Shear Modulus and Damping Ratio of Organic Soils

ORIGINAL PAPER

Shear Modulus and Damping Ratio of Organic Soils

P. Kallioglou Æ Th. Tika Æ G. Koninis ÆSt. Papadopoulos Æ K. Pitilakis

Received: 18 May 2007 / Accepted: 11 May 2008

� Springer Science+Business Media B.V. 2008

Abstract The paper presents results from a labora-

tory investigation into the dynamic properties of

natural intact and model organic soils by means of

resonant-column tests. The natural intact organic

soils were sands, cohesive soils and peats with

varying content of calcium carbonate. The model

organic soils were formed in laboratory by mixing

kaolinite and paper pulp. The influence of various soil

parameters, such as strain level, confining stress, void

ratio, plasticity index, organic content and secondary

consolidation time on shear modulus, G, and damping

ratio, DT, is presented and discussed. The test results

on natural organic soils show that only high organic

contents (OC C 25%) have significant influence on G

and DT at both small and high shear strains. For the

model organic soils, however, a significant influence

of even lower values of organic content

(5% B OC B 20%) on G at small strains and DT at

both small and high strains is observed.

Keywords Shear modulus � Damping ratio �Dynamic properties � Resonant-column �Organic soils � Peat

1 Introduction

It is well known in Geotechnical Engineering that

among the key parameters controlling the response of

soil to dynamic loading is shear modulus and

damping ratio. It is also widely accepted that the

response of soil to both static and dynamic loading

depends mainly on the level of strain induced to it.

Soil behaviour ranges from linear elastic to inelastic,

depending on the level of strain, and may be divided

in three zones (Dobry 1991; Jardine 1992; Hight and

Higgins 1994). At small shear strains, c, the stress–

strain relation is linear elastic, soil shear stiffness has

its maximum value, G = Gmax, and damping ratio its

minimum value, DT = DTmin. The upper strain limit

of this range is called linear elastic threshold shear

strain, cte, and depends on soil type. When the strain

exceeds the linear elastic threshold shear strain, but

remains below another upper strain limit, the stress–

strain relation becomes non-linear elastic, and is

accompanied by stiffness degradation and damping

increase. The latter upper strain limit is called

volumetric threshold shear strain, ctv, and depends

also on soil type and stress state. When the strain

exceeds the volumetric threshold shear strain, ctv, the

stress–strain behaviour becomes inelastic with sig-

nificant stiffness degradation, damping increase and

plastic strains development. Consequently, passage

from elastic to inelastic behaviour corresponds to ctv,

defined as the strain at which excess pore water

pressures or plastic strains start to build up.

P. Kallioglou (&) � Th. Tika � G. Koninis �St. Papadopoulos � K. Pitilakis

Department of Civil Engineering, Laboratory of Soil

Mechanics, Foundations’ & Geotechnical Earthquake

Engineering, Aristotle University of Thessaloniki,

54124 Thessaloniki, Greece

e-mail: [email protected]

123

Geotech Geol Eng

DOI 10.1007/s10706-008-9224-1

Organic soils, which according to their definition

contain a varying proportion of organic matter,

include peat (remains of dead vegetation in various

stages of decomposition), gyttja (plant and animal

remains deposited in lakes) and organic clays, silts

and sands. Table 1 presents a classification system of

soils according to the content of the organic matter,

proposed by Karlsson and Hansbo (1981). Organic

soils have long been recognized as problematic

materials, because of their low shear strength, high

compressibility and permeability and considerable

secondary consolidation deformations. They are

characterized by an inhomogeneous and anisotropic

structure and differ greatly from inorganic soils with

respect to their engineering properties. There are,

however limited experimental data, regarding the

dynamic properties of such soils. Most of the

previous investigations were concerned with the

dynamic properties of soils with very high organic

contents, such as peats (Shannon and Wilson 1967;

Kramer 1993, 1996, 2000; Stokoe et al. 1996;

Boulanger et al. 1998; Wehling et al. 2003).

2 Objectives and Scope

With expanding urban development, there is an

increasing demand of building large infrastructure

constructions at sites with even problematic soils. For

example, organic soils and peats are often encountered

within the foundation soil of large embankments and

bridges. The design of these constructions requires the

knowledge of the engineering behaviour of such soils

and more particular, the seismic design requires the

knowledge of their shear modulus and damping ratio.

This paper presents the results of a laboratory

study on the dynamic properties of natural and model

organic soils by means of resonant-column (RC)

tests. The tests were carried out in the context of site

seismic response studies in Greece and Cyprus and

also an investigation into the dynamic problems of

seismically problematic non liquefiable soils, consid-

ered in the Greek Seismic Code (GSC 2000).

3 Testing Procedure

The tests have been performed in the RC apparatus,

designed by Drnevich at University of Michigan

(Drnevich 1967). The apparatus is of fixed-free type

and allows both the longitudinal and torsional vibra-

tion of a solid cylindrical specimen (diameter 35.7/

71.1 mm and height/diameter ratio 2:1). The speci-

men is placed in a triaxial cell, installed on a concrete

base, which is fixed to the ground (passive end). It is

surrounded by fluid (water) and subjected to an

isotropic confining stress, ro, (up to 700 kPa) and

back pressure, ub. The dynamic excitation (force or

moment) is subjected to the specimen by means of a

system of magnets and coils, connected to the top base

plate attached to the specimen (active end). The

simple harmonic longitudinal or torsional vibration

applied to the active end, produces longitudinal or

shear waves respectively, which propagate down to

the specimen base (passive end), where they reflect.

The excitation frequency is changed until resonance

in the first mode of vibration is achieved, and this

occurs at a phase of 180o between excitation and

velocity of active end. The resonance frequency,

amplitude of vibration and acceleration are measured

at the active end of the specimen. These values with

the characteristics of the specimen (geometry and

mass) and the apparatus (mass and stiffness of active

end) together are used for the estimation of propagat-

ing longitudinal and shear wave velocity, Vp and Vs,

Young’s and shear modulus, E and G, longitudinal

and shear damping ratio, DL and DT, and axial and

shear strain, e and c, respectively. In this paper results

for the torsional vibration are only presented. Calcu-

lations were made according to ASTM D4015-92.

Table 1 Classification of soils according to the organic

content (Karlsson and Hansbo 1981)

Soil group Organic content

in weight % of

dry material

(\2 mm)

Examples of

designations

Low-organic soils 2–6 Gyttja-bearing clay

Dy-bearing silt

Humus-bearing sand

Medium-organic soils 6–20 Clayey gyttja

Silty dy

Humus-rich sand

High-organic soils [20 Gyttja

Dy

Peat

Humus-rich topsoil

Geotech Geol Eng

123

Each specimen, after it had been trimmed to its

nominal dimensions, was installed in the triaxial cell

base and then enclosed by a membrane. The appa-

ratus was assembled and saturation of the specimen

followed by increasing both the back and cell

pressure, but keeping a constant effective stress

(r0o & 30 kPa). Saturation degree was evaluated by

estimating Skempton’s parameter B. After the com-

pletion of saturation procedure, the specimen was

consolidated at various levels of r0o. Length and

volume changes of the specimen were continuously

measured. Two types of dynamic excitation were

imposed: small-strain loading and a sequence of

loadings with increasing strains. The former was

applied sometimes during consolidation stage and

always after the completion of primary consolidation,

whereas the latter was applied always after the

completion of primary consolidation. As the test is

considered to be non-destructive, r0o was usually

increased to the next level, in order to assess the

dependence of dynamic properties on r0o.

4 Tested Soils

The tested soils were intact natural organic soils,

retrieved from various sites in Greece and Cyprus,

using either rotary core or thin wall tube sampling

(shelby plastic or metal), as well as model organic

soils. The latter soils were formed in laboratory in

order to study the effect of the organic matter on the

dynamic properties, as in natural organic soils there is

always the combined effect of natural sedimentation

process, stress history, soil composition and structure.

The organic content, OC, of the soils was measured

by ignition in a muffle furnace at 440 or 750�C,

(ASTM D2974-00). The natural organic/peaty soils

are classified according to their organic content,

Table 1, and their plasticity into the following groups:

(i) Calcareous organic sands. Table 2 and Fig. 1

present the physical properties and the grading

curves of the sands respectively. These belong to

the recent holocene–pleistocene marine and

fluvial deposits, encountered near the coastal

zones of Aegion (S1), Larnaca (S2s, S3s, S5s)

and Limassol (S4), as well as at Nissi peatland

deposits (Cristanis 1994), the latter being depos-

ited in the intramontane basin of Edessa (S6).

The sands were normally consolidated, apart

from sand S1 (OCR = 4), and non-plastic (NP).

The organic matter of the samples, apart from

S6, consisted of semidecomposed roots and

seaweeds, which although they were very of

light weight, as compared to the mineral mass,

they covered a significant part of the sample

volume (up to 1/3 of the specimen volume for

soil S5s). All sands were also characterized by

the presence of high calcium carbonate content,

CC, ranging between 22% and 55%. This was

determined using either HCl method or radio-

graphic method (RD) as a percentage of the dry

mass of the soil.

(ii) Organic cohesive soils. Table 3 and Fig. 1

present the physical properties and the grading

curves of the soils respectively. These belong

either to the recent holocene–pleistocene mar-

ine and fluvial deposits, encountered near the

coastal zones of Aegion (C1, C2 & C3), Volos

(C4), Argostoli (C6) and Larnaka (C8s and

C9s), or at the lake deposits of Volvi (C5) and

Drama (C7s) basins. The soils were normally

consolidated to slightly overconsolidated

(OCR = 1–1.5). The organic matter of the

samples either had an amorphous structure

within the mineral matrix, or consisted of

semidecomposed roots and seaweeds (C8s and

C9s). In the latter case, although the mass of the

organic matter was small, as compared to the

mineral mass, it covered up to 1/3 of the sample

volume. Some soils (C1, C2, C3, C8s and C9s)

were also characterized by the presence of high

calcium carbonate content, ranging between

21% and 36%.

(iii) Peats. Two natural peats, P1 and P2s were

tested. Table 4 presents the physical properties

of the soils. Peat P1 had an amorphous

structure and was retrieved from Philippi

peatland, located in the intramontane basin of

Drama in northern Greece (Cristanis 1987).

Peat P2s had a highly fibrous structure and was

retrieved from the lignite deposit basin of

Ptolemaida-Kozani in northwestern Greece.

Both peats are considered to be non-plastic

(NP), since it was not possible to perform

Atterberg limits tests due to their nature. They

were also normally consolidated. Although

their ash content was between 38% and 52%

Geotech Geol Eng

123

https://www.researchgate.net/publication/256418244_The_genesis_of_the_Nissi_peatland_northwestern_Greece_as_an_example_of_peat_and_lignite_deposit_formation_in_Greece?el=1_x_8&enrichId=rgreq-6b541d7e-33d6-4911-8935-cae945ee2993&enrichSource=Y292ZXJQYWdlOzIyNTkwNDMyOTtBUzoxOTg1Mjg4MTE5NjY0NjRAMTQyNDM0NDM2NTgyMA==

Ta

ble

2P

hy

sica

lp

rop

erti

eso

fn

atu

ral

calc

areo

us

org

anic

san

ds

(NP

)

Tes

taD

epth

(m)

r0 mb

(kP

a)

Sam

pli

ng

met

ho

dd

Gs

D50

(mm

)

Cu

=D

60

D1

0c o (k

N/m

3)

wo

(%)

e oS

r

(%)

FC

e

(\7

5l

m)

(%)

OC

f

(%)

CC

g

(%)

US

CS

So

ild

escr

ipti

on

S1

14

.0–

14

.61

34

PL

2.6

69

0.1

20

5.7

19

27

0.7

04

10

02

31

22

2S

MD

ark

-gre

yto

bla

cksi

lty

san

dw

ith

seaw

eed

s(M

ediu

mo

rgan

ic)

S2

sc4

.0–

4.5

57

M2

.58

50

.17

06

.71

84

01

.01

81

00

26

13

55

SC

-SM

Dar

k-g

rey

silt

y-c

lay

eysa

nd

wit

h

seaw

eed

s(M

ediu

mo

rgan

ic)

S3

sc2

.68

50

.18

06

.32

02

60

.69

99

81

81

34

6S

C-S

MD

ark

-gre

ysi

lty

-cla

yey

san

dw

ith

seaw

eed

san

d4

%sh

ells

wit

h

dia

met

er[

2m

m(l

ayer

of

seaw

eed

sat

the

bas

e)(M

ediu

m

org

anic

)

S4

6.7

–7

.58

1P

L2

.75

20

.09

12

1.0

19

29

0.8

52

94

32

82

6S

MD

ark

-gre

ysi

lty

san

dw

ith

roo

tsan

d

seaw

eed

s(M

ediu

mo

rgan

ic)

S5

s9

.5–

10

.28

7M

2.7

36

0.0

95

–1

75

21

.44

89

84

52

53

0S

C-S

MD

ark

-gre

ysi

lty

-cla

yey

san

dw

ith

po

cket

so

fse

awee

ds

and

7%

shel

ls(d

iam

eter

[2

mm

)(H

igh

org

anic

)

S6

9.0

–9

.61

07

PL

2.6

73

0.0

65

–1

65

91

.68

09

45

32

54

2S

MB

lack

,si

lty

san

dw

ith

fib

rou

s

stru

ctu

re(H

igh

org

anic

)

aS

pec

imen

sh

adn

om

inal

dim

ensi

on

s:D

o=

7.1

cm,

Ho

=1

4.2

cm,

apar

tfr

om

tho

sein

dic

ated

wit

hin

dex

s,w

hic

hh

adn

om

inal

dim

ensi

on

s:D

o=

3.6

cm,

Ho

=7

.1cm

bE

stim

ated

in-s

itu

ver

tica

lef

fect

ive

stre

ss.

Wh

ere

dat

aw

ere

no

tav

aila

ble

,th

eu

nit

wei

gh

ts,c,

abo

ve

and

bel

ow

gro

un

dw

ater

tab

leas

sum

edeq

ual

to1

8an

d2

0k

N/m

3,

resp

ecti

vel

yc

So

ils

S2

san

dS

3s

wer

ere

trie

ved

fro

mth

esa

me

bo

reh

ole

and

dep

thd

M:

Sh

elb

ym

etal

tub

e,P

L:

Sh

elb

yp

last

ictu

be

eF

C:

Fin

esco

nte

nt.

Gra

din

gte

sts

wer

eco

nd

uct

edw

ith

ou

tso

ilp

re-t

reat

men

tfo

ro

rgan

ican

dca

lciu

mca

rbo

nat

eco

nte

nt

fO

rgan

icm

atte

rco

nte

nt

gC

alci

um

carb

on

ate

con

ten

t

Geotech Geol Eng

123

(ASTM D4427-92) and they may be alterna-

tively described as high-organic soils (ash

content greater than 25%), they are referred

to as peats in this paper, because of their

characteristic structure, odor, colour and high

organic content (ASTM D2487-00, Karlsson

and Hasnbo 1981).

The model organic soils were formed in laboratory

by mixing kaolinite (K) and pure paper pulp (P) at

contents of 5, 10 and 20% of total dry mass. The paper

pulp was initially shredded into very small fibrous

pieces and mixed with distilled water by means of a

blender. The mixtures were prepared in a slurry

condition at an initial water content ranging from

1.25 and 1.75 times the liquid limit of the soils. This

condition may be considered as replicating the depo-

sitional conditions of young deposits under overburden

pressure. To avoid segregation and achieve uniformity,

the mixtures were constantly mixed, matured for

several days and then were placed in three split moulds

(inside diameter: 71.1 mm, height: 270–400 mm),

where they were consolidated under one-dimensional

conditions to a vertical stress of 50 or 100 kPa. In order

to study the effect of the presence of salts in pore water,

as it is the case for organic soils near coastal areas, a

mixture of kaolinite and 10% paper pulp with distilled

water containing NaCl (0.18 N solution) was also

prepared. To avoid osmotic effects during the test on

this mixture, water with the same salt concentration

was used inside the pore water and volume change

measuring system as well as in the cell. Table 5

presents the physical properties of the model organic

cohesive soils, as well as kaolinite. As shown in the

above table and also exhibited in Fig. 2, the increase of

organic content results in an increase of liquid limit,

LL, plasticity index, PI, void ratio, e, and soil

compressibility, Cc, as in natural organic soils. It

may thus be inferred that the behaviour of the model

organic soils used in this study resembles that of natural

organic soils.

5 Test Results and Discussion

It is well known that natural soils are structured

materials. As stated by Mitchel (1976), the term

‘‘structure’’ means the combination of ‘‘fabric’’

(particle arrangement) and interparticle ‘‘bonding’’.

For the intact organic soils in this work, the presence

of organics indicates the existence of an inhomoge-

neous and inherently anisotropic fabric, while the

presence of calcium carbonate, which may act as

cementing agent at particle contents, indicates pos-

sibly the existence of a bonded structure and thus an

extra component of strength and stiffness.

The resonant–column test results of each soil

group are presented in the following paragraphs. For

each group the results for the shear modulus first and

for damping ratio then at small and high strains are

described and discussed.

Fig. 1 Grading curves of

natural organic sands and

cohesive soils

Geotech Geol Eng

123

Ta

ble

3P

hy

sica

lp

rop

erti

eso

fn

atu

ral

org

anic

coh

esiv

eso

ils

Tes

taD

epth

(m)

r0 mb

(kP

a)

Sam

pli

ng

met

ho

dd

wo

(%)

c o (kN

/m3)

LL

(%)

PI

(%)

CF

f(\

2lm

)

(%)

Gs

e oS

r

(%)

OC

g

(%)

CC

h

(%)

US

CS

So

ild

escr

ipti

on

C1

13

.6–

14

.21

30

PL

25

19

27

10

22

2.7

26

0.7

34

91

13

22

CL

Dar

k-g

rey

tob

lack

clay

wit

hsa

nd

(Med

ium

org

anic

)

C2

47

.0–

47

.64

61

PL

26

19

29

10

22

2.6

83

0.7

07

98

15

23

CL

Dar

k-g

rey

clay

(Med

ium

org

anic

)

C3

34

.2–

34

.83

34

PL

25

19

31

12

23

2.7

29

0.7

14

94

13

21

CL

Dar

k-g

rey

clay

(Med

ium

org

anic

)

C4

49

.8–

50

.05

19

R2

32

03

91

98

2.7

91

0.6

44

99

62

CL

Bro

wn

-red

clay

(Med

ium

org

anic

)

C5

20

.0–

20

.62

54

PL

29

18

40

19

24

2.7

14

0.7

93

10

08

–C

LG

rey

clay

wit

hsa

nd

(Med

ium

org

anic

)

C6

4.5

–5

.51

00

PL

51

17

59

30

26

2.6

50

1.3

42

10

06

–C

HD

ark

gre

ycl

ayw

ith

san

dan

dsh

ells

(Med

ium

org

anic

)

C7

s5

6.0

–5

7.0

47

5P

L5

21

61

03

40

51

2.2

80

1.0

59

10

03

3–

MH

Bla

ckcl

ay(H

igh

org

anic

)

C8

sc1

1.0

–1

1.5

99

L5

41

77

14

04

72

.77

11

.49

81

00

25

36

CH

Gre

ycl

ayw

ith

abu

nd

ant

seaw

eed

s,

shel

lsan

dth

inh

ori

zon

tal

lay

ers

of

san

d(H

igh

org

anic

)

C9

sc4

21

73

7e

8e

21

2.5

47

1.0

85

10

02

53

1C

HC

9s

was

sim

ilar

toC

8s,

bu

tit

had

ath

ick

lay

ero

fsa

nd

atth

eb

ase

(Hig

ho

rgan

ic)

aS

pec

imen

sh

adn

om

inal

dim

ensi

on

s:D

o=

7.1

cm,

Ho

=1

4.2

cm,

apar

tfr

om

tho

sein

dic

ated

wit

hin

dex

s,w

hic

hh

adn

om

inal

dim

ensi

on

s:D

o=

3.6

cm,

Ho

=7

.1cm

bE

stim

ated

in-s

itu

ver

tica

lef

fect

ive

stre

ss.

Wh

ere

dat

aw

ere

no

tav

aila

ble

,th

eu

nit

wei

gh

ts,

c,ab

ov

ean

db

elo

wg

rou

nd

wat

erta

ble

assu

med

equ

alto

18

and

20

kN

/m3,

resp

ecti

vel

yc

So

ils

C8

san

dC

9s

wer

ere

trie

ved

fro

mth

esa

me

bo

reh

ole

and

dep

thd

M:

Sh

elb

ym

etal

tub

e,P

L:

Sh

elb

yp

last

ictu

be,

R:

Ro

tary

core

eD

eter

min

edu

sin

gth

ew

ho

lesp

ecim

enm

ass

fC

F:

Cla

yF

ract

ion

.G

rad

ing

test

sw

ere

con

du

cted

wit

ho

ut

soil

pre

-tre

atm

ent

for

org

anic

and

calc

ium

carb

on

ate

con

ten

tg

Org

anic

mat

ter

con

ten

th

Cal

ciu

mca

rbo

nat

eco

nte

nt

Geotech Geol Eng

123

5.1 Calcareous Organic Sands

Figure 3a presents the variation of small-strain shear

modulus, Gmax, with isotropic effective stress, r0o, at

24 h confinement time for the tested calcareous

organic sands. It should be noted that c values for

small size (index s) specimens (c = 26 9 10-6 -

72 9 10-6) are one order higher than the corre-

sponding values for large size specimens

(c = 0.9 9 10-6 – 15 9 10-6). The insitu mean

effective stress, r0oinsitu, also indicated in the above

figure was determined using the value of the coeffi-

cient of earth pressure at rest, ko, estimated either

from ko triaxial tests or using Jaky’s (1944) equation

for normally consolidated soils (1 – sin u0). It is

shown that Gmax increases linearly with increasing r0oin a log–log plot. Lower values of Gmax are indicated

for the high-organic sands S5s and S6. Moreover, the

Gmax values for the medium-organic sands S2s and

S3s (small specimens) measured at higher strains, are

either comparable (S2s), or even higher (S3s) than the

corresponding values of the other medium-organic

sands (S1 & S4). This may be attributed to the higher

content of calcium carbonate of sands S2s and S3s,

indicating a larger component of stiffness due to the

interparticle bonding.

Considering the test results at effective confining

stresses equal to and above the r0oinsitu, the shear

modulus of the sands can be expressed as a function

of effective confining stress, shear strain, void ratio,

Table 4 Physical properties of natural peats (NP)

Testa Depth

(m)

r0mb

(kPa)

Sampling

methodcGs wo

(%)

eo co

(kN/m3)

Sr

(%)

OCd

(%)

CCe

(%)

HCl/

RD

USCS Soil description

P1 85.8–86.0 682 PL 2.137 101 2.297 13 96 48 – Pt Black, clayey peat with amorphous

structure

P2s 35.4–35.9 548 R 2.441 58 1.953 14 86 62 – Pt Brown-black, peat with shells

and intense fibrous structure

(fibers with horizontal

orientation)

a Specimens had nominal dimensions: Do = 7.1 cm, Ho = 14.2 cm, apart from that indicated with index s, which had nominal

dimensions: Do = 3.6 cm, Ho = 7.1 cmb Estimated in-situ vertical effective stress. Where data were not available, the unit weights, c, above and below ground water table

assumed equal to 18 and 20 kN/m3, respectivelyc PL: Shelby plastic tube, R: Rotary cored Organic matter contente Calcium carbonate content

Table 5 Physical properties of model organic cohesive soils and kaolinite

Mixture Testa wob

(%)

cob

(kN/m3)

LL

(%)

PI

(%)

CF (%)

(\2 lm)

Gs eob Sro

b

(%)

OCc

(%)

USCS

Kaolin K 49 17 54 28 49 2.692 1.331 99 0 CH

Kaolin + 5% paper pulp P–5 56 16 70 44 – 2.616 1.512 98 5 OH

Kaolin + 10% paper pulp P-10-A 69 15 90 58 – 2.580 1.818 98 10 OH

Kaolin + 10% paper

pulp + NaCl

P-10-Bd 59 16 112 71 – 2.580 1.520 100 10 OH

Kaolin + 20% paper pulp P-20 86 14 210 122 – 2.369 2.177 94 20 OH

a Specimens had nominal dimensions: Do = 7.1 cm, Ho = 14.2 cmb Initial parameters at resonant–column testsc Organic matter contentd Mixture prepared with solution of distilled water and NaCl (0.18 N)

Geotech Geol Eng

123

organic content and calcareous content by the

following expression:

G ¼ A cð Þ � f r0o� �

� g eð Þ � h OCð Þ � k CCð Þ ð1Þ

where: A(c), f(r0o), g(e), h(OC) and k(CC) are

functions of c, r0o, e, OC and CC respectively.

The regression analyses of these data resulted in

Eq. 2.

G¼ 830

1þ17:35�c0:597�r0ð0:681�c0:045Þ

o �e�0:99

�OC�0:104�CC0:657 R2¼0:922� �

ð2Þ

where: c, OC and CC are expressed as percentages

(%) and r0o and G are expressed in kPa.

The normalized G values predicted from the above

equation are compared with the experimental data at

a shear strain close to the minimum shear strain used

in the tests on both large and small size specimens,

c = 6.6 9 10-5, in Fig. 4.

The normalized shear modulus, G/Gmax, is plotted

versus shear strain in Fig. 5a for all sands at an

effective isotropic stress approximately equal to or

higher than r0oinsitu. For sands S2s, S3s and S5s, the

measured G values were normalized by the Gmax

value, determined from equation (2) at c = 10-6. For

medium-organic sands, the degradation G/Gmax

curves agree with the range of corresponding curves

presented in literature for reconstituted inorganic

sands containing fines (Kallioglou 2003). High-

organic sands exhibit higher linearity in G/Gmax

curves than medium-organic. The magnitude of r0oaffects the position of the G/Gmax curves both for

medium-organic and high-organic sands, Fig. 6a. In

Fig. 2 Variation of (a) organic content, OC, with liquid limit,

LL, and (b) compression index, Cc, with void ratio, eo, for

model organic soils

Fig. 3 Variation of (a) small-strain shear modulus, Gmax, and

(b) small-strain damping ratio, DTmin, with isotropic effective

stress, r0o, for natural calcareous organic sands

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123

particular, at a given shear strain level, c, an increase

of r0o results in an increasing linearity of G/Gmax

curves. The influence of r0o on G/Gmax-c curves is

limited at stress levels lower than r0oinsitu or of the

order of 90 to 140 kPa and diminishes at stresses

exceeding the latter range.

The variation of small-strain damping ratio,

DTmin, with isotropic effective stress, r0o, at 24 h

confinement time is plotted in Fig. 3b. DTmin remains

either constant, or decreases with increasing r0o. The

range of DTmin values is from 1.4% to 1.8% for the

medium-organic and from 2.5% to 4.1% for the high-

organic sands at c B 10-5 for the range of stresses

examined (r0o = 30–400 kPa). These ranges com-

pare with the corresponding range of DTmin between

0.7% and 1.9% for inorganic sands containing fines

Fig. 4 Comparison of normalized shear modulus, G/[g(e) 9

h(OC) 9 k(CC)], obtained from Eq. 2 with the corresponding

results from the tests on natural calcareous organic sands

Fig. 5 Variation of (a) normalized shear modulus, G/Gmax,

and (b) damping ratio, DT, with shear strain, c, for natural

calcareous organic sands at effective isotropic confining stress,

r0o, approximately equal to or higher than insitu stress, r0oinsitu

Fig. 6 Effect of effective isotropic confining stress, r0o, on

variation of (a) normalized shear modulus, G/Gmax, and (b)

damping ratio, DT, with shear strain, c, for natural calcareous

organic sands S4 and S6

Geotech Geol Eng

123

(Tika et al. 2004). A small increase in DTmin of

cemented over non-cemented sands has been reported

in literature (Chiang and Chae 1972; Saxena et al.

1988). Since, however, all sands tested in this work

contained calcium carbonate, the higher DTmin values

observed for the high-organic sands indicate that the

organic matter starts to have an influence on DTmin at

an organic content exceeding 25% approximately.

The variation of damping ratio versus shear strain

is plotted in Fig. 5b. The DT versus c curves for the

medium-organic sands are within the range of

corresponding curves presented in literature for

inorganic sands containing fines (Kallioglou 2003),

whereas for the high-organic sands exhibit higher

linearity than the medium-organic sands. The mag-

nitude of r0o affects the position of the DT curves

both for medium-organic and the high-organic sands

and at a given shear strain level, c, with an increase of

r0o resulting in a decrease of DT, Fig. 6b.

5.2 Organic Cohesive Soils

5.2.1 Natural Intact Organic Soils

Figures 7a and 8a present the variation of small-strain

shear modulus, Gmax, with isotropic effective stress,

r0o, at 24 h confinement time for the tested medium-

organic and high-organic cohesive soils respectively. It

should be noted that the tests on the high-organic soils

of this group were conducted on small size specimens

and the c values (c = 53 9 10-6 – 230 9 10-6) are

up to two orders higher than the corresponding values

for the large size specimens of medium-organic soils

(c = 1.2 9 10-6 – 10 9 10-6). The insitu mean

effective stress, r0oinsitu, also indicated in the above

figures, was determined using the value of the coeffi-

cient of earth pressure at rest, ko, estimated either using

Jaky’s (1944) equation for normally consolidated clays

(1 – sin u0), or as function of PI and OCR for

overconsolidated clays (Brooker & Ireland, 1965).

The angle of shearing resistance, u0, was evaluated

from the empirical correlation of u0 and PI (Kenney

1959). A linear relation between Gmax and r0o in a log-

log plot is observed for each tested soil for both normal

consolidation and overconsolidation states.

Kallioglou et al. (2008) studied the small-strain

stiffness of natural intact inorganic cohesive soils

with calcium carbonate content less than 5% and

expressed Gmax by the following equation:

Gmax ¼ 6290� 80� PIð Þ � r00:50o � e�0:63 ð3Þ

where: Gmax and r0o are expressed in kPa and PI as

percentage values (%). Kallioglou et al. (2008) also

confirmed that the above equation holds for the

laboratory Gmax value of natural intact inorganic

cohesive soils containing calcium carbonate up to a

content of 25%.

To account for the effect of stress history, void

ratio and soil composition and plasticity on Gmax,

Gmax values at r0oinstitu for large size specimens only

were normalized by the void ratio and plasticity index

functions of the above equation and plotted versus

r0oinstitu at c B 10-5 in Fig. 9. As indicated in the



stress, r0o, for medium-organic cohesive soils

Geotech Geol Eng

123

above figure, at a given r0oinstitu, the medium-organic

soils (OC = 6–15% and CC = 0–23%) showed

either comparable, or lower values of normalized

Gmax than the estimated from the above equation.

The results for the shear modulus at high strains

are shown in Figs. 10a and 11a & b for the medium-

organic and the high-organic cohesive soils respec-

tively at an effective isotropic stress approximately

equal to or higher than r0oinsitu. For the high-organic

soil C7s the measured G values were normalized by a

Gmax value at c = 7 9 10-5, because of the plateau

observed in G-c curve at strains c\ 2 9 10-4,

Fig. 11a. In the above figures, the G/Gmax-c curves

are compared with those presented in literature for



stress, r0o, for high-organic cohesive soils

Fig. 9 Variation of normalized small-strain shear modulus,

Gmax/[f(e) 9 g(PI)], with insitu mean effective stress, r0oinsitu,

for natural organic cohesive soils


and (b) damping ratio, DT, with shear strain, c, for medium-

organic cohesive soils at effective isotropic confining stress,

r0o, approximately equal to or higher than insitu stress, r0oinsitu

Geotech Geol Eng

123

inorganic cohesive soils (Kallioglou et al. 2008;

Vucetic and Dobry, 1991; Sun et al. 1988). The

degradation curves follow the trend of increasing

linearity with increasing plasticity; in particular for

the medium-organic soils, the G/Gmax curves either

agree with, or exhibit a higher linearity than the

corresponding curves, proposed in literature for soils

of the same plasticity, whereas for the high-organic

soils the G/Gmax curves exhibit a higher linearity for

c\ 10-3. The magnitude of r0o was observed to have

a negligible effect on the position of the G/Gmax

curves for the stress range studied (r0o = 110–

400 kPa).



confinement time is plotted in Figs. 7b and 8b for the

medium-organic and the high-organic cohesive soils

respectively. DTmin either remains constant or

decreases with increasing r0o. The range of DTmin

values is between 1.8% and 4.2% for the medium-

organic cohesive soils at c B 10-5 and at r0oinsitu.

This range is similar with the corresponding of

DTmin = 1.4–4.7% for inorganic cohesive soils (Kal-

lioglou et al. 2008). No clear effect of the organic

content on DTmin is observed possibly due to

different composition of natural soils tested.

The DT versus c curves for the medium-organic and

high-organic cohesive soils, shown in Figs. 10b and

11c respectively, indicate that there is no clear effect of

soil plasticity on them. Moreover, these curves differ

significantly from the corresponding curves presented

in literature for inorganic cohesive soils on the basis of

soil plasticity (Vucetic and Dobry 1991).

5.2.2 Model Reconstituted Organic Soils



24 h confinement time for the tested model organic

cohesive soils as well as kaolinite for comparison. A

linear relation between Gmax and r0o, in a log–log plot,

is observed for each tested soil for both normal

consolidation and overconsolidation states. At a given

r0o, Gmax decreases with increasing organic content

above 5%. The addition of salt (NaCl) in soil P-10-B

results in an increase of Gmax to values equal or above

the corresponding for soil P-10-A and even kaolinite.

The normalized shear modulus, G/Gmax, is plotted

versus shear strain in Fig. 13a at r0o = 90–110 kPa,

apart from soil P-20 for which data at r0o = 40 kPa

only were available. The degradation curves of the

model organic cohesive soils are practically coincident

with that of kaolinite, irrespectively of organic content

(OC = 5–20%) and stress level. This behaviour is in

agreement with the results on natural medium-organic

cohesive soils showing either negligible or small effect

of medium organic content (OC = 6–15%) on degra-

dation curves. It can thus be concluded that for

medium-organic soils the plasticity of the mineral soil,

rather than of the organic soil, controls the position and

Fig. 11 Variation of (a) shear modulus, G, (b) normalized

shear modulus, G/Gmax, and (c) damping ratio, DT, with shear

strain, c, for high-organic cohesive soils at effective isotropic

confining stress, r0o, approximately equal to or higher than

insitu stress, r0oinsitu

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123

shape of G/Gmax curves. The magnitude of r0o has

either a slight (P-10-B), or a negligible effect (P-5 & P-

10-A) on the position of the G/Gmax curves for the

stress range studied (r0o = 90–200 kPa), Fig. 14a.

The presence of salt (NaCI) in soil P-10-B results in

higher degradation of G/Gmax curve.

The variation of small-strain damping ratio, DTmin,

with isotropic effective stress, r0o, at 24 h confine-

ment time is plotted in Fig. 12b. A slight to moderate

decrease of DTmin with increasing r0o is observed.

DTmin increases with increasing organic content and

this may be attributed to the increasing flexibility of

the soil mass due to the presence of organic fibers.

However, the addition of salt (NaCl) in soil P-10-B

results in a decrease of DTmin. These observations

indicate a significant effect of both the organic matter

content and pore water chemistry on DTmin. The range

of DTmin values at c B 10-5 is between 2.1% and

4.8% and is similar with the corresponding of natural

intact organic cohesive soils tested, Fig. 7b.


for model organic cohesive soils is plotted in Fig. 13b.

The damping ratio curves shift to higher values of DT

with increasing organic content. Similarly with the

natural organic cohesive soils, these curves differ

from the corresponding curves, presented in literature

on the basis of soil plasticity (Vucetic and Dobry

1991). The magnitude of r0o has slight or negligible

effect on the position of the DT versus c curves for the

stress range studied (r0o = 90–200 kPa), Fig. 14b.



stress, r0o, for model organic cohesive soils and kaolinite


and (b) damping ratio, DT, with shear strain, c, at effective

isotropic stress r0o = 40–110 kPa for model organic cohesive

soils and kaolinite

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5.3 Peats



24 h confinement time for the tested peats. The insitu

mean effective stress, r0oinsitu, also indicated in the

above figure, was determined using the value of the

coefficient of earth pressure at rest, ko, estimated using

Jaky’s (1944) equation for normally consolidated soils

(1 - sin u0). A linear relation between Gmax and r0o, in

a log–log plot, is observed for both soils. The Gmax

values of the tested peats (Gmax = 15.9–27.8 MPa at

r0o = 39–374 kPa and wo = 101% for P1 and

Gmax = 60.7–73.1 MPa at r0o = 111–396 kPa and

wo = 58% for P2s) are higher than the corresponding

values reported in literature for peats (7–11.3 MPa for

r0o = 66–200 kPa and w = 152–240% by Boulanger

et al. 1998, and 0.15–11 MPa for r0o = 1.5–12.5 kPa

by Kramer 1993). Obviously, the high Gmax values of

peats P1 and P2s may be attributed to their lower water

contents, as well as to the fact that for most of the stress

range examined, apart from the highest ones, the peats

were overconsolidated.

The results for the shear modulus at high strains

for both peats are shown in Fig. 16a & b at an

effective isotropic stress approximately equal to

r0oinsitu. The measured G values were normalized by

the G value at c = 2 9 10-5, Fig. 16a. Both peats

exhibit strong linearity, similar to those reported for

very plastic clays (PI = 200%) and other peats in

literature, Fig. 16b. The effect of r0o on the position

of the G/Gmax curves was not studied due to the upper

limit of confining pressure (ro \ 700 kPa) in the

resonant-column apparatus.

Fig. 14 Effect of effective isotropic confining stress, r0o, on

variation of (a) normalized shear modulus, G/Gmax, and (b)

damping ratio, DT, with shear strain, c, for model organic

cohesive soils Fig. 15 Variation of (a) small-strain shear modulus, Gmax, and


stress, r0o, for peats

Geotech Geol Eng

123



confinement time is plotted in Fig. 15b. As shown,

DTmin decreases with increasing r0o. The range of

DTmin values is between 2.3% and 2.4% at c B 10-5

and at r0oinsitu and agrees with the values for peats

given in literature.


for peats is plotted in Fig. 16c. As shown, the peats

exhibit high linearity in DT curves. These curves

agree with the lower bound curve presented in

literature for peats and high plastic clays with

PI = 200% (Vucetic and Dobry 1991).

5.4 Effect of Secondary Consolidation Time

on Shear Modulus and Damping Ratio

For all the organic soils tested in this work, primary

consolidation was completed within 24 h. The effect of

time on Gmax and DTmin was studied by conducting

tests of long duration under constant confining stress

and recording the variation of Gmax and DTmin with

secondary consolidation time of soils. A linear increase

of Gmax with logarithm of secondary consolidation

time was observed. DTmin either remained constant or

decreased with logarithm of secondary consolidation

time, Fig. 17. The influence of secondary consolida-

tion time on Gmax can be expressed in terms of the

following parameter NG (Marcuson and Wahls 1972):

NG ¼Gmax tð Þ � Gmax t ¼ 48 hð Þlog t

48 h

� �� Gmax t ¼ 48 hð Þ

ð4Þ

where Gmax tð Þ: small-strain shear modulus at a given

time t; Gmax t ¼ 48 hð Þ: small-strain shear modulus at

48 h consolidation time.

Fig. 16 Variation of (a) shear modulus, G, (b) normalized

shear modulus, G/Gmax, and (c) damping ratio, DT, with shear

strain, c, for peats at effective isotropic confining stress, r0o,

approximately equal to insitu stress, r0oinsitu


(b) small-strain damping ratio, DTmin, with consolidation time

at effective isotropic confining stress, r0o, equal to and higher

than insitu stress, r0oinsitu

Geotech Geol Eng

123

Similarly, the following parameter ND can be used

in order to quantify the effect of secondary consol-

idation time on DTmin:

ND ¼DTmin t ¼ 48 hð Þ � DTmin tð Þlog t

48 h

� �� DTmin t ¼ 48 hð Þ

ð5Þ

The variation of parameter NG with plasticity

index of both natural and model organic soils at the

insitu mean effective stress, r0oinsitu, is shown in

Fig. 18. The results of medium-organic soils are

within the range of inorganic clays given in literature,

whereas high-organic soils exhibit higher values of

NG. The effect of time on DTmin for the above soils

was either negligible (ND = 0 for S1 & C3) or small

(ND = 0.15 for C2 & P1, ND = 0.21–0.25 for S6, C1

& C7s) irrespectively of organic content.

The variation of NG with of secondary compres-

sion index, Ca, obtained from RC tests for model and

natural organic cohesive soils, as well as peats is

presented in Fig. 19. An increase of NG with

increasing Ca is observed.

The influence of secondary consolidation time on

G/Gmax-c and DT-c curves was studied for the natural

high-organic cohesive soil C7s, Fig. 20. It is shown

that with increasing consolidation time the G/Gmax

curve moves upwards, whereas the DT curve down-

wards. This influence is stronger for DT curves and it

diminishes for G/Gmax curves with increasing con-

solidation time.

5.5 Linear Elastic and Volumetric Threshold

Shear Strains

The variation of linear elastic and volumetric thresh-

old shear strains, cet and ct

v, with plasticity index at

effective isotropic confining stress, r0o, approxi-

mately equal to insitu stress, r0oinsitu, for the natural

organic, as well as the model organic soils at

r0o = 40–110 kPa, is presented in Fig. 21. As shown,

medium-organic soils exhibit similar linear elastic

threshold shear strains values, cet, as inorganic soils.

For the high-organic soils both threshold shear strains

are higher than the corresponding for the medium-

organic soils. For high-organic cohesive soils of high

plasticity also the linear elastic threshold shear strains

approach the values observed for peats.

6 Conclusions

For the tested calcareous organic sands the following

conclusions can be drawn:

– The presence of organic matter starts to have a

significant influence on Gmax and DTmin of the

sands at contents exceeding 25% approximately.

High-organic sands (OC = 25%) exhibit lower

Fig. 18 Variation of NG with plasticity index, PI, at effective

isotropic confining stress, r0o, approximately equal to insitu

stress, r0oinsitu for natural and model organic soils (open

symbols indicate medium-organic and closed symbols high-

organic soils)

Fig. 19 Variation of NG with secondary compression index,

Ca, at effective isotropic confining stress, r0o, approximately

equal to or higher than insitu stress, r0oinsitu for natural and

model organic soils. The numbers in the parentheses indicate

the effective stress level.

Geotech Geol Eng

123

Gmax and higher DTmin values than the medium-

organic sands (OC = 8–13%).

– The G/Gmax and DT versus c curves for medium-

organic sands are similar with those observed for

inorganic sands containing fines, whereas high-

organic sands exhibit a higher linearity in both G/

Gmax and DT curves. For both medium-organic

and high-organic sands, the magnitude of r0oaffects the position of the G/Gmax and DT versus ccurves.

For the tested organic cohesive soils the following

conclusions can be drawn:

– Medium-organic intact soils show either compa-

rable, or lower normalized small-strain shear

modulus, Gmax/[f(e) 9 g(PI)], than the corre-

sponding for inorganic cohesive soils. Both

intact natural and model reconstituted organic

cohesive soils show a decrease of Gmax with

increasing organic content. No clear effect of the

organic content on DTmin was observed for the

natural medium-organic cohesive soils, possibly

due to their different composition. An increase of

DTmin with increasing organic content was indi-

cated by the model organic cohesive soils. The

pore water chemistry may also affect significantly

both Gmax and DTmin.

– Medium-organic cohesive soils (OC = 6–15%)

exhibit either similar G/Gmax curves, or a more

linear behaviour than the inorganic soils of the

same plasticity. High-organic cohesive soils

(OC = 25–33%) exhibit higher linearity than

the inorganic soils of the same plasticity. For

both medium-organic and high-organic cohesive

soils, the magnitude of r0o has negligible effect on

the position of the G/Gmax curves. There are

indications that the degradation curve may be

influenced by pore water chemistry.

Both peats tested exhibit a strong linear response

similar to that of very plastic clays (PI = 200%).

The influence of secondary consolidation time on

Gmax is quantitatively similar for the medium-organic

soils to that of inorganic soils and higher for the high-

organic soils, as compared with that for the inorganic

soils of the same plasticity.

Threshold shear strains depend on both soil

plasticity and organic content. Medium-organic soils

indicate linear elastic threshold shear strain values

Fig. 20 Effect of secondary consolidation time on variation of

(a) normalized shear modulus, G/Gmax, and (b) damping ratio,

DT, with shear strain, c, for natural high organic cohesive soil

C7s at isotropic effective stress r0o = 360–400 kPa

Fig. 21 Variation of linear elastic and volumetric threshold

shear strains, cte and ct

v, with plasticity index, PI, at effective

isotropic confining stress, r0o, approximately equal to insitu

stress, r0oinsitu

Geotech Geol Eng

123

similar to those of inorganic soils of the same

plasticity. For high-organic soils both threshold shear

strains are higher than medium-organic soils of the

same plasticity.

As previously recognized, organic soils are inher-

ently variable materials and the results of a laboratory

investigation involving a limited number of tests and

type of soils are not sufficient to define the behaviour

of these complicated materials with great precision.

Nevertheless, it is hoped that the findings of this work

may contribute to the understanding of the dynamic

properties of organic soils, and its results could be

applicable to organic soils at other sites, that were

formed under similar geologic and depositional

conditions.

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