Methods of determining creep, long-term strength and ...

Publisher’s version / Version de l'éditeur:

Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la

première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à [email protected].

Questions? Contact the NRC Publications Archive team at

[email protected]. If you wish to email the authors directly, please see the first page of the publication for their contact information.

https://publications-cnrc.canada.ca/fra/droits

L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site

LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.

Technical Translation (National Research Council of Canada), 1969

READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.

https://nrc-publications.canada.ca/eng/copyright

NRC Publications Archive Record / Notice des Archives des publications du CNRC :https://nrc-publications.canada.ca/eng/view/object/?id=14d51ca2-bade-40d0-a9e9-0bb7de42437b

https://publications-cnrc.canada.ca/fra/voir/objet/?id=14d51ca2-bade-40d0-a9e9-0bb7de42437b

NRC Publications ArchiveArchives des publications du CNRC

For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous.

https://doi.org/10.4224/20386669

Access and use of this website and the material on it are subject to the Terms and Conditions set forth at

Methods of determining creep, long-term strength and compressibility

characteristics of frozen soilsVyalov, S. S.; Gorodetskii, S. E.; Ermakov, V. F.; Zatsarnaya, A. G.; Pekarskaya, N. K.; National Research Council of Canada. Division of Building Research

NRCTT ｾ 1364

NATIONAL RESEARCH COUNCIL OF CANADA

TECHNICAL TRANSLATION 1364

NRCTT -1364

METHODS OF DETERMINING CREEP, LONG - TERM STRENGTH

AND COMPRESSIBILITY CHARACTERISTICS OF FROZEN SOILS

BY

S. S. VYALOV ET AL.

STATE COMMITTEE OF THE COUNCIL OF MINISTERS CU. S. s. R)

FOR CONSTRUCTION

PUBLISHER

NAUKA. MOSCOW, 1966

TRANSLATED BY

H. R. HAYES AND V. POPPE

THIS IS THE ONE HUNDRED AND EIGHTIETH OF THE SERIES OF TRANSLATIONS

PREPARED FOR THE DIVISION OF BUILDING RESEARCH

OTTAWA

1969

PREFACE

The study of frozen ground mechanics and its application

in engineering practice has been more widely developed in the

Soviet Union than elsewhere. Prominent among literature in

this field are compilations or manuals describing laboratory

or field procedures to be carried out prior to engineering

construction.

The work translated here describes laboratory procedures

for testing of strength and deformation properties of frozen

soil to be carried out in connection with foundation design.

The editor Dr. S.S. Vyalov, who is also one of the contribu

tors, is one of the leading Soviet scientists in this field.

The translation has been undertaken because of the growing

interest in North America in construction procedures on frozen

ground.

The Division wishes to record its thanks to Mr. H.R. Hayes

and Mr. V. Poppe, Tl'anslations Section, National Research Council,

for translating this paper, to Mr. P.J. Williams of this

Division and Dr. H.B. Poorooshasb, University of Waterloo, who

checked the translation.

Ottawa

June, 1969

R.F. Legget

Director

Title:

Authors:

Publisher:

NATIONAL RESEARCH COUNCIL OF CANADA

Technical Translation 1364

Methods of determining creep, long-term strength and compressibility characteristics of frozen soils

(Metodika opredeleniya kharakteristik polzuchesti, dlitel'noiprochnosti i szhimaemosti merzlykh gruntov)

S.S. Vyalov, S.E. Gorodetskii, V.F. Ermakov, A.G. Zatsarnayaand N.K. Pekarskaya

Research Institute of Foundations and Underground Structures,Academy of Science U.S.S.R., State Committee of the Councilof Ministers (U.S.S.R.) for Construction

(Nauchno-Issledovatel'skii Institut Osnovanii i PodzemnykhSooruzhenii, Akademiya Nauk SSSR, Gosstroi SSSR)

Nauka, Moscow, 1966

Translators: H.R. Hayes and V. Poppe, Translations Section, National ScienceLibrary

The aim of this work is to provide a unified method of

determining the Ions-term strength, creep and compressibility of

frozen soils. The authors examine the fundamentals of frozen

soil rheology, methods of testing frozen soils for long-term

strength, creep and compressibility, also practical methods of

processing test data and definitions of propprties required in

the calculation of frozen soils in terms of lirniting states.

This book is intended for workers in industrial and scientific

research laboratories engaged in the study of the mechanical pro

perties of frozen soils.

General Editor

Professor S.S. Vyalov,

D.Sc. (Eng.)

TABLE OF CONTENTS

Foreward. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

I. General mechanism of frozen soil deformation. 8Rheological processes in frozen ground..................... 8Deformation pat terns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Compressibility of frozen soils.. 15Long-term strength... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

II. General requirements for tests. 23Preparation of specimens ;........... 23Instrument and test condition requirements. '" 24

III. Methods of creep and long-term strength testing with uniaxialcompression , .. .. 26

Instruments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Rapid load action tests.................................... 27Long-term load action tests................................ 29Processing experimental data and determining creep

characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Determining long-term strength characteristics...... 40Simplified method of determining creep characteristics..... 42Processing experimental data and determining creep1 characteristics of long-term strength............. . . . . . . . 44

IV. Methods for long-term strength testing at shear under creepcondi tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Ins trumentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Tests at rapid load action................................. 47Tests at long-term load action.......... 49Processing experimental data and determining

characteristics of long-term strength. 52

V. Methods for compression testing. 55Instrumentation " 55Testing procedure.......................................... 56Processing experimental data and determining compression

characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

VI. Simplified method for creep and long-term strength testingwith the aid of a dynamometric device :........ 65

Description of the method.................................. 65Instrumentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Experimental methods...................... . . . . . . . . . . . . . . . . . 72Processing experimental data and determining characteristics

of creep and long-term strength.......................... 75

Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

References '" , '" .. 93

Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

-4-

METHODS OF DETERMINING CREEP, LONG-TERM STRENGTH

AND COMPRESSIBILITY CHARACTERISTICS OF FROZEN SOILS

Foreword

Frozen soils, because of the presence in them of ice and unfrozen water,

possess clearly defined rheological* properties - the capacity to develop

imperceptibly slow deformations (creep) and to lose strength during prolonged

load action. Volumetric consolidation deformations also develop in plastic

frozen soils. These characteristics must be taken into account when

studying the mechanical properties of frozen soils and in evaluating frozen

soils to be used as building foundations, media in which buildings are

erected, and construction material.

Frozen soils should be evaluated in terms of two limiting states

strength and deformation.

The evaluation of frozen soils for strength (bearing capacity) consists

in determining the load at which, during a given period of time (the useful

life of the bUilding), a state of limiting equilibrium occurs in the soil;

this is the ultimate load, and if it is exceeded the soil fails or loses

its strength. The methods of the limiting equilibrium theory (the theory

of plasticity) are used for the calculations, while allowing for the varia

bility of strength characteristics in time. Methods of calculating the

bearing capacity of frozen soils used for building foundations have already

been dealt with in published literature(1,2), as also have methods of eva

luating frozen soils used as protective enclosures in sinking excavations

by the artificial freezing method(3).

When evaluating frozen soils for deformations, the load calculated is

that at which deformation during a given period reaches the maximum permiss

ible for the structure. Calculations are made by methods employed in the

creep theory, for which it is necessary to know the deformation growth

pattern and the deformation characteristics of the frozen soil.

Methods of calculating for deformations in protective enclosures of

frozen soils are given in reference 3.

Methods of evaluating frozen soil foundations for deformation are not

yet sufficiently well established and for this reason they are at present

restricted to the calculation of ultimately stabilized settlements. For

these calculations the method generally accepted in soil mechanics is used,

but allowing for the variability of the compressibility characteristics in

relation to load and soil temperature, which vary with depth(l). The bearing

* Rheology - the science of the deformation and flow of solids.

-5-

capacity (strength) of the foundations of industrial and civic buildings

composed of hard-frozen soils are evaluated on the basis of long-term

strength characteristics.

All the above calculations pertain to those cases in which it is inten-

ded to maintain the soils used for building foundations, media or material

in a frozen state. In addition it is necessary to take into consideration

the temperature regime of the frozen soils, since their mechanical properties

depend largely on this factor. In view of the complexity of solving problems

of strength and creep at a temperature that varies in space and time (which

is usually the case in actual conditions), it is permissible to employ

approximation methods: computing the effect of temperature change in time

by introducing into the calculation the dependence of the deformability and

strength characteristics on the temperature of the frozen soil, and computing

the effect of temperature change in space by dividing the given frozen mass

into a series of zones with averaged temperature values, i.e. reduce the

problem to evaluating a mass with non-uniform characteristics. In order to

make these calculations, it is necessary to know: for deformation calcula

tions, the relation between stress and deformation and the pattern of deve

lopment in time, as well as the compressibility characteristics; and for

strength calculations, the strength characteristics (at compression and

shear) and their variation in time. Determination of all these character

istics must take into account their relationship to the temperature of the

frozen soil.

The aim of the present work is to standardize the methods of determining

the characteristics of long-term strength, creep and compressibility under

laboratory conditions.

In the first section, which is of a general nature, the basic patterns

of creep and long-term strength of frozen soils are examined.

These patterns were revealed as a result of earlier research. The

research data and validation of the patterns have been dealt with in publi

shed works(l-lO). These works also provide a more detailed background to

questions relating to the theory of frozen soil rheology and its practical

application.

The main sections of the present work are devoted to the testing of

frozen soils for long-term strength, creep and compressibility, to practical

methods of processing experimental data and to the determination of calcu

lated characteristics.

The rheological patterns and the methods of establishing them set forth

in this work are also valid in principle for non-frozen clay soils.

The procedures were worked out on the basis of research conducted by

the former V.A. Obruchev Permafrost Institute, Permafrost Department of the

Moscow State University, and the Permafrost Institute, Siberian Division

-6-

of the Academy of Sciences U.S.S.R.

The ideal method of determining the strength and deformability charac

teristics of frozen soils is to test for creep in the presence of a complex

stress state, e.g. triaxial compression, or distortion and compression,

which permits the invariant relation between all the stress and deformation

components and time to be determined. However, these methods and the

necessary apparatus are still in the ､･ｶ･ｾｯｰｭ･ｮｴ｡ｬ stage. Therefore, in the

present work we shall examine test procedures for the simplest forms of

stress state, employing standard equipment for testing thawed soils and

rock. The instruments are modified slightly for testing frozen soils. Here,

of course, we shall have to contend with the well-known defects of these

instruments, partiCUlarly of the instruments used for shear tests.

The proposed ｬｯｮｾＭｴ･ｲｭ strength and creep test procedures apply to

uniaxial compressions and shear tests. The first of these provides the

basis for ･ｳｴ｡｢ｬｩｳｨｩｮｾ the characteristics and pattern of deformability

used for evaluating frozen soils with respect to deformation (creep) and

for determining the characteristics of long-term strength at compression,

which may be used for evaluating the strength of frozen clay soils (which

do not p o s s e s s "internal friction"). Shear tests enable us to determine the

cohesive forces which vary in time and the "internal friction", both of

which are needed to calculate the strength (bearing capacity) of frozen

sandy, sandy silt and silty clay soils.

Special attention is given to a simplified method of testing by means

of a dynamometric instrument. Since this instrument is new, a diagram,

description and brief summary of the theoretical principles of the method

are ｾｩｶ･ｮ in the text.

Another simplified method of determining the characteristics of long

term ｳｴｲ･ｮｾｴｨ which can be recommended is N.A. Tsytovich's method of testing

by ball stamp depression. The relevant test procedures are given detailed

treatment in the cited works(1,2,7,lO,11).

A special section of this work is devoted to compressibility tests of

frozen soils. It is necessary to conduct these tests in order to detErmine

the compressibility characteristics used in calculating the ultimate settle

ment of the foundations of buildings erected on frozen plastic soils.

The selection of the form of testing is governed by evaluation require

ments. Here we should take into consideration the fact that the calculations

and tests set forth in this work are not intended to meet quantity or bulk

requirements, but are for use in the planning of particularly important

structures and structures for which no frozen soil parameters have been

given in standard specifications. Finally, the indicated tests may be

applied in the investigation of the mechanical properties of frozen soils

-7-

for research purposes.

This booklet was compiled at the Permafrost Laboratory, Research

Institute of Foundation Soils and Underground Structures (formerly the

V.A. Obruchev Institute of Permafrost Studies) by a group of authors:

S.S. Vyalov (Section I), N.K. Pekarskaya (Sections II and IV), S.E. Gorodet

skii (Section III), A.G. Zatsarnaya (Section V), S.S. Vyalov and V.F. Erma

kov (Section VI) with the cooperation of E.P. Shusherina (Moscow State

University). The work was carried out under the guidance of Professor S.S.

Vyalov, D.Sc. (Eng.).

Observations and wishes expressed by organizations and individual

specialists have been taken into consideration in the compilation of the

text. To these the authors convey their sincere gratitude.

-8-

I. GENERAL MECHANISM OF FROZEN SOIL DEFORMATION

Rheological Processes in Frozen Ground

Stresses are divided into normal cr, which act perpendicularly to a

ｾｩｶ･ｮ section, and tangential (shear) T, which act parallel to the section.

Deformations are measured in relative units and are divided into relative

linear (relative elongations) E and relative angular (relative shears) y.

The relationships examined below are written to conform with components cr

and E, but they remain valid also for components T and y with the appropriate

changes in the values of the parameters in the formulae.

Deformations are either elastic, which recover when the load has been

removed (reversible), or plastic, which do not recover when the load has

been removed (non-reversible).

Depending on the nature of the relationship between stress and defor

mation, distinction is made between linear deformations, which are directly

proportional to the stress, and non-linear deformations related to the

stress in other ways.

Depending on the rate of development of the deformation process, defor

mations are regarded as either instantaneous, which occur at the speed of

sound, or deformations which develop over a period of time, i.e. viscous.

Instantaneous and slow deformations may be partly reversible (elastic)

and partly non-reversible (plastic) and may be linear or non-linear.

A reversible deformation which develops over a period of time is called

a visco-elastic or elastic reaction deformation; it recovers over a period

of time (reversible elastic reaction). A residual plastic deformation which

develops over a period of time is sometimes called a plastic reaction.

Variations in the stress-deformation state of a body in time are called

rheological processes. These processes are manifested in the following

forms:

creep, i.e. the development of a deformation over a period of time, even

when the stress is unchanged (continuing viscosity);

relaxation, i.e. diminution (weakening) of stress required to maintain

constant deformation;

loss of strength, i.e. decrease of that stress level which causes

failure of the body with an increase in the time of bad action.

The creep process may be represented in the form of a graph. For this,

time t is plotted on the graph along the axis of the abscissae, and the

relative deformation E caused by the action of a continuing stress cr, along

the axis of the coordinates. Usually, a series of creep curves is construc

ted, for which tests are carried out on a series of specimens of one type

to which different stresses (constant for a given specimen) are applied.

-9-

Foreach stress there is a corresponding creep curve (Fig. 1).

Deformation of frozen soil is made up of an initial conditionally

instantaneous (Ei n i t)

deformation (Fig. 2a, section OA) which occurs imme

diately after the application of a load, and a deformation which develops

over a period of time E(t) (sections AB and AD)

E = Ei n i t

+ E(t). (1)

The process of development of slow deformations includes:

the first stage of creep, or the stage of attenuating (irregular) creep

(Eat) with decreasing rates of d e f'o r-m.t t.Lon (Fig. 2a, section AB);

the second stage of creep, or the stage of visco-plastic flow (steady

state creep) Ef

at a more or less steady rate of deformation (section BC);

the third stage of creep, or the stage of progressive flow E at anpr

ever-increasing rate (section CD)*. In tensile stress and ;,hear tests

(when the area of the specimen decreases) this stage always ends in "brittle"

failure for compact frozen soils with a low moisture content or "viscous"

failure (which is accompanied by substantial plastic deformations) for

heavily ice-impregnated, plastic frozen soils. In compression tests (when

the area of the specimen increases) this stage ends in "brittle" failure for

soils of the first type, or in the complete flattening of the sample, without

visibly disturbing its wholeness, for soils of the second type.

The process, which includes all the above-mentioned stages, is called

the process of non-attenuating creep; it develops under fairly large stresses.

At low stress levels the second and third stages of deformation are

practically non-existant, and in this case the entire process is callea

attenuating creep (Fig. 2b). This process takes place at an ever-decreasing

rate of deformation, which either reaches the ultimate, (virtually) stable

value Eu l t'

or develops unrestrictedly, but at a decelerating rate, tending

to zero ("long-lasting creep").

Partial recovery of the deformation takes place when the load is removed

from the specimen at any moment of time (Fig. 3).

An initial virtually instantaneous deformation Ei n i t

(Fig. 3a, section

0-2) recovers immediately on removal of the load (section 3-4), and in this

case the recovery of this deformation may be either full or partial, depen

ding on the magnitude of the load. In the first case, the entire initial

deformation is elastic (Ei n i t

= Eel) and, correspondingly, the initial sec

tor 0-2 of the loading curve is equal to section 3-4 of the unloading curve.

* Editor's note: The length E is apparently erroneously indicated in thepr

original Fig. 2a, and is corrected here.

-10-

In the second case, the initial deformation computed from the elastic Eel

(section 0-1) and the plastic Ep l

(section 1-2) parts: Ei n i t = eel + Ep l'

in which case only Eel (section 3-4 equals section 0-1) recovers.

The initial deformation is called substantially instantaneous because

in practice the loading does not occur "instantaneously", i.e. at the speed

of sound, but occupies a certain length of time.

An attenuating (irreGular) creep deformation recovers over a period of

time only partially (section 4-5 of the curve), i.e. consists of a defor

mation of elastic reaction £el(t) (section 5-6) and of plastic reaction

Epl(t) (segment 5-7).

A deformation with a steady plastic-viscous flow, like one with a pro

gressive flow, is absolutely irreversible.

The total deformation of creep E at any instant of time t consists of

the recovering, i.e. elastic Eel(t) and the residual, i.e. plastic £(t)

parts (Fig. 3b).

( 2 )

These forms of deformation are separated in the event that it is necessary

to study the elastic properties of the soil (for example, in calculating

the short-term effect of loads, and of unloading) and are determined on the

basis of unloading tests.

Deformation Patterns

The main characteristic of the deformative properties of frozen soil

is the relationship between the stress a and the total deformation £ (which

includes the elastic and plastic parts).

The relationship between stress and deformation in conditions where

creep is encountered is determined with regard to the period during which

the load is applied, since for each time t value the magnitude of this

deformation (at one and the same stress) will be different and constantly

increasing. Similarly, in the stress-deformation diagram a series of curves

is obtained, each of which characterizes the relationship between stress and

deformation at a given moment of time t (Fig. 4).

Curve to corresponds to the initial (substantially instantaneous) defor

mations, curve too corresponds to the ultimate, stabilized deformations and

is obtained from long-term tests leading to the stabilization of the defor

mations. The intermediate curves correspond to different instants of the

time of load action. Curves for different t values mayor may not be

similar.

The nature of the stress 0 - total deformations E curves for any given

moment of time t depends on the type of soil (Fig. 4b). Usually these curves

-11-

consist of two sections, the boundary of which is the point of gradient

change N (0). Each section of the curve conforms to definite patterns.

The section ON (where 0 < as) may be linear, deformation being directly

proportional to the stress, or non-linear; in the section NM (where a > 0 )sthe stress usually depends on strain in a non-linear manner.

In order to simplify the calculations, it is sufficient for practical

purposes to assume that the stress-deformation curve for different instants

of time t are mutually similar and that each of them is described by a

single non-linear relationship. Usually an exponential relationship is

assumed and then the interdependence of stress and deformation at any moment

of time t will be expressed by the following equation (which is verified by

experimental data):

ma = A (t)E: ,

where A(t) - deformation coefficient, kg/cm2

;

m<l - hardening coefficient (dimensionless value).

Coefficients A(t) and m are determined experimentally as parameters

of the curves shown in Figure 4. Coefficient m depends to a negligible

degree on soil temperature and time of load action, and may be taken as

constant for a given soil.

Coefficient A(t) depends on the composition of the soil, its temperature

and the time of load action. With accelerated loading, coefficinet A has

a maximum value A = Ai n i t

and is the coefficient of initial deformation, i.e.

corresponds to curve t shown in Figure 4a. With an unlimited, long-termo

load action coefficient A has a minimum value A = Am, being the coefficient

of the ultimate stabilized deformations when the creep process acquires an

attenuating character, or tends to zero if the process is of a non-attenua

ting character.o

Coefficient A may be expressed by the modulus of deformation E = E

having the relationship

( I - m m I-mA(t) = E t)E = E (t)a ,

where E(t) is a quantity which varies in time.

If the parameter m has a value close to unity, coefficient E(t) assumes

the significance of a linear modulus of deformation

A(t) = E(t).

The value of coefficient A(t) may be used in deformation calculations

when calculating for some moment of time t. In this case the value of A(t)

corresponding to the moment of time, determined directly from the stress

deformation graph, is substituted in the calculation. Where it is necessary

to determine the development of deformations over a period of time it is

-12-

necessary to know the deformation rates.

The pattern of change in time t of deformation £ caused by stress 0

which varies in time, may be determined from the equation:

m£ =

o(t) + So(v)K(t-v)dv.

Ai n i t 0

( 4 )

in cm2/kg (force)'hr is the function of creep

mE

At a constant load (0 const) the expression takes the following formt

A 0 + 0 ｾ K(t)dt,init 0

where Ai n i t

is the initial deformation coefficient in kg(force)/cm2

;

m is the hardening coefficient (m<l);

v is a variable of integration;

K(t) _ 1 deEm)- 0 dt

which characterizes the change in the rate of deformation in time. This

function is related to the time variable coefficient of deformation A(t) in

( 6 )

equation (3) in the following way:

K(t) = ｾｦｇＨｾｊThus it is sufficient to determine experimentally either K(t) or A(t).

The first terms in equations (4) and (5) describe initial deformation,

and the second terms, the deformation which develops in time. If the initial

deformation is negligible, which is characteristic for frozen soils, the

first term may be ignored.

Deformation equations differ, depending on which creep theory is

accepted. Equation (4) accords with the non-linear successive theory, which

permits the effect of the previous load variation to be taken into consider

ation. For a constant load 0 = const, this equation, which takes the form

of equation (5), becomes identical to equation (3), if K(t) is expressed in

terms of A(t) in accordance with relation (6),

Le. A(t) = A 1 + ｾｴｋＨｴＩ､ｴＮinit 0

Equations (3) - (5) are correct in the event that the stress-deformation

curves for different moments of time t are mutually similar. However, if

these curves are not mutually similar (which is indicative of dissimilarity

of the creep curves for different stresses 0), or consist of two sections,

the deformation equation will be more complex(1,3). In particular, the

deformation equation may consist of several terms, which reflect different

stages of deformation and which are characterized by creep function K(t)

values.

The form of the creep function K(t) (or the deformation coefficient

A(t) depends on the properties of the frozen soil and is determined from

-13-

creep test data.

The form of function K(t) may differ, depending on the nature of the

deformation process. If the process is attenuating or "long-lasting", this

function is such that where t = 00 its value is zero, but with a non-attenu

ating process it assumes a constant value.

In order to simplify calculations for the majority of frozen soils

(which are checked during tests), we can, within a range of small stress

intervals, assume that

K(t ) = a a-I- t ,ｾ

which corresponds, in accordance with expressions (5) and (6), to the

following value of coefficient A(t) in equation (3)I

A(t)

where

1 + --l.. t aA

i n i tｾ

ｾ｛ｫｧＨｦｏｲｃ･Ｉ . hraJ and a < 1 (dimensionless

cm 2

( 7' )

value) are ｰ｡ｲ｡ｭ･ｴ･ｾｳＬ

( 8 )

(7) or

definable by experiment; Ai n i t

is the initial (where t = 0) value of

coefficient A. In this case it may be found that a depends on the value of

stress 0; the variability of a in relation to 0 indicates dissimilarity of

the creep curves.

Where values of K(t) or A(t), are those given by expressions

(7'), equations (5) or (3) will assume the following form:

£ = ol/m[ 1 + leta] dmAi n i t ｾ

where Ai n i t

is the coefficient of initial deformation; and m < I is the

hardening coefficient.

If the initial deformation £init = 0 is ignored, i.e. if we assume that

Ai n i t

= 00, which is entirely permissible for practical calculations, the

value of parameter A(t) is simplified thus

and the deformation equation (8) takes the simple form:

dm

£ = (ft a]

(7")

(8' )

Equations (8) and (8') are correct for constant stress 0, but they can

also be used in cases where the load increase is slow and uniform.

The effect of the temperature of the frozen soil is accounted for by the

following relationship of parameters Ai n i t

and ｾ in equations (8) and (8')

(parameters m and a do not depend on temperature)

where 8 is the temperature, without the minus sign,

( 9 )

a k kW[kg . hr /cm 2

• deg ]; w[kg/cm 2• deg ]

and k < 1 (dimensionless value) are parameters, definable by experiment,

where k may prove to have a value close to unity.

The expressions in formula (9) are correct only for soil in a frozen

state, i.e. for a temperature 8, not exceeding the thawing temperature of

the soil.

For a constant temperature the data

directly in equations (8) or (8'), which

(10 )E = o (1

(8+U k W

in formula (9) is substituted

assume the form

)

1/ m

+ l ta

w

(10' )or

respectively.

For a temperature which varies in time according to a certain pattern

8(t); the formulae in (9) are substituted in integral equations (4) or (5).

and the law of deformation is derived by integrating these equations.

In addition to (8), the following are other possible forms of defor-

mation equations:

and

(8" )

(8" , )

where parameters Ai n i t,

Ak

(initial and final deformation coefficients) a.

b and a are determined experimentally.

If the initial deformations are disregarded, the l/Ai n i t

terms are left

out of these equations. Equation (8"') reflects the attenuating process of

deformation, where t ｾ 00 deformation assumes the final value € = ｛ｾｊｬＯｾk Ak

Equations (8') and (8") reflect the process of deformation by the so-called

law of secular attenuation, when, where t ｾ 00, the rate of deformation tends

to zero, but the magnitude of the deformation itself tends to infinity.

If a steady visco-plastic flow with an approximately constant speed

(see Fig. 2a, section Be) is the principal phase of deformation, the defor

mation pattern is determined by the following equation

t = K (0-0 ) nf

(11 )

-15-

where E = ｾｾ = const is the constant rate of relative ､ｾｦｯｲｭ｡ｴｩｯｾ in the

stage of steady plastic-viscous flow in l/hr;

a is the applied stress in kg (force)/cm2

;

af

is the maximum stress beyond which there is a constant rate of flow,

in kg (force)/cm 2;

K is the coefficient which characterizes the viscous properties of the

soil, in l/hr (cm 2/kg)n;

n>l is a dimensionless quantity.

Equation (11) may be expressed graphically by a rheoloGical curve

constructed in t - a coordinates (Fig. 5). The curve has a point of change

of gradient B; up to this point the flow develops slowly; beyond it the rate

increases sharply. Roughly speaking, the curve may be considered as a broken

straight line and the law of deformation can be expressed by two linear

equations

Kl Ｈ｡Ｍ｡ｾＩ where a<a f'ｾ p

(12)

t = K2 (a-a f) where a>a f'p P

where a f is the stress beyond which the visco-plastic flow rate increasesp

sharply;

K 1 and K2 are the values inverse to the ratio of viscosity for the first

and second sections of the curves, respectively, in cm 2/hr . kg.

The effect of the frozen soil temperature on the process of steady

visco-plastic flow is taken into account by the temperature dependence of

parameter K in equations (11) and (12)

1

K = U(8+1)q (13)

where 8 is the temperature without the minus sign, in °C; U [hr/degq

(kg/cm 2)n] and q < 1 are experimentally definable parameters.

Where there is a wide range of stresses, deformation may be considered

as the sum of the initial deformation Ei n i t,

the attenuating deformation

Eat and the deformation of steady visco-plastic flow Ef

(14)

where Ei n i t

+ Eat are determined by means of equation (5), in which the

function is assumed to be such as to reflect only the attenuating process

of the deformation; Ef

is determined by equation (11).

Compressibility of Frozen Soils

Under a specific conditions frozen soils posses plastic properties and

when subjected to a load they are capable of becoming compacted over a

period of time without the soil thawing. Such soils are called plastic

frozen, and the settlement of building foundations in such soils should be

-16-

computed with respect to the second limiting state, i.e. in terms of defor

mations with allowance for compressibility (consolidation), determinable by

experimental loads or compression tests. The following characteristics are

typical for plastic-frozen soils.

Medlum- and fine-grained sand,and sandy loam .

Sandy-clayey-silt, clay.

Sandy-clayey silt, clay heavilyimpregnated with ice .

oTemp. C

> -0.3

> -0.5

> -1.5

< -4

Total moisture

content, %

>30

<50

>50

>70

A

h

Compression deformation is made up of the initial deformation which

occurs immediately after the application of a load and deformations which

develop in time. The deformation which develops in time includes the

visco-clastic portion which recovers in time after removal of the load,

and the residual portion (see Fig. 3a). This deformation is always of the

attenuating type.

The relationship between the compression load p and the stabilized

deformation of plastic-frozen soil compression (relative compression) e

is non-linear (Fig. 6). A frozen soil compression curve usually has an

alternating character. Two sections can be distinguished: in the first

section, CB, the curve is convex; in the second, BD, the curve is concave.

A frozen soil compression curve may be represented more simply in the form

of a broken line CA 1A 2 D consisting of three sections. In the pressure inter

val corresponding to sloping sectors CAl and A2D the compressibility of the

frozen soil is negligible, but in the load interval which corresponds more

or less to the steep sector AIA 2 maximum compressibility is noted.

The relationship between load p and relative compression e (compression

relationship) in general is expressed by the formula

(15)

where a (p) is the reduced coefficient of compressibility, which is detero

mined experimentally. It depends on the magnitude of the compressing load,

the type and temperature of the frozen soil, and is expressed in cm 2/kg.

The reduced coefficient of compressibility a is a quantity, inverselyo

proportional to the general modulus of volumetric deformations E , whicho

also depends on the properties of the soil, its temperature and the external

load

where SＲｾＲ

1 - ｬＭｾ is a parameter which depends on the lateral expansion

-17-

(16)

(Poisson) ratio ｾ of the frozen soil.

The ultimate (stabilized) settlement of plastic-frozen foundation soils

is computed in the way as in calculations for thawed soil, but taking into

account (a) the temperature variation of the frozen soil with respect to

the depth of the compressible layer and (b) the dependence of the compress

ibility coefficient a on this temperature and on the magnitude of theo

load. For example, the settlement of an independent foundation, according

to SNiP(12) is determined by the formulan

S = ｾ Pihl

i=l

(17)

layer to depth 2hs'e

ifor each ith-layer

Pi

layer and the esti-

base of the foundation after

equal to the weight of the

i=lthe pressure under the

(actual) pressure p tna

where p = p - p * iso 0

deducting the natural

excavated soil;

hs

is the thickness of the equivalent layer;

zi is the distance from the centre of the given

where Pi is the additional (to the natural) pressure in the centre of the

given ith-layer, determinable by methods commonly employed in soil mechanics;

n is the number of layers into which the depth subject to compression

is divided;

hi is the depth of the ith-layer;

8i

is a dimensionless coefficient dependent on the lateral expansion

(Poisson) ratio of the ith-layer(12);

Eo(i) is the modulus of volumetric deformation of the ith-layer.

The value of the modulus of columetric deformation Eo(i) for each ith

layer into which the foundation layer subject to compression is divided must

be assumed to correspond to the average pressure Pi in this layer and the

estimated soil temperature 8i

of this same layer.

In calculating settlement by the equivalent layer method (Tsytovich's

method), the following formula is used:n

The value of the compressibility coefficient ao i

=

must correspond to the average pressure Pi in the given

mater soil temperature 8i

in the same layer.

* sic. This should read Po = p - Pnat' (Translator).

-18-

Long-term Strength

Strength, in the broad sense of the word, refers to the capacity of a

material to resist f'a i Lu r e and the development of large residual deformations

which distort the shape of the body. In the narrow sense, strength refers

only to failure strength.

The main characteristic of strength is its ultimate value (R, 0 ), i.e.. us

the stress which causes failure of the material. In frozen soils, as in

other visco-plastic materials, this characteristic is a variable quantity

which depends upon the load action time.

In conditions where non-attenuating creep occurs in frozen soil, there

may be three critical states (see Fig. 2a):

First, the onset (at moment of time tf)

of the stage of steady flow at

a constant rate (point B);

Second, the onset (at moment of time t ) of the stage of progressivepI'

flow at an increasing rate of deformation (point e);

Third, soil failure (at moment of time t , point D).p

In terms of strength, the third state, soil failure, should be taken

as the ultimate state. However, in frozen soils SUbjected to plastic

deformation in compression tests (when the area of the working section

remains unchanged), failure may not occur; the failure of the specimen takes

place without its uniform character being disturbed. In this case the

limiting state will be the second state, the onset of progressive flow, since

it leads to loss of rigidity. Insofar as the bearing capacity of the ground

has still not been exhausted during the onset of progressive flow, it is

recommended that the achievement of deformations of a given maximum value

should be accepted as the ultimate state of frozen soils SUbject to plastic

deformation (without failure).

If in testing a series of identical samples at different stresses,

with a constant value for each sample, the process is found to be non

attenuating, the time taken to achieve failure (or transition to the pro

gressive flow stage) and deformations of the given ultimate value varies in

inverse proportion to the stress (see Fig. 1).

The relationship between the stress and the time within which failure

or ultimate deformation occurs characterizes the diminution of strength

(resistance) of frozen soil. This relationship is illustrated graphically

by a long-term strength curve, which is constructed by plotting the failure

stress along the axis of ordinates, and the time within which failure or

ultimate deformation occurs, along the axis of abscissae (Fig. 7).

The following variable quantities, which depend upon the time of load

action are in line with the stated strength characteristics:

-19-

Strength limit, i.e. the stress which causes failure of the frozen soil

in those forms of loading in which this failure is clearly defined;

Conditional strength limit, i.e. the stress at which deformation

reaches a value 50% higher than that of the deformation at which the pro

gressive flow stage began

€ 1.5€·p pr

It is necessary to distinguish the following:

Instantaneous strength R , i.e. the stress which causes failure wheno

a load is applied instantly, theoretically at the speed of sound. In

practice, the load is applied more slowly and, as a result of the tests, we

determine the sUbstantially instantaneous strength, which corresponds to the

concept of temporary resistance. This strength is somewhat less than true

instantaneous strength. For frozen soils subject to plastic deformation

(without failure), the conditionally instantaneous strength is assumed to

be the stress at which under rapid loading conditions deformation reaches

a level equal to 20% of the initial height of the sample:

Long-term strength R(t) or Rl t,

i.e. the stress which causes failure

after a given interval of time t.

For frozen soils sUbject to plastic deformation the long-term strength

characteristic is assumed to be the stress at which deformation after a

given interval of time reaches a maximum value. In metallurgy this stress

is also known as the creep limit;

The long-term strength limit or the ultimate long-term resistance 000;

Roo, i.e. the maximum stress at which progressive flow and failure do not

occur.

(18)R(t) =

diminution of strength R in relation to time t of the

> Roo) is expressed by the formula

B

Instantaneous strength is used when evaluating (in terms of strength)

frozen soil for the effect of short-term loads, long-term strength when

evaluating the effect of loads over a finite given period of time, long

term strength limit when evaluating the effect of loads over a very long

period, for example the useful life of permanent building structures, and

in cases when the occurrence of non-attenuating deformations is not per

missible.

The pattern of

load action (when R

t+l'In -s-

where R(t) is the strength at a given moment of time t, kg/cm 2 (in any type

of deformation: compression, shear, etc.); B (kg/cm 2) and B are parameters

determinable by experiment, and here B and the unit in the denominator of

the formula must have the same dimensionality (minutes, hours) as that of

-20-

Ro

the values of t being substituted in the formula. In order to simplify the

formula, the unit in the denominator may be ignored.

Where t = 0, formula (lS) gives the instantaneous strength

B

In 1-B

Where t = t , and t is the loading time, formula (JS) determines the00·

substantially instantaneous strength

Ro

Bt +1

In _0_

B

(20)

(to' Band 1 are in minutes).

The long-term strength limit is determined by the expression

(21)R

00

In tooB

where too (lOOB 0.05) r.-h and B is the number of years.

The value of R in formula (IS), where t = 00, is found to be zero, which

indicates the conditional nature of the theoretical concept of the long-term

strength limit. However, with a sufficiently large value of t the diminution

of R will be so small that for practical purposes it can be disregarded.

Such a value t = too is also given by formula (21), deduced from the condition

Roo - R l oo = 0.05,R I a a

where Roo is the theoretical value of R(t), t being 100 years, and R l o o the

estimated value of the long-term strength limit.

The relationship of the strength of frozen soil to temperature is

defined by the formula

(22)

where e is the temperature of the frozen soil without the minus sign; v

(kg/cm 2• deg) and p (a dimensionless quantity) are parameters determinable

by experiment, in which p may prove to be close to unity.

The formula is valid where 8 does not exceed the thawing temperature

of the frozen soil, i.e. only when the soil is in a frozen state.

The above strength characteristics relate to a simple stress state-uni

axial compression, or extension and simple shear, the parameters for formulae

(lS) - (22) having values appropriate to the given form of testing. The

above characteristics may be used:

For comparative evaluation of the strength properties of frozen soils

and for studying the behaviour of ttlese soils under the long-term effect

of a load;

Thus, parameters Band B in equations (18) - (21) are

-21-

As characteristics in ･ｶ｡ｬｵ｡ｴｩｮｾ the strength of frozen clayey soils,

which are not subject to "internal friction".

The load resistance (strength) of frozen soils under conditions of a

complex stress state is defined in terms of the state of ultimate equilibrium

and the effect of the time of load action. ｾｨ･ state of limiting (ultimate)

equilibrium (Ultimate stress state) is characterized by the formation in the

soil of sliding surfaces and by the development (on these surfaces) of the

same ratio of tangential (T) and normal (0 ) stresses as that at which then

shear resistance of the soil at a given moment of time t is ultimate. If

this resistance is exceeded, soil failure or loss of rigidity will result.

The shear strength T of frozen soil is a variable quantity which depends

on the time of load action t. The pattern of variation of T in time and

the dependence of this quantity on temperature are described by formulae

(18) - (22). Shear strength also depends on the magnitude of the effective

normal stress a .n

functions of an. Accordingly, a graph of the long-term shear strength of

frozen soils is represented by a series of long-term strength curves, where

each curve corresponds to its normal stress an value (Fig. 8).

The condition of ultimate stress may be represented by a shear diagram

the relationship between the ultimate shear breaking strength T and then

effective normal stress o. For frozen soils, taking into account then

variability of shear strength in time, the shear pattern is shown as a

series of curves, each of which corresponds to a specific time t of the

action of the shearing load.

Normally, the relationship between shear resistance and normal stress

for frozen soils is non-linear. However, it is sufficient for practical

purposes to assume this relationship as linear, approximating the shear

pattern by a series of straight lines (Fig. 9). The upper line (where

t = t ) corresponds to the conditionally instantaneous shear strength T ,o 0

the lower line (where t = t ) to the ultimate long-term T , and the inter-00 00

mediate lines (where t = ti)

to the shear strength at the given moment of

time T( t ) .

The segments cutoff by the lines on the axis of ordinates determine

the "cohesion" of frozen soil c, and the slope of the lines the "angle of

internal ｦｲｩ｣ｴｩｯｮＢｾＮ These characteristics serve as basic parameters of

frozen soil strength. The cohesion and internal friction of frozen soils

are variable quantities which depend on the time of action of the shearing

load; their value varies from maximum, conditionally instantaneous c ando

ｾｯＧ to minimum, ultimate long-term cw and ｾｯｯ［ intermediate values c(t) and

ｾＨｴＩ correspond to the cohesion and internal friction at the given moment

-22-

of time (t). ｾｨ･ cohesion and internal friction of frozen soil depend also

on temperature 8.

The angle of internal friction Q for frozen sandy soils may in practice

be treated as constant, depending neither on e nor on t.

The division of shear strength into cohesion and internal friction, and

the concepts themselves, are arbitrary, since the nature of these forces is

the same. By cohesion we imply that part of the shear strength which is not

related directly to the normal stress, and by internal friction, that part

of the shear strength which is related to the normal stress.

Shear patterns of frozen soils are constructed from test data obtained

with instruments designed for soil investigations under conditions of complex

stress state: instruments for triaxial compression, torsion and compression,

etc. If these instruments are not available, the tests may be carried out

with cutting instruments - plane-parallel or wedge. A rough shear diagram

may also be constructed, using uniaxial compression and pure shear test data

as a basis.

The condition of ultimate equilibrium of frozen soil can be expressed

as a formula, which follows from an examination of the shear diagram (see

Fig. 9).

T(t) = c(t) + a tan ｾＨｴＩＬ

(24)T(t) = c(t)

where T(t) is the ultimate shear strength, which is a function of time, in

kg/cm2

; c(t) is the cohesion, variable in time, in kg/cm 2; Q(t) is the angle

of internal friction, variable in time; a is the normal stress, in kg/cm 2•

The angle of internal friction Q of frozen clayey soils may be close

to zero, then the condition of ultimate equilibrium is transformed:

a f(t)us

where 0 f(t) is the ultimate uniaxial compression strength of the frozenus

soil, variable in time, in kg/cm 2•

Formulae (23) and (24) are used for evaluating frozen soil strength

and rigidity (the latter formula for soils without friction).

-23-

II. GENERAL REQUIREMENTS FOR TESTS

Preparation of Specimens

Before commencing soil tests, it is necessary to define the main

characteristics of the physico-mechanical properties of soils generally

used to describe thawed soils (texture, water properties, natural moisture,

etc.). In addition, for frozen soils the phase composition of the moisture

at a given temperature is determined, if this is stipulated as a requirement.

The method used in this case is the one devised by the former Permafrost

Institute of the Academy of Sciences, U.S.S.R. For an approximate evaluation

of the phase composition it is possible to use the curves for unfrozen water

previously obtained for the principal soil types(13).

Where the cryogenic structure of the frozen soil is non-homogeneous

(stratified and reticulate), the water and ice contents and the unit weight

are determined differentially - for aggregates of frozen soil and for the

sample as a whole in accordance with the rules of instruction of the Perma

frost Institute(14,15).

The degree of completeness with which the general characteristics of the

physico-mechanical properties of the soil are determined will depend on the

stated requirement in each individual case.

Frozen soil testing is conducted with disturbed and undisturbed samples.

Depending on the requirement, undisturbed samples are taken from a layer of

frozen or thawed soil. In the latter case the samples are frozen artifi

cially. Undisturbed soil samples are taken with special samplers (cutting

cylinders) (Fig. 10) and a press. Samples of each series should be identical

and should therefore be taken, where possible, from the same level. For

layered soils the samples are cut so that the direction of stratification

is different in relation to the loading: in one series of samples, parallel

to the stratification, in another series, at right angles to it.

It is also desirable to prepare several control samples from soil

stratified at an angle of 45° to the effective force.

Frozen soil core samples are prepared in premises, where the tempera

ture is below freezing. It is most expedient to work frozen soil at tempe-000

ratures between -2 and -S C. At temperatures above -2 C the soil begins to

thaw; at temperatures below -So or _6°c the soil is difficult to work on

account of its increased hardness; apart from this, at lower temperatures

cracks may form in the interlayers and ice lenses contained in the soil.

Disturbed soil samples are prepared in accordance with the methods

usually applied in testing unfrozen soil. The soil in an air-dry state is

pulverized, passed through a sieve with a 1 mm mesh, then brought to the

given degree of moistness. If the requirement calls for preparation of

specimens with a low moisture content, uniform moistening may be achieved

by ｭｩｸｩｮｾ previously cooled soil w1th snow.

carried out in premises where the ｴ･ｾｰ･ｲ｡ｴｵｲＰ lS below freezinr.)

The moistened soils is placed in mouId s , the wa lLs of wh l c h are evenly

smeared with a thin ｦｩｬｾ of vaseline, and therl compacted tu the required unit

ｷ･ｩｦｾｨｴＮ

Specimens prepared from disturbed or und l s t u r-ccd tha,,:ed soil are

artificially 1'1" ,:':"n under conditions which e ns ur-e t ha t the re q u La Lt e cryo-

ｲｾ｣ｮｬ｣ tcxttlreis f'o r-n.e d du r i nr- tr-'d-::; ｦＺＧ･ｴｾ＾ｾｩｮｧｰｲｯｬＮﾷ｣ｾＭﾷ［［ＬＺｾ

In order to obtain f r oz e n ;;oil wi t l.o u t ice .inc LusLo ne (of compact

texture), the specimens are i'rozen at t e.npc r-a t.u r-e » be Low -3ClOC. To obtain

npe c lrnc nc c on t a Ln l nrt icp I n c l us Lons (of laycrc'c: and reticulate s t r-u c t ur-e )

, - 0 r: °c d\-)the s pe c Lrne na are frozen a t a hi er t c.npc r-a t ur-c ｾＭｨ -, -) ｾ a n auove .

To obtain specimens of layerr,d t e x tur-e , ｃｲ･ｃＧＺｾｩ nr; is cfCected by c o o Lt ng one

s Lde of the sample wi th mol s t.ur e s c e pi ns; t.owa r-d s Ulf' ｦｲＧ｣･ｾｾｩｮＮ｛ＧＢＮ e drte .

After fr'pczing, the s amp Le s a re carefully trLmnie o at bo t.h ends so that

their surfaces are smooth and parallel to each other. Then the samples ear-

mar ke d for uniaxial compressiun and s he a r' t e s t.s In a ｷｰ｣ｬｻｾ･ tester are freed

from their forms by means of an adapter and a nrcss. Snmples earmarked

for compres s ion and shear t es t s in a cut t i rw apc':J ra t us are trans fe r red to

the forms in which they will be tested.

To protect them from the effects of e xpo s ure , the s amp Les are wrapped

in (para-rubber tape?).*

The prepared frozen soil specimens are dept at ttlC same temperature

as that of the subsequent tests for at least 24 hours.

It is convenient to use automatically controlled ultrathcrmostats for

keeping the samples at the required constant temperature. Ultrathermostats

are installed in a room, the temperature of which must be 10w2r than that

at which the samples will be tested, since the temperature of an ultrather

mostat is controlled by hc a t Lng .

The specimen is taken out of the ultrathermostat and placed in the

tester. The prepared specimen is kept in the tester at the given tempera

ture for at least 2Cl-3Cl minutes, after which the test can be started.

Instrument and Test Condition Renuirements

The mechanical properties of frozen soils can be tested with instruments

designed for unfrozen soils, rock and other materials, but, because of the

unique features of frozen soil, some of the indicated instruments have to

be modified.

Instruments for testing frozen soils must be capable of withst:=tnding

heavy loads (of up to several tons) and at the same time provide for tests

* In Russian: para lent a . (Transl.)

-25-

covering a wide range of load variations, since the strength of frozen soil,

depending on a number of factors (soil type, soil temperature, duration of

load action) varies from a fraction of a kilogram to more than 100 kg/cm 2•

The instruments must also be such as to ensure that the tests can be

conducted at the stipulated load increment rate (in rapid tests) and at a

constant stress for long periods of time (in creep tests). These require

ments may be met by using presses and test apparatus with several scales, or

instruments with different capacities.

Tests of highly dispersed frozen soil (clay and loam) with a temperature

° ° °close to 0 C (from 0 to -5 C), and long-term tests necessitate the use of

presses and instruments designed for small stresses, like those intended

for ｴ･ｳｴｩｮｾ unfrozen soil.

For frozen sandy soils and for all types of soil with a sufficiently

°low temperature (below -5 C), a high ice content and a rapid failure

condition, it is necessary to use presses and instruments designed for

large loads (3 - 5 tons and over), like those used for testing cemented

rock.

When testing frozen soils it is necessary to keep the temperature of

the specimen virtually constant during the entire test. This condition

applies with particular force where the temperature is high (close to OoC).

Permissible temperature variations in various ranges are as follows:

°Testing temp., C

Permissible temp.deviation, °c

up to -2

±O.l

-2 to -5

±0.2

-5 to -10

±0.5

below -10

±1.0

The soil can be kept at a constant temperature in receptacles with

automatic temperature control (refrigeration chambers, cabinets)* or in

natural underground laboratories and pits insulated to minimize temperature

variation.

Measures must be taken to protect frozen soils from the effects of

weathering when conducting long-term tests. There are various methods of

accomplishing this ifor example, with rubber sheathing, coatings, insulating

pads of sawdust and other materials). The method selected will depend on

the specific conditions and the type of test.

* If special receptacles are unavailable, type FAK 1.5 sectional refrigeration chambers are recommended. These have a working area of m2 and aminimum temperature of -10, -12°C.

-26-

III. ｾｅｔｈｏｄｓ OF CREEP AI,rD ｌｏＺｾｇＭｔｅｾｾｾｓ＿ｒｅｎｊｔｾ TESTING

AT UNIAXIAL COMPRESSION

Instruments

1. Various types of hydraulic and electromechanical presses, as well

as instruments used to test unfrozen soils (lever presses, compression stands,

etc.), may be used for uniaxial compression tests.

2. In selecting instruments for uniaxial compression tests of frozen

soils, allowance should be made for specimen deformation by an amount not

less than 20% of its initial ｨ･ｩｾｨｴ［ maintenance of a given load for pro

ｬｯｮｾ･､ periods when conducting creep tests (within 5%).

3. Short-term tests are usually conducted with hydraulic and electro

mechanical presses; creep tests are conducted with lever presses and creep

machines, if they permit a constant load to be maintained for prolonged

p e r Lod s of time. The most convenient lever presses are those designed by

Gidroproekt,* which have sectorial levers for 0.5 and 1.0 ton. Among the

hydraulic and electromechanical presses, preference is Given to testing

.nac h t ne s equipped wi th refrigeration cabinets (for example, ZDMK 30t type

testing machines).

4. Instruments for testing frozen soils at uniaxial compression are

fitted with devices for measuring the axial and radial deformation of the

specimen. Measuring devices intended for single and continuous measurements

may be used to record deformations. Automatic deformation recording is

necessary in certain cases during rapid testing (paras. 10 - 11).

The measuring devices must meet the following requirements:

The measuring range in terms of the axial deformation of a specimen

should not be less than 20% of its original height; the deformation measure

ment should be accurate to within 0.01 mm.

They should be capable of measuring the radial deformation of a speci

men. For determining maximum radial deformation values, the Poisson ratio

for frozen soils may be taken as 0.35.

5. For the measurement of axial deformations, clock-type indicators,

rheostat and resistance data units and other devices may be used. Selection

of the method of measuring will depend on the availability of equipment

and the purpose of the tests. It is advisable to use special data units for

measuring radial deformations. Such a device and the method of applying

it to a specimen are illustrated in Figures 11 and 12.

* The S. Ya. Zhuk All-Union Research Development Institute of HydraulicStructures.

-27-

6. Specimens used for uniaxial ｣ｯｾｰｲ･ｳｳｩｯｮ tests are cylindrical in

shape with an hid ratio of 2, where h is the height of the specimen, and

d is the diameter, which must not be less than 4 ｣ｾＮ When testing coarse

grained soils and soils with ice intercalations, the diameter of the speci

men should be 12 - 15 cm.

7. In uniaxial compression tests, special attention should be paid to

ensuring that the top and bottom surfaces of the specimen are parallel, that

they are clearly formed and that they are centred on the plates of the

testing machine. The specimen is positioned on a ring of the same diameter

as the specimen inscribed in the centre of the lower plate. The top and

bottom surfaces of the specimen are carefully cleaned with fine emery paper.

8. The specimens must be protected from the effects of exposure during

long-term tests. This is accomplished by placing the specimen to be tested

in an elastic rubber sheath, the diameter of which is larger than that of

the specimen itself. The sheath is held in place by rubber bands mounted

on the upper and lower plates of the instrument (see Fig. 12).

Rapid Load Action Tests

9. Rapid load action tests are carried out to determine the substanti

ally instantaneous value of the limiting strength (temporary resistance)

o ｾｯ and to determine the relationship between stresses and deformationso us

owhich characterize the stress-deformation state at the initial moment of time

10. In order to obtain all the indicated characteristics, the instrument

to be used for the tests is fitted with an automatic recorder and attach

ments which permit both axial and radial deformations of the specimen to be

measured (data units, dial gauges).

11. The tests consist in subjecting frozen soil specimens to a continu

ously increasing load. The load is applied evenly and gently, but is in

creased rapidly so that the whole procedure is completed in approximately

30 seconds. The test ends with the failure of the specimen or the achieve

ment of an axial deformation value equal to 20% of the initial height of

the sample.

During the test the automatic recorder traces the compression pattern

in coordinates of load P (kg) - absolute deformation A (mm), and the radial

deformation gauge indicates the increase in the diameter of the specimen

(see Fig. 11).

12. The nature of the stress-deformation patterns obtained in uniaxial

compression tests of frozen soils depends on the type and temperature of

the soil.

For brittle frozen soil the stress curve has a peak (Fig. 13, curve a);

for plastic frozen soils and frozen soils subject to viscous deformation,

deformation increases continuously with compression and the stress-defor-

-28-

mation curve does not have a peak (Fig. 13, curve b).

13. The characteristics of strength and deformability (para. 9) are

determined as follows. The resulting P-A curves are reconstructed in E-O

coordinates (E - relative deformation, 0 - stress), thus giving arbritary

and actual compression curves for each test.

14. In order to construct an arbitrary curve we determine

a) stresses 0 as the quotient of the division of the effective load P

by the initial area of the specimen Fo

p

o = F kg/cm2

;

o

b) the relative deformation E corresponding to the selected P,

t.hE = h '

where h is the initial height of the specimen;

t.h is the variation in the height of the specimen, i.e. the amount of

absolute deformation A;

c) the resulting 0 and E values are plotted on the arbitrary compression

curve (Fig. 14).

15. When constructing an actual compression curve, the arbitrary defor

mation (E) values are plotted along the axis of the abscissae, and the

respective values related to the variable (increasing) area of the specimenP

a = F along the axis of ordinates, where F = Fo

+ t.F (t.F is the increase in

the size of the area).

The increase in the size of the area is determined from radial deforma

tion measurements.

16. From the actual compression curve (Fig. 14, l' and 2') we can

determine the conditionally instantaneous strength a ｦｾｯ and establishus 0

the relationship between stresses and deformations:

a) The value of 0 f is defined as the maximal stress a on theus

compression curve l' (if the failure is of a brittle nature), or as the

stress at which deformation E reaches a value equal to 20% of the initial

height of specimen 2' (if the failure is of a viscous nature).

b) The relationship between stresses and deformations is established

by the generally accepted methods of processing experimental data (see

para. 43-56). As a result, we are able to determine the form and parameters

of this relationship, in particular the coefficient of initial deformation

Ai n i t and the coefficient of hardening m in equation (3). If the initial

portion (see Fig. 14) of the curve is almost straight, the angle of slope

of this line will determine the modulus of total linear deformation

0/ 2E = €' kg cm , which characterizes both the total purely elastic (reversible)

and the total residual deformations. In order to determine the modulus of

-29-

purely elastic deformations, unloading tests are carried out and E is

determined from the load release curve. In both cases these moduli depend

on the velocity of the load action (static moduli). In order to determine

the modulus for true elastic deformations, the load should be brought to

bear on the specimen instantaneously. This is achieved either by dynamic

tests or by very rapid application of the load.

17. The arbitrary compression curve is used to determine ultimate

strength and to establish the relationship between stress and deformation

in the event that variation in the cross-sectional area of the specimen is

not taken into account. These characteristics are determined in accordance

with paragraphs 18, 43-56.

18. If the purpose of the tests is simply to determine the value of the

actual instantaneous limiting strength, automatic recording and radial

deformation measurement are not absolutely necessary, but the test must

include axial deformation measurement* and subsequent measurement of the

final cross-sectional area of the specimen if the failure was of the viscous

type.

19. The mean arithmetic values of the limiting strength (temporary

resistance) 0 , the coefficient of initial deformation Ai it and theusa n

coefficient of hardening m, which are given in Appendix 1, are taken as

their calculated values.

Long-term Load Action Tests

20. Long-term load action tests are conducted to determine the calculated

characteristics of creep and long-term strength of frozen soils. These

tests consist in determining deformations € evolving in time t when subjected

to constant stress 0.

21. The tests are conducted with a series of identical specimens of

frozen soil. In uniaxial compression tests the number of specimens in a

series is 8 - 10.

22. The specimens are subjected to different stresses, each stress

remaining constant for the duration of the given test, and the soil tempera

ture remaining constant for the entire series of tests.

Axial and radial deformations are measured during the test.

23. The load applied to each of the specimens is determined as some

fraction of the "instantaneous" strength (0 ) determined by rapid actiono

load tests (para. 16).

The first specimen is subjected to a compressive stress 01, approxima

tely equal to 0.9 of ° , and the second and succeeding specimens to ever-o

* It is not absolutely necessary to equip the apparatus with a deformationmeasuring device when testing brittle frozen soil.

-30-

> 03 > 04 •••.• ' the values of which are deter-､･｣ｾ･｡ｳｩｮ･ｳｴｾ･ｳｳ･ｳ 01 > 02

mined from the expression

0. = 0 [1. - Q...-)'l 0 10

where 0i

is the stress applied in the given test; 00 is the ｵｬｴｩｾ｡ｴ･ strength

at rapid load action; n is the factor which for specimens 1 to 9 is assumed

to be equal to the series number of the specimen beine tested. For the 10th

and ｳｵ｣｣･･､ｩｮｾ specimens (if more than 10 are tested), the value of n may be

taken as 9.25, 9.50, 9.75, etc.

24. In uniaxial compression creep tests the cross-sectional area of the

specimen increases in proportion to the deformation. Thus, in order to

maintain a steady stress, the load must be increased during the test in

proportion to the increase in the area of the specimen. The value of the

effective load at any moment of time is determined from the expression

P = of kg, where a is the stress in the specimen which must be maintained

at a constant value, in kg/cm 2; F is the area of the specimen in cm

2•

25. The most efficient way of varying the effective load P needed to

maintain constant stress a = const is by means of an automatic adjusting

device (creep machine). If this device is not available, load P may be

varied by the usual load increment method.

26. To facilitate computation of the value of load P it is necessary to

compile a subsidiary table containing the indicated ijrowth intervals of the

diameter of the specimen 6d and the corresponding values of the calculated

area F and the ｡｣ｴｩｮｾ load P (at 0 = const). The load on the specimen is

increased when the increase in the area of the specimen reaches no more

than 5%.

27. If the tests are conducted without the stress being automatically

controlled, it is necessary to record the lateral deformation and to increase

the load P as soon as the area of the specimen varies by the amount indicated

above. The corresponding value of load P is obtained from the table. If

the tests are conducted with automatic load control, the radial deformation

gauge is connected to the automatic control system of the instrument, which

alters the load in accordance with the variation pattern of the specimen

area.

28. The frozen soil specimen is placed in the press, great care being

taken to ensure that it is correctly centred and kept at the given tempera

ture for not less than 20 - 30 minutes prior to the test.

Smoothly and guarding against impact, the load, which is gradually

increased to the given value, is applied to the sample. The time during

which the load reaches the given value must be the same in all the tests and

should be approximately 30 seconds.

-31-

29. The deformation gauge or the automatic measuring device, is set at

zero before the load is applied. However, measurement of creep deformation

begins the instant the load reaches the given value. The readings at this

instant are taken as zero readings.

The measurements are entered in a log book, the form of which is given

in Appendix 2.

30. The deformation rate for each interval of time between measurements

is calculated during the test

Ai-Ai_ l

v = t -t mm/min,i i-l

where v is the rate of deformation; Ai-Ai_ l

is the deformation increment;

ti-ti_ l

is the time variation. The values of v are given in Appendix 2,

column 12.

31. The time intervals between deformation measurements are selected

taking into account the deformation rate of the specimen and the stage of

deformation in which the creep process takes place:

a) In the irregular creep stage (see Fig. 2, sector AB) the time inter

vals between readings are assumed to be as follows. At the beginning, if the

deformation rate is high, readings are taken at least every minute. As the

deformation rate decreases, i.e. when deformation increases are no longer

recorded during a one minute interval, the intervals between readings are

progressively increased to ｾｴｩ = Ｒｾｴｩ｟ｬＧ Accordingly, readings are taken

every 2, 4, 8, 15, 30 minutes, 1 hour, 2 hours, etc., but no less frequently

than every 8 hours. In selecting the time interval, we must allow for the

fact that the deformation increase during ｾｴ between subsequent readings

should not exceed 1.0 mm, otherwise the time between readings will have to

be adjusted.

b) If in not less than three successive measurements the deformation

rates are practically uniform, it is assumed that the stage of constant

velocity flow has been reached (see Fig. 2a, sector Be). In this stage

the deformation measurements are made at uniform intervals of time. The

time interval between readings is assumed to be equal to the value of bt

between the final readings during the transition from the irregular creep

stage to the stage of constant velocity flow.

c) In the progressive flow stage, the onset of Which is characterized

by an increase in the rate of deformation, the readings are again taken

more frequently. The interv.al between readings is decreased in stages in

proportion to the increase in the deformation rate, and is determined by the

relationship ｾｴｩ = 1/2 ｾｴｩ｟ｬＧ

Having regard to the specific test conditions which determine the nature

of the deformation of the specimen, it may prove expedient to modify the

-32-

8bove relation slizhtly and ta;(c ｲ･｡､ｩｮｾｳ either ｾＱＰｲ･ｏｾ lesG frequently,

depending on how the deformation process develops.

32. 'I'h e t e s t s are considered complete if:

a) The specimen Pails (for brittle soils).

b) The deformation of the specimen reaches a value 50% higher than the

deformation at which ｴｾｬ･ｳｴ｡ｾ･ of ｰｲｯｾｲ･ｳｳｩｶ･ flow occurred (for soils

subject to viscous ､･ｦｯｲﾷＺｮ｡ｾｩｯｮＩＮ

c) ｓｴ｡ｨｩｬｩｺｾｴｩｯｮ Gf ､｣ｦｯｲｭ｡ｴｾｯｮｏｃｃｴｬｲｾｳＬｾｮ｜ｾｽｽｩ｟｣ｨ case stabilization

is considered to have [leon r e ac he d if the increase of relative deformation

E does not exceed 0.0001 during the ｦｯｬｬｯｷｩｮｾ intervals of time:

6 hour s , for sandy Lc arn - 12 hours, :'01' loam and clay - 24 hours.

for sand -

33. Taking into account tne fact that the process of frozen soil creep

may be extremely ｰｲｯｬｯｮｾ･､ arId under small stresses may extend to several

months or even years, the duration of the tests is limited to an interval

of time long enough to permit the creep and 1011g-term strength characteris-

tics to be determined. In this, CCl.;3e, some of t.h e tests in a p:;i ve n series

will not include all the sta',;es of ､･ｦｯｲｭ｡ｾＺｯｮＬ bUG \"1111 be terminated at

the star,:e of irrctjular C'"CCP (if the rate uf ＧＺＧＺＺｾＨＩｾＧｉＺｬ［ｾＧＬ［ on.: bt>in·" measured

continually d e c r-e a s e s for each s ub s e que n t. ;'·>.',(i· r1f':), 'Ji':n t he steady flow

stage (if the deformation rate is constant).

The maximum time interval for the t.es t s Ｌｾｳ (;ctt'r';;\;:lc,i with respect

to the purpose of the te s t s and the t.e c hn ic aI ｙＧＨＡＺ［ＨｪｕｬＧＨ［ＬＮＬｾｾＺ

a) If the tests are conducted to de t e r-m l ne the ｣［Ｇｪ［［ＬＺＧ［Ｉ｣ＺＭｊｾｲｪｾｊｴｩ｣ｳ of frozen

soi Is for a lonr,-term load (for example t he found" t 4on ,304 J 3 of ou rLd i ng s ) ,

the duration of the tests will depend upon t e c hn i c al Ｈｯｬ［Ｚ［［､･ｲﾷ［ｾｴＺｌｯｮｳＬ but

must not be less than 10 - 15 days.

b) If the tests are conducted to determine the c l iar-u c t e r Ls t Lc s of

frozen soils SUbjected to a load for a limited, short period of time

several hours or days (for example, for static evaluations of protective

enclosures of frozen soil formed when cutting various holes and trenches

with the aid of artificial freeZing), the maximum duration of the tests

should correspond to the period during which it is required to keep the

soil in a frozen state.*

34. On completion of each test, a creep curve is constructed (see Fig.

2). For this we take from the log book (see Appendix 2) the absolute defor

mation (.\") values (col. in and the time (t.) va Lue s corresponding to them1 1 ｾ

(col. 3). we determine tI.'- r-e La t Lve deformation E: ;: .\./h (where h is the1

initial height of ｴＺｬ｣［ｾＩ･Ｈ［ｩｭ･ｮＩ and construct a g r aph in coordinates of

E: = t.

* Literally "pe r-Lod o ;' -JO ':: f the frozen ''';I''ounei''. Transl.

-33-

As a result of testing all the specimens in a given series we obtain

a series of creep curves (for a given soil temperature) in which each

curve corresponds to its constant compressive stress value (Fig. 15a)

01 > 02 > 03·

35. Tests have been carried out correctly if the resulting series of

creep curves satisfies the following conditions:

a) The creep curves do not intersect or lie upon each other.

b) A straight line drawn parallel to the axis of ordinates for any

moment of time t intersects at least five creep curves, in which case it

will be possible to construct curves in ｳｴｲ･ｳｳＭ､･ｦｯｲｭｾｴｩｯｮ coordinates

through these points (para. 41).

37. Where it is necessary to differentiate between recovering and

residual creep deformations and, in addition, to isolate elastic initial

deformations, creep tests are carried out by unloading the specimens.

38. Each specimen is unloaded after being tested. The load is removed

quickly, and immediately afterwards the axial deformation of the sample is

measured. Subsequent deformation measurements are carried out in 2, 4, 8,

15, 30 seconds, 1,2, 4, 8, 15 ... minutes, respectively, so that the

intervals of time between readings are always increased by a factor of two

ＨｾｴｩＫｬ = ＲｾｴｩＩＧ The test is continued until the deformations are stabilized

(in accordance with para. 32c).

Tests may also be carried out by loading/unloading the specimens in

stages. The number of test cycles (loading-unloading) at one temperature

must be at least five or six.

39. Using the data obtained for each test, a curve is traced in relative

deformation - time coordinates (see Fig. 3). Curve 3 - 5 reflects the

process of deformation recovery in time.

Sector 3, 4 of the curve denotes the extent of the instantaneously

recovering (initial) deformation. Section 4, 5 denotes the magnitude of

the deformation which recovers in time.

Processing Experimental Data and Determining Creep Characteristics

40. The deformation patterns of frozen soils and their deformative

characteristics, which serve as the requisite parameters for creep calcula

tions, are determined on the basis of test data. The relationship between

stress and deformation and the pattern of deformation variation in time are

considered to be such basic patterns. Creep curves obtained as a result of

tests serve as the source material for these patterns.

41. The relationship between stress and frozen soil deformations, taking

into account the time factor, is characterized by the series of curves at

-34-

Figure 15b. These curves are obtained by reconstructing the creep curves

(Fig. 15a):

a) At least five or six points (corresponding to different moments of

time t of load action) are plotted on the axis of abscissae of the deforma

tion-time diagram (Fig. 15a). The points should be evenly distributed along

the axis of abscissae.

b) From each point tl, t2, t3 ... a straight line is drawn parallel to

the axis of ordinates; the points at which these lines intersect the creep

curves (each of which corresponds to its own value of 01, 02, 03"') denote

the values of deformation E caused by stresses 01,02,03'" at given

moments of time tl, t2, t 3 ...

c) The points of intersection (except those located in the progressive

flow sector) are plotted on the relative deformation-stress diagram. The

result of this reconstruction is a series of curves showing the relationship

between stress 0 and deformation E at given moments of time t of load action.

The actual compression diagram for the initial moment of time (to) is plotted

on the graph (Fig. 15b).

42. To establish the relationship between stress and deformations, an

empirical formula is selected which must correspond satisfactorily to the

experimental tesults. The analytic expression of the relationship between

stress and deformation and the parameters of the relationship are determined

by the usual methods of compiling empirical formulae.

43. The relationship between the stresses and deformations of frozen

soils is usually expressed by exponential equation (3) in the form

o = A(t)Em,

thus, in selecting an empirical formula, we should first of all verify this

equation. To verify the validity of the exponential equation and the

determination of its parameters A and m, the deformation - stress chart is

reconstructed in logarithmic coordinates. For this the logarithmic values

of the stresses are plotted along the axis of ordinates, and along the axis

of abscissae, the corresponding values (allowing for the sign) of the loga

rithms of the deformations (Fig. 16). As a result of such a reconstruction,

if the stress-deformation relationship is expressed by an exponential

equation, a series of straight lines in which each line corresponds to a

specific time of load action is obtained on a lno - InE graph. The line

denoted by index t reflects the connection between stresses and deformationso

at the initial moment of time of load action. The parameters of this line

(Ai 't is the coefficient of initial deformation in kg/cm 2; m. 't is thenl lnl

hardening coefficient) are either determined directly from a lno - InE graph,

or they are calculated analytically.

-35-

44. In order to determine parameters A" Ｎｾ｡ｾ､ m, ;t from the graph, the..cnl" J..n..c

upper line on the Ino - InE graph is continued u:1til it intersects with the

axis of ordinates. The portion cut off by this ｾｩｮ･ on the axis of ordinates

represents the value y = InAi n i t,

hence Ai n i t

= e Y. Then, allowing for the

selected scale, the tangent of the angle of inclination of the upper line

to the axis of abscissae is determined from the Ino - InE graph, which also

determines the value of the coefficient

6. On (5)

mi nit = 6. On E)

45. In order to determine parameters Ai n i t

and mi n i t

analytically, a

system of equations is formulated

where

curve

!n n

In Ai n i t

+ mi n i t L In E =L l n (5

n I n I n

l"n 'init ｾ 1n E + mi nit 4= (In E)' ｾ (In E Ln a),

n is the number of experimental points on the stress-deformation

for the initial moment of time t .o

In reconstructinr, stress-deformation curves in logarithmic coordinates

a variety of instances is encountered:

a) The stress-deformation curves are sufficiently well aligned (i.e.

the experimental points plotted on the logarithmic graph lie in straight

lines), while for all moments of load action time these lines are parallel

to each other (Fig. 17a).

b) The stress-deformation curves straighten out,* but these lines for

different moments of time ti

are not parallel to each other (Fig. 17b). More

probable i" the case in which only the line for the initial moment of time

t is out of parallel to the rest. In this case the hardening coefficient iso

is a constant value (m = const) for all moments of time t > t. However,o

coefficient is equal tofor the initial moment of time t , the hardeningo

some value of mi n i t

different from the value for other moments of time t.

c) The stress-deformation curves straighten out* but are inflected and

take the form of refracted lines (Fig. l7c).

d) The stress deformation curves do not even out in logarithmic

coordinates.

46. If all the stress-deformation curves even out in logarithmic coordi

nates and, in addition, they are all parallel to each other (m = const), then

equation (3) is correct.

Assuming, in conformity with expression (7") for frozen soils, an expo

nential relationship between the coefficient of deformation A and time, the

deformation equation r,ay be represented in the form of equation (8')

* Spryamlyayutsya (Translator).

-36-

m ｯｾ｡ (25)E ="'[1- •

If the results of verifying the applicability of equation (2S) (see

paras. 47 - 49) prove unsatisfactory, the applicability of equations (8),

(8") and (8" I) should be verified. Verification of the validity of these

equations and determination of the parameters which go into them should be

carried out in accordance with the rules contained in paras. 29, 32, 33 of

:lcction VI.

47. Parameter m in this equation is determined similarly to the one

dealt with in paras. 43, 44 and 45. Different values of t are calculated

in this way. The mean arithmetic value is taken as the calculated value

of the hardening coefficients m 1ca c

m =calc

n

ｾi=l

n

where n is the number of found values of the hardening coefficient m. forl

different moments of time t ..l

48. To verify the validity of equation (25) and the definition of

parameters ｾ and a, graphs are constructed (Fig. 18) in coordinates

mE

o- t and

mIn £- - Int.

o

To construct an Emlo - t graph, relative deformation (E.) values andl

corresponding stress (Oi) values for each selected moment of time ti

are

taken, either directly from the creep curves (see Fig. 15a) or from the log

book. The value of the hardening coefficient m is determined in accordance

with para. 47.

49. If on the Em/o - t graph the experimental points form a single

curve and such a curve evens out in logarithmic coordinates, this constitutes

confirmation of the validity of equation (2S).

The parameters ｾ and a of this equation are either determined directlym

from the In £- - In t diagram (Fig. 18b), or they are calculated analyticallyo

similarly to the determination of parameters A and m dealt with inini t init

paras. 44 and 4S.

SO. If all the stress deformation curves even out in logarithmic

coordinates, but the lines for different moments of time are not parallel

to each other, then the equation

o = A(t)Em(t) and Em(t) = ｾ t a, (26)ｾ

in which the hardening coefficient m = met) (para. 51) depends on the time

of load action is correct.

(27)

£m(t)from the In

o

-37-

51. To determine the hardening coefficient m = met) a diagram in m - t

coordinates is constructed (Fig. 19). Using the normal method of compiling

empirical formulae, an analytical expression of the relationship between the

hardening coefficient m and time t is then selected.

52. Parameters ｾ and a in equation (26) are determined

- In t diagram, or they are calculated analytically.

53. If the stress-deformation curves even out in logarithmic coordinates,

but are inflected (see Fig. 17c), it means that these curves consist of two

sections: the first relating to small stresses ｯｾｯｳＧ and the second to

large stresses 0>'0 , where 0 is the stress determinable by the coordinates s

of the intersection point in the In 0 axis. The values of parameters A and

m in this case are determined for each of the sections separately.

54. If the stress-deformation curves do not even out in logarithmic

coordinates, it means that the relationship between the stresses and defor

.mations are not described by equation (3). In this case, to establish the

relationship between stresses and deformations another analytical expression

which corresponds to the experiment results should be selected. In particu

lar it is recommended to try an equation of the form

£ = Bota(o),

also an equation of the form (8") and (8" I).

55. The validity of equation (27) can be verified by a graph constructed

in In £ - In t coordinates (Fig. 20). If the experimental points foro

different stresses 0i lie in a straight line on this diagram, equation (27)

is valid. In order to make use of equation (27) with respect to aI, a2, a3

function a = a (0) (Fig. 21) is established.

56. When equation (27) is analyzed it can be shown that coefficient B

depends on the value of the applied stress 0. In an exceptional case, if

coefficient 0 is linearly related to the stress 0, but the relationship of

coefficient B to the stress is described by an exponential equation of then

form B = 00 , deformation equation (27) takes the form

m bo£ = ao t , (28)

awhere m = n + 1 and b = o'

57. To allow for the effect of temperature on the process of deformation

of frozen soil it is necessary to determine the parameters K, wand W in

equations (9) and (10). For this it is necessary to carry out creep tests

on several (at least three) series of specimens at different temperatures

e below freezing and process the results of the tests in the following

manner:

-38-

a) For each series of specimens, the values of moduli of deformation

(A) at different moments of time are determined by the method laid down in

paras. 43, 44 and 45.

b) Curves are constructed for the variation of the moduli of deformation

A in time for each temperature (Fig. 22a).

c) These curves even out in In A - In t coordinates (Fig. 22b) and from

the resulting diagram the values of parameters ｾ for each temperature are

determined.

d) A diagram showing the relationship between parameter ｾ and tempera

ture 8 is constructed (Fig. 22c).

e) The curve showing the relationship between parameter ｾ and tempera

ture is transformed* on a ｉｮｾ - In(8 + 1) diagram, where e is the tempera

ture of the frozen soil, ignoring the minus sign (Fig. 22d).

Parameter w is defined as the section cut off by the straight line

obtained in the ｉｮｾ - In(e + 1) system on the axis of ordinates; parameter

k is defined as the tangent of the angle of inclination of this line to the

axis of abscissae.

Parameter W is determined by rectifying the diagram of the modulus of

initial deformation Ai n i t

- temperature 6 in coordinates of In Ai n i t

- In

(6 + 1) and occurs as the section cut off by the resulting straight line on

the axis of ordinates.

58. The relationship between stress a and constant rate of plastic

viscous flow t is determined from a rheological curve (see Fig. 5) which is

based on creep curves. For this:

a) on each creep curve we mark off a linear portion corresponding to a

flow with almost constant velocity: t = const (see Fig. 2a, section BC);

b) the rate of steady plastic-viscous flow t = const is defined as the

tangent of the angle of inclination of the linear portion of the creep curve

to the axis of abscissae;

c) a graph (see Fig. 5) is constructed, with stress a values plotted

along its axis of abscissae and the t rates corresponding to these stresses

along its axis of ordinates. The resulting curve also reflects the relation

ship between the stress and the relative rate of steady flow (for a given

soil temperature).

59. To verify the validity of equation (11), which characterizes the

relationship between stress a and rate of plastic-viscous flow t = const,

and to determine parameters K and n, for this equation, the rheological

curve is transformed into logarithmic coordinates**. First on a diagram

* Spryamlyaetsya. (Transl.)

** Spryamlyayut reologicheskuyu krivuyu v logarifmicheskikh koordinatakh.(Translator).

-39-

constructed in a - £ coordinates, we determine the stress af

beyond which

constant velocity flow occurs. Then a In(a - af)-lnE: diagram is constructed

(taking into account the resulting symbol) (Fig. 23a).

If the points plotted on such a logarithmic diagram lie in a straight

line, it means that equation (11) is valid.

Deviation of the points from the straight line may be due to inaccurate

determination of the af

value. In this case, a more accurate value should

be obtained from the a - E: diagram (see Fig. 5) and the rheological curve

rectified anew in coordinates of In(a - af)-lnE:.

60. If the rheological curve in logarithmic coordinates has an inflection

point as and is represented by a broken line (Fig. 23b), the parameters K *and n are found separately for the two parts of this line: for the section

of the line from the point of inflection (for which reason the line is

extended to intersect the axis of ordinates) and for the section beyond the

point of inflection. The relationship between stresses and plastic-viscous

flow rate in such a case is as follows

a ｾ as

a ,s

where 6a = a - af'

61. Parameters Kand n in equation (11) are determined from a logarithmic

diagram in the In£ - In(a - af) system of coordinates (see Fig. 23), the

construction sequence of which is set out in para. 59. The section cut off

by the line on the axis of ordinates (axis of In£), determines the value of

InK, and the tangent of the angle of inclination of the line to the axis of

abscissae determines the value of n. Parameters K and n may also be deter

mined analytically in a similar manner to that indicated in para. 45.

62. Allowance for the effect of the frozen soil temperature on the plas

tic-viscous flow process is reflected by the relationship of parameter K

in equation (11) to the temperature e. This relationship is determined by

expression (13). Coefficients U and q of this expression should be deter

mined in the same way as parameters wand k described in para. 57, then

a) rheological curves are constructed for different (at least three)

soil temperatures, and after curves are constructed for different (at least

three) soil temperatures, and after rectification of these curves in loga

rithmic coordinates, the value of parameter K is determined for a different

temperature 8;

b) the resulting values of K are plotted on the diagram, the value1

of InK being plotted along the axis of ordinates, and the value of In(8 + 1)

* Blank space in Russian text (Transl.)

-40-

along the axis of abscissae, where e is the soil temperature without the

minus sign.

The section cut off by the resulting curve along the axis of ordinates

determines the value of InU, and the tangent of the angle of inclination

of the straight line to the axis of abscissae determines the value of q.

Determining Long-Term Strength Characteristics

63. Long-term strength tests with uniaxial compression are carried out

to establish the pattern of strength diminution in time and to determine

the strength of frozen soils at different times of load action.

64. To determine the long-term strength characteristics of frozen soils,

we can utilize creep tests on a series of identical specimens (paras. 21

33), providing that such tests be carried either to the failure point or

to the point at which the deformation value exceeds by 50% the deformation

at which the progressive flow stage began.

65. The number of specimens tested in accordance with the requirements

of para. 64 should not be less than five or six. The first of these

specimens is tested under a load equal to 0.9 of 00' where 00 is the condi

tionally instantaneous strength (para. 16 or 18). The load applied to the

remaining specimens is assumed to be progressively less, as specified in

para. 23. The load applied to the last specimen of a given series must

be such that failure (or the achievement of deformation value € 1.5€)p pr

occurs within the given time.

The indicated time interval is established depending on the purpose of

the tests and technical considerations:

a) if the specimens are tested for the purpose of establishing the

overall pattern of strength diminution and of evaluating frozen soils with

respect to long-term load action (e.g. in building foundation soils), the

maximum time before failure or the achievement of deformation value € =P

1.5€ should be at least 10 - 15 days;pr

b) if the tests are conducted for the purpose of evaluating frozen

soils subjected to a load for a limited, short time (hours or days), the

maximum time before failure or the achievement of deformation value

€p = 1.5€pr should correspond to the period of time the frozen soil will

be in use.

66. For greater precision in the selection of test loads and control, a

curve of long-term strength is constructed during tests (para. 67). Subse

quent loads are allocated in such a way that there are at least five or six

points on this curve in a given time interval and the distance between these

points along the axis of abscissae is increased.

-41-

67. The results of tests involving a series of specimens, each specimen

having been tested under a constant load (creep test), are entered as

shown in Appendix 3 and used for the construction of a long-term strength

curve (Fig. 24), which characterizes the relationship between the strength

of the frozen soil and the time of load action.

The long-term strength curve may be obtained directly from a series of

creep curves (Fig. 24). For this the deformation value E = 1.5E isp pr

determined on each of the creep curves, i.e. for each stress value, 01, 02,

03, etc. The resulting points are transferred to the axis of abscissae,

and from this we determine time t1, t2, t3 ... taken to achieve deformations

the portion cut offInB

of a = - --S-, fromby this line along the axis of ordinates gives

which we find parameter B = e-a S.

Parameters Sand B may also be calculated analytically, using equations

in which E = 1.5E for every given stress 01,02,03 .... These are plottedp pr

along the axis of ordinates of the long-term ｳｴｲ･ｮｾｴｨ diagram (Fig. 24b).

The corresponding values of time t1, t2, t3 ... at which deformation reached

the value E = 1.5E which was also determined from creep curves, arep pr

plotted along the axis of abscissae of the diagram. The curve constructed

from the resulting points is also a ｬｯｮｾＭｴ･ｲｭ strength curve.

68. The long-term strength curve conforms to equation (18). To verify

the validity of this equation and to determine the calculated parameters B

and S, for this equation, a graph is constructed with value ｾ plotted along

its axis of ordinates, and In(t + 1) or, when simplified, In(t), along the

axis of abscissae. If the resulting points lie in a straight line, equation

(18) is correct. The tangent of the angle of inclination of the line1

obtained from the diagram determines the value of S' and

the value

n n n

a ｾ Int + i 4= Clnt) 2 = ｾＨｾｬｮｴＩ ,

where n is the number or experimental points; a is a subsidiary value for

the calculation of parameter B.

69. Using the resulting parameters Band S, we calculate from formula

(18) the strength values at uniaxial compression for any given moment of

time t of load action.

The ultimate long-term strength is determined from formula (21).

70. If the requirements call for determination of the ultimate long-term

strength only, an approximation of this characteristic can be found by

uniaxial compression tests in which the specimen is loaded in stages.

° =i

-42-

The magnitude of each stage of the load is determined from the formula

° n.o l,

ｾ

where 0i is the stress for each i stage; 00 is the ultimate strength with

rapid load action; ni

is a factor which is assumed to be equal to the series

number of the stage.

71. Each stage of the load is maintained to the point at which stabili

zing deformation occurs (para. 32c), and so on until, at one stage in the

series, stabilization does not occur, but deformation begins to develop at

a practically constant rate. Then the next control stage of the load is

applied. The last two stages are each maintained for three days in order

to ensure that the process of deformation is in the steady creep stage.

72. The results of the staged loading tests are plotted on a graph

constructed in relative deformation € - time t coordinates (Fig. 25). The

ultimate long-term strength 000 will be included between the maximum loads

at which deformations are stabilized and the minimum load at which flow

begins. It is safe to assume that the value of 000 will be equivalent to

the first of these values.

73. The relationship of the strength of frozen soil ° (t) at any moment

of time to temperature 8 is calculated by means of equation (22), parameters

v and p of which are determined as follows:

a) a long-term strength curve is constructed for each given temperature

(at least three) and parameters Band B are determined (paras. 67-69);

b) substituting the found values of Band B in formula (18), we calcu

late the ° (t) values at the given moment of time for each temperature;

c) from the resulting data we construct a graph showing the relationship

between strength ° and temperature 8 (Fig. 26a), which is then reconstructed

in logarithmic coordinates Ino - In(e + 1), where 0 is the temperature

without the minus sign (Fig. 26b). Rectification of the curve in the latter

case confirms the validity of formula (22); the portion cut off by the

resulting straight line on the axis of ordinates will determine the value

of In v, and the tangent of the angle of inclination of the line, the value

of p .

Simplified Method of Determining Creep Characteristics

74. The method* recommended here may be used to obtain rough estimates

of creep characteristics when it is not possible to prepare the required

number of identical specimens (para. 21) or when it is necessary to reduce

the overall test period.

* This method of determining creep characteristics of unfrozen clayey soilswas developed and proposed by R.S. Meschyan.

o is the ultimate strength witho

to be equal to the series number

-43-

75. The creep characteristics are determined from the results of testing

two identical specimens, each of which is loaded by a different method.

76. The first specimen is loaded in stages. The magnitude of each stage

is determined as a fraction of the value of the conditionally instantaneous

ultimate strength 0 , found by rapid load action tests. The load for theo

first stage is assumed to be close to 0.1 of the value of 00,

In the second

and subsequent stages the load is progressively increased, the load values

being determined by the formula

where 0i is the stress being determined;

rapid load action; n is a factor assumed

of the loading stage.

77. Each stage of the load is maintained for the same time period, the

length of which depends on the soil texture and the test conditions. For

sandy and low-temperature frozen soils, each load is maintained for a

shorter period, while for clayey, particularly high-temperature frozen soils,

the load is maintained for a longer period.

In all cases the stages must be maintained for at least 24 hours.

78. Stage loading tests are conducted in a similar manner to creep tests

(paras. 24 - 31). The first stage is applied to a prepared specimen, after

which the axial and cross-sectional deformations are measured. The time

intervals between readings are fixed in accordance with para. 31. During

the test the magnitude of the acting load is adjusted (paras. 24 - 27) so

that the stress in the specimen remains constant.

79. When the given time has elapsed, the load is rapidly but smoothly

increased to 02, definable in accordance with para. 70, the test is then

conducted as for the previous stage. As soon as the period of action of

the second loading stage has elapsed, additional loading is applied to the

specimen, and so on until the test has been completed.

The number of loading stages should not be fewer than six or seven.

The test is considered complete if, during one stage of the series (but not

less than the 6th), progressive flow, characterized by an increase in the

deformation rate, is achieved.

The results are plotted on a graph constructed in relative deformation

time coordinates (see Fig. 25).

80. The second specimen is tested for creep at one constant value of

applied stress 0 const.

The test is conducted in accordance with the requirements cited in

paras. 24 - 31. The duration of the test depends on technical resources,

but must not be less than 6 - 8 days.

-44-

81. The value of the given stress is calculated so that by the end of

the set time period (6 - 8 days) progressive flow will have occurred. The

value of stress 0 is determined as a fraction of the value of the

conditionally instantaneous ultimate strength and is assumed to be equal to

0.4 00,

82. If, during the test, the specimen fails in less than 6 - 8 days or

the deformations become stabilized, the test must be repeated, the value of

the applied stress 0 = const having been appropriately decreased or in

creased.

83. A creep curve is constructed during the test (see Fig. 2). In order

to do this, values of absolute deformation A. (col. 8) and the correspondingl

times ti

(col. 3) are taken from the log book (Appendix 2); then theA.

relative deformation E= hl

is determined, h being the initial neight of

the specimen. From this data a graph is constructed, the relative defor

mation E being plotted along its axis of ordinates and the corresponding

time t along its axis of abscissae.

Processing Experimental Data and Determining Creep Characteristics

84. The deformation patterns of frozen soils and their deformative

characteristics are established on the basis of test data. The relationship

between stress and deformation and the pattern of variation of deformation

in time (para. 40) are the main patterns.

85. The relationship between stress and deformation characterized by

the series of curves shown in Figure 15b is established through the following

reconstruction of the creep curve obtained from staged loading tests (see

Fig. 25):

a) on the axis of abscissae of the deformation-time diagram within the

sectors corresponding to each loading stage (except the last) in which the

deformation process occurred in the progressive flow phase, we plot at least

five or six points (corresponding to different moments of time t of load

action). The points must be evenly distributed along the axis of abscissae;

b) from each point tl, t 2, t 3... a straight line is drawn parallel to

the axis of ordinates; the points at which these lines intersect with the

creep curve at each loading stage determines the value of deformations El,

E2, E3 ... caused by stresses 01,02,03", at given moments of time tl, t 2,

t3 ... of load action.

The results are processed in aocordance with paras. 42 - 57. Parameters

A(t) and m of equation (3) are determined as a result of such processing.

86. The pattern of variation of deformation in time K(t) (a function of

creep) is determined from data obtained from tests carried out on the

second specimen with a constant load. To determine the pattern of variation

-45-

of deformation in time, the resulting creep curve is reconstructed in rate

of deformation t-time t coordinates.

This curve is then reduced to a single load. For this, the ordinates

of the £-t curve (except those in the progressive flow portion) are divided1

by the quantity --, where m is an exponent, determined in accordance witham

para. 85.

87. The analytical expression of the creep function K(t) and the para

meters of this relationship are determined by the normal method of compiling

empirical formulae. The form of the creep function should correspond to

coefficient A(t), determined experimentally with staged loading (para. 85).

Correspondence of the creep function K(t) and coefficient A(t) (see Section

I) confirms the validity of the fast method of determining creep character

istics recommended here.

88. If the creep function K(t) and the coefficient of deformation A(t)

do not correspond, it means that the creep curves are not mutually similar.

In this case, the recommended method cannot be used, and these characteris

tics should be determined by the usual method (Section III, paras. 20-57).

-46-

IV. METHODS OF LONG-TERM STRENGTH TESTING IN SHEAR

UNDER CREEP CONDITIONS

Instrumentation

1. The strength of frozen soils in shear is tested by means of the

shear apparatus developed by the Gidroproekt and commonly used for testing

unfrozen soil, and the wedge tester (Fig. 27) developed by the All-Union

Research Institute of Mine Surveying and used for testing the shear strength

of cemented soils(17).

2. The shear apparatus is used for testing frozen soils at stresses

not exceeding 25 - 30 kg/cm 2 (para. 3), the wedge tested for stresses higher

than 25 - 30 kg/cm 2• The application of the wedge tester at lower stresses

is possible if testing is done within the range of low values of the normal

stress. If testing is to be done within a wide range of stresses, it is

recommended to use both instruments (the shear apparatus at stresses below

25 - 30 kg/cm 2 and the wedge tester at higher stresses).

3. The shear apparatus developed by the Gidroproekt is designed for

horizontal stresses of up to 7.5 kg/cm 2 and vertical stresses of up to 12.5

kg/cm 2• If testing is to be done at higher stresses (up to 25 - 30 kg/cm

2) ,

the apparatus must be modified: the cable diameter of levers of the hori

zontal and vertical loads is increased and the area of the specimen is

reduced. To reduce the area of the specimens, a metallic ring with an

internal diameter of not less than 50.5 mm is inserted into the cutter of

the instrument.

4. The wedge tester consists of several (at least three) pairs of

cast iron casings. Each pair of casings ensures shearing at a definite

angle of inclination of the specimen (see Fig. 27). For each angle of

inclination a, there is a specific constant ratio of normal and tangential

stresses 0 IT. Different ratios of normal and tangential stresses aren n

achieved by changing the angle of inclination of the specimen.

5. A specimen of frozen soil is placed between two casings (see Fig.

27). The lower casing (3) is stationary, while the upper casing (2), to

which the load is applied, moves and cuts the sample at an angle to the

horizontal a. The load P is applied vertically but because of the inclined

position of the specimen, it divides into a normal (0 ) and a tangentialn

(1 ) components.n

6. Tests in the wedge tester are conducted at an angle of inclination

of the specimen of from 30 to 60 - 70°. It is not recommended to deviate

from these limits, since at an angle of less than 30° the specimen is

crushed and at angles exceeding 60 - 70° it turns over.

-47-

Load P on the wedge tester is created by hydraulic or mechanical

presses (paras. 1-3, Section III). Lever presses may be used in tests

on weak soils. To reduce the effect of friction between the plate of the

press and the tester, the pressure on the upper casing of the press is

transmitted through a set of metallic rollers (13 - 15) interconnected by

a chain*. The deformations are determined by means of measuring devices

(para. 5, Section III).

7. In the case of the wedge tester, the ratio of the normal (an) and

the tangential (Tn) stresses depends on the angle of inclination a; these

stresses are found by means of the following formulae:

P kg/cm 2,a =E

cos a,n

psin kg/cm 2,T = F

a,n

(29)

(29 I )

where a is the angle of inclination of the specimen; F is the area of shear,

cm 2; P is the vertical load, kg (the ratio ｾ is expressed through S).

8. The specimens of frozen soil used in shear tests are of cylindrical

shape. Rectangular specimens may also be used in the wedge tester. The

measurements of specimens used in the Gidroproekt shear apparatus are:

h = 50 mm, d = 71 mm.

The measurements of specimens used in the wedge tester are: d = 71 mm,

h = 100 mm. Larger testers can also be constructed. Special packing is

used for testing smaller specimens. Separable semidisks of appropriate

thickness are inserted from both ends to compensate for the small size of

the specimens; inserts of various thickness with the radius of the concave

surface equal to the radius of the sample are used to compensate for the

small diameter of the latter.

9. When preparing specimens for tests in the wedge tester, special

attention should be paid to the precision of grinding the ends of the

specimen, since even a slight deviation of the end plane from an angle of

90° to the axis of the specimen has a considerable bearing on the

experimental results.

Tests at Rapid Load Action

10. The purpose of these tests is to find the instantaneous (maximum)

values of basic parameters determining the strength of frozen soil: the

cohesion (c ) and the angle of internal friction ＨｾＩＮ The shear strengtho 0

* On using a roller chain, the coefficient of friction is very low and maybe taken as zero.

-48-

of frozen soil is determined without preliminary compaction, i.e. frozen

soil is regarded as being overcompacted*.

11. The tests in the Gidroproekt apparatus are carried out at different

values (at least three) of the normal load in accordance with the task in

hand. The tests should be repeated at least three times, but if very

scattered results are obtained the number of parallel tests is increased.

12. A specimen of frozen soil is placed in the shearing part of the

apparatus and is kept there for 20 or 30 minutes. It is then subjected to

the given normal load (0). Immediately after that the specimen isn

subjected (rapidly but without hitting) to an increasing shearing load (T).

The loading is done by means of shot or weights. The duration of the test

is checked by a stopwatch. The time interval between the start of loading

and the end of the test must be 30 seconds.

The test is regarded as complete when the specimen has failed or

continuous shearing of soil has begun.

A sample is taken from the shearing zone after testing to determine

the moisture content.

13. Resistance to rapid shear (TO) is determined by dividing the

failure load T by the area of the cross-section of specimen F. These data

are recorded in a log book (Appendix 4).

14. The results of tests on given soils at given temperatures are

represented in the form of a rapid shear diagram (on - Tn) (Fig. 28).

The conventional instantaneous cohesion (c ) and the angle of internalo

friction ＨｾｯＩ corresponding to the rapid loading of frozen soil of given

temperature are determined graphically from this diagram. The cohesion is

found as a section of the ordinate cut off by a straight line, and the

angle of internal friction as the angle formed by this straight line and the

abscissa. The results obtained are recorded in a table (Appendix 5).

15. For certain frozen soils the relationship between T and cr is re-n n

presented by a curve. In this case the curve is replaced by a broken

straight line consisting of two sections and the values of c and ｾ are

determined separately for each section. When the calculation method used

does not make it possible to apply the values obtained, the curve may be

replaced by one averaged straight line.

* High dispersion frozen soils (clays and clay loams) with temperatureshigher than -2 or -3°C, and sandy soils with temperatures exceeding -0.5 0C,

display a certain compressibility. It would be better to test the shearstrength of such soils after preliminary compaction. However, since thisis difficult to accomplish, even these soils are tested without preliminary compaction.

-49-

16. Tests in the wedge tester are carried out at different (at least

three) angles of inclination of the specimen a determined by the task in

nand. It is recommended to use a = 30, 45 and 60°. The test must be

repeated at least three times.

17. A specimen of frozen soil is placed in the ｣｡ｳｩｮｾ of the tester,

which is mounted below the press at a given angle of inclination a, and is

kept there prior to the start of the experiment for 20 or 30 minutes.

18. An increasing vertical load (p) is applied to the specimen rapidly

but without hitting it. The duration of the test is checked by a stop

watch. The time interval between the start of loading and the end of test

must be 30 seconds. The test is completed when the specimen fails or

continuous shearing sets in. The results are noted in a log book (Appendix

6) .

19. A sample is taken from the shearing zone after testing to determine

the moisture content. The shear strength Tn and the normal stress an are

found for each angle of inclination a by means of formulae (29) and (29').

20. The test results are recorded in the form of a diagram of shear

(Fig. 28). The instantaneous cohesion (co) and the angle of internal

friction ＨｾｯＩ are found from the diagram (paras. 14 - 15).

The results obtained are noted in a final table (Appendix 5).

21. If it is required to determine c and ｾ for a wide range of normalo 0

stresses, the test results obtained with the Gidroproekt apparatus and the

wedge tester are recorded in a common diagram of rapid shear, and Co and ｾｯ

are found from it as described in paras. 14 and 15.

22. If apart from the shearing tests, the uniaxial compression of given

soil was also tested (at rapid load action), the results of these tests are

also recorded in the diagram of shear. The compression force causing

failure (00)

is recorded along the abscissa and a semicircle with the centre0

0at the point an ｾ is constructed on the section obtained. The straight

line (or a curve) based on the results of shear tests must form a tangent

to the circle and this serves as a check of the accuracy of results obtained.

Tests with Long-term Load Action

23. The purpose of the tests is to determine the shear strength, the

cohesion and the angle of internal friction of frozen soil for different

durations of the shearing force.

24. As in the case of rapid shear, the tests are carried out by applying

different (at least three) normal loads (in the shearing apparatus) and at

different (at least three) angles of inclination of the specimen a (in the

wedge tester). The values of the normal load are determined by the task

in hand.

-50-

25. A separate series of long-term shear tests for different values (at

least six) of the shearing load T (shearing apparatus) or the vertical load

P (wedge tester) is carried out for each normal stress on (shearing appara

tus) or angle of inclination of the specimen a (wedge tester).

Eighteen to twenty identical specimens of frozen soil are prepared for

a cycle of such tests at the same temperature and three different normal

stresses (or angles of inclination).

26. Each series of samples (at on = const or a = const) is tested at

different (constant for'the duration of each test) values of the shearing

stress T (shearing apparatus) or the ratio P/F = S (wedge tester). Then

deformation of the specimen is measured in the course of the test (para. 31,

Section III). Each sample is tested to failure or until the value of defor

mation is Ap

1.5Ault'

27. The load applied to each specimen is determined as a certain fraction

action (paras. 13 and 19)

or a (wedge tester). The

or S (wedge tester) equal

of the instantaneous strength durins shear determined in the tests with

for the same values of ° (shearingn

first specimen is tested at T (shearingn

ｴｯｾｏＮＹ of the value of the instantaneous

rapid load

apparatus)

apparatus)

strength. The second and all subsequent specimens are tested at progressi

vely lower values of T or S: T1 > T2 > T3 .•• , or Sl > S2 > S3' .. , whichn

are determined in accordance with para. 23, Section III. The load on the

last specimen must be such that failure or deformation Ap

= 1.5Ault does

not occur prior to the expiry of the given time interval, which is determined

by the task in had in accordance with para. 33, Section 111*.

The progress of the test and the selection of loads are checked by

plotting long-term strength curves (para. 41) in the course of investigations,

and these serve for checking (para. 66, Section III) the loads applied to

subsequent specimens in the given series.

28. The constancy of stress in the course of the test is ensured in the

same way as during uniaxial compression, the only difference being that

owing to the reduction in the working area of the specimen, the load on

shearing is reduced proporttonally to the reduction in the working area.

29. If the change in the area of the specimen does not exceed 5%, the

load acting during shearing is reduced by a value equal to the product of

the given stress and the changed area of the specimen.

* If the selected load is small, the specimen will not fail in the giventime interval and the test will result in stabilization of deformation(para. 32, Section III), or flow at a constant rate.

-51-

30. The loads required to ensure the constancy of stress during the

test are calculated prior to testins and their values are recorded in a

table. The load at a given deformation of the ｳｰ･｣ｩｾｬ･ｮ is determined

directly from the table and the load is reduced as required (manually or

by means of automatic control).

31. The frozen soil specimen intended for testins in the shearing

apparatus is placed in the shear apparatus; the indicator measuring the

deformation is set at zero. The specimen is kept in the apparatus for 20

or 30 minutes prior to testing and is then sUbjected first to normal and

later to shearing loads of Given value.

32. The load is transmitted uniformly without impact, and is increased

evenly until it reaches the given value. The time interval during which

the load reaches the ｾｩｶ･ｮ value must be the same for all tests (20 - 30

sec).

The deformation of the specimen is measured from the moment the load

reaches the given value. The setting of the indicator corresponding to this

moment is regarded as the zero setting.

33. The soil specimen intended for testing in the wedGe tester is

placed in the casing of the apparatus mounted beneath the press at a given

angle of inclination a.

The mounted specimen is kept in the apparatus for 20 or 30 minutes.

It is then sUbjected to the given vertical load P (see para. 32) and its

deformation is measured.

34. The rate of deformation v is calculated for each time interval be

tween the measurements, as outlined in para. 30, Section III.

35. The time intervals between the measurements of deformation are

selected in accordance with the stage and rate of deformation (see para. 31,

Section III).

36. The data obtained in the course of these tests are recorded in log

books (Appendix 7).

The time recorded in columns 2 and 3 of the log book is measured in

minutes in the first hour of testing and later in hours. The deformation

indicator readings are recorded in column 5. The absolute deformation Ai

(column 7) is determined as a difference between the given and the "zero"

readings corrected for the deformation of the apparatus.

The deformation increment (column 8) is calculated as a difference

between the given and the preceding deformation. The loads T and P (columns

10 and 11) (shear tester) on P (wedge tester) are recorded with allowances

for changes in the course of testing (para. 29). The deformation rate

(column 9) is calculated by dividing the deformation increment by the time

interval corresponding to this increment.

1.SAu l t

is determined

The results obtained are

-52-

37. If the purpose of the test is to determine the ultimate long-term

shear strength only, the specimens are loaded in stages.

To construct a diagram of shear, it is essential to carry out at least

three tests at different values of the normal load (shear apparatus) or angle

of inclination of the specimen (wedge tester) which are constant for the

duration of each test. Each test is conducted at different stages of the

shearing load T (shear apparatus) or vertical load P (wedge tester). Each

loading stage is determined according to instructions in para. 70, Section

III.

38. Each loading stage (T or p) is maintained until deformation is

stabilized (para. 32, Section III). On increasing the load, no stabilization

will occur in a subsequent stage and the deformation rate will remain

practically constant. ｾｨ･ next loading stage is then applied for checking

purposes. The last two stages are maintained for three days each to make

certain that deformation is taking place in the steady creep phase. The

test is then terminated. In the course of ｴ･ｳｴｩｮｾＬ the deformation is

recorded in accordance with paras. 3la and 31b, Section III.

Processing Experimental Data and Determining the Characteristics of Long

term StrenGth

39. The experimental data recorded in the log book (Appendix 7) are

used for plotting the curves illustrating creep at shear. Time t (column 3)

is plotted along the abscissa and the corresponding values of the absolute

deformation Ai (column 7 in the log book) for the given values of L

nor S

along the ordinate. This results in a family of creep curves for each

value of the normal stress an (shear apparatus) or the angle of inclination

of the specimen a (wedge tester). Each curve corresponds to a constant

value of Tn or S (see Fig. 24).

40. Time t corresponding to deformation Ap ｾ p

from the creep curves for each value of T or S.n

recorded in Appendix 8.

41. Each family of creep curves is replotted to give its own curve of

long-term strength (Fig. 24). For this the values of T1, T2, T 3. • •. (shear

apparatus) or S1, S2, S3'" (wedge tester) are plotted along the ordinate,

while the time during which the deformation reached A = 1.SA It (t , t ,P U PI P2

t ... ) is plotted along the abscissa.p 3

The number of curves illustrating the long-term shear strength corres

ponds to the number of different normal stresses a or angles of inclinationn

of the specimen a (Fig. 29a).

42. The values of Sand B in equation (18) are found from the long-term

strength curves in accordance with paras. 68-69, Section III, if R(t) in

T and the normal stressn

c and ｾ are determined in

-53-

equation (18) is substituted by T(t) or Set). The values of Band B at

shear are determined for each normal stress 0 or angle of inclination ofn

the specimen a.

43. The values of T(t) or Set) for different 0 or a at any given momentn

of time t are calculated by substituting the obtained values of Band B in

equation (18). The ultimate long-term shear strength Too or the value of Soo

are determined by means of equation (21).

44. The shear diagrams are constructed for different given moments of

time (Fig. 30). If tests are conducted in the shear apparatus, the diagrams

are based on the values of the shearing force Tn (the ordinate) calculated

(para. 43) for the given moments of time and the corresponding values of

the normal stress 0 (the abscissa). In the case of tests in the wedgen

tester, Tn and on are calculated from the values of S (equations (29) and

(29')) determined for the given moments of time and different angles of

inclination of the specimen a. Each diagram of shear corresponds to its

own time to failure. If tests are conducted simultaneously in the shear

apparatus and the wedge tester, the results are recorded in one common

diagram (para. 21).

45. If a given soil is subjected to both shear and uniaxial compression,

the test results are also plotted on the diagram of shear in accordance with

instructions in para. 22. The values of compression strength recorded on

the diagram refer to the same moments of time as those used in the construc

tion of the diagram.

46. The characteristics of strength - the cohesion c(t) and the angle

of internal friction ｾＨｴＩ of frozen soil for any moment of time ti,

are

determined as parameters of the straight line in the shear diagram corres

ponding to the given time of load actions (see Fig. 30). The value of c

is found from the segment of the ordinate cut off by the straight line and

the angle ｾ is the angle of inclination of this straight line towards the

abscissa.

If the relation between the shearing stress

on is expressed by a curve on the shear diagram,

accordance with instructions in para. 15.

47. Parameters Coo and ｾｯｯ are determined from the shear strengths cal

culated by means of equation (21).

48. The results of tests with loading in stages are used in approximate

determinations of indices of the ultimate long-term shear strength. This

involves plotting deformation versus time as shown in Figure 25.

Deformations (A) is plotted along the ordinate and time along the

abscissa. A new diagram is constructed for each value of ° (shear appan

ratus) or the angle a (wedge tester). For each loading stage there is a

-54-

corresponding value of the shearing force T (shear apparatus) or the

vertical force P (wedge tester). Each diagram indicates that some loads

lead to stabilization of deformation (E = 0), while other loads result in

a constant rate of flow (E = const). The value of the ultimate long-term

strength will lie between the greatest load resulting in stabilization of

deformation and the smallest load leading to a constant rate of flow. To

be on the safe side, the ultimate long-term strength may be taken as equal

to the greatest load resulting in stabilization of deformation.

49. In the case of tests in the shear apparatus, the values of Too are

obtained directly from the curves A versus t. In the case of tests in the

wedge tester, they are calculated by means of equations (29) and (29') by

substituting into them the values of Poo

determined from the curves for

different angles a. The data obtained are used for the construction of a

shear diagram and the determination of Coo and ｾｯｯＧ

50. If it is required to determine c and ｾ of frozen soil in the case

of brief load action, they are found directly from the test data by re

plotting the long-term strength curves on the shear diagrams. Calculations

by means of equation (18) may be omitted.

51. If use is made of the Gidroproekt shear apparatus, this replotting

is done as follows.

The given time tp 1'

for which it is required to determine c and ｾ is

plotted on the abscissa in the long-term strength diagram (see Fig. 29).

A perpendicular is drawn from this point intersecting the T versus tn p

curves plotted for different values of a The points of intersectionn

which determine T for the given moment of time t at different values ofn PI

an are projected to the ordinate in the shear diagram (see Fig. 29b). The

corresponding values of a are plotted along the abscissa. The resultantn

straight line will represent the shear at the given moment of time t andp 1

C and ｾ are determined from it.

52. In the case of the wedge tester, the procedure is as follows. The

long-term strengths are plotted in accordance with instructions in para. 41

for different values of a (see Fig. 29a). The given time t , is plottedp

on the abscissa. A perpendicular is drawn from this point and its inter-

section with the S - t curves will determine S at the given moment of timep

and angle a. By substituting these values of S and a into equations (29)

and (29'), we can calculate T and a , construct a diagram of shear, andn n

determine c and ｾ for the given moment of time tP l

(Fig. 29b).

-55-

v. METHODS OF COMPRESSION TESTING

Instrumentation

1. The compression of frozen soils can be determined by means of com

pression devices (lever presses, consolidometers) intended for testing

unfrozen soil, with due consideration being given to requirements mentioned

in paras. 2 and 3. It is recommended to use the following devices:

a) the devices designed by the Central Research Institute of the

Ministry of Communications, consisting of four consolidometers (the area

of working rings of 40 cm 2) and four lever presses with a total lever arm

'I'atio of 1 : 40(18);

b) the devices designed by the Central Research Institute of the

Gidroproekt, consisting of a consolidometer with an area of working rings

of 60 cm 2 and a lever press with a lever arm ratio 1 : 20 (table model);

c) the devices designed by the "Burovaya Tekhnika" plant (K-l),

consisting of a lever-disk press and a consolidometer with an area of

working wheels equal to 60 cm2(19).

2. The compression device (the consolidometer) used in testing frozen

soils must satisfy the following requirements:

a) all parts must be made of corrosion resistant materials; the instru

ments ｭ･｡ｳｵｲｩｮｾ deformation must be mounted directly on the stamp or the

bottom plate of the consolidometer;

b) to avoid plastic pressing out of ice from the consolidometer, the

perforations in the stamp and the bottom plate must not exceed 0.5 mm, while

the gaps between the stamp and the working rings must be less than 0.1 mm;

c) the working rings of the consolidometer must serve also as sampling

devices (for this, one of their edges is sharpened by bevelling from the

outside), the thickness of ring walls must not be less than 0.03 - 0.04 of

the diameter;

d) the ratio of the height of the working ring to its internal diameter

must not exceed 1 3 when testing frozen soils with a massive cryogenic

texture and a total moisture content not exceeding 50%; in the case of soils

with layered and reticulate texture and a moisture content exceeding 50%,

this ratio must be at least 1 : 3 and not higher than 1 : 1.5.

3. The lever press used in testing frozen soils must be chosen in

relation to the maximum compacting load (para. 16). This requirement is met

by presses with a capacity of 0.5 - 1.5 ton. It is recommended to use

presses with load application from below.

4. Deformation is measured automatically or by individual readings of

dial indicators. Owing to a negligible rate of compressibility of frozen

soil, it is recommended to use measuring devices with an accuracy to O.OOlmm.

ｾ '. ., -1 t ＧｾＬＮＮ -d' a t C>VI a nz l e ,," IR"o ','" tel r e s pe c t "0j-'ilIO Ｈｪ･ｖｾｌｃ･ｓ S(10U.l:....... JP U;"3C'Q, JLiOUrJ.ltt-.: c .... ［ｬｾ 0.1 _lS....L U,,- :.Jv ＮｾＭＮｩ 1 .L _' L.- 0

ｉｾ｡ c h other.

5. ｾｨ･ deformation of the apparatus is determined by calibration

｡｣｣ｯｲ､ｩｮｾ to existing methods(20) in a room with a negative temperature

corresponding to the temperature of subsequent tests and under the same

loads as in the test.

ｾｨ･ calibration results are recorded in Appendix 9 and are used in the

construction of a curve ＨｆｩｾＮ 31) required for the calculation of actual

d'?formation.

G. The size of test specimens must correspond to that of working ｲｩｮｾｳＮ

The specimens must have thoroughly cleaned (with a ｳｴｲ｡ｩｾｨｴ blade knife) and

pol j ,;hed (with thin sandpaper) top and bottom surfaces wh I c h must be

nara]]eJ to each other.

'I , The height of the specimen is measured (at least six times) with a

slide gauge to within 0.05 mm; this also confirms whether the top and

bot tom cur-f'a c e s are really parallel.

8. In compression testing of frozen soils from beneath planned

structures, use must be made of undisturbed specimens with natural ice

content and temperature.

9. The compressibility of frozen soils used as a building material in

various earth structures is found from the results of tests on artificial

specimens with a ｾｩｶ･ｮ ice content, temperature and cryogenic texture.

ｔ･ｳｴｩｮｾ Procedure

10. Compression testing is done to determine the following indices of

compressibility of frozen soils:

a) the compressibility of soil under any given ultimate ｬｯｮｾＭｴ･ｲｭ load;

b) the recovering deformation (e )* and residual deformation (e ).rec "res '

c) the reduced coefficient of compressibility (ao);

d) the compression modulus of deformation (E ).c

11. The indices of compressibility of frozen soils are determined by

measuring linear deformations. Other methods (based on changes in porosity

and weisht) are not used.

12. The temperature regime must remain constant (for instructions see

Section II).

If it becomes impossible to maintain a constant temperature throughout

the entire test, a drop in temperature (by not more than IOC) for a brief

period of time is permissible. However, it is essential that the given

* In contrast to preceding chapters, the follOWing symbols are used in thepresent chapter: e - relative deformation; E - coefficient of porosity.

-57-

temperature is reestablished and maintained until deformation becomes

stabilized.

13. In order to determine the indices of compressibility of frozen

soils which characterize the extent of compactness of the latter (e, ao'

Ec)'

the specimens are tested under a load which is increased in stages,

with each stage being maintained until deformation becomes stabilized.

14. The number and magnitude of loading stages are determined by the

type of frozen soil and its temperature:

a) the loading of sandy soils must be done in stages, which are being

increased by successive amounts of 3 - 4 kg/cm 2;

b) it is recommended to load clayey soils (clay, clay loam) with a

temperature below _2°C in stages which are being increased by successive

amounts of 3 - 4 kg/cm 2, and of not more than 1 - 2 kg/cm 2

, if their temper

ature is above _2°C.

15. The load in the first stage depends on the structure of frozen soil:

a) on testing soils with a natural structure, the load must correspond

to the natural pressure Pb determined from the following equation:

(30)

where H is the depth from which the specimen was taken (in m); y is the

unit weight of frozen soil (t/m 3) ;

b) on testing soils with an artificial ｳｴｲｵ｣ｴｵｾ･ and a temperature

above _2°C, the load in the first stage must not exceed 0.5 kg/cm 2, and for

soils with a temperature below _2°C it may be taken as 0.5 - 2 kg/cm 2•

16. The load in the last stage, i.e. the maximum compacting pressure,

depends on the load rating. If the load rating is not known, use may be

made of the ultimate strengths given in corresponding specifications.

In accordance with eXisting specifications SN 91-60(21), the maximum

compacting pressures may be taken as follows:

a) For sandy soils and soils with a temperature below _2°C, the com

pacting pressure may exceed the rated strength (see table) by a factor of 2.

-58-

Rated strengths of frozen soils

Strength at the "lax. mean

Soil"lonthly temp. of soil at

the level of foundationbase (rn )

I -0.5_ l ..... -2.5 -1. 0ｾＮＯ

Fine sand, sandy loar:1 2.0 5.0 7.0 8Clay 10ar:1 and clay 2.5 4.0 6.0 7Sar:1e but silty ..., " '< " 4.0 6L..GU _J. U

Clay solIs ' ｾＧ contentwi cn')f organic a dmi xtures

Iranging fro"l 3 to 12% 1.5 2.5 3.5 5

Note: Rated strengths for intermediate temperatures are

determined by interpolation.

b) F f '1 '+-' t t b -?oC, the ｣ｯｭｰ｡｣ｴｩｾｾ｟ｾor razen SOl s ｷｬｾｮ a er:1pera ure a ove - lib

pressure may exceed the rated strength by a factor of 3 or 4.

17. Prior to each test, frozen soil is compressed from all stdes to

ensure maximum contact of the top and bottom surfaces of the specimen with

the stamp and the bottom plate of the consolidometer. This is done as

follows:

a) The soil specimens with a temperature above _1°C are placed for 30

seconds under a load equal to the maximum compacting pressure.

b) The soil specimens with a temperature below _1°C are placed for 1

min under a load equal to the maximum compacting pressure.

18. The changes in deformation with time are observed during each

loading stage. The subsequent loading stage is applied after (nominal)

stabilization of deformation in the given stage.

The deformation is considered to be stabilized if its increment does

not exceed 0.002 mm in the following intervals of time: 6 hours for sand,

12 hours for sandy loam, 24 hours for clay and clay loam.

The deformation is considered to be stabilized also if its increment in

the course of a test is less than 1% of total deformation under a given load

in the intervals of time given above.

19. To determine e and e , the load is removed from the specimensrec res

after the compaction under the given load has been completed.

20. Depending on requirements, the load is removed either after each

loading stage or at the end of the loading cycle. In the latter case the

load is removed gradually and in stages corresponding to the loading stages.

21. The recovery of deformation with time is measured while removing

the load. Readings of measuring instruments are taken every minute and later

in accordance with instructions in para. 18.

-59-

22. The readiness of all details of the apparatus, mainly of its

penetrating parts (stamp and bottom plate), and the passage of the stamp

through the operating rings are checked prior to each test (check for

ellipse) .

23. The weight of the load (PJ

, kg) is determined for each loading stage:

PI = pFN,

where F is the area of the soil specimen calculated from the internal

diameter of the working ring (cm 2) ; N is the ratio of the lever arms of the

press (for example 1 : 20 or 1 : 40); p is the load applied to the specimen

(kg/em 2) •

24. Weight and dimensions (the internal diameter) of working rings are

determined and recorded in Appendix 10.

25. The specimens are prepared for testing in accordance with instruc

tions in Section II. A prepared specimen is weighed together with the

working ring on technical scales to within 0.01 g. The temperature in the

weighing room must correspond to the testing temperature. The results of

weighing are noted in Appendix 10 (VII, Column 1).

26. The height of the specimen is measured in accordance with para. 7

and recorded in Appendix 10 (VI, Columns 1 - 6).

27. The specimen is placed in the consolidometer. The stamp and the

devices for measuring the deformations are mounted, after which the specimen

is kept in the consolidometer for at least 20 or 30 minutes.

28. The readings are taken from deformation measuring devices set at

"zero" and are recorded in Appendix 11, columns 8 and 9. The specimen is

then compressed (para. 17) and the readings are repeated.

29. The deformation measuring devices are again set at "zero"; the

initial readings are taken and recorded in Appendix 11. The first loading

stage is then applied. The stopwatch is released at the same time and sub

sequent readings are taken.

30. The readings of measuring devices are taken in accordance with

para. 18. The established pattern is retained in all subsequent loading

stages.

31. In tests carried out in accordance with paras. 19 and 20, the load

is removed from the specimen until it reaches a value equal to that in the

preceding stage. Having reduced the load, the deformation is measured

(para. 21) and the results recorded.

32. When the recovery of deformation is complete, which is determined by

reading the indicators in accordance with para. 18, the ｾｯ｡､ is again reduced

to a value corresponding to that in the preceding stage, and so on until

the load has been removed completely.

-60-

33. In all tests, the temperature is measured together with deformation.

It is recorded by automatic devices or from individual readings and is

noted in Appendix 11, ｣ｯｬｵｾｮ 7.

34. After the stabilization of deformation in the last loading stage

(or the last unloading stage, if the tests were conducted by removing the

load in stages), the test is regarded as complete and the consolidometer is

quickly dismantled (in a few minutes).

35. The soil specimen is removed from the consolidometer together with

the ring. Pressed out moisture may be present on the surface of the speci

men. It is recommended to remove it with filter paper. The specimen is

then weighed (together with the ring) to within 0.01 g on technical scales

located in the same room. The data is recorded in Appendix 10, VIII,

column 1.

36. The weighed specimens and the ring are put in a porcelain cup, placed

in a thermostat and dried to a constant weight at 100 - 10SoC. The

weighing results are recorded in Appendix 10, VII, Column 4.

Processing ｅｾｰ･ｲｩｭｾｮｴ｡ｬ Data and Determination of Compression Characteristics

37. The initial ｨ･ｩｾｨｴ of the specimen is determined to within 0.01 mm

from the results of measurements carried out in accordance with para. 7. It

is calculated as the arithmetic mean (hi n i t)

of the number of measurements

(n) made with a slide gauge:

hh , + h 2 + h 3 ... + h n

init = n

38. Having determined the dimensions of the specimen (the height and the

diameter), the weight of the ring (q ), the combined weight of the frozenr

specimen and the ring prior to (qfr) and after testing (q1fr)' and the

weight of the dry specimen (qd)' the following soil characteristics are

calculated:

a) the volume of the specimen (to within 0.01 ｣ｭＳＩｾ

V = hi nit F cm3

, (33)nd 2

where F = ｾ is the area of the specimen (cm 2) and d is the internal

diameter of the ring (cm);

b) the unit weight (to within 0.01 g/cm 3) :

y =q - qfr r / 3.

V g cm ,(34 )

c) the unit weight of the skeleton (to within 0.01 g/cm 3):

qdy s = V g/cm 3; (3S)

d) the initial coefficient of porosity (to within the first three

decimal point s ) :

(36)

-61-

Yuw - Ys

Ys

where y is the unit weight of soil (g/cm3

) ;uw

e) the total moisture content (Wt o t)

and ice content (i) of the

specimen prior to testing (to within 0.05%):

( 37)

(38 )

where Wun f

is the unfrozen water content(13);

f) the total moisture content (W'tot) and ice content (i') after

testing (to within 0.05%):

W'tot

i' = W'tot - Wun f'

(39)

(40)

The results are recorded in Appendix 10, VI, columns 11-12, and VII,

column 9.

39. The test results (Appendix 11, V, columns 8 and 9) are used to

determine the ｡｢ｳｯｬｾｴ･ deformation of soil and apparatus (column 12) to

within the first three decimal points, This is calculated as a mean (A )m

of two indicator readings (or two recordings of automatic devices) as

follows:

Am

(41)

(42)

where AI and All are deformations of specimens calculated as differences

between the given and the initial readings of the first and the second

indicators (mm).

The absolute deformation of soil A = 6h is calculated with corrections

for calibration (Appendix 9, VIII, column 6) and is recorded in Appendix

11, column 13.

A = A - Am ap'

where A is deformation of the apparatus (rom).ap

40. The relative deformation of soil is determined for every load and

all time moments of its application to within the first four decimal points

or 0.01%. It is calculated by means of equation (43) and is recorded in

Appendix 11, column 14.

Ae = or e

hi nit

A. 100%,

hi n i t

(43)

(44)

-62-

where A is the absolute deformation of soil (mm); hi n i t

is the initial

height of the specimen (mm).

41. The results recorded in Appendix 11 are used to construct the

following:

a) the .consolidation curves, i.e. the curves illustrating the relation

between the relative deformation and the time under a constant load (Fig.

32), which serve to indicate the stabilization of deformation

e = f(t);

b) the compression curve, i.e. the curve illustration the relation

between the relative deformation and the load (Fig. 33)

e = f(p).

42. The compression curve is based on the final deformation of soil,

i.e. on the stabilized deformation in each ｬｯ｡､ｩｮｾ stage. It is constructed

by plotting the load values (in kg/cm 2) along the abscissa, and the relative

deformation (e) along the ordinate.

43. The curve illustrating the relation between the relative deformation

and the load is used to determine the reduced coefficient of compressibility

a. This coefficient is expressed as the ratio of the increment of theo

relative compression deformation Ｈｾ･Ｉ and the increment of the load ＨｾｰＩＬ

and is determined as the tangent of the angle of inclination towards the

abscissa of a strajght-line passing through two points on the compression

curve within the selected interval of compacting loads (see Fig. 33)

a = tan ao P2 - Pl

The load intervals ＨｾｰＩ and the corresponding changes in soil deformation

Ｈｾ･Ｉ are determined by plotting and are recorded in Appendix 12, columns

4 - 5.

44. If it is required to determine the coefficient of compressibility

a expressed as a ratio of the change in the coefficients of porosity ＨｾﾣＩ

and the increment of the load ＨｾｰＩＬ i.e.

ｾ£

a = ｾＮ

P

this is done as follows:

a) the coefficients of porosity (£ ) under all given loads areP

calculated:

A= e is the relative

hi n i t

A£ = £ h (1 + £ ),

P 0 init 0

where £0 is the initial coefficient of porosity;

deformation of soil:

(45)

-63-

b) the E-p compression curve is constructed by plotting the change in

compacting pressures along the abscissa and the corresponding change in the

coefficient of porosity along the ordinate (Fig. 34);

c) the curve illustrating the relation between the change in the

coefficient of porosity and the pressure is used to determine the

coefficient of compressibility a as the tangent of the angle of inclination

towards the abscissa of the straight-line passing through two points on the

curve within the selected interval of compacting loads

( 46)

45. The data in Appendix 12, columns 5 or 6, are used to determine the

compression modulus of deformation which is a reciprocal of the specific

coefficient of compressibility.

Ec

1a

o

P 2 - P 1

kg/cm 2. (47)

46. The results of tests carried out by removing the load from the

specimen are used to determine the recovering deformation of the soil and

the apparatus (Appendi x 12). It is cal cula ted as a mean (A' ) of de formam

tions (A'I and A'II)' recorded by two measuring deVices, with the help of

the following formula:

A'm

A'I + A'II2 mm. (48)

9, VII,

determined

- A and relative -rec(Appendix

6. It is

with corrections for calibration

The recovering deformation of soil (absolute

e ) is calculatedrec

column 6) and is recorded in Appendix 12, II, column

from the following expressions:

or

Arec

A'm

A' ap ,

e'm

e'ap'

(50)

where A' is the absolute elastic deformation of the apparatus in mm;ap

e' is the relative elastic deformation of the apparatus; e' = A' /hi

'tap m m n r

is the relative elastic deformation of the soil and the apparatus.

47. The absolute residual deformation of soil (A ) is determined asres

a difference between the full (A), i.e. stabilized deformation under a cer-

tain load and the deformation which has recovered with time (A ) once therec

load was removed

A = A - Ares rec

(51)

-64-

The relative residual deformation is calculated as follows:

where

eres

eap (52)

eres

Ares

hi n it

.

-65-

VI. SIMPLIFIED METHOD OF CREEP AND LONG-TERM STRENGTH

TESTING BY ｲｾｅａｎｓ OF A DYNAMOMETER

Description of the method

The method of creep and long-term strength testing described here has

been developed* to simplify these tests. It renders it possible to deter

mine the rheological properties by testing a single specimen (or two, if

a check is required).

This methods is as follows:

A soil specimen is sUbjected to a load through an elastic element, i.e.

the dynamometer, by straining the latter. The position of the dynamometer

is then fixed. The stress transmitted to the specimen through the dynamo

meter induces the creep strain in the specimen which in turn releases the

dynamometer and reduces the stress in the latter.

Such a lowering of stresses lasts until the deformation of the speci

men becomes stabilized and an equilibrium sets in between the load trans

mitted to the specimen and the internal resistance forces in the soil. If

the given initial stress in the specimen is close to the conditional

instantaneous strength, the stabilization of deformation will correspond to

the ultimate equilibrium and the final stress to the ultimate long-term

strength of soil.

The dynamometer tests may be regarded as creep tests under a stress

which changes with time or as relaxation tests during varying deformation.

The changes in the stress and deformation are interdependent and are

determined by the rheological properties of soil.

The suggested method may be used for tests with different types of

loading (compression, rupture, shear). Below we describe a device used in

compression testing but essentially the same apparatus and the same mathe

matical treatment can be applied in other tests as well.

The diagram illustrating the compression tests and the shapes of

resulting curves are shown in Figures 35 and 36.

As shown in Figure 35, the stressing device (7) applies a load on the

soil specimen (1) through the dynamometer (4) and the stamp (3). The de

formation of the soil sample is recorded by the indicator (2). The indica

tor (5) shows the stressing of the dynamometer and its release in the

course of the test. Having applied the initial load P (and the initialo

strain to the specimen and the dynamometer corresponding to this load), the

position of the dynamometer (4) is secured by fastening the stressing

* The method was suggested by 3.S. Vyalov; the inventor's certificate No.161133, January 21, 1964.

-66-

device (7) to the stand (6) in such a way that the total height of the

dynamometer (t") remains constant throughout the test:

t = l' + t " = const.

The stressing of the dynamometer leads to the formation of initial

compression strain (A') in it. In the course of the test the dynamometero

is released by a factor of A'(t), so that its total strain in the given

moment of time will be (Fig. 36a):

A' = A' - A'(t).o

As the dynamometer is being released, this strain is reduced with time to

a certain final value Ak corresponding to a stabilized condition.

The load applied to the specimen through the dynamometer gives rise

to initial deformation A" in the specimen. This deformation increases ino

the course of the test by A"(t) which is equal to the release of the

dynamometer A'(t), so that the total deformation of the specimen in the

v,iven moment of time will be equal to (Fig. 36b):

A" = A + A"(t).o

This deformation will increase until it reaches its final value Ak corres

ponding to a stabilized condition.

Equation (53) is equivalent to:

A = A' + A" = const.000

(56)

By substituting the expressions for A' and A" from equations (54) ando 0

(55) into equation (56) and by considering th8t A'(t) A"(t), we find that

A = A' + A" = const.o

The force created by stressing the dynamometer and applied to the

specimen will be equal to:

pet) = EA' kg, (58)

where E is the modulus of deformation of the dynamometer (kg/cm), and A'

is the deformation of the dynamometer (em). This force changes from its

initial value Po to its final value Pk

corresponding to a stabilized

condition (Fig. 36c).

The tests yield data on the development of deformation in the dynamo

meter (A') and the sample (A"), and on the reduction of the force pet), as

shown in Figure 36. These data are used to determine the creep and the

long-term strength of the given soil.

For the determination of creep properties, the testing arrangement may

be regarded as a system consisting of two series-connected elements. The

first element is elastic (the dynamometer) and obeys Hook's law (58), the

-67-

second element is plastic-viscous (the soil specimen) which obeys a certain

as yet unknown creep law. In its simplest form, this law may be represented

as follows:

pet) = <p(AI!) !)Jet), (59)

where ｾＨａＢＩ is a function describing the relation between the load and the

deformation of soil at the initial moment of time t = 0, while !)J(t) is a

function which describes the development of deformation with time (the creep

function) .

The deformation of the system dynamometer-specimen is determined by

equation (57). By ｳｵ｢ｳｴｩｴｵｴｩｮｾ equations (58) and (59) into (57), or (which

is the same) by comparing equations (58) and (59), we obtain:

EA' pet)!)J (t ) = ｾ (A") = ｾＩＧ (60)

where <p(A") is a function which depends on the soil properties and is

determined experimentally. The most likely form of this function is the

experimental relationship ｾｩｶ･ｮ in equation (3), i.e.

ｾＨａＢＩ = A (A")minit .

Then equation (60) may be written as follows:

EA' pet)1/J(t) =

A (A")m A. (A")minit lnit

(61)

(62)

where pet) is the load which varies with time and is applied to the specimen

via the dynamometer; A' and A" are the corresponding deformations of the

dynamometer and the specimen which vary with time; E is the modulus of

deformation of the dynamometer; Ai n i t

is the coefficient of initial soil

deformation; m is the coefficient of strengthening of soil. We should note

that A" in equation (62) can be also found as follows:

A" = A - A'o '

where A = A' + A" is the total initial deformation of the dynamometer (A")o 0 0 0

and the specimen (A").o

Function 1/J(t) characterizes the creep of soil and is equal to:

!)J(t) = A(t)Ai n i t '

(62' )

where A(t) is the coefficient of soil deformation from equation (3) which

varies with time.

Therefore the data on the reduction in the force pet) (or in the

deformation of the dynamometer A') and on the development of deformation of

the specimen (A") with time can be used to find the creep function !)J(t) by

means of equation (62). Having found this function and by considering

-68-

equation (59), we obtain the law of deformation of a given soil in the

following form:

A" - [ pet) ]l/m _ rpc.t)]lIm- A

i n i t¢(t) - lATtT

To simplify the calculations, in all equations the deformations are

given in absolute values in centimetres, while the loads are in kilograms.m

Consequently, E is expressed in kg/cm and A in kg/cm (parameters ¢ and m

are non-dimensional). During final processing of experimental data it isA I

essential to substitute A and P by the relative deformation €' = ｾ andA" D

E" = h (non-dimensional value, and the stress a = ｾ (kg/cm2

) , where h is

the initial height of the specimen and F is the area of its cross-section.

In the same way, the true values of parameters E and A expressed through

E and A will be equal to:

(64)

Equation (62) can now be modified as follows:

EEl a(t)¢(t) = A.. (E")m = A.. (E")tr: '

lnlt lnlt

where the value of ｾＨｴＩ is the same as in equation (62).

Equation (63) will now assume the following form:

E" = [ a(t ) -J l/m = [a (t )] 11mAinit¢(t) A(t)

A and P can be converted to E = ｾ and a = ｾ when plotting the diagrams

shown in Figure 38.

Let us now proceed to the determination of strength characteristics of

soil specimens.

These characteristics are found in the following way. If the given

initial load on the specimen (P ) created by stressing the dynamometer willo

vary, then for each value of Po there will be a corresponding value of final

load Pk.

For the ultimate long-term strength Poo

there will be the final

value of the load Pk

= Poo

' obtained in the tests with the initial load

close to the breaking load, i.e. P ｾ P (the breaking force P iso max max

determined in preliminary tests).

Furthermore, the value of Pk

depends on the ｾｩｧｩ､ｩｴｹ of the dynamometer

i.e. on its modulus of deformation E. The true value of the ultimate long

term strength is obtained when use is made of an infinitely rigid dynamo

meter, i.e. when E = 00 and consequently deformation is zero A(t) = O. In

this case A" = A" const and equation (62) assumes the following form:o

(65)

-69-

On comparing equations (65) and (62) we obtain the following ratio of the

change in the load on testing with an absolutely rigid dynamometer pet) to

the change in the load pet) on testins with a flexible dynamometer with a

modulus of deformation E ｾ 00.

(66)

),. ,o

(x")Iil

Epet) _ ｐｄｾ _PTtT - ｾＮ (),.,,)m

lnlt

The ultimate ｬｯｮｾＭｴ･ｲｭ load Poo calculated by considering the flexibility

the dynamometer E and corresponding to the final load in the presence

an absolutely rigid dynamometer will be equal to:

p 00 = P. r, A' 0K •

Ai n i t (),. 'k)m

of

of

This formula may be written also in the following form:

P r A" 1P k A.. (),.ff)!il = Pk r*

.i n i t k l k

(66 I )

or as

(66")r, = Pk

ｬＭｾｾ r 1 - ｾ｝ｯｾ｝ + lr

m

- 0 l J

where Poo is the ultimate long-term load (kg); Pk

is the final load obtained

on testing with a flexible dynamometer (kg); E is the modulus of deformation

of the dynamometer (kg/em); A' and A" are initial deformations of theo 0

dynamometer and the specimen respectively (em); ),.k and Ak are final defor-

mations of the dynamometer and the specimen (cm); A. 't and m are soillnl

characteristics mentioned earlier.

In the determinations of the long-term strength, the rigidity of the

dynamometer may be ignored only if the following condition is satisfied:

ｬｾ mJ. 1 ± 6, (67)

where 6 is the permissible error.

We should also note that since certain approximations are permissible

in the determination of stabilization of deformation, the same approximations

may be used in calculating the ultimate long-term strength.

Instrumentation

1. The apparatus for testing the strength and the creep of frozen

soils by the dynamometric method must render it possible to apply the loads

to the specimen, up to and including the breaking load, quickly but

uniformly, and to deform the specimen to an extent not less than 20% of its

initial height. The total deformation of the system specimen-dynamometer

must remain constant throughout the test.

-70-

2. The apparatus* specially developed for the ､ｹｮｾｭｯｭ･ｴｲｩ｣ testing of

frozen soil is shown ｳ｣ｨ･ｾ｡ｴｩ｣｡ｬｬｹ in Figure 37. It is used in compression

ｴ･ｾｴｩｮｾ of specimens with natural and artificial structure. A load is

applied to the specimen by mechanical, ｭ｡ｾｵ｡ｬ or combined (mechanical and

manual) methods. The apparatus is desiGned for testin; cylindrical frozen(

s o i I specimens of L:o d i ame t e r s . ｾＧｊｨ･ＺＺ testing; specimens with d Lme n s Lo ns

､ｩｦｦ･ｲＰｮｾｦｲｯｾ those essential to replace the plates

of the spec imen - d = 35 7 or d 2 = 45 ') :-::m1 " .. OJ c: ,

cr03;:-,,-sect j on ? = 10 cm 2 or ? = 16 ｮＬｾ 2 t nc- 1 2 ......J.. ,

the respective areas of the

ｨ｣ｬｾｨｴ = 01 = 80 mm or

h 2 = 100 rnrn ; the ratio of the height of ｾｲｨ･ s pe c i rte n to its d i ame t e rv >-

hid = '2.2. ｾＧ［ｬｃ 'nxi;;;u:n c ompr-e s s Lnr; force on mc c han i c a I Lo ad Lnr; - 1,000 kg,

'1:1 Ｂ［｡ｾｵ｡ｬ 1,'2din" - 1,500 ｫｾ［ the ma xLmu:n c ompr-e s s I ng stress in the

ＺｾｾｾｈＮＧＧＲｩＺｾｬＨ［ｮ G = Ina -1 ｾｾＬｾ［Ｚ＼ CTTl2• The ､･ｦｯｲｾＮ｡ｴＮｩｯｮｳ are mea s ur e d to within

0.01 - 0.002 mm; the stresses in the specimer1 are ::1easured to within

0.0] - 0.15 ｫｾＯ｣ｭＲ (the accuracy of stress ::1easurements depends on the

ＮＧｬｃｃｕｾﾷＭＧＺｬｃＬｙ of t h c Lnd i c a t o r of d e f'o r-rna t Lo n s in the dynanome t e r and the

r if'; I d it y C' f' the 1 a t t e r ) .

The rate of ､ｩｳｰｬ｡｣･ｾ･ｮｴ of the ｬｯ｡､ｩｮｾ screw; on ｾ･｣ｨ｡ｮｩ｣｡ｬ loading

40 ＺｾｉｾＯｉＢＱｩｮ［ on manu a I Lo ad t nr; the rate nay vary over a ","ide range of values.

4. The ､ｹｮ｡ｾｯｭ･ｴｲｩ｣ apparatus consists of the following ｾ｡ｩｮ units:

ｾ｡ｮｵ｡ｬ and mechanical axial loadings devices; a standard dynamometer (from

0.2 to 5 tons in capacity) with an indicator of deformation of the dynamo

meter (with divisions for every 0.01 mm); a device for measuring the

deformation of the ｳｰ･｣ｩＺｾ･ｮ and the bearing plate with guiding sleeves.

5· Tile axial loadins device 1s intended for mechanical or manual

op or-a t Lo n . The device for mec ha n t ca I load inC'; consists of (see Fig. 37) a

r e v e r-s Lb Le , t.wo-ep ha s e c ur-r-e n t mo t o r- (1), gear drive (2), s c r ew drive (3)

and loading screw (21), which is joined to the lower cross gear (4) by the

stop screw (5). The electric motor and the screw drive are assembled on a

plate which is joined from below to the bearing plate (20) by means of

three supports. The device for manual loading of the specimen consists of

the crank (IS) and the loading screw (14). The standard dynamometer (10)

transmits the force from the loading device to the soil speci::len (18).

The deformation of the dynamometer at the time of load application and in

* The apparatus was developed and produced at the Laboratory of Frozen SoilMechanics, the ｾ･ｳ･｡ｲ｣ｨ Institute of Foundations and UndergroundStructures. Its design was developed by V.F. Ermakov.

-71-

the course of the test is measured by the indicator (11), and the deformation

of the specimen by the dial type indicators (7) with divisions every 0.01

0.002 mm* which are set by means of a clamping device mounted on the

bearing plate (20). The bearing plate (20) is joined to a frame provided

with legs which contain the screws for mounting the bearing plate in a

horizontal position. The guiding sleeves (6) for the movement of longitu

dinal drives (16) are mounted on the bearing plate in a strictly vertical

position.

6. In mechanical loading the force from the electric motor (1) is

transmitted to the loading screw (21) via the screw gear (2) and (3) and

then via the cross gear (4 and 13) and the longitudinal gear (16) to the

loading screw (14), the dynamometer (10) and the specimen of frozen soil

(18). The specimen is unloaded by reversing the rotation of the electric

motor (1). The manual loadinE is accompJished by turning the upper

loading screw (14) by means of the crank (15). To prevent any skewing of

the specimen on applying the load and in the course of the test, the load

is applied strictly through the centre of the specimen. To achieve this,

the specimen is mounted on the cylindrical stamp (19) which is set up

strictly in the centre of the bearing plate (20), while the dynamometer (10)

is mounted between the mobile guides (9) and (12) sliding along the drives

(16). The stamp (17) with two supports (8) for the indicators (7) is

mounted on the specimen.

7. For a general evaluation of the rigidity of the entire system, or

if the deformation of the specimen is determined not from the indicators

(7) but from the indicator of the dynamometer (11), the apparatus should

be calibrated. In this case a rigid metallic cylinder is placed on the

cylindrical stamp (19) instead of the specimen (18). The supports which

support the legs of the indicators for measuring the deformation of the

apparatus are screwed into the cross drive (13) from both sides. The load

is applied to the apparatus in stages either manually or mechanically.

The deformation of the apparatus and the dynamometer, and the load are

determined after each loading stage (the load is determined by reading the

dynamometer). The data obtained is used to construct the 6\ - P (deformation

load) curves. Then the deformation of the specimen at any moment of time

may be found from the equation:

\"(t) = \" + \'(t) + 6\ (68)o '

* It is desirable to connect the indicators of the dynamometer and thespecimen to an automatic recording device.

-72-

where A"(t) and A'(t) are the true deformation of the specimen and the

deformation of the dynamometer at the given moment of time t; ｾａ is the

deformation of the apparatus found from the calibration curve; ａｾ is the

initial deformation of the specimen.

Experimental Methods

8. The dynamometric testing device is used to determine the long-term

strength and the creep. Two tests are required to find the long-term

strength: the first involves a rapid application of the load (up to the

failure of the specimen) to determine the conventional-instantaneous

strength (the temporary resistance a ); the second is a long-term test witho

the initial stress close to the instantaneous strength, which is used to

find the ultimate long-term strength am. The creep characteristics are

determined by a long-term test at any arbitrary value of the initial stress.

9. The tests to determine the conventional-instantaneous soil strength

a are conducted either directly in the dynamometric apparatus with ao

rapid (but smooth and uniform) application of the load, or in conventional

devices by methods described in Section III. The dynamometric tests are

carried out as follows:

The frozen soil specimen (18) with carefully cleaned and mutually

parallel top and bottom surfaces, which has been kept at the temperature of

subsequent tests for 24 hours, is mounted on the cylindrical plate (19)

(see Fig. 37). The stamp (17) with supports (8) for the indicator (7) is

placed on the free surface of the specimen. The lower movable guide (9) is

mounted on the stamp (17). The standard dynamometer (10) is placed between

the lower (9) and the upper (12) movable guides. By turning the crank (15),

the upper loading screw (14) is brought to the upper guide (12) (the force

from the loading screw (14) to the guide (12) is transmitted through a ball)

in such a way that the hand of the indicator (11) of the dynamometer (10)

will move slightly and return to zero. The load is applied uniformly to

the specimen after careful centering. The test lasts approximately 30

seconds and leads either to the failure of the specimen or to axial defor

mation equal to 20% of the initial height of the specimen.

10. If it is required to determine the type of relationship between the

stress and the initial deformation, the apparatus is provided with a

recording instrument for measuring the axial deformations of the specimen

and the dynamometer. The data obtained is used to plot the P - A" curveso

(the load versus the soil deformation) or the a - € curves (the stresso

versus the initial relative deformation). In this case a = PIF and

EO = ａｾＯｨＬ where F is the area of the cross-section of the specimen in cm 2

and h is its initial height in cm.

-73-

11. The ultimate long-term strength is determined at ｐｾ 0.95 Pma x'where P is the instantaneous breaking load found in accordance with

maxpara. 9. The creep characteristics are determined at any initial load Po

but not below 0.5 P ,since at P < 0.5 P the proportional relationshipmax 0 max

between Po and pet) at the given moment of time is disturbed. It is

recommended to use P = (0.7 - 0.8) p . If the long-term strength ando max

the creep are to be determined simultaneously, the tests are conducted at

p ｾ 0.95 P ,i.e. as in the long-term strength determinations. In thiso max

case it is recommended to check the results by repeating the test at

P = (0.7 - 0.8) P .o max

12. The determinations of creep and long-term strength characteristics

are conducted as follows. The frozen soil specimen (see Fig. 37) is mounted

between the upper (17) and the lower (19) cylindrical stamps, then centred

and kept there at the given temperature for at least 20 - 30 minutes prior

to testing. The indicators for measuring the deformation of the dynamometer

(11) and the axial deformation of soil (7) (or the recording instruments

measuring the deformation) are set at zero.

A compressing load is then applied to the specimen by turning the

crank (15), which serves to exclude the effect of roughness of top and

bottom surfaces of the specimen on the experimental results. The

compressing load amounts to (0.2 - 0.3) Pma x

and is applied for a period

of 5 minutes. The readings are taken from the indicators (7) and (11) and

the load is removed. After an interval of 10 - 12 hours (at the temperature

of the test), the indicators and the recording instruments are set at zero.

13. The initial load P is applied manually or mechanically. It iso

applied smoothly and uniformly but sufficiently quickly (10 - 15 seconds).

The test is regarded as successful if the initial load application

does not result in fracturing of the specimen and the latter does not skew

throughout the entire test; otherwise the test has to be repeated.

The increasing load and deformation of the specimen are measured for a

subsequent determination of the relationship between the stress and the

initial deformation on applying the load*.

14. After the application of the initial load Po' the position of the

dynamometer is set automatically and further testing consists in reading the

ｩｮｾｩ｣｡ｴｯｲｳＮ These readings are taken after 5, la, 15, 20, 30, 45, 60, 90

sec, 2, 3, 4, 5, 7, 10, 20, 30, 45, 60, 90 min, 2, 3, 4, 5, 6, 8, 12, 24

hours and then every 24 hours. In the presence of recording instruments,

* It will be shown later that if the test is repeated with a differentvalue of Po' the measurement of increasing deformations may be omitted.

-74-

the deformations are recorded automatically, and the indicator readings

serve as a control only.

Since the main development of deformation and the corresponding drop

in the stress take place in the initial and relatively short interval of

time (minutes or hours), the readings taken in the course of the first

hour must be very accurate (especially in the first 5 or 10 minutes).

The test is considered complete when stabilization of deformation sets

in (relative stabilization). In the determination of the uttimate long

term strength, the stabilization is considered complete if the incrementA"

of relative deformation of the specimen E" = h does not exceed 0.5 . 10- 4

in 24 hours. For a more precise determination of 0 00 (if this is specifically

asked for), the test is considered complete when the relative deformation

of the specimen does not exceed 0.25 . 10- 4 in 5 days.

When the specimens are 80 and 100 mm high, the respective absolute

deformations are A" = 0.004 - 0.005 mm in 24 hours and A" = 0.002 - 0.0025 mm

in five days. In creep tests the criterion of stabilization is taken in

accordance with instructions in paragraph 32, Section III.

15. The measurements described in paragraph 14 are used to calculate

the deformations of the dynamometer and the specimen which vary with time.

The deformation of the dynamometer is found by means of equation (54) by

using the readings of the indicator of the dynamometer. The deformation

of the specimen is found from equation (55) by using the readings of the

indicators of the specimen (or by using the readings of the indicator of

the dynamometer and recalculating the data by means of equation (68), if the

indicator of deformation of the specimen is not used). The results of

these measurements or recordings made by recording instruments are noted

in a log book (Appendix 13). The data are then used to plot the AI - t

and the A" - t curves (see Fig. 36a and b)*.

16. The measurements of deformation of the dynamometer A' determined in

accordance with instructions in paras. 14 and 15 are used to find the load

transmitted to the specimen through the dynamometer. The load is calculated

by using equation (58):,

pet) = EA' kg, (69)

where E is the modulus of deformation of the dynamometer in kg/em, and A'

is the deformation of the dynamometer in em.

* The recording of deformations of the dynamometer AI and the sample A" whichvary with time is essential if the tests are conducted to determine thecreep characteristics. If the long-term strength only is required, itis sufficient to register AI and the initial deformation of the specimenA".

o

-75-

In the same way we determine the initial load

P = EA' kg00'

the load which changes with time

pet) = EA'

and the final load

(69' )

(69")

(69' , , )

where ａｾＬ A' and Ak are the initial deformation, the deformation which

changes with time, and the final (stabilized) deformation of the dynamometer

in em.

The calculated values of pet) are used to plot a curve showing the

change in the load P with time t (Fig. 36c).

17. In the course of the test it is essential to check the changes in

the cross-section of the specimen and the corresponding changes in its

area F, since this will affect the value of the stress a = P/F. If the

change in the area does not exceed 5% (which corresponds to a change of 8%

in the diameter of the specimen), it may be ignored and the stress a may

be related to the initial area of the specimen (i.e. the area prior to

testing). However, if the change does exceed 5%, it is essential to

calculate a and to relate it to the true area of the specimen.

The area of the cross-section of the specimen may be checked by

measuring the cross-section after testing. In special investigations and

in particular when studying the cross-deformations due to creep, it is

expedient to mount indicators of cross-deformations on the specimens (see

Section III, paras. 4, 5, 24, 25, and 26).

Processing Experimental Data and Determining the Characteristics of Creep

and Long-term Strength

18. The creep tests are carried out to determine the pattern of

development of deformation with time. For this it is essential to determine

by means of equation (59) the form of the function ｾＨａＢＩ describing the

relation between the load and the deformation, and the form of the creep

function ｾＨｴＩ characterizing the pattern of development of deformation with

time.

19. The form of the function ｾＨａＢＩ may be determined from the data on

the initial loading of the apparatus (see para. 13), or from the experimental

data on the instantaneous strength (see para. 10), by plotting the relation

between the load P and the initial deformation of the sample A" (Fig. 38a).o 0

The equation of the curve obtained in this way determines the form of the

function ｾＨａＢＩＮ The corresponding empirical formula is selected by the

usual methods of processing experimental data(23)

m =

-76-

20. The most likely form of the function ｾＨａＢＩ is the exponential

relationship (61), i.e.:

4J(A") = A . (A")minlt .

To check the validity of this relationship and to determine A i n i t and m,

the load-deformation curve is replotted in logarithmic coordinates (Fig.

38b). The distribution of experimental points on this diagram indicates

the validity of equation (61). From the diagram we find y = In Ai n i t

; then

Ai n i t

= ey. The angle of inclination of the straight line towards the

abscissa determines a = arc tan m and hence

lllnPo

lllnA"o

The values of Ai n i t

and m may also be found analytically in accordance

with instructions in para. 45, Section III.

Equation (64) is used to express A. it through the relative deformationA P In

ｾ = h and the stress 0 = p' Ai n i t

can also be found directly from the

J1avram if the latter is constructed in a - E coordinates.

21. The deformation equations examined here are based on the assumption

that the relation between P and All at any moment of time is described by

a 3inrrlc form of function qJU"), Le. the power of this function ill is

constant for all moments of time t. The validity of this assumption and

the values of Ai n i t

and m determined in accordance with para. 20 are checked

by conducting parallel tests on two similar specimens.

22. The tests mentioned in para, 21 are performed at two values of the

initial load P ( ) and P / .) determined in accordance with para. 11. Theo 1 0 ｾ 2

results are plotted (Fig. 38c) to show the variation of deformation of the

dynamometer Ｈａｾ and A;) with time, corresponding to the different values of

the initial load PO C l

) and PO

( 2 ) ' The creep functions ｾＨｴＩ determined by

means of equation (62) are identical (since this function does not depend

on the value of Po) if Po > 0.5 Pma x'

and therefore:

EA I ( 1 ) E

Ai n it

( AII ( 1 ) )m = Ai n it

A'2

On presenting this expression in logarithmic form and by considering that

:\ II = A - A' we obtain:o '

m =

A' ( t>1 n 7""A-'-,-----'-

( 2 )(70)

-77-

where "o(d = "'0(1) + ,,11 0(1) and "0(2)= "'0(2) + ,,11 0(2) are the total

initial deformations of the dynamometer (,,') and the specimen (,,") foro 0

PO(l) and PO

( 2) ' respectively, ,,' (1) and ,,' (2) are the deformations of the

dynamometer at a given moment of time t. for P ( ) and P ( )' respectively.l 0 1 0 2

23. To determine m by means of equation (70), it is necessary to take

any arbitrary time ti,

find the corresponding values of "'(1) and "'(2)

(see Fig. 38c), and by substituting these values into equation (70) find m.

It is required to carry out at least three such determinations for

different values of ti,

The validity of equation (61) is confirmed if the

values of m coincide. If it is found that m varies with time, further

treatment may be carried out in accordance with para. 51, Section III.

Since variation of m makes the equation considerably more complicated, it

may be taken as constant if its variation does not exceed 20%.

24, The values of m for different t. determined in accordance withl

para. 22 must coincide with the values determined on initial loading in

accordance with para. 20. However, if it is found that m is constant for

all values of ti

but differs from m on initial loading (t = 0), the

discrepancy may be ignored in order to simplify the creep equation, and

for initial loading take m found by means of equation (70), i.e. we may

take m = const. for any time t from the beginning of loading to the onset of

stabilization of deformation. The coefficient Ai n i t

which forms part of

equations (61) - (63) can be found from the following expression:

Ai n i t

= Po kg/cmm,

(71)o")rn

o

where P is the initial load; ,," is the initial deformation of the specimeno 0

resulting from this load; m is a parameter determined by means of equation

(70) in accordance with paras. 23 and 24. To express the coefficient Ai n i t

in kg/cm 2, it is recalculated by means of equation (64).

25. The next step is to determine the creep function ｾＨｴＩ in equation

(59). This function is found from equations (60) or (62), but we must

first calculate E,,' = pet) and <PeA") = Ainit(A")m, where ,,' and A" are the

deformations of the dynamometer and the specimen, which are obtained from

experimental results (see Fig. 36a and b).

It is best to express E,,' and <p("") in the form of curves as in

Figures 39a and b.

These factors are expressed as follows: ,,' in em, E in kg/em, E,,' in

kg, ,," in em, Ai n i t

in kg/cmm,

<p(A") = AinitC>..,,)m kg.

26. The creep function ｾＨｴＩ is determined by substituting E,,' and <p(,,")

for different moments of time ti

from the curves in Figures 39a and b into

equation (60) or (62). The results calculated by means of equation (60) or

-78-

(62) are expressed in the form of the curve shown in Figure 39c.

The initial ordinate of such a curve must be equal to unity, since:

EA i Po 0

A• • ( AII ) m = p '" l.lnlt 0 0

27. If control tests were performed with similar specimens at different

values of PO(l)' PO( 2) ' etc., in accordance with paras. 21 and 22, the

results of all tests are plotted on Figure 39c. The experimental points

must lie on the same curve, which will serve as a check of the validity

of equation (62) and of "parameters Ai n i t

and m.

28. The form of function ｾＨｴＩ is determined by selecting an empirical

formula which best describes the curve in Figure 39c. The empirical formula

is selected by the usual mathematical methods of processing experimental

results.

29. The most likely form of function ｾＨｴＩ is the expression derived

from equation (62'):

'4J ( t )A(t )

= =A. ｾ tｬｮｾ

1

Ai n i t t a1 + ｾ

(72)

which corresponds to equation (7').

To check the validity of this equation and of parameters ｾ and a (Ai n i t

has been determined earlier), the equation must be modified as follows:

A= In ｩｾｩｴ + a In t. (73)

Ai n i t

and

temperature

A" does not exceed 5% ofo

will simplify the de for-

equation (60) assumes

the final deformation Ak, it may be ignored, which

mation equation, In this case function cp (A") from

the following form:

Figure 39c must now be replotted on a logarithmic scale (see Fig. 39d)

with coordinates In [ilJ (t) - IJ - Int.

The parameters are expressed as follows: a and ｾＨｴＩ are non-dimensional-m -m

factors, A. 't in kg/cm Ｌｾｩｮ kg/cm . hr a, t in hours Ｈｾ and t maylnl

also be expressed in minutes). Equation (64) is used to express

ｾ in true dimensions. The dependence of Ai n i t

and ｾ on the soil

is expressed by equations (9) (see also para. 57, Sec. III).

The fact that experimental points lie on a straight line in Figure 39d,

confirms that equation (72) may be used to describe the creep function. The

deformation pattern of frozen soil in this case will be described by

equation (8).

30. If the initial deformation of the specimen

cp(A") (A" )m (74)

-79-

These values are plotted on Figure 39b. The curves will emerge from the

Po i n t A" = 0 as has been shown by the dotted line in Figure 39b.o '

Equation (60) which serves to calculate the values of the creep

function ｾＨｴＩ will assume the following form:

EA'ｾＨｴＩ =' (75)

(A" )m

These values are plotted on Figure 39c. Since A" = 0, ｾＨｴＩ at t = 0 willo

tend towards infinity as has been shown by the dotted line in Figure 39c.

31. If the initial deformation is ignored (A" = 0), equation (72) whicho

determines the form of the function ｾＨｴＩ will assume a simple form corres-

ponding to equation (7"):

(76)

(76')

The validity of this equation is checked by modifying it as follows:

In ｛ｾ (t) ] = In (t) + ex In t,

and by distribution of experimental points plotted on a diagram of the

type shown in Figure 39d, on which the ordinate denote s In ｛ｾＨｾＩ ] = ｉｮｾ (t )

and the abscissa In t. The inclination of the resultant straight line again

defines ex, while the section cut off by this line on the ordinate is equal1 -m ex

to In r' which is expressed in kg/cm . hr. This is converted toex hm

kg/cm- z . hr by means of the following formula: ｾ = ｾ -- .F

The dependence on the temperature of frozen soil is expressed by formula

(9) and is found in accordance with para. 57, Sec. III.

The deformation pattern of frozen soil is defined by equation (8').

32. Apart from equation (72), the creep function ｾＨｴＩ may be expressed

in the following ways:

ｾＨｴＩ1

= (bt + 1)1 + Ai n it

ex In

or1

ｾＨｴＩA

i n it Cinit- ) -atA

kA

k1 e

( 77)

(78)

In this case the law of deformation of frozen soil will be defined by

equations (8") or (8"').

The validity of equations (77) and (78) is checked by modifying them

as follows:

kxY = me + c, (79)

-80-

for equation (77) : t,1 1

kwhere y = rn =b'

c := -b'

1 1· for equation (78) :1

x :=

ijJTTI - y :=ｾ［ m := -,

1:: a A ,and

init

Ai n i t _ 1 ' cA

k

Ainit,

Ak

k := -a, and x = t.

The logarithmic form of equation (79) is as follows:

In(y - c) := Inm + kx. (80)

By plotting this equation in In(y - c)-x coordinates, we obtain a straight

line.

Factor c is determined previously from three points on the y - x curve2

by means of the equation c := y 1Y 2 - Y 3_2- , where y 1 and y 2 are the ordinates

Y1 + Y2 - Y3

of arbitrary points Xl and X2 on the y - x curve, while Y3 are the ordinates

of point X3 equal to:

(82)

(81)

and (78 ) assume more simple forms:

1J; (t ) A(t) := 1=

In(bt 1)a +

1J;(t) A(t)1

1 e-a t)A

k

(l -

The validity of equation (77) or (78) is confirmed by the constancy of

c at different values of Xl and X2 and the tendency of experimental points

to I'o rrn a straight line when plotted on a semi-logari thimic scale in

accordance with equation (80). The same diagram also provides the parameters

of equations (77) and (78).

33. If the initial deformation of the specimen is ignored (see para. 30),

equations (7 7 )

and

that

1 k:= -a and x = t.Ak'

34, The strength of given soil is determined by means of rapid and long

term tests. The tests with rapid loading give the substantially instanta

neous strength (temporary resistance) 0 , while the long-term tests perforo

med until the deformation becomes stabilized give the ultimate long-term

The validity of these equations is checked as in para. 32, except

in this case the parameters will be as follows: for equation (81) y := t,

ｾＬ c = - ｾＬ k := ｾ and x := 1J;(E); for equation (82) y := ｾＬ m := ｾＬk

m

strength 0 00 •

35. The substantial instantaneous strength (temporary resistance) is

oo

found from the following expression:p

max-F- kgzcrn", (83)

-81-

where Pma x

is the breaking load on the specimen in kg found in accordance

with para. 9; F is the true cross-sectional area of the specimen (see para.

17) .

36. The ultimate long-term strength is found by means of the following

formula:P

CIO

F (84)

where F 1s the true cross-sectional area of the specimen at the moment of

termination of the test in cm 2 (found in accordance with para. 17); PCIO is

the ultimate long-term load in kg found by means of equations (66) - (66"),

or directly from equation (69"'), if the rigidity of the dynamometer is

extremely high and satisfies the equation (67). The final load P in

equations (66) and (69"') is found experimentally in accordance with

paras. 9, 11 and 16.

ａｐｐｾｎｄｉｘ 1

Results of compression tests at rapid load act 10n

Type of soilStructureLocation

Temperature of specimen e, °c

ICD[\J

I

9

ｾｾ Re ma r-k s

m

Test Unit wt. Tot. moist. Ice cant. Condit. inst. 'I'e s t period Coeff. of Coeff.

No. y, g/cm 3 cant. Wt ot'% i , '" limi t of str. t, min. init. deform. strengt10

a0'

kg/cm 2 Ai n i t,

kg/cm 2 ening,

- -

1 2 3 ｾ 5 I C '7 8i

I

APPENDIX 2

Log-book of compression tests at long-term load action


Sp ecimen No.-";eight p , g

Height h, cm

Diameter d ｾ ernArea F, ern

Stress 0, kg/cm 2

Ln i t . load P = of, ;';8Temp. of specimen 8, CSample ｾｯｮｴ｡ｩｮ･ｲ for moist.

cant. determination no. *

IｾＺｯ

.o

15

Hemarks

Type offailure,time ｾｦ

appearanceof fractures,skewing, etc.

1.4- ').L,J12

v

Axial deforrr;.

rate Load, 1cmp.\.-L liP kO" 8 0('

ｴｾＭｴｾＭｬｬＢｾＢ v

l l- :

nem/min I

65

" Ax i a I i Radial.:... t'o r deform.

• -- I Readings

43

ｾ･ｲＬｴＢ 1 I "iclJcUQ.'.u"Start Ofl between I I ｲｬｧｲｮｾｭ

test, r-e ad l ngs j l ｕｾＢﾷ ..

t -to I t.-t ... 'rJgTnr'mi l-l I l l-l. I

min (hI') I min (hI')

2

Time ofread.

fir min

Deform. increment

AbsoLute deform. Ｖｾ = ｾｩＭｾｩＭｬＧ mm

Axial I Radial I Axial IRadial

x, 1 r • (d,) : I1 l J. i '

I I

I I I I I 'r '--r-sH ｬｯｔＭｾ 1 1:------+-----I I

1

Date

* A sample for moisture content determination is taken after the test in accordance with Sec. II. The moisture

content recorded in a separate log-book.

:',:- ｾＭ ::. r , ｾ .....--,--_.

Type of sojl:,tr'uc;:u",e

Ｎ［ｾＺ［ＺＺ･ 1'<3.:

',':1 ｾ - ｹｾ

:'::' -.. >.' .....ｾＧｾＭ - '- ., - .)

t

I

L-

I:.e:r:a!'.',";>,

,.....,p -l ｾＬｮＺｴｴ

c-' 1 .

If

!

. ,

---+------4-'I!

I

1,J

ＭＭｔＭＭＭＭＭｾ I'o t a I ｛ＭＭＭｔＭＭＭＭＭＭＭｩｰＭ［［ＺｪｾＭＭＭＺｾｲｾｬ･Ｍｪ｟｣ｦｾｉＺＭＭＭＭＭＭＮｾＭＭＭＭｲＭＭｾｲ［ｾＲｾ - ------, ｵＺＺｾ］］ＺＺＺ［［ＺＺＺｦ

1 I . '- 'Jef'e'r-'. I or.s e 1 i\cl. ;">:::"1 ,', -: Ｂｾｾｗ de

" •• ,-' ,TLOISe. '. ＬｾＢＬＮ ! r» o t- • _ " ' pry," ＬＮ｟ＮＧｾ no,ＧＧＭＰＬｉｾｌＬｴ Nt. n t I .cCe ｟ＧＩ｣ｲ｟ｾＺＺ［ 'it J1.: t 11J',I. __ d .".t _. u ,,'1.0. ,e'L

'k·lt, grr./cm3Iwon".,.!cont.la Kg/cm2

0; fluw I ｃｾｩｾＰＺ［Ｎ I Lrogre;<s;"j" : h.;".:', ""-'0"1 -II t t' 'I i ,; I I at"·,, y. ｾ［Ｌ I pat e I s> 1 "'N C 'E:' ' ｾ - •

I ' I ! - .; -:) ｾ '.' .1>-' J • :.' I' '-' 0 r i r : r: -:. i ;,'i t .-'

, I . '. C '. I' LII j t f' I I , '. ,

Ii i c.. (' r' '. I' ! : ;:;ll L, :::'. I I t n i t .1LI. L. 't-' I

I . ｉｾｉ I -----l-----+----,- ----+--------+-'.'--il . I! r I __ G IC .:5 ｾＫ 5 U I ,. ! ,_I I ｾ :

I ｾ 1---+-----+-------+Iii I ' i

. I ,I 'i· I I

I

: I I

I' I II I '.

APPENGIX 4

Log-book of rapid shear resistance tests (shearing ｾｰ｡ｲ｡ｴｵｳ［

Type of soilStructure

Temperature of specimen, 8, orLocation

ｾｾｾｴ I, .Normal Horizontal Istress breaking load Container

Date Test an' i jDurat10C no. for 'wei,

'lO'jkg / cm2 . Tn' of ｴｾｳｴ moisture -

'I, ,(glkg/cm 2 t, min . determin. speci

ｾ

1 ,J 3 Ij 5 6 7 8

APPENDIX 5

Results of determinations of rapid shear resistance of frozen soil


Temperature of specimen 8, °cLocation

Unit wt. Total Normal Condit. Angle of

Testof soil moist. Ice stress inst. Cohesion internal

y cont. cont. 0 limit of C friction RemarksNo.

gm/cm 3Wt ot'

% i, %n

s t r . , T ° deg.kg/cm 2

kg/cm 2 o kg/cm 2 <j),

1 2 3 4 5 6 Ci 8 9

APPENDIX 6

Log-book of rapid shear resistance tests (wedge tester)

IcoV1

I


Temperature of specimen 8, °cLocation

Angle ofBreaking Duration

Container

DateTest inclination

load of test,no. for Wt. of Additional

No. of spec.P, kg min

moist. spec. g remarksa, deg. determin.

1 2 3 4 5 6 7 8

f\FPENDIX 7

Log-book of shear tests at long-term luaa action

no.moisture

load T

kg/cm 2

ｳｾＧＺＧＲＮｲｩｲ［Ｖ apparatus;

ｫｾＨＯ｣ｭＺ F ,_""., , ｊ｜｟ｾ

ｪ･ＺＬＡＬＺｾ｡Ｑ TOAd P = lQ t;l

ｾＩ k r:10

ｩｩｴｊｲｩＲｯｮｴＺｾＱi n it La l

InitJ21

F2r the ｜ｊｩ､ｾｯｰｲｯ･ｫｴ

Temperature- 9, °cSample ｣｣ｮｾ｡ｩｮ･ｲ for

d et er:nina t i on.. o r-r.a I s t r e s s a:;,

S:le;:_:r..rirH3 s t r-e s s T

Type of soilStructureLocationSpecimen o.weLgh t p, gmHeight, h , em

Diameter U i em

Area F, ern

Ien

Deform. Correct.meas. for deform.

mm of apparatus

I'I'Lrne

I b e t.we c r:

I ... I Start of i reading. s

:+test t , It.-t.

Da t e nr- ":i n .L 1 1- 1

I 2LtnJ((.rl l"in,,'hr)!I i I

5 6 7

rnm

ｬｾ

APPENDIX 8

Results of shear tests at long-term load action


a * kg/cm 2• a, deg

n 'Temperature of specimen 8, °c

'I'o t a lIce Stress

Time tmoist. duringP

Test Unit wt.cant.

cont. 1n'

Swhich

No. y, g/cm 3

Wt ot'JI r , % kg/crn 2 deform.

Remarks/0

becomesA = 1.5 A

P pr

1 2 3 4 5r:

7°

I I I I

* Such a record is compiled for each value of normal stressa or angle of inclination of the specimen a.

n

-88-

APPENDIX 9

Log-book of calibration of compression apparatus

I. Apparatus no.II. Type of apparatus

III. Indicator nos.IV. Area of plate, cm

z

V. Lever arm ratio of pressVI. Weight of units not balanced by counterweights

VII. Deformation of the apparatus(tests performed three times)

Wt. ofIndicator readings, mm Deform. of apparatus, mm

load Load

kg kg/cm zI II I II

1

ｾＭｾ4 5 6

I

VIII. Results of calibration

Mean deform. ofMean Calc. *apparatus based

deform. of deform. ofLoad on calibrationkg/cm z data, mm

apparatus apparatusA mm A romm' pr'

A1 Az A3

1 2 3 4 5 6

* Determined graphically from the calibrationcurve.

APPENDIX 10

Determination of unit weight, unit weight of skeleton, initial coefficientｾｘｰｯｲｯｳｩｾ｟ｾｮ､ ice content of given soil

I. Laboratory number of specimenII. Hing (cylinder) number

III. Weight of ring (cylinder) (qr)' ke;IV, Internal ring diameter (d ), em

V, Area of specimen (F), cm2r

v l , Tv1casLlred and o a Lcu I a.t cu values

Un I t wt. I Init .

of Skeletonlcoeff. ofYS porosity

g/cm 3 "0

13129

ｾＭ･ｩｧｨｴＭｾｾＧｾｾｾｬｾ mm II ｖＭ［［ＭｾＭ of Wt. of spec. 1 Wt. of I -"." spec, 'I, with ring spec" .. ｾｉ Unit wt;.

Icm ' (c,v1inder) I y g z cm

hlh2h3h .. hsh6avg'l v q" ,.,fr.g

+qfr.r.g.'1'07- --8---+---- ----+---10 11·---+------+--

11 I !II-t-VII. Determination of ice content prior to testing

Wt of Wt of Iwt of Wt of'.-it of Wt of Total lunrro"nl 'frozen frOZen[China cup with

dry soil water i tit .i c espec. ring and

mo s . I wa er tspec., g cup. g

g g cant " %Icont .,* % co% .with dry soil

ring, g

'+3g

ＭｾＭｉ4 5 6 I 7 8 9

I rI

I I I I

* Determined by calorimetric methods

VIII. Determination of ice content after testing

Wt of Wt of ｾｉｴ of Wt of Total Unfrozen Icefrozen frozen dry water, moist. water cant.spec. spec. soil, g g cont., % cant " % %with afterring testing,after I

Itesting,g

g I1 2 3 4 5 6 7

I, ,

APPENDIX 11

Log-book of compression tests

I. Laboratory no. of specimenII. Type and no. of apparatus

III. Indicator no.IV. Testing conditions

V. Measured and calculated valuesI

'.0o

I

Time of reading Time Readings Abs. deform. oft interval soil and apparatus

ｾｴＮ offrom moment as shown by Abs. Rel.Press. of applic. Temp. of meas. instr. deform.load p, hr min of given ｴ･ｳｾ e, of soil

deform.ate Pe' kg kg!cm

2

loading C I II of soilI II A A, mID e

stage t, hr m

1 2 3 4 5 6 7 8 9 10 11 12 13 14

D

APPENDIX 12

I. Log-book of results of compression tests

Rel. Compres.

Total deform. modulus of

Unit wt. moist. Ice cont. Pressure increments Reduced deform.

y gm/cm 3 cont. i % intervals in each coeff. of E kg/cm 2

Wt ot'% tot' kg/cm 2 compress.

n ,

lip, loadingv

stage, lie 0.0

, cm 2/kg

1 2 3 4 5 6 7

II. Log-book of determinations of recoveringand residual deformation

Unit Total Ice Press. Tot. soil Recovering Residual

wt. I moist. cont. p deform. deform. deform.gm/cm cont. i , % kg/cm 2 e

n, % of soil of soil

Wt ot'% e

rec'% e r e s'

%

1 2 3 4 5 6 7

--

I'-DI--'I

APPENDIX 13

Log-book of dynamometric tests at long-term load action


Sample no.Weight p, gHeight h, emDiameter d 2 emArea F, cmTemperature 6, °cSample container

for moisturedetermination no.

Dynamometer no.Modulus of compressibility

of dynamometer E, kg/emInitial deform. of dynamo-

meter '\', emT i t i 1 J8 d r; ;ｾ I'l L la _, a !" , Kg

Initial stressOa , kg/cm 2

Initial deform. 8f specimen

｜ｾＩ mm

I'-0

roI

e

ess.orm.timeof

ewing

I Ti me intervalAbs. deform. IInstrument readings of spec., !iJ11 Jeform.

Time of!

Date from start of ILoad, T6mp. Remar;,zsreading of test (sec, dynamometer kg C'

Axial Radial Axial Radialmin, hr)

deform. deform.mm

1 2 3 4 c:: 6 7 8 9 10 11J

Deform. of dynamometer andspecimen oncompres., tim

of compress.,load on comprnature of defof specimen (

of appearancefractures, skif any, etc. )

-93-

References

1. Vyalov, S.S. Reologicheskie svoistva i nesushchaya sposobnost merzlykhgruntov (Rheological properties and the bearing capacity offrozen soils). Izd-vo Akad. Nauk SSSR, 1959.

2. Tsytovich, N.A. Osnovaniya i fundamenty na merzlykh gruntakhtions on frozen soils). Izd-vo Akad. Nauk SSSR, 1958.

(Founda-

3. Vyalov, S.S., Gmoshinskii, V.G., Gorodetskii, S.E., Grigor'eva, V.G.,Zaretskii, Yu.K., Pekarskaya, N.K. and Shusherina, E.P. Prochnosti polzuchest merzlykh gruntov i raschety ledogruntovykh ograzhdenii(Strength and creep of frozen soils and design of ice-soil enclosures). Izd-vo Akad. Nauk SSSR, 1962.

4. Brodskaya, A.G. Szhimaemost merzlykh gruntov (Compressibility offrozen soils). Izd-vo Akad. Nauk SSSR, 1962.

5. Vyalov, S.S., Pekarskaya, N.K. and Shusherina, E.P. Metodika ispytaniimerzlykh gruntov na szhatie i sdvig s uchetom polzuchesti(Methods of compression and shear testing of frozen soils withallowances for creep). Merzlotnye Issledovaniya, No.2, Izd-voMGU, 1961.

6. Materialy po 1aboratornym issledovaniyam merzlykh gruntov (Data onlaboratory investigations of frozen soils). Izd-vo Akad. NaukSSSR, Moscow, No.2, 1954; No.3, 1957; No.4, 1961.

7. Principles of geocryology (Permafrost studies). Part 2. Engineeringgeocryology. Izd-vo Akad. Nauk SSSR, 1959.

8. Pekarskaya, N.K.at teksturyto texture).

Prochnost merzlykh gruntov pri sdvige i ee zavisimost(Strength of frozen soil at shear and its relation

IZd-vo Akad. Nauk SSSR, 1963.

9. Prochnos t 1 polzuches t merzlykh gruntov. (Sbornik s t at e i ) . (Strengthand creep of frozen soils) (Collection of papers). Izd-vo Akad.Nauk SSSR, 1963.

10. Tsytovich, N.A. Ob oprede1enii si1 stsepleniya svyaznykh gruntov pometodu sharkovoi proby (Determination of cohesion forces incohesive salls by the ball probe method). Dokl. Akad. Nauk SSSR,111, No.5, 1956.

11. Tsytovich, N.A. Instruktivnye ukazaniya po opredeleniyu sil stsepleniyamerzlykh gruntov (Instructions for determining the cohesionforces in frozen soils). Materialy po laboratornym issledovaniyammerzlykh gruntov, 2, Izd-vo Akad. Nauk SSSR, 1954.

12. Stroitel'nye normy i pravila (Construction norms and rules). Part II,Section B, Ch. I, Gos. izd-vo lit. po stroitel'stvu arkhitekture istroitel'nym materialem, Moscow, 1962.

13. Nersesova, Z.A. Instruktivnye ukazaniya po opredeleniyu kolichestvanezamerzshei vody i l'da v merzlykh gruntakh (Instructions fordetermining the amount of unfrozen water and ice in frozen soils).Materialy po laboratornym issledovaniyam merzlykh gruntov, 2,Izd-vo Akad. Nauk SSSR, 1954.

-94-

14. Polevye geokriologicheskie (merzlotnye) issledovaniya (Geocryologicalfield investigations). Metodicheskoe rukovodstvo, (Handbook),Part I. Izd-vo Akad. Nauk SSSR, 1961.

15. Pchelintsev, A.M. Instruktivnye ukazaniya po opredeleniyu ob'emnogovesa, vlazhnosti i ob'emnoi l'distosti merzlykh gruntov v polevykhlaboratoriyakh (Instructions for determining unit weight,moisture content of frozen soils in field laboratories). Materialypo laboratornym issledovaniyam merzlykh gruntov 2, Izd-vo Akad.Nauk SSSR, 1954.

16. Instruktsiya po opredeleniyu kharakteristiki soprotivleniya sdvigusvyaznykh gruntov (Instructions for determining the shearresistance of cohesive soils). Ministerstvo elektrostantsii.Otdel inzhenernoi geologii (Ministry of Power Stations, Divisionof Engineering Geology), 1957.

17. Fisenko, G.L. Opredelenie stsepleniya i koeffitsienta vnutrennegotrenlya pcluskal'nykh gornykh porod Korkinskogo mestorozhdenlya(Determination of cohesion and coefficient of internal frictionof semiconsolidated rocks of the Korkinskii deposit). Issledovaniyapo voprosam marksheiderskogo dela, 27, 1953.

18. Troitskaya, M.N. Posobie k laboratornym rabotam po mekhanlke gruntov(Handbook of laboratory investigations in soil mechanics). Izd-voMGU, 1961.

19. Kompressionnye ispytaniya ovraztsov glinistykh porod v odometrakh (vremennaya instruktsiya (Compression testing of clay solI samplesin odometers (preliminary instructions). Izd-vc VSEGINGEO, Moscow,1959.

20. Rukovodstvo po laboratornomu opredeleniyu fiziko-mekhanicheskikhkharakteristik gruntov pri ustroistve osnovanii sooruzhenii(Instructions for laboratory determinations of physico-mechanicalproperties of soils on laying the foundations of structures).Gos. izd-vo lit. po stroitel'stvu i arkhitekture, Moscow, 1956.

21. Tekhnicheskie usloviya proektirovaniya osnovanil i fundamentov navechnomerzlykh gruntakh (Technical considerations in designingfoundations in permafrost). (SN91-60).

22. Chapovskii, E.G. Laboratornye raboty po gruntovedeniyu i mekhanikegruntov (Laboratory investigations in soil science and soilmechanics). Gosgeoltekhizdat, Moscow, 1958.

23. Bronshtein, I.N. and Semendyaev, K.A. Spravochnik po matematike(Handbook of mathematics). Izd-vo Nauka, 1964.

-95-

Time t

.

! ｾｾｾｾ］Ｚｴ］］］ｴＺ］］ＺＺｉ］ＶＬｾ L.l-_-'-_......... ......__\.-<0

w

Fig. 1

Creep curves of frozen soil at differentstresses 01 < 02 < 03

e II eI I

Time t

- - ..=-..=-:.-w---:-,..

tp<" t,

Time t

Fig. 2

Creep curvesa - non-attenuating; b - attenuating

a

w

Time t 7 Deform. E

Fig. 3

Division of deformations into recovering(E 1) and residual (E ) types

e resa - creep curve; b - stress

deformation diagram

-96-

a c. ,1:,,;;

oｉＭＭｲＭＭｾ］ＺＺＺｴＺＺＮＮＮＭＭＺ｣Ｍe

M...

ol

Fig. 4

Diagram of stress (0) deformation

(E) relationship, allowing for creep

a - series of curves for

different moments of time

to < tl < t2 < t 3 < too of load

action; b - 9urve for one of the

moments of time t i

Fig. 5

Rheological curve of frozensoil: relationship betweenstress (0) and deformation

rate (£) in the steadyplastic-viscous flow stage

e

｣ｾＭＭＭＭＭＭＭＭ

p, kg/cm 2

D

Fig. 6

Relationship between load andrelative compression of

frozen soil on compression

Fig. 7

Curve showing long-termstrength of frozen soilrelationship between

magnitude of failure loadand time in which failure

occurs)

-97-

.l----ll- 6"

r/1

Time, t

,

ｾｾＺＺＺＺＺ］］］ｴ［ｮＬＢｾ '-- 6/1

rJ)

Fig. 8

Diminution of shear strength (Tn)

with time at different normal stresses

Fig. 9

Shear diagram of frozen

soils for different moments

of time to < tl < t 2 < t3 <too

of action of shear load

Fig. 10

Probe (1) and adapter (2)

4

Fig. 11

Diagram of radialdeformation gauge1 - spring collar;

2 - measuring slidewire; 3 - sliding contact;

4 - connecting lead

-98-

I

2

J

":It---- II

:-"l't+-- 5

Fig. 12

Mounting specimen for uniaxial compression test

1 - upper plate; 2 - rubber band;3 - rubber sheath;

4 - pick-up of radialdeformation gauge; 5 - specimen

6 - lower plate

L.- A

p b

Fig. 13

Frozen soil compression diagrams:brittle (a) and sUbject to

plastic deformation (b)

Fig. 14

Frozen soil compression diagrams;1 and 2 - arbitrary;I' and 2' - actual

6 6; OJ 6.6,,5656,68 69 ｾｏ

bl

o t,

Fig. 15

t1 t

J

a

t. t5

64

t, t

1-D\D

I

Reconstruction of frozen soil creep curves as curves showingrelationship between stress and deformation

a - creep curves for different stresses; b - stress-deformationcurves for various times of load action

-100-

tn 6

Fig. 16

Diagram for determining parameters A and mplotted in logarithmic coordinates

ln6 h ln6C ｾｮ､Q

.-,

ＬＬｾＭＭＬ}lnAI ｉｽｩｾｾＺｾｲＬｾ I/

J

t. t,

.,ｾｮ l. 0 LoE 0 lot 0

Fig. 17

Relationship between stress and deformationfor different load action times

plotted in logarithmic coordinates

til

6"

o

Q

t

b

\lit

-101-

",

o t

tnt

Fig. 18

Time function F(t)a - plotted in normal coordinates;

b - plotted in logarithmiccoordinates

tn6,{'-- _

o

Fig. 20

Verification of equation

£ = ｂ｡ｴｾＨ｡Ｉ by rectification

in logarithmic coordinates

Fig. 19

Dependence of hardeningcoefficient m on time t

a

Fig. 21

Dependence of coefficientｾ on stress a

-102-

Fig. 22

Determination of parameters wand k of frozen soil atdifferent temperatures

a and b - curves showing variation ofmodulus of deformation

A in time plotted in ordinary andlogarithmic coordinates;

c and d - curve showing variation ofparameter ｾ with temperatureplotted in ordinary and logarithmic coordinates

arctan n

-tnt

d b tn(6-tp

-Lnt

Fig. 23

Rheological curves plotted inlogarithmic coordinates

-103-

tp Time,, hr

tｰｾ

QI

oL..L-,-_.J__---L_--:-_...I.- --l__

ｾｾｾＬＮ［

Fig. 24

Construction of curve of long-term strengthduring compression, (shear) from creep curves

a - series of creep curves for differentfailure stresses;

b - curve of long-term strength duringcompression (shear)

t -0

6 L 6 ｾ 6.J - •

2"'J<r.. ｾ r.

II

(,

-:Time, t 0 8

p

Fig. 25

Growth of deformation in timewith staged loading

Fig. 26

Temperature (8) dependence of strengthof frozen soil during compression

plotted in ordinary (a) andlogarithmic (b) coordinates

a

-104-

bp

I

Fig. 27

The wedge apparatus developed by theAll-Union Research Institute of Mine Surveying

a - general view; b - schematic drawing;1 - specimen; 2 - movable casing;

3 - stationary casing;4 - set of metal rollers

acorn' an' kg/cm 2

Fig. 28

The conditional-instantaneousshear resistance and a

of frozen soil com

-105-

I

....ｾｾｉ II I

".LJ--..L-L-l_-

d", 6"1 6"J 6n·kg / cm2

oc, d.l d.J DC, <Jes"

Fig. 29

a) Family curves illustrating the long-termstrength of frozen soil during shear in relation to a

(shearing apparatus) or a (wedge tester) nb) Reconstruction of curves denoting the

long-term strength obtained for different valuesof a in the shear diagram

n

f•. kg/cm 2t,

6".kg/cm 2

Fig. 30

Shear of frozen soil fordifferent durations of load action

ｄＮｄＶＱＭＭＫＭＭｉＭＭｾＮＮＬＭＭｉＭＭＴＭＭＫＭＭＱ

D.DI'L...---L_l-----.L----l_..L-----L.---l

ｾＮｍｍ

Fig. 31

Calibration curves forfour compression devices

-106-

,

Fig. 32

Curves illustrating thedependence of relative

deformation e on time twith load application

in stages

Fig. 33

Variation of relativedeformation of frozen

soil (e) with load(compression curve)

,','t

Q P, PI

Fig. 34

Variation of the coefficientof porosity of frozen

soil with load (compressioncurve)

Fig. 35

Diagram of dynamometric apparatus1 - specimen; 2 - indicator ofdeformation of the specimen;3 - plate; 4 - dynamometer;

5 - train indicator fordynamometer; 6 - stand;

7 - stressing device

-107-

Fig. 36

Curves obtained in tests with the dynamometric apparatusa - deformation of dynamometer;b - deformation of specimen;c - variation of load with time

-108-

IJ

7

J

1

1 -

Fig. 37

Design of dynamometric apparatus1 - electric motor; 2 - gear drive;

3 - screw drive; 4 and 13 - lowerand upper yoke; 5 - stop screw;

6 - guiding sleeve; 7 - strainindicator for specimen;8 - support for strainindicator for specimen

9 and 12 - lower and upper movableguides; 10 - dynamometer; 11 - strain

indicator for dynamometer;14 - upper loading screw; 15 - crank formanual loading; 16 - longitudinal rod;

17 and 19 upper and lower end bearing plates;18 - soil specimen; 20 - base plate;

21 - lower loading screw

-109-

a

).'A"o

Fig. 38

Relation between load and deformation of soila - relation between P and initial deformation of soil A"b - the 16ad-deformati8n curve on a logarithmic scale and

o

determination of Ai n i t

and m from equation (61);

c - determination of Ai n i t

Rnd m from results of two

parallel tests with different initial loads pO(l)and PO

( 2 )

0.:. P(t) 11 b

I "' __.............

...... 1--'/ I

Ｚｾ I I

ifl I

II t

·tn{Wti"l d

ｾｲｾｷ arc

ｾＱtana

ii t Ln t

Fig. 39

Determination of creep function ｾＨｴＩ

a - development of deformation of dynamometer with time;b - development of deformation of soil specimen with time;

curve illustrating the creep function ｾＨｴＩ［

c - ｾＨｴＩ - t curve;d - same on a logarithmic scale

Methods of determining creep, long-term strength and ...

Documents