods (ultrasonic method) with special reference to the elasticity of ice. Canadian Journal of Research, vol. 5, p~ 601-618. ·

Brockamp, B. and Wolcken, K. ( 1933) The running time curves and ice thickness meas­urements between West Sta~ion and 120 km marginal distance. Wiss. Ergebnisse Deut. Gronland ....:. Expedition Alfred Wegener 1929 und 1930-31, vol. 2. Leipzig: F. A. Brockhaus.

Brutsaert, W. ( 1964) The propagation of elastic waves in unconsolidated unsaturated granular mediums. Journal of Geophysical Research, vol. 69, no. 2.

Bull, C. B. B. ( 1955). Values of gravity on the inland ice in North Greenland. Meddelelser· om Gronland, Bd 137, no. 1. ·

Burmister, D.M. and Stoll, R.D. ( 1963) Static and dynamic response ·of granular soilS. Columbia University, Department of Civil. Engineering and Engineering Mechanics, Technical ,Report 1 for U.S~ Navai Civil Engineering Laboratory, Contract NBy 32198.

Butkovich, T.R. and Landauer, J.K. (1960) Creep of ice at fow stress. U.S. Army Snow, Ice and Permafrost Research Establishment (USA SIPRE) Research Report72.

Chang, T.S. and Kesler, C.E. (1956) Correla.ti.on of sonic properties of concrete with creep a.IJd re~a.xation. ·University of Illinois, Department of Theoretical and Applied Me.chanics, T and AM Report 94. ·

Crary, A.P. (1954) Seismic studies on Fletcher's Ice Island, T-3. Transactions American -Geophysical Union, vol. 35, no. 2, April, p. 293-300.

( 1955) Seismic soundings in polar .ice. Geographical Review, vol. 45, no. 3, July, p. 428-430. · · · ·

_____ ; Cotell, R.D.; and Oliver, J .. ( 1952) Geophysical studies in the Beaufort Sea., 1951. Transactions American Geophysical Union, vol. 33, April, p. 211-216.

Dorsey, N.E. (1940) Properties of ordinary water substance. New York: Reinhold Pub-lishing_ Corp. ·

Ewing, M. and C~ary,A.P. (1934) Propagation of elastic waves in ice, Part II. Physics, vol. 5, p. 181-184.

-----,--------; and Thorne, A.M., Jr . .(1934) Propagation of elastic waves in ice, Part I. Physics, _vol. 5, no. 6, p.165-168.

Foster-Miller Associates, Inc. ( 1961) A feasibility study of t~st method for determining the dynamic properties of soil. Contract Report to u:s~ Army Engineer Division, New England. ·

Fry, Z.B. (1963) Development and evaluation of soil bearing capacity, :foundations .of structures - field vibratory test data. U.S. Army Engineer Waterways Experiment Station, Technical Report No. 3-632.

Good by, J. E. and Kaplar, C. W. (in prep.) Ice crystal structure in frozen. soils and arti­ficially frozen ice. USA CRREL Research Report 156.

LABORATORY DETERMINATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE 25

Hardin, B.O. et al. (1961) Discussion of paper by F .E. Richart, Foundation Vibrations, 1960. Journal of Soil Mechanics and Foundations Division, ASCE, Proc. yaper 2564.

Hellbardt, G. (1955) Seismische Versuche aufeiner Eisplatte (Seismic investigations on an ice plate). Ze itschiift fii1 Geophysik, vol. 21, no. 1, P·. 41-4 7.

Hess, H. (1940-41) On the elastic constants of ice. Zeitschrift ti.ir Gletscherkunde, vol. 27, p. 1-19. USA SIPRE Translation 4, 1950. . ' ·

Iida, K. ( 1940) On the elastic properties of soil, particularly in relation to its water con­tent. Bulletin of the Earthquake Research Institute, Tokyo Imperial University,

. vol. 18, p. 675-690.

Imbert, B. ( 1958) Ice cover and glacial relief. Symposium on Antarctic Research, Welling­ton, New Zealand (unpublished).

Ishimoto, M. and !ida, K. ( 1936, 1937) Determination of elastic constants of soils by means of vibration methods: modulus of rigidity and Poisson's ratio. Bulle~in of the Earthquake Research Institute, Tokyo Imperial University, vol. 14, p. 632-657 ( 1936) and vol. 15, no. 2, p. 67-85 ( 1937).

Joe sting, H.R. ( 1954). Geophysical exploration in Alaska. Arctic, vol. 7, no. 3 and 4, p. 165-175~

Jones, R. (1958) In-situ measurement of.the dynamic. properties of soil·by vibration methods. Geotechnique., vol. Y'III, p. 1·21.· ·

Joset,. A. and Holtzsg,herer, J.J. (1954) Exp~dition Franco-Islaridaise au Vatnaj~kull mars­avril 1~51. Resultats des sondages seismiques (French-Icelandic e.~pedition· to Vatnajokull in March-April 1951. Results of Seismic Soundings). Jokull, vol. 4,. p. 1-33 (text in French). ·

Kaplar, C.W. (1963) Laboratory determination of the dynamic moduli of frozen soils and of ice. Proceedings: International Conference on Permafrost, Purdue University.

Kesler, C.E. and Higuchi, ·Y. (1953) Determination of co.mpressive strength of concrete by using its sonic. properties. Proceedings, American Society for Testing Materials, vol. 53, p. 1044-1052.

Koch, K.R.( 1885) Beitrage zur Kenntniss der Elasticit~t ·des Eises (The elasticity of ice). Annalen der Physik, 3rd Ser, vol. 25,p.438-450. . . .

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Lagutin, B .. L. and Shul'man, A. P. ( 1946) "0 metodakh roscheta ledianykh perepray" ("Methods of calculating the load carrying capacity of ice eros sings") in Data on the problem of ice crossings. Trudy Nauchno-Issledovatel'skikh Uchrezhdeniya Seriya 5, Vyp. 20, Glavneye Upravleniye Gidrometeorologicheskoy Sluzhly Gidro­meteoizdat Sverdlovsk, Moscow. U.S •. Army Corps of Engineers, New England Divi· sion, ACFEL 'franslation 25, 1954, p. 4~-63.

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Leet, L.D. (1950) Earth waves. Cambridge, Mass.: Harvard University Press; Harvard Monographs in Applied Science, no. 2.

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Love, A.E.H. (.1892) A treatise on the mathematical theory of elasticity. Cambridge: Uni-. , versity Press, 4th edition, 1927 •.

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26 LABORATORY DETERMiNATION OF DYNAMIC MODULI OF FROZEN SOILS AND OF ICE

. '

Nakaya, tJ. (1959) Visco-elastic properties of snow and ice in the Greenland Ice Cap. USA SlPRE Research Report 46.

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Oliver, J.; Crary, A.P.; and Cotell, R.D. (1954) Elastic waves in arctiC' pack ice. Trans­actions American Geophysical Union, vol. 35, p. 282-292.

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Thiel, E. and Ostenso, N.A. (1961) Seismic studies on Antarctic ice shelves. Geophysics, vol. XX:VI, no. 6, p. 706-715.

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Tsytovich, N.A. (1940) An investigation of the elastic and plastic deformation of frozen ground. Trans. Akad Nauk SSSR, vol. 10• p. 5-36.

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LABORATORY DETERMINATION OF DYNAMIC MODULI OF_ FROZEN SOILS AND OF ICE 27

Tsytovich, N.A. and Sumgin, M.I. (1937) ''Deformation of frozen ground under vertical load" in Osnovaniia mekhaniki merzlykh gruntov (The principles of mechanics of frozen ground). Moscow: Izdatel'stvo Akad Nauk SSSR, Chap. 5. USA SIPRE Translation 19, Chap. 5, 1959.

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W~lcken, K.(1961) Seismic ice-thickness measurements on Novaya Zemlya, 1932-33. Polarforschung, vol. 5 (\12), p. 87-91.

..

I

·APPENPIX A: TEST RESULTS

TABLE AI

TABULATION OF THE MEASURED FUNDAMENTAL RESONANT FREQUENCIES FOR DYNAMIC MODULUS TESTS

29

Specjme;, Flexural Longitudinal Torsional Flexural . Longitudinal Torsional

No. Terrip •. Freq. Temp, Freq. Temp. Freq. oF. cpa . oF. cps oF. cps

Specimen Temp, Freq. Temp; Freq. Temp. Freq. No. oF. cps oF. cps oF . cps

SP-300 30. 0 1626 29. 2 6530 29.6 3690 SNHT-307 26.4 1549 25, 3 6100 25.6 3410 (Horizontal 24.9 1728 i!4. 2 6820 24. 5 3920 -(Vertical· 20. 7· 1637 20,0 6300 20.3 3680

Beam) 20. 3 1734 19.6 6908 19.9 3970 Beam) 13.0 1734 12. I 6530 12.4 3840 9. 9 1745 9.0 7110 9. 5 4055 2. 0 178j I. I 6730 1.4 3960 2. 7 1782 0.4 7050 1.0 4063· -7.7 181~ -8. 5 6840 -8. 2 4023

14,3 1782 -16. 5 7210 15. 7 4129 17.0 1850 -18. 5 7253 -18.0 4160 SNHT -308 25. 8 1558 25,0 6120 25. 3 3470

, (Vertical 20.0 1655 20,0 6320 19.9 3635 SP-301 29.9 1638 28.7 6800 28.8 3960 Beam); 12. I 1723 10,4 6600 10.9 3820

(Horizontal 25.2 1775 24.7 7020 25. 0 4096 2. 0 1793 o. 9 6730 1.3 3890 Be.am) 19.8 1792 19. I 7142 19.4 4140 -7. 6 1835 -8.0 6900 -7.9 3980

10.7 . 1825 10.-0 7310 10. 3 4190 1.5 1830 -0. 2 7332 o. 6 4200 SNHT-309 27.0 1558 26, 2 6100 26.4 3430

13. 0 1837 -13. 8 7367 -13.7 4242 (Vertical 19.8 1684 19. l 6400 19.4 3670 16.0 1862 -17.0 7422 16.7 4295 Beam) II. 9 1734' II. 0 6630 II. 3 3880

0, 7 1804i -0,7 6820 -0. 2 4000 -8.7 1813 -9. 0 6900 -9. 2 4044

SM-154 * 29.8 1440 29.8 5890 29.8 3640 (Horizontal· 21. 0 1520 21.0 3690 SNHT-310 25. 3 1593 23, 9 6!30 24,3 3625

Beam) 14.0 1550 14.0 6350 14.0 3770 (Vertical 17.6'1707 15. 7 6400 16. 3 3870 2. 0 1569 2. 0 6400 2. 0 3800 Beam) 13. 5 1743 12.8 6530 13. l 3910

II, 0 1569 -14.0 6550 -13.0 3850. 3. 3 1832 1.8 6750 2. l 3980 -9. 0 1885 -10, 0 6850 -9.7 40 II

SM-200 31. 4 1471 30. I 5559 28. 8 3270 (Vertical 23. 3 1521 23.4 6200 23. 5 3530

Beam) II. 5 1558 10.5 6400 9. 5 3680 SEBT-304 24.8 1228 24. 2 4813 24. 3 2748 1.0 1608 o. 0 6500 -2. 0 3690 (Vertica! 19.8 1317 20,7 5146 19.7 a93o

,• -8. 7 1615 -9.0 6900 -8. 0 3740 Beam) 9. 5 1491 8. 9 5869 9. I 3320

o. 9 1533 -0.4 6030 0. I 3460 -II. 7 1638 -13, I 6220 12.6 3580

SMT-306 30. I 1243 30.0 4664. 29.9 2623 I

(Vertical 25. 8 1539 25.6 5759 25. 7 3230 SEBT-305 24.9 1191 24, 5 4612 24.6 2720 Beam) 22. I 1639 21.4 6100 21. 8 3450 (Vertical. 22.4 1305 21. 5 5337 21.8 2980

17.7 1696 17.4 6300 17.5 3580 Beam) 9. 5 1510 8. 9 5869 9. I 3345 8. 6 1763 7. 9 6510 8. 0 3640 2. 0 1588 1.1 6210 1.3 3510

-·o. 6 1827 -I. 5 6610 -1.1 3760 -8.8 1638 -9.6 6350 -9.4 3690 -9.7 1893 -10.3 6800 -10. 2 393.0

SEBT-306 24.6 1203 24. 3 5078 24.4 2828 SMT-307 30,6 1100 30 .. 5 4633 30. 5 2500 (Vertical 20, I 1347 19.6 5359 19.6 3070 ·(Vertical 26. I 1470 25. 5 5811 25. 7 3349 Beam' 22.4 1549 21.6 6220 21.8 3550

Beam) 10, I 1460 9. 6 5890. 9. 7 3410 0. 8 1539 0. 0 6200 0, I 3560

17, I 1629 16.6 6380 16.9 3680 -9. 5 1594 -10, 2 6400 10,0 3670 7. 2 1706 6. I 6650 6. 5 3860

-0 .. 8 I'V95 -2.0 6800 -I. 6 3970 SEBT-307 24.2 1202 23. I 4789 23. 5 2757 10. 2 1911 -II. 2 6920 -10. 9 4077 (Vertical 22. 3 1243 21. 5 5059. 21. 8 2827

Beam) 8. 9 1449 7. l 5659 8. 2 3240 SMT-308 30,7 1110 30.7 4581 30.6 2421 2. 2 1520 I, 9 5891 . 1.7 3380 (Vertical 26, 5 1439 26. 2 5782 26. 3 3270 -9.2 1549 -10; 2 6200. -9.9 3470

Beam) 22, 3 1569 21. 5 6230 21. 9 3480 ;

17.8 1639 17. 5 6410 17.6 3670 '7, 8 1708 7. I 6740 7', 4 . 3880

-0, 8 1806 -I. 7 6910 -I. 3 3940 -9. 7 1920 -10, 5 7100 -10. 3 4014

SEBT-308 z'4. 9 1337 24, 5 4637 24.6 2889 (Vertical 19.5 1480 19.0 5358 19.2 3140

RPrtm) . 7. 4 !603 6, 0 5901 . 6, 4 3430 3. 'i 1674 2. 4 6140 2, 8 3540

SMT-309 30.4 1049 30. 2 4633 30. 3 2511 -10.0 1738 . -II. 0 6300. 10.7 3680

(Vertical, 25,9 1459 25. 5 .5781 25.6 3300 Beam), 22.9 1549 22. 5 6120 22.6 3480

17.2 1647 16.7 6320 17.0 3660 8, 4 1719 7. 8 6720 8. I 3870 0, 2 1792 -0.9 6900 -0. 3 4043

10, 2. 1831 -II. 4 7010. -10,8 4073

SNHS-150 30. 3 1242 29.5 5114 29.0 2683 (Vertical 17.7 1334 17. 5 5335 16. 5 3180

Beam) 9. 5 1396 8, 5 5391 8. 0 3220 -0, 5 1408 -1.0 5444 -I. 5 3330 -7.0 1439 -8,0 5444 -7.0 3340

SMT-310 30,0 1273 30.9 4873 30. l 2623 ~(Vertical 26. 5 1619. . 26. 4 5734 26. 5 3300

Beam) 22. I 1773 . 20, 9 6320 21. 5 3620 17.9 1863 17. 5 6500 17.6 3750

8, T 1920 8. 1 6730 : 8. 2 3820 . ~0. 3 2000 -1.7 6920 -1.1 3860 -9. I 2045 ~ 10. 2 7! II -9.8 4030

SNHS 152 * 29.0 1334 30. 0 5335 31.0 2290 (Horizontal 20. 5. 1418 20. ·5 5400 20. 5 3030

Beam) 10. 5 1405 II. 0 5600 11.0. 3110 3. 2 1500 2. 0 5670 2. 0 32so

-6. 0 15?0 -6.0 5723 -6. 0 5250

SNHS 153 * 29. 0 1332 . 29.0 4966 29.0 2910

SNHT-30_6' 24,6 1646 23. 5 6170 23. 9 3545 (Vertical 20.0 1707 19.8 6300 19.7 3660

Beam) 1!. 7 1783 10.4 6590 10. 8 3840 -0.4 1797 -0 •. 9 1?600 -0.7 3900

(Horizontal 17.0 1470 17.0 5035 . 17.0 3050 Beam) 9. 0 1510 9. 0 5535 9. 0 3290

-3, 0 1556 -3. 0 5670 -3.0 3370 -15.0 1510 -15,0 5890 -15,0 3400

-8. 5 i850 -9. 1 6890 -8. 9 3990 ~ NOTE: Physical data on specimens are given in Table Ill.

30

Specimen No.

SFS-374 (Vertical

Beam)

SFS-375 (Vertical

Beam)

SFS-376 (Vertical

Beam)

SFS-377 (Vertical

B<'am)

SFS-378 (Vertical

Beam)

SYS-376 (V<>rlical

Beam)

SYS-377 1 Vertical

Beam)

SYS- 378 iVertical

B<>am)

APPENDIX A

TABLE AI (CONT'D)

TABULATION OF THE MEASURED FUNDAMENTAL RESONANT FREQUENCIES FOR DYNAMIC MODULUS TESTS

Flexural Longitudinal Torsional Flexural Longitudinal

Temp. Freq. Temp. Freq. Temp. Freq. "F. cps oF. cps oF. cps

Specimen No. Temp. Freq. Temp. Freq.

"F. cps 'F. cps

31.1 1090 30.8 4581 30.4 2421 SYS-379 30.4 1106 30.0 4453

28. 3 1306 Z8.Z 4990 27.8 2795

24.3 1420 l3. 6 5279 23.8 2929

(Vertical 25. 1 1112 24.6 4687

Be;._m) 20.7 1233 20. I 5189

22.0 1490 20.7 552? 21.0 3080 14.9 I 300 14.4 5447

12. 3 1561 I L 5 5713 11.5 3280 7. I 1411 5. 8 5680

5. 3 1591 4, l 5833 4. 7 3440 -0.6 1499 -1.7 5781

-2. 3 1621 - 3. 5 5922 - 2. 9 3470 -9.5 !554 -10. I 5924

-9.0 1646 -7.9 6000 -8.7 3580 S"'~S-380 30.6 1120 30.4 4264

30.4 1038 30. I 4056 30. I 2490 (Vertical 25. 7 1296 24.8 4769

28.2 1242 27.6 4687 27.8 2782 Beam) 20.7 1428 19.8 5338

24. 5 1350 24. 2 4928 24. 3 3080 13.6 1549 12.0 5569

21.5 1445 20.7 5568 21.1 3230 7- 2 1593 6. I 5691

13.4 1524 II. 2 5736 13.0 3384 o. 6 !676 0.3 5781

6. 0 1568 5. 2 5834 5. 4 3510 -·9. 5 1725 -II. 7 . 6120

-2. 3 1593 -3. 5 6010 - 2. 9 3570 -8.8 1602 -9.6 6100 -9. 1 3590

SBC-307 29. I 781 28, 8 3230

31.0 1038 30. 5 4319 30,9 2291 (Horizantal 24.7 979 24. 3 4000

28.3 1212 28. 3 4633 28. 2 2839 Beam) 19. 8 1041 19. 2 447 3

23. 9 1398 23.0 5000 23.4 3070 9. 3 1202 8. 0 4894

22. 5 1420 21. 5 5560 21.8 3190 - i. 6 1296 -3. I 5278

II. 4 1557 10.6 580 I 11.0 3450 -7.0 1376 -8. 7 5358

4. 8 1581 4. 2 5980 4. 6 3490 -2. 3 1616 -2. 9 6120 -2, 7 3565 SBC-307A 30. 3 666 30. 2 2910

-8. 5 1621 - 10.0 6150 -9. 2 3610 (Horizontal 25. 0 970 24. 3 3970 Beam) 19. 5 1090 18. 7 4498

31.8 1069 31.0 4160 31.2 2091 9. I 1255 7. 9 5144

27. 5 1294 27. I 5110 26. 9 2746 -2. 7 I 398 -3. 8 5469

24. 5 1388 23.4 5248 23. 6 2925 -8. 7 1429 -10. 5 5702

21. 9 l42'l 21.6 5560 22.0 .3140

14.0 1543 12. 4 5790 13. 5 3280 SBC- 308 25. 3 3880

5. I 1574 3. 4 5890 4. 3 3435 (Ho rizoatal 19. 9 1111 19. 2 4476

-3. 2 1610 -4. 3 61!0 -4.0 3480 Beam) 10. 5 !262 9. 2 5000

-7- 8 1626 -9.4 6300 -8.0 3 560 0, 0 1337 -I. 5 5224 -8. 7 1408 -10.4 5436

30. 7 1130 30. 4 4160 30. 5 2391

27- 9 1347 n. 1 5012 27- 6 2828 SBC-309 30. 3 863 29.9 3570

24. 2 1499 23. 6 5258 23. 7 3020 (H~rizontal 25. 9 1105 25. 3 4370

21.5 1549 20. 7 5680 20. 9 3140 Beam) 19. 2 1238 18. 3 4790

I i. 4 1651 10:8 5847 ··to, 9 3370 9.-3 '136"5 8. 5 5333

4. 4 1676 3. 4 5890 3. 8 3450 -0.6 1438 ~ 2. I 5623

-3. I 1686 -3. 8 6090 -3, 3 3560 -9. 5 I 520 -10.7 5781

-5. 4 1696 -6. 2 6110 -6.0 3660

SBC-309A 31. 9 852 31.7 3670

30. 0 1079 29. 8 4317 29. Q 2312 (Horizontal 25. 5 1191 24.4 4739

26. 0 1049 25. 8 4517 25. 8 2461 Beam) 19. 2 1252 17. I 5123

21. I 128.6 20. 4 5000 20. 6 2809 8. I 1346 7. I 5448

15. 6 1408 14, 7 5334 14.9 2920 -I. 8 !38'l -3. 2 5612

6. 8 I 524 5. Q 5618 6. 1 3100 -7. 5 1470 -9.4 5769

- L 6 1534 - ~) . ! 5781 -2. 7 3230

-10. 7 1558 -11. 3 5'l2.4 -11. 5 1330 SBC-31C 30.0 739 29. 6 3360 (lbrizontal 24, 5 1020 23. 8 4264

29.9 1120 zq. 4 4161 29. 6 22'l2 Beam) 21.0 1040 19.9 4487

26. 3 IOQ 1 25. u 4266 25. 7 2431 B. 8 1293 7. 3 5045

25. 2 11l0 24. 6 4318 24. 8 2452 -I. I 1382 -2. 5 5447

21.0 1!00 20. 4 5090 20.6 2728 -9. I !448 -10.7 5758

lb. 2 IL28 14. b 527'l 15. 6 2950

7. 6 I 306 6. 4 5590 6. 8 3080

-L 0 1389 -2.0 5690 - -1.6 3250 SFFC- 366 30. 1 382 29. 7 1851

-I L 3 1444 - 12. 8 5891 - 12. 3 3350 (H~rizontal 25. 4 510 24.9 2222 Beam) 21. 9 610 21. 5 2648

lO. 0 1059 29. 5 4474 29.9 2382 10.0 667 9. 7 2849

24.9 1091 24. 4 4528 24.6 2594 -2. 5 752 -3. 2 3170

21. 3 1243 20. 7 4'l95 20. 9 2757 -7.8 822 -9. 5 3350

16.6 I 343 15. I 5224 I 5. 8 2941

7. 2 1423 6. 4 5545 6. 7 3080 SFFC-366A 30.0 391 29. 5 1840

o. 3 1449 - \. 3 5758 -0. 5 3280

-12. 2 154'l -13. 4 5891 -13.0 3390

(Horizontal 26.6 489 25.7 2213 Beam) 20. 0 57 3 19. 2 2543

10.6 651 10: 5 2870 -3. 2 750 -6.6 3380 -7.8 771 -9.2 3630

Torsional

Temp. Freq. oF. cps

30. 1 2412 24. 7 2500 20.2 2819 14. 5 3030 6. 0 3150

-I. 5 3230 -10.0 3310

30. 5 2402 25.0 2695 20. I 2960 12. 7 .3150 b. 4 3200 0. 4 328C

-10. 3 3760

2iL 'l 171~

24.4 2161 19.4 239 i H. 3 2674

-2. 7 2930 -8. 4 3010

30. 2 1637 24. 5 2172 18. 9 2471 8. 3 2865

-3, 5 3040 -9.9 3 I 30

19. 5 2561 I Cl. 0 2746 -I. 0 2945 -9.7 3020

30. l 1910 25. 4 2361 18. 7 2697' 8. 7 ·2920 -I. 5 3090

-10. 2 3255

31. 5 1980 24.6 2697 17.4 2839 7. 5 3060

-2. 9 3150 -8. 5 3200

30. 0 1764 24.0 2271 20. 2 2481

7-9 2869 -I. 9 3010

-10. 2 3090

29. 9 !Ill 25. I 1212 21. 5 1419

9. 7 1550 -3.0 1598 -9.0 1909

29.7 I I 51 26. 2 1202 19.4 1470 10. 2 1540 -4.0 I 793 -8.7 2122

APPENDIX A

TABLE Al (CONT'D)

TABULATION OF THE MEASURED FUNDAMENTAL RESONANT FREQUENCIES FOR DYNAMIC MODULUS TEsrS

Flexural Longitudinal Torsional Flexural Longitudinal Torsional

Specimen Temp. Freq. Temp. F:req. Temp. Freq. No.

Specimen Temp. Freq Temp. Freq. Temp. Freq. No.

oF. cps oF. cps oF. cps oF. cps oF. cpa oF. cps

SFFC-367 30.4 364 2.9.4 1734 2.9.4 1010 SI-668 2.7. 7 1419 2.7. or; 5436 2.7.0 3040

(Horizontal 2.4. 7 469 2.4. 3 2.2.2.1 2.4. 5 1283 (Vertical 23.8 142.9 2.3. 5 5467 2.3. 2. 30";0

Beam) 19.9 531 19.6 2614 19.9 142.8 - II. 0 609 10.6 2.848 10.7 1539

Beam). 2.1. or; 1440 2.0.6 ";540 19.6 3080 1";.6 1470 15.5 5550 I';. 3 3130

-l. 4 699 -2..4 3250 -2..2. 1792: II. 4 1485 10. I 5";90 9. 5 3180

-6.7 771 -8.3 32.80 -1.2 2.171 4. 7 1515 3. 5 5680 3. 5 32.10 _.,_ 0 152.9 -6:5 ";735 -8. or; 32.60

SFFC-368 30.8 341 30.5 1588 30.5 874 -8.0 152.9 -9.8 5758 -10.5 32.70 (Horizontal 2.6. 9 470 lb. 2. 2.091 26.3 1140

Beam) 19. l 578 17.8 2.542. !8. I 1439 -12. ~ 1534 -14.7 ";780 -14.0 3280

12.. 3 650 ll. 9 2778 12.0 1578 SI-670 28.3 1418 28.0 5457 28.0 2980 -2.. 6 765 -3.5 3190 -3. 3 1782. (Horizontal 26. I 1418 25.9 5480 25.9 2990 -7.8 82.2. -9.3 32.80 -8. 2. 1782. Beam) 21.2 1434 20.8 5534 21. I 3040 - 12.6 1449 12. 2 5560 12.6 3070

SFFC-369 31.4 351 30.9 1618 31. I 831 1.5 1469 0.0 5579 0. 8 3110 Horizontal ·2.6. 5 460 2.5. 7 2.102. 2.5. 9 113:1 -8. 5 15!5 -8.7 56bo -8.7 3150

Beam) 2.1. 2. 561 2.0. 5 2.634 2.0. 8 1377 6. 5 733 8. 0 2.859 8. I 1589 SI-671 31.6 1397 31. 5 5418 31. 3 30 !5

-3.0 753 -4.8 32.40 -3. 7 !762. (Horizontal ~8. 6 1409 28.6 5423 28. 5 3020 6. 3 831 -7. I 3330- -b. 7 1811 Beam) 25.6 1414 25.8 5448 25. b 3035

2.0. 2 142.4 19.8 5480 20.0 3070 12.8 1439 12.. 9 5546 12.9 3140

SAP-148 2.9. 4 1082 29. 0 3870 28. 3 2380 1.5 1460 0. 4 5579 1.0 3155 (Vertical 2.0. 5 1112 20. b 4Ib0 20.8 2360

.. -9.8 1480 -10.2 5624 -10.0 3170

Beam) b. 3 1143 6. 4 4370 b. 5 25b0 -I. 5 1194 -2. 5 4b85 -3. 5 2b80 SI-672 28.6 1397 28.6 5423 28.6 3040

-12.. 0 1235 - 12. 0 4475 -12.0 2710 (Horizontal 25. 4 1414 25. 3 5457 25.4 3045 Beam) 20.0 1424 19.4 55! I 19. b 3060

SAP-150 26.9 831 26. 9 3450 2b. 9 2191 I 2. 3 1439 12. 3 5551 12.0 3 I 15 (Horizontal 22.0 913 22. 0 3750 2.2.. 0 2233 3. 8 1454 2. 5 5584 3. 0 3130

Beam) 13.0 980 13. 0 4055 13. 0 23b0 -7.0 1480 -6. 3 5624 -6. 2 3180 2. 0 1000 2. 0 43b8 2. 0 2452

-8.0 1049 -10.0 4474 -8.0 2540 SI-673 28. 9 1360 28.9 5407 29.0 ,2990 (Horizontal 25. I 1368 25. 2 5435 25. 2 3010

Beam) 21. 5 1371 21.4 5468 21. 4 3050 S!-664 27.6 1407 26. 4 5480 2b. 0 3000 10.4 1403 10. 3 5534 10. 2 3095 (Verti~l 22. 6 1425 22. 0 5545 21. 4 3010 2. 9 1418 3. 0 5559 3. I 3130

Beam) 19.8 1435 17. 4 5557 18. b 3030 -7. 6 1434 -8.7 5646 -7. 8 · 3'220 13. 2 1445 12. 4 5579 II. 5 3040 9. 7 1460 8. 8 5b45 8. 8 3070 Sl-674 31.0 1339 30. 8 5329 30. 7 3010 3. 1 1470 l.b 5b68 0.5 3110

-3. 5 14.80 -2. 5 5755 -4. 2 3130 (Horizontal 28. 4 1346 28. l 5340 28,0 3015

Beam) 26.4 l34b 2b. ~ 5357 ~-2 3o-25 -7. 5 - 1500 -8. 5 5783 -8.0 3150 21. 5 1368 21. 0 ) 5423 21. 2 304~

-12. 3 1510 t 3. 9 5858 - 13. 'l 3170 9. 4 1381! 8. 5 5457 9..0 307d 3. 3 1409 1.7 5511 2. 5 3120

SI-6b5 28.8 1425 28. 3 5334 27. 9 3060 (Vertical 26.0 1435 25. 4 5351 24. 8 3%0 Be~m) - 2,1. 0 1440 20. 2 5368. 20. 4 3 80.

14.0 1450 13. 4 ' 5435 - 13.0 3100

- 10. 2 1431 -jO. 6 ~559 -10. 9 31 50

Sl-675 2H. 4 I 3<)3 28. 0 5435 28. I 3000 (Horizontal 24.4 1403 23. 7 546!! 23. 8 3020

7. 7 1480 7. 2 ~56o 6. 8 3180 3. 0 ISIS 2. 4 56L3 2. 4 3220

Beam) 20.7 141. 20. 2 5511 20. 2 3075 II. I 1434 10; 2 5559 10. 5 3110

-5. 0 1521 .::.~, 5 5657 -5. 5 3240 3. 8 1449 2. 7 5613 3. 2 3120 -7. 5 1529 -8. 0 5b70 -8. Q 3270 -10. 3 1469 -10. 2 5655 - 10. 2 3143

- 12. 5 1548 I 3. 8 5747 - 13. I 3280

S1-b67 29. 6 1480 29. 9 5445 30. I 2055 SI-(P)** 27.7 1582 27. 5 5781 27. 2 3280 (Vertical 26. 8 1495 25. 4 5533 24. 9 Z'-'80 (Horizontal 25. 0 1593 25. 0 5781 25. 0 3280 Beam) 22. 2 1500 20. 8 5569 2(}. 2 1005 Beam) 20. 5 1593 20. 2 5789 20. 2 3285

15. I 1520 I 6. I 5635 15.4 3030 12. 7 1608 12. 0 5833 12. 3 3290 9. 7 I 525 8. 'l 56b'l 8. 4 lOBO 5. 7 1612 5. 9 5853 5. 4 3290 2. 6 I 530 o_ 4 5679 I. 2 3100 - -6. b 1621 -7. 2 5890 • 7. 2 3300

-6.0 1540 -8. () 5770 -7. 5 3 I 50 -7. 7 !54-9 -9. 5 5782 -8. 5 3170

-II. 6 I 578 I 3. 0 :>835 - 12. 3 3185

NOTES: Vertical beams wcr<' frozen in ,·ertical position from top to bottom - icc lcnst•s in soil specimens orient.,d normal to longitudinal axis of beam.

Horizontal beams wt're frozen in horizontal position from top to bottom - ice lenses in soil specimens oriented parallel to longitudinal axis of beam.

ALNICO bar magnets used with all test specimens. except those marked with asterisk("). Dim<'nsions of bar magnets: 3/16 x 3/16 x 2 inches. Weight: I h gr<u11s per piiir,

* ALNICO cylindrical magnets used with.these specimens. Dimensions of cylindrical magnets: 3/ 16-inch diam.,ter x l. 8 inches. Weight: IZ grams per pair.

** ·Specimen was cut from natltrally frozen lake ice from Portage Lake, Maine, in March 1953.

31

32 APPENDIX A

Bx1o• 15xl05

·;; Q. 7

.; !::::: u ~ U)

6 <I ...J L&J

~

0

U)

·~ :::> ...J :::> 0 0 2

I I I I I I I I I I I I

.. EL (LONGITUDIN~~

ll . -.-

~ 7 .. ' • . . . b.

I~ ~ . /::.

. 6 6. '--------0

~--f- -.·-Et (FLEXURAL) _ 0 0 .

~~ Cl ~ -/ 0 -~ -

-

(.1

Cl

~ 14 .; !::::: u 9 w 13 > w ~ ~

...J 12 <I z

0 :::> ~

(; z

r r I I I

~--r-l--•7-~

~~ ~ v--- -~

~ •/ • - .. r -~·

-· .. • -· .. -

--

-

-

w 4 0 II ...J

; ·- ~

' -._

3 1 l

39 20 10 0 -10 TEMPERATURE, °F

-20 10

20 10 0 TEMPERATURE .·F

-20 30 -10

a. Modulus of elasticity VI. temperature( I) b. Lon9itudlnal wave velocity vs. temp.,ature 9xlc:i 5

Ill Q.

.; 3 ~

'• I I I I r .- u

: ' .; !::::: 8 u

I r r f. . f. 1. I I I I I I I I I I I 1-r ~ -~

.a -·~.-~.

~ ~ •

~ ~ ~ • • , . 0 ~ a:: ~ 2 0

U)

Ill _j __,....- .. • • •. --.-., ~

•. •

9 "' > L&J

7 > <I ~

~ ~

~

~

:::> ...J :::> 0 0 2

c)

. -

-;

--

...J <I z 0 6 c;; a:: 0 ~

~

~

~

-- ;>

0 l

30 20 10 0 -10 -20 !5 _L

30 -10 -20 20 10 0 TEMPERATURE. °F TEMPERATURE, °F

c. Modulus of rigidity vs. temperature d. Torsional wave velocity vs. temperature

O.Br-T-.,.--, 1 ..........--,--r-..,...--,r-'o-r·,1..........-.....,....-r-'T"'<-."'"T'""T1-'T"'< 11r~ 1 .-r--.-r-"T-, _ Wet Unit .Water

wj~ 0.6

::t Q ..... 0.4 <I a:: fJ)

z 0 fJ)

0.2 fJ)

6 !l.

0

""~--;-~-~---, ~~--t- ----6~ 0

Specimen T~ay 'Number Symbol

Number* Weight Content pc{ o/o'

~sP-3oo 0 • H~-11 12.9 14~ 5

SP-301 6 • HB-11 131 12.. 7 -- - -*ffB(-).indicates test beams frozen froin top to bottom in horizon-- tal position. Ice lenses oriented parallel to longitudinal axis of

beam, in a horizontal plane. ·

NOTES

' In graphs a and b solid symbols represent values comp~ted using fundamental longitudinal frequencies. Open symbols rep- ' resent values computed using fundamental flexural frequencies.

In graph e symbols indicate values computed using each. value of modulus of elasticity, ELand Ef, as shown in graph a and .. a corresponding .value of Gin graph c. . ·

' Th!' curves for ·Poisson's ratio in graph e were computed from values taken from curves in graphs a and c.

30 20 10 0 -10 -20

TEMPERATURE I °F

e. Poisson's' ratio vs. temperature(Zl

Figure Al. · Dynamic elasticproperties of frqzen Peabody gravelly sand vs temperature.

"' a.

~ ~ u f-(/)

5 <l _.J

w

~

0

rn ::::> _.J

::::> 0 0 ~ t-

w 4

"' a.

~ ~ e J:e a:: ~ 2 0

(/)

::::> _.J

::::> 0 0 ~

c;

I _t

0.8 .I-

wl~ 0.6

::I_

0 f-- 0.4 <l a::

U)

z 0 (/)

0.2 (/)

0 a..,

0

APPENDIX A 33

I I I

I

t:::. t:::.

~ ~-----:-:--

-~-- 0 -Ef(FLEX~

/0 • -v • n·

;Z~ t:::.

: LONGITUDINAL) I -

I!

4 -~ _l _l _1

30 20 10. - 0 -10 .. -20 TEMPERATURE, °F

a. Modulus of e-iosticity vs. temperature< 1 l

I I_ I

• ~ ..--· .. -. ..-f-----R

~ .

.. -. --

.30 .20 10 0 .. -:-10 -20 TEMPERATURE. °F

c. ~odulus of rigidity_ vs. ter:nperature

i ~~ -~ . -- --·: -r-- -·~ ---- -'---=

-· _·.

-;--of- ~ ~ • ,..

--· -

30 ~0 10. . 0 . . . -10 -20 · · TE'ftoiiPERATURE, °F . · · - ·

. e: Po!:sson's ratio. vs. temperot~re< 2 l . ~· ...

u : ' 13

>­f-u 0 _.J

w > w ~ ~

<i 12 z 0. ::> f-(.9

z 0 _.J

I

~· X 103

-

--

-

I I I

~ ~-

.........-:1 .. 1_.....---- • v· -

.. -

I ..• -

--

~

-

All -

_l _l 1 1 1 l 1

30 20 10 0 -10 -20 TEMPERATURE ,°F

b. Longitudinal wave_ velocity vs. temperature 8xiQ 3

u

: ' ~ ~ u 0 _.J

UJ > w 7 > <l ~

_.J

<( z 0 iii a:: 0 f-

> 6

I I I I I I I I I t-

t-t- • t-

t-t-

t-

t-,,· /

t-t- .. ··.1

t-·

t-

30 20 10 0 -10 -20 TEMPERATURE. °F

d. Torsional wave velocity vs. temperature

*HB( ) i;,dicates test beams frozen from top to ·bottom in h~rizon­tal position. Ice lenses oriented parallel to longitudinill axis of· beam, in a horizontal plane.

7-VB( ) md1cates test beams frozen from top;to bottom m vert1cal position. Ice lenses oriented nor~al to longitudinal axis of beam.

.. In graph_~- a and b'.solid sytnbols represe'nt values computed -·using fundarnentil.! longitudinal fre_SJ~encies. Opel' sytnbols r<;p­resent value_s_ compu;ted using fundamental fle.xur-al frequencies·.

In graph e symbols indicate values 'computed using ~ach value of modulus of elasticity, ELand Ef, as shown in graph a and a corresponding value of Gin graph c. .. .

• . Thd curves fo.r Poisson's ra't-io in graph e w_ere' corpputed from values take~ from curv<'s in graphs a and c. ·

F:igure :A2. Dyn~mic:elastiC:properties ()[ froz~n .Mcfyama.ra concrete ,sand ys temperature.

34

• a.

> ..... 0 ...... (/)

Cl _J

laJ

I£. 0

.. a.

,: ..... Q § a:: I£. 0 (/)

:::» ,_J

:::» 0 0 ~

<£

3

2

0

0.8

IU~ 0.6

=1. 0 j:

0.4 4( a: (/)

z 0 (/)

0.2 (/)

5 ll.

0

30 20 10 0 -10 TEMPERATURE, °F

a. Modulus of elasticity VI. temperature< 1 >

I I

19 t..,_

-&--~--~ "'"' .,A • ,. .

/

~-

30 20 10 0 -10 TEMPERATURE. °F

c. Modulus of r1C)idity vs. temperature

30 20 10 0 ..;10 TEMPERATURE, °F

e. Poisson's ratio vs. temperoture(2)

.APPENDIX A

-20

--

----

-20

-20

u Q)

~

.; t: 0 0 _J w > IU

~ ~

_J Cl" z Q :::» ..... a z 0 _J

:;;.

30 20

b. longitudinal wave velocity vs. temperature 8xl05

>­t: 7 0 g UJ >

~ 6 Cl 3t _J

Cl z ~ 5 a:: 0 ....

4

I I

-··-) 1- -

·-f-vA.-- •

--- 'iL

/f ... . J •

./ lOr r;-

~!- -•

~

30 20 10 0 -10 -20 TEMPERATURE, °F

d. Torsional wave velocity vs. temperature

Specimen Tray . Wet Unit Water

Number Symbol Number* Weight Content

pcf %

SMT-306 0 • VB-9 136 15.1

SMT-307 a • YB-9 14l 14.l

SMT-308 ll. • YB-9 143 lZ. 5

SMT-309 v • YB-9 14l ll.l

SMT-310 ):( )( YB-9 139 lz.".l

*VB(.) 1nd1cates test beams frozen from top to bottom 1n verhcal position. Ice lenses oriented normal to longitudinal axh of beam.

NOTES

In graphs a and b solid syml:lols represent values computed using fundamental longitudinal frequenciu. Open symbols rep­resent values computed using fundamental flexural frequencies.

In graph e symbols indicate values computed using each value of _modulus of elasticity, EL and Ef• as shown in graph a and a corresponding value of G in graph c.

The curves for Poisson's ratio in graph e were computed from values taken from curves in graphil a and c.

'· ,ltin/A~. fl}yaa,.,c elasUc Properties of frozen bi,ead,. .lieN amara coacrete·.-nd and East Bostou till · ·.- •• temperature. · ·

.. a.

.; 1-0 1-Ul <I ...J w I.L. 0

Ul :::> ...J :::> 0 0 ~

w

.., a.

>-1-e £> a:: I.L. 0

Ul :::> _J

:::> 0 0 ::t

~

2

0

0

wl~ 0.6

=t Q 1- 0.4 <I a::

!:" z 0 Ul

0.2 Ul

6 CL

0

APPENDIX A 35

u • ~

.; t: (.) 0 ...J w > w ~ ~

...J <C( z 0 :::> 1-0 z 3 ~

~-~·(f--1'--'--'---:2-:>-o=-'"_.__.__.__., o-::---L--'--'--'--'o':--'__.~.__.__._ __ ,'="o-'--'--L--'--="' -20

TEMPERATURE, °F

a. Mod":' Ius of elasticity vs. temperature< 1 >

I I I

-~ . ·-~,. ~-· •

......... I(_ ,l.-

u • .. ~ .; t:: (.)

0 ...J lU > w > <I ~

...J <I z 0 c;; a: 0 1-

30 20 10 0 -10 -20 TEMPERATURE. °F

c. Modulus of rigidity vs. temperature

30 20 10 0 -10 -20 TEMPERATURE. °F

e. Poisson's ratio v~. tomperoture12>

14&10"

..

2

II

0

9

7

6

5

4

I I I I

r-r-r-1-

-~---""

tr - v--' -

/~ - •

,... / '/" - .,fll" --r-r-r-

.... -1- -1-

1- -I

20 10 0 -10 -20 TE~PERATURE,°F

b. longitudinal wave velocity vs. temperature

I I I I 1-

1-

~-:! 1- - -

·---~ ---~ 0

1- ,;/ ~ 1-

1- -r 1-

1-

1-

1-

_l 1 l

30 20 10 0 -10 -20 TEMPERATURE, °F

d. Torsional wave velocity vs. temperature

Specimen Tray Wet Unit Water

Number Symbol Number* Weight Content pcf o/o

SNHT-306 0 • VB-9 133 12. 3

SNHT-307 A & va~9 128 13. I

SNHT-308 If ,. VB-9 1 35 13. 9

SNHT-309 )::{ )I( VB-9 I 33 13. 2

SNHT-310 " • VB-9 131 14. I

*VB( ) indicates test beams frozen from top to bottom in vertical position. lee lenses oriented normal to longitudinal axis of beam.

NOTES

In graphs a an:l b solid symbols represent values computed using fundamental longi~udinal frequencies. Open symbols rep~ resent values computed using fundamental flexura) frequencies.

In graph e symbols indicate values computed using each value of modulus of elasticity, ELand Ef, as shown in graph a and a cor responding value of G in graph c.

The curves for Poisson's ratio in graph e were computed from values taken from curves in graphs a and c.

Figure A4. Dynamic elastic properties of frozen blend, Manchester fine sand and East Boston till vs temperature.

36

·;; Q.

.; !:::: u ..... U)

~

..J w u.. 0

U)

:::::> ..J :::::> 0 0 -~

w

0

2 106 X I I

"' a.

.;

..... i5 ~ a: u.. 0

en :::::> ..J :::::> 0 0 ~

<£

0 1

0.8 I

wj~ 0.6

::l

2 ..... 0.4 ~ a: U)

z 0 U)

0.2 U)

6 Cl.

0

30 20 10 0 TEMPERATURE, °F

a. Modulus of elasticity vs. temperature< 11

I I

.t

~ '. . ., ~ - ~

v ~)I.e )I

)(

• l/ ~ /t~ )(.

30 20 10 0 -10

TEMPERATURE. °F

c. Modulus of rigidity vs. temperature

I I

~ I ~ • • ..!)(-.. r~

... ,. l . • ~ v ~-

0 .... .-:---[A v t:;. .- ~--):t-r-- -=-t:.: -

.. ~ -$

~~ ~ 0 } 0

jJ

30 20 10 0 -10 TEMPERATURE. °F

e. Poisson's ratio vs. temperoture< 2l.

APPF;NDIX A

-20

--

-

20

-

--

---

-20

12xl0 5

u ... ~·I I > !:::: u 0 ..J

~ 10

w ~ 31:

ci 9 z i5 :::::> ..... t5 z 0 8 ..J

7

u

:: ......

.; !:::: 7 u 0 ..J ~

>

"' 6 > c ~

..J ~

z 0 5 u; a: 0 .....

> 4

I I I I I I I I I I I I I

./ "'•1..--- I

1-1-

.. I( • • 1-

..... / • 1-

~ "/ "" 1- v· 1-

~~/ ~

1-

1-

1- 7 -1- ; ... · -1-

I 1- -

• 1- -1- I -1- -~

1- -1-1-1- -

l_ I

30 20 10 0 -10 -20 TEMPERATURE ,°F

b. longitudinal wave velocity vs. t_emperoture

I I I I I I I'

1-1-1-

.,

~ . ~ ~

~ •j.,

-------e

~

.,~

/ 'Ill

~ v • ~ J/)(

0

~ 1)( ~

30 20 10 0 -10 -20 TEMPERATURE, °F

d. Torsional wove velocity vs. temperature

Specimen Tray Wet Unit Water

Number Symbol Number* Weight Content

pcf o/o

SEBT-304 0 • VB-9 137 11. 2

SEBT-305 t:;. • VB-9 145 7. 0

SEBT-306 p ~ VB-9 144 9. 4

SEBT-307 ):t )( VB-9 132 5. 7

SEBT-308 v • VB-9 144 12.2

*VB( ) md1cates test beams frozen from top to bottom in vertical position. Ice lenses oriented normal to longitudinal axis of beam .

All specimen material finer than No. 4 sieve· except SEBT-308 which passes ~~~.

NOTES

In graphs a and b solid symbols rspresent values computed using fundamental longitudinal frequencies. Open symbols rep­resent values computed using fundamental flexural frequencies.

In graph ·e symbols indicate val~es computed using each value of modulus of elasticity: ELand Ef, as shown in graph a and a corresponding value of G in graph c.

The curves for Poisson's ·ratio- in graph e were computed from values taken from curves in graphs a and c,

Figure A5. Dynamic elastic properties of frozen ·East Boston till vs !emperature.

wl~

·;;; a.

.; t: (.)

1-(/)

3 <l _J

w lJ.. 0

(/)

:::> _J

:::> 0 0 ~

w

en Q.

2

0

0.8

0.6

r-

1-

::l

Q 1- 0.4 <l a:

_(f)

z 0 (/)

0.2 (/)

6 (l.

0

I

~

APPENDIX A 37

- u Ql

c 6

c ----- --· 6 c

---2• .; t:

c ___ ......

• • Et (FLEXURAL) Ji. k._......- •

~ ~ •

.U 0 _J

w // ~ V.:,:o

~ /J ~ EL (LONGITUDINAL) -

c/ • •

~: 0 • • •

c~

> w > <l 3: _J

<l z 0 :::> 1-(5· z 0 _J

~

1 _l I I

30 20 10 0 -10 -20 TEMPERATURE, °F

a. Modulus of elasticity vs. temperature< 1 l

I

- u

- : - ·:

.; t:

• -• ~ ~ .. ~

(.)

g w > ILl

~ > <l 31:

• _J

• <l z Q (/)

ex: 0 1-

30 20 10 0 -10 -20 TEMPERATURE' °F.

c. Modulus of rigidity vs. temperature

I I I I I I I I I I I I I --

-

--

c 6 -

-- l -

- -~ - . .0 -· --]!;' c

~ o---- --r- • -r-:---- 0 • 0 0 -

• r--- 0 -

• • • • 1 _I

30 20 10 0 -10 -20 TEMPERATURE' °F

e. Poisson's ro!io vs. temperoture< 2l

13xl03

I . I I ._ r--r-- -

1- -1- -

12 -r- -

II

10

1- • ~ ,___

-

1-

·~ -

1- --

1-~ -v· -• • 1- v • -

1- • r- • r-r-1-1-

9 1-r-1-

8 _l_ 1 l _j l 1 I I I

20 10 0 -10 30 -20 TEMPERATURE ,°F

b. Longitudinal wove velocity vs. temperature ax 103

7

6

5

4

I I I I I I I I I I I I

1--

1-

• • • 1-.--.--

~ -·__.J> .t _...l___.?

r- / I •

•

30 20 10 ' 0 -10 -20 TEMPERATURE' °F

d. Torsional wove velocity vs. temperature

Specimen Tray Wet Unit Water Symbol Weight Content

Number Number* pcf 'Vo

SNHS-150 0 . . VB-Z 109 41.5

SNHS-lSZ 6. • HB-3 109 za. 1

SNHS-153 c • HB-3 liZ 31.4

*HB( ) indicates test beams frozenfrom top to bottom in horizon­tal position. Ice lenses oriented parallel to longitudinal axis of beam, in a horizontal plane.

*VB( ) indic-ate~- test be;;_ms 1roz.en from top to bottom in vertical position. Ice lenses oriented normal to longitudinal axis of beam.

NOTES

In graphs a and b solid symbols represent values computed using fundamental longitudinal frequencies. Open symbols rep­resent values computed using fundamental flexural frequencies.

In graph e symbols indi·cate values computed using each value of modulus of elasticity, ELand Ef, as shown in graph a and a corresponding value of G in graph c~

The curves for Poisson's ratio in graph e were computed from values taken from curves in graphs a and c.

Figure A6. Dynamic elastic properties of frozen New Hampshire silt vs temperature.

38 APPENDIX A

-~

Q. 4 .; '::: u 1-(I)

3 ~ ....1 w II... 0

(I) 2 :::::1 ....1 :::::1 0 0 ~

w

0 30 20 ' 10 0 -10 -20

TEMPERATURE, °F

a. Modulus of elasticity vs. temperature( 1 >

4xlo• I I

--

"' Q.

.; 3 1- -§ ~ -a:: -II... 2 0 -(I)

:::::1 ....1 :::::1 0 0

~ -u---4 -~

~~--__. --*-1 -

~

~ l v• .-

0 I

30 20 10 0 -10 -20 TEMPERATURE 1 °F

c. Modulus of rigidity v1. temperature

0.8

)I(

I

ICJ o.6 WN

:L I 0 )(

j: Q4 ~ a:: (I)

z 0 (I)

0.2 (I)

0 Cl.

p~~30~~~~2~0~~~~10~~~~0~~~~-~10~~~-~20

TEMPERATURE, °F

e. Poissson's ratio ws. temporoturo<2>

u • ~ .; '::: u 0 ....1 w > w ~ ~

....1 ~ z 0 :::::1 1-<:5 z 0 ....1

~

u : ~ .; 1-0 0 ....1

"' >

"' > c it ....1 ~ z 0 u; a:: 0 1-

12xl01

I I I I I I I I I )I I - -

!- -r-r ~~.-... ._

-·~ I _...

- V' ,.,.......I

-- ,( -- / • -

:.:1 ..,. f•·

!w

10

9

• - -_I

~ --

8

. -1 l I l l 7

20 10 0 30 -10 -20 TEMPERATURE,°F

b. LonCJitudlnal wave velocity v1. temperature ex 101

7

6

5 t•

30 20 10 0 -10 TEMPERATURE 1 °F

d. Torsional wave velocity vs. tem~rature

Specimen Tray Wet Unit Water Symbol Weight Content Number Number*

pcf o/o

SFS-374 t:. • VB-9 119 2.6. 5

SFS-375 ':;] • VB-9 12.3 2.3. 0

SFS~376 c • VB-9 12.5 zo. 5

SFS-377 ):( )( VB-9 12.4 2.1. 5

SFS-378 0 • VB-9 12.3 2.3. 7

*VB( ) mdtcates test beams frozen from top to bottom 1n vertlcal position. Ice lenses oriented normal to longitudinal axis of beam.

NOTES

In graphs a and b solid symbols represent values computed using fundamental longitudinal frequencies. Open symbols rep­resent values computed using_ fundamental flexural frequencies.

In graph e symbols indicate values computP.d using each value of modulus of elasticity, EL and Ef, as shown in ·graph a and a corresponding va]ue of G in graph c.

The curves for Poisson's ratio in graph e were computed from values taken from curves in graphs a and c.

Figure A7. Dynamic elastiC properties of frozen Fairbanks silt vs temperature.

.. Q. 4

> !::: ~ ~ en 3 c .J

"' IL. 0

en 2 :::> .J :::> 0 0 2

iJ

0

2lll01

1-

1-

APPENDIX A 39

u • ~ > ~

u g "' >

"' ~ ~

.J c z 0 :::> ~

(; z 0 .J

~

30 20 10 0 -10 -20 TEMPERATURE, °F

a. Modulus of elasticity vs. temperature( 1)

I I ' ' ' ' u • . =

"' > ~

u

~r" ~.--: ~~

_.)l(y -

g

"' >

"' Jl ~· -> c ~ ·-

12•105

' ' I I I TTTT TT T T T I I ~

t--t- • t-

~--~ I :.__, t-

~,/', t- • t-t- 9 -

r- r/! -r- r t-t- -

t- v: t-

"" .,

10

9

8

t-r-

7 I I I I I I I I

30 20 10 0 -10 -20 TEMPERATURE,°F

b. Lon9itudinGI wave velocity vs. temperature 8lll05

' ' ' ' I I r 1 I I I

~

7

"

I I I

r- "' ___. ~-~-6

t- •• ~J--~ vf<~ t-

} - .J c z 0

;--r-/j

'/ t- -

0 30

wl~ II

:l Q ~ 0.4 c a: en z .0 VI

0.2 VI 0 :l.

0 30

~ a: 0 ~

> 20 10 0 -10 -20

TEMPERATURE. °F

c. Modulus of rigidity vs. temperature

20 10 0 -10 -20 TEMPERATURE. °F

e. Poisson's ratio vs. temperoture(2)

5 t-

~VI ---

~ 4 I I I

30 20 10 0 -10 -20 TEMPERATURE, °F

d. Torsional wave velocity vs. temperature

Specimen Tray Wet Unit Water

Number Symbol Number* Weight Content pcf o/o

SYS-376 0 • VB-~ 1Z.6 z.z.. 9

SYS-377 A • VB-9 130 z.z.. 3

SYS-378 p II VB-9 130 Z.O. I

SYS-379 ~ )I( VB-9 131. . 19.8

SYS-380 v • VB-9 11.6 z.o. z. *VB( ) indicates test beams frozen from top to bottom in vertical

, position. Ice lenses oriented normal to longitudinal axis of beam.

'NOTES

In ·graphs a and b solid symbols represent values computed using fundamental longitudinal frequencies. Open symbols rep­resent values computed using fundamental flexural frequencies.

In graph e symbols indicate values computed using each value of modulus of elasticity, ELand Ef, as shown in graph a and a corresponding value of G in graph c.

The curves for Poisson's ratio in graph e were computed . from values taken from curves in graphs a and c.

Figure AS. Dynamic elastic properties of frozen Yukon silt vs temperature.

40

·;;; 0. 4 -; !::: ~ 1-en

3 <l _J

LIJ

IJ.. 0

en 2 ::::l _J

::::l 0 0 ~

w

0 30 20 10 0 -10

TEMPERATURE, °F

a. Modulus of elasticity vs. temperature< 11

2 X 106

., 0.

-; 1-§ ~ a: IJ.. 0

en ::::l ..J ::::l 0 0

• .,;-.A~ r ~·~ " -, . --· ~

~

... ~ ~

0 30 20 10 0 -10

. TEMPERATURE. °F

c. Modulus of rigidity vs. temperature

wj~ 0.6

::l Q 1- 0.4 <l a:

!'l z 0 en

0.2 (/)

0 Cl.

0 30 10 0 -10

TEMPERATURE, °F

e. Poisson's ratio vs. temperoture< 21

APPENDIX A

-20

--

-

--

-20

-20

10 X 103 )(, /·.,

u Q)

:$ 9

>-!::: u 9 ~ 8

LIJ

~ 31:

;l 7 z 0 ::::l 1-<:5 z 0 6 ..J.

5

f-f-t-

-~

.... • f-

/111.../

~ f- ·V f-f-f-

f- f. . t-f- A t-

30

•. I .. ,... • I I I

~/ ~-.

•

v -...

-_;

-

-

--

-

I

20 10 0 -10 -20 TEMPERATURE,°F

b. longitudinal wave velocity vs. temperature 6 X 103

u :l: ' -;

5 !::: u 0 . ..J. w > ILl 4 > c 3t ..J <l z 0 3 u; a: 0 1-

> 2

f- )(. ~ j( I

f-

~----~..-----;, ~ t-

• .......,

• v • f-

~· f- r-•:

f- .,;~ .-

f-r- • -

r-

30 20 10 0 -10 -20 TEMPERATURE, °F

d. Torsional wove velocity vs. temp~roture

Specimen Tray Wet Unit Water Symbol Weight Content Number Nwnber*

ocf o/o SBC-307 0 • HB-11 100 54,1

SBC-307A ll. • HB-11 110 37. 2

SBC-308 If " HB-11 88 85.0

SBC-309 ~ )I( HB-11 95 60.8

SBC-309A 'il • HB-11 90 73.8

SBC-310 c • HB-11 107- 41. 6

*HB( ) indicates test beams frozen from top to bottom in horizon­tal position. Ice lenses oriented parallel to longitudinal axis of beam. in a horizontal plane.

NOTES

In graphs a and b solid symbols represent values computed using fundamental longitudinal frequencies. Open symbols rep­resent values computed using fundamental flexural frequencies.

In graph e symbols indicate values computed using each value of modulus of elasticity, ELand Ef• as shown in graph a and a corresponding value of G in graph c_. _. .

The curves for Poisson's ratio in graph e were computed from values taken from curves in graphs a and c.

· Figure A9. Dynamic elas~ic properties of frozen Boston blue clay vs temperature.

APPENDIX A 41

"' a.

>­~

~ ~ (f)

<l ...J w

1>.. 0

Vl ::::> ...J ::::> 0 0 ~

w

o~~-3Lo-LJ-~~2~oJ-~L-~,o~~-LJ-~o-L~~~--,~o~~~-~2~o

TEMPERATURE. °F

Vl ::::> ...J ::::> 0 0 ~

I

,;

0

0.8

wl~ 0.6

:::1._

Q ~ 0.4 <l a::

Vl

z 0 (f)

0.2 (f)

0 n.

0

a. Modulus of elasticity vs. temperatur~1 1 l

X I I

/I&

~-~ ~---"1-.Jf

-rJ ~-~_,. .. -

30 20 10 o· -10 -20 TE.MPERATURE. °F

c. Modulus of rigidity vs temperature

I I I I I I

---. -...

• -

-A

;. • A -~· .. I- " v y)l( -

~---!--- ~

r-- • )I( ):{ -)I( -.fJ • -

6. .. • ~ p • -6. p" ____

---\1 F---- 0 p ):{

0

~ 0 \1~ -

~ ~ p ):{ -

~ ):{ If -

30 20 10 0 -10 -20

TEMPERATURE. °F

e. Po1sson's ratio vs. temperature(Z)

u • ~ >-!:::: (.)

g w > w ~ ·~

...J <( z 0 ::::> ~

~ z .0 ...J

2 ~.~~30~~-L~2~o-L~~~~o~~-L~~o-L~~~~~-L~

TEMPERATURE ,°F

>­~ 3 u 0 ...J lL1 >

~ 2 <(

~

...J <l z Q Vl a: 0 ~

I

0

·b. longitudinal wave velocity vs. temperature

I I r I I

• ~ f-

~---.-...-·· ·~

~~,..-.....

>/~ ,. /,.

f- "' q -

-

-

_l

30 20 10 0 -10 -20 TEMPERATURE. °F

d. Torsiona I wave velocity vs. temperature

Specimen Tray Wet Unit Water

Symbol Weight Content Number Number* pcf o/o

SFFC-366 0 • HB-11 Ill 33. 5

SFFC-366A 6. ... HB-11 108 33.4

SFFC-367 p " HB-11 l 09 35. 6

SFFC-368 ):!; )I( HB-ll 108 34. 5

SFFC-369 \1 • HB-11 I 08 35. 3

*HB( ) indicates test beams frozen from top to bottom in horizon­tal position. Ice lenses oriented parallel to longitudinal axis of beam •. in a horizontal plane.

NOTES

In graphs a and b solid symbols represent values computed using fundamental longitudinal frequencies. Open symbols rep­

. resent values computed using fundamental flexural frequencies.

In graph e symbols indicate values computed using each value of modulus of elasticity, ELand Ef, as shown in graph a and a corresponding value of Gin graph c. .

The curves for Poisson's ratio in graph e were co~puted from values taken from curves in graphs a and c.

Figure AlO. Dynamic elastic properties of frozen Fargo clay ~s temperature.

42

• 2 Q.

; !:::: ~ .... (I)

'"' _J

ILl

... 0

(I)

~

...J ~

0 0 ::lE

w

0

., a.

.; 1-0 ~ a:: LL 0

en ~

..J ::::> 0 0 ~

~

0

0.8

wj~ 0.6

::1.

2 1- 0.4 <[

0::

en z 0 en

0.2 en 0 Q

0

APPENDIX A

a a, I I I I I I I I I I I -.- I

&10 •

I

• ~A Et (FLEXURAL} 0 .--~~___::-:.::

----- --::-4-.--~ __.o-1,~ • -r~ EL (LONGITUDINAL l

-

-

-I L .l

30 20 10 0 -10 -20 TEMPERATURE, •F

a. Modulus of elasticity vs. temperature(!)

I I I I I

... • -·-r----a .•.

·-·--·11 ..

30 20 10 0 -10 -20 TEMPERATURE. °F

c. Modulus of rigidity vs. temperature

I I -

--

-. -

.:. ~

~----------

---~ A 0

0. -- 0~

~ r-D.~ ---tf. ---I'-

~ • 1----r-....

/ .. / -

• -~

30 20 10 0 -10 -20

TEMPe-RATURE. °F

e. Poisson's ratio vs. temperoture 121

0 .. ~

; I-

0 0 ..J w > ILl

~ • _J .. z 0 ::::> .... (; z 0 _J

-;;

0

: ' ; ~ 0 0 ..J 1&.1 > ILl > .. • _J .. z 0 u; a:: Oo 1-

>

1-1-1-

9 ~103 ---- ---- ..... /

• v r 1-

L 1- •

8

r v. 1-

/ 1-

1-r------ 1-··· .• v

1--- / ---- -·------·-

1- ·;

7 • }() 20 10 0 -10,

TEMPERATURE ,°F

b. lon4Jitudinal wave velocity vs. temperature 6KI0l

---

·-·

...

-20

,...,I I I I I I I I I I I I I T- r- IITI.

-

f-------· 1------~

5

_;.--•--·----· -- 1----

--· . ~ 1-

1-~ ..

1-.... .....

4 _1_ _L

-20 30 20 10 0 -10

TEMPERATURE. °F

· d. Torsional wave velocity vs. temperature

--~1 Specimen Tray

Wet Unit Water Symbol Weight Co'"""' Number Number*

pcf "!o .

SAP-148 D. • VB-2 62 3 71

SAP-150 • HB-3 71 l80 '------·

*HB( ) indicates test beams frozen from top to bottom in horizon­tal position. Ice lenses oriented par·allel to longitudinal axis of beam, in a horizontal plane. ·

*VB( ) indicates test beams frozen frorn top to bottom in vertical position. Ice lenses oriented normal to longitudinal :,xis uf beam.

NOTES

In graphs a and b solid symbols represent values computr·d using fundamental longitudinal frequencies. Open symbols r<'p­resent values co1nputed us_ing ~undan1ental flexural fre-quencies.

In graph e symbols indicate values comf)uted using each valut: of modulus of elasticity, ELand Ef, as shown in graph a and a cor-re~~rondtng value of Gin graph c.

The curve~ for Poisson's ratio in graph e were computtJd from values taken from c.1rves in graphs a and c.

Figure All. Dynamic elastic properties of frozen Alaska peat vs· temperature.

.,. a.

>­f-

u f­V)

<l ....J ILl

l.l. 0

V)

::::> ....J ::::> 0 0 ~

APPENDIX A

0 . ~

>­f-(.)

0 ....J

12x IO:s I· I•

--~

I -

-

I I ! E

.... 41• ~·~.,-,r'

~ 10

I&J

~ ~

....J <l 9 z 0 ::::> l-ei z 3 8

-

f-

43

I I I I. r ~ r I' " I -

I :

-•l ---J-J -·-· ~- ~ )I(

o~~~~~~~~~~~~~~~~~-~-~~~~~~~~-

30 w 0 -20 _I .L l_ I 7

20 10 0 30 -10 -20

en a.

~ f-0 C)"

a:: IJ... 0

V)

::::> ....J ::::> 0 0 ::f

C)

0

wl~ 0.6

:::t

'2 f- 0.4 <l a:

~ z 0 V)

0.2 rn 6 a.

TEMPERATUR-E. °F

a. Modulus of elasticity vs. temperature1 1 l

I I I I I I I ...,--,-

I

- 0

: - ...... -

; ~ 7 u 0 ....J ~

> ILl 6 >

- <l ~

- ....J <l - z -~ .... -. ~--·.,Jil -..-·· _-_.,. -- -0 5 u;· a::

- 0 1-

- > 4

30 20 10 0 -10 -20 TEMPERATURE. °F

c. MQdulus of rigidity vs. temperature

20 10 0 -20 TEMPERATURE, °F

e. Poisson's ratio vr,. t.,.,.,_roture(Zl

TEMPERATURE,°F

b. Longitudinal wave velocity vs. temperature

I ·r I

f-

--

f-

-~, ~"· -·""' 1- -

f-.. -··

f-

l

30 20 10 0 -ro -20 TEMPERATURE. °F

d. Torsional wave velocity vs. temperature

Sp..,.cinu:n Tray Wet Unit

Number Symbol Number):C Weight pcf

SI-670 6 "' HB-10 56

SI-671 a • HB-10 55

SI-67Z 0 • HB-10 56

SI-673 f1 If HB-10 55

SI-674 )l; )I( HB-10 55

SI-675 \1 ... HB-10 55

*HB( ) Indicates test beams frozen from top to bottom in horizon­tal position. Ice lenses oriented parallel to longitudinal axis of beam, in a horizontal plane.

NOTES

. In graphs a and b solid symbols represent values computed using fundamental longitudinal frequencies. Open sym·bols rep­resent values computed using fundamental flexural frequencies.

In graph e symbols indicate values computed using each value of modulus of elasticity, ELand Ef, as shown in graph a and a corresponding value of Gin graph c.

The curves for Poisson's ratio in graph e were computed · from values taken from curves in graphs a and c.

Figure A12. Dynamic elastic properties of artificially frozen ice (tray HB-10) vs temperature.

44 APPENDIX A

-~ 2xl0 6 Q.

> t: (.)

1-U) <(

...J w 1.1.. 0

U)

:::> ...J :::> 0 0 ~

u.i

o~~~3o~~~~~~L...J~~~o~~~~o~~~~~-L~~

"' Q.

')-

1-

9 ~ a:: 1.1.. 0

U)

:::> ...J :::> 0 0 ~

,;

2 X 106

I

0

TEMPERATURE, °F

a. Modulus of elasticity vs. temperature< 1 l

I

~~ ·-· .. -,...--~ ...... -~·--- ~· ·~· .. .. ~ ..

30 20 10 0 -10

TEMPERATURE' °F

c. Modulus of rigidity vs. temperature

0.8 T. TTT T I I I I

wj~ 0.6

:l )I( )I( •• )I( )II • ... •

-!1~-,.):(. ~ . ~ • rJ )I(

f-•--... o.:! P--r~-~--w- ~ -'0"

.'\1 • '\1 ~ r-....l2.~- •-'JL • <;; ~ .. .. ~

t::. t::. t. t::. t::. t::. t::. t::.

Q 1- 0.4 <( a:: U)

z 0 U)

0.2 U)

6 Q.

0 30 20 10 0 -10

TEMPERATURE, °F

e. Poisson's ratio vs. temperature12 l

-.--.-

----

-20

-

---

---

---

-20

u •

---

T T r T T

~ 12 -

>-t: (.) 0 ...J w > w ~ J:

I

ci 10 z 0 :::> 1-<:5 z 3 9

8

----

f-•

~

f-

f-

f-

f-.

f-.

~

f-. _l _l

~·J •

~-·-a. )I -~-

.)(_~.

-·~· . .

~-·- II ..

• II.

I

30 20 10 0 -10 -20 TEMPERATURE ,°F

b. Longitudinal wave velocity vs. temperature 7x 103

u

: ......

> t: 6 (.)

0 ...J l4J > w 5 > <[

3t

...J <(

z 0 4 u; a:: 0 1-

> 3

T T I I I I I I r 1 r I r· r r r r --

-

: ... .---- -:~J !-~ -~.: .. -~~~~

~ J-

-

f- -

-f:'

~ .

~ I

30 20 10 0 -10 -20

TEMPERATURE' °F d. Torsional· wove velocity vs. temperature

Tray Wet Unit

Specimen Syrpbol Weight Number Number* pcf

SI-664 c • VB-5 54

SI-665 t::. • VB-5 55

SI- 667 X( )I( VB-5 56

SI-668 '\1 • VB-5 56

~.

*VB( ) indicates' test beams frozen frpm top to bottom in vertical position. Ice lenses oriented· normal to longitudinal axis of beam.

NOTE::;

In ~raphs ·a 'and b solid symbols repr'esent values computed using fundamental longitudinal frequencies. Open sym,bols ~ep­resent values computed using fundamental flexural frequenCies.

In graph e symbols indicate values computed usin!l each value of modulus of elasticity, ELand Ef, as shown 1n graph a and a corresponding value of Gin graph c.

The curves for Poisson's ratio in. graph e were computed from values taken from curves in graphs a and c.

. Figure A13. Dynamic elastic properties of artificially frozen ice (tray _vB-5) vs temperature.

.. Q.

.; !::: u ..... U)

<l ...J w

"'-0

U)

::r ...J ::r 0 0 ~

w

"' Q.

2

0

I

0

0.5

wl~ 0.4

::::1..

2 ..... 0.3 <l 0::

(f)

z 0 (f)

0.2 (f)

6 CL

0.1

L.

I

APPENDIX A 45

I I I I I I I T T

EL (LONGITUDINAL l -

~=~--=~ ___ oW t-=i=--oe-:-c

_ Et (FLEXURAL)

---

I

30 20 10 0 -10 -20

TEMPERATURE, °F

a. Modulus of elasticity vs. temperature< 1 l

I I I I

-· -•r-----•-~- •

.I

30 20 10 0 -10 -20

TEMPERATURE. °F

c. Modulus of rigidity vs. temperature

I I T I T. T

-

~·--·--·-..__. , -_.Q.-.-

--o-o __..2--

--:::.s;r. c -0

I

..., -<

-1

30 20 10 0 -10 -20

TEMPERATURE. °F

e. Poisson's ratio vs. temperoture 121

u . ~ 12

>--!::: u g w > w ~ ~

I

;;i 10 z 0 ::r ..... <:5 z 0 9 ...J

8

u

: :: .;

7 !::: u 0 ...J UJ > w 6 -~ ~

...J <l z 2 5 U) Q: 0 1--

> 4

[ [ TT ----

~

r-..... .....

- -·-· - -··--·· -·-f.--•

- -

- ---< -1

r- -1 I I I I I I I I I

30 20 10 0 -10 -20 TEMPERATURE ,°F

b. Longitudinal wove velocity vs. temperature

I r -T [ I I r r r I -, r T T f.- -

..... f-

""'

·-·-· ---·--· ·-

I I I I I I

30 20 10 0 -10 -20

TEMPERATURE. °F I

d. Torsional wove velocity vs. temperature

Specimen Ice Length, in.

Cross-sectional Weight, Density, area, sq in. lb lb/cu. in. No. Type

SI-(P) Clear 9. 95 2.24 0.725 0.0326

Horizontal Beam (Optic AxPs of crystals oriented no'rmal to longi­tudinal axis of beam.)

'NOTES

In graphs a and b solid symbols represent values computed using fundamental longitudinal frequencies. Open symbols rep­resent values computed using fundamental flexural frequencies.

In graph e symbols indicate values computed using e.Cch value of modulus of elasticity, ELand Ef' as shown in graph a and a cor responding value of G in graph c.

The curves for Poisson's ratio in graph e were computed from values taken from curves in graphs a and c .

Figure A14. Dynamic elastic propertiesof Portage Lake (natural) ice vs temperature.

Unclassified 1

Security Claaaification

DOCUMENT CONTROL DATA - R & D (Seciirlt'f claasHicetlon of IItle, ~of obatrect and iride•lnl-ototfGft muat h ent~red'when the overeU report Is ·~l•••llled) .

I. ORIGINATING ACTIV11\' (Co~,. cudiM) za. I'EPORT SECURITY CLASSIFICATION

Cold Regions Research & Engin~ering Laboratory U. So Arn1y Terrestrial Sciences Center Hanovera New Hampshire

Unclassified ab. Gi"OUP

t. R_IE~OIIIT TITLI:

LABORATORY DETERMINATION OF THE DYNAMIC.MODULI OF FROZEN SOILS AND OF ICE

"· DlliCIIIUfDTIVK NOTIEa (Type of ropottt _,d lnclual .. e •tea)

Research Repo.rt · I· AU THORCII (j/tlr~l ...... , middle lnltlel, leet ,.._)

Chester W. Kaplar

e. RL!tPO .. T DATil 7& TOTAL NO. OP' PAGES

January .1969 48 84!1. CONTRACT 011! Q .. ANT NO. 8411. CRI81NATOR"I Jn:POR"f NUIInlllR(a)

b. PRO.JI:CT NO. -Research Report 163

c.

d.

DA Task 1 T062112Al300 1 ... OTHIIR REPORT NOIII (Any other nUIIIbeN .lhel mey be eaal .. ed ,.,. NJIOrf)

This document has been approved for public release a'nd sale; its distribution is unlimited

••· suPPI'Lll~oelllNTAillv NoT;r;s Co_ sponsored by u. a~oNaoRINe MILITA~~tv Acnv•Tv

Office,· Chief of Engineers , Cold Regions Research and Engineering Laboratory

Directorate of Military Construction U.S. Army Terrestrial Sciences Center ~p,~iin~~:r;};t~~}~\';,i~i~~an~h Hanover, New Hampshire

11. A.IT.ACT ~ ~

This report presents a summary of results of labor~tory investigations of frozen soils and ice to determine the elastic moduli by the dynamic (sonic) method. The elastic moduli were indirectly obtained by measuring the fundamental resonant frequencies of flexural,. .longitudinal, and torsional vibrations induced in prismatic beams by electromagnetic means. Vibration tests were performed on a total of 56 specimens representing 12 different materials (8 natural soil types, ranging from coarse-grained to fine-grained; Z blended soils; a natural peat; laboratory-frozen ice and natural lake ice, a.t temperatures ranging from approximately +32F to -lOF). Elastic wave velocities (longitudinal and torsional) were computed for each material in· the range of test temperatures studied. All soils were saturated or were close to saturation. The dynamic moduli of elasticity of the frozen soils were found to increase with a decrease in temperature, the greatest rate of increase occurring between +32F and +20F. Coarse granular soils gave the hig~est values and clays the lowest in the ratio of more than 4 to 1. Dynamic Young's modulus, E, computed from flexural vibrations was usually lower than dynamic E computed from longitudinal vibrations. Average values of dynamic Poisson's ratio for all soil types computed from average values of E and G (longitudinal vibrations) ranged from 0. 26 to. 0. 38. Values of Poisson's ratio for the various soil types did not conform to any logical pattern related to temperature or soil type. The dynamic moduli of elasticity of ice showed only slight dependence on temperature, and test values were more consistent than those of the soils. Natural lake ice was

(Cont 1 d)

~------------------------~~~~·'· ... ------------~~--~----~ DD ,_ 14 73 ... ~LAC •• 00 ~O-.M t•71, t JAN •• WN C .. , ..ev •• o•eo ... •Tc ~o,. A,...Y u••· Unclassified

security cleulfication

Unclassrfit·d Security Classification

14.

Frozen soil Ice

KEY •OROS

Dynarnic moduli of Plasticity Vi brat ion Elastic wave veloc1ty Young's rnodulns Poisson's ratio

Abst r·act (Coi1t'd)

least temperature dependeni and gavf~ the rnost consistent results. Dyna1nic moduli of ice E (longitudinal vibration) and G co1npar~d closely with values reported by other investigators. Average values of Poisson's ratio for ice wcr·e r e a s on a b 1 e but 1 e s s c on s i s t e 11 t , r a 11 g i 11 g f r· o rn 0. 30 to 0. 41.

LINK A LtNK 8 LINK C

~01. f. . .. ROLE .WT ROLE WT

Ullclass)fu:~d

~euraty Cl .. alflcation