experimenta.1 study on elastic moclul:i of c:layey sediments under. undrained'...

Journal of Geosciences，osaka City University Vo1. 21， Art. 1， p. 1-16. March， 1978

Experimenta.1 Study on Elastic Moclu，l:i of C:layey Sediments under. Undrained' State

Koichi NAKAGAWA and Tsuneo OKUDA

(with 2 Tables and 16 Text Figures)

Introd.uction

Elastic modulus under infinite small strain level is one of the fundamental quantities

to understand the stress strain behavior of sediments. Among many factors that influ-

ence the elastic modulus， physicochemical factors may play important role in mechanical characteristics of clayey sediments.

Measurements of elastic moduli of sediments by means of dynamic method have

been applied by various authors from different points of view. Also， several chemical analysis of sedin1ents and physicochemical arguments related with bonding forces inter圃

clay-particles have been reported.

Effects of confining pressure or octahedral mean stress on elastic wave velocity in

granular substance such as sand were studied theoretically by T AKAHASHI & SATO (1949)

and GASSMANN (1951)， and experimentally DUFFY & MINDLIN (1957)， HARDIN & RICHART

(1963)， HARDIN & BLACK (1968)， etc. Effects of strain level on elasticity wereαamined experimentally by HARDIN & DRNEVICH (1972) and SEED & IDRISS (1970). Effects on

triaxial consolidation and strωhistory were examined by HARDIN & BLACK (1968) and

AFIFI & RICHART (1973). Frequency effects on rigidity of clayey sediments were re-

po巾 dby NAKAGAWA (1975).

On the other hand， a physicochemical treatment of bonding forces of interparticle in water-electrolyte-clay mineral system was theoretically made by OLPHEN (1963). The

effect of diffuse electric double layer on compressibility WaS examined by BOLT (1956)

based on consolidation test. Relationships between mechanical and chemical character-

istics were investigated by WHITE (1958) and by GRIM (1962). Statistical discussions of

the thermally activated process in deformation such as creep of clay were made by MURA帽

YAMA & SHIBATA (1958)， MITCHELL et al. (1969) and ITO & MATSUI (1975). The report of reseach referred to physicochemical aspect of the elastic modulus of clayey sediment， however， have apparently not been published to date.

In this paper， we shall indicate the results of measurement of elastic moduli and chemical analysis of various clayey sediments in Osaka area， and discuss briefly the

relationship between elastic modulus and physicochemical factors.

The authors would like to express their appreciation to Prof. T. KASAMA for his

』ト

2 Koichi NAKAGAWA and Tsuneo OKUDA

encouragement during the study. Thanks are due to Dr. M. TSURUMAKI， Dr. Y.T. IWASAKI and Dr. Y. N1SHIGAKI for tbe contiolJing discussion and criti:cal reading of the

manuscrlpt.

Method

Elastic wave velocities

The dynamic elastic moduli in this study have been determined by the measurement

of P and S wave velocities and densities. P wave velocity was measured by the ultrasonic

pulse transtnIssion method. For measurement of the S wave velocity， the three methods were l1sed in accordance with the sti:ffness of specimen.. The measurement of S wave ve-

locity in the sti:ff specimens with lower void ratio characterized as higher rigidity than

109 dyn/cm2 were carried out by the ultrasonic pulse transmission method. Contrarily， for the veηT soft specimens as higher void ratio than liquid limit state， the S wave velocity was measured by specially arranged shear pulse method consisting of high power shear pulse

generator and magnetic pick up. The velocity was calculated from the relation of path

length and travel time of shear pulse.

'Peclmen

Displ~çement :-analyzer Lineαlizet

v. F. Co附 erter

X-y

Re1corder・

B. T.

Osdlloscope

Frequency

Counter

Fig. 1. Schematic diagram of experimental equipment of resonance column method.

The resonance column method was applied to determine the S wave velocity for the

other most specimens except very sti:ff or soft samples above mentioned. The resonance

column method used in this study was essentially simi1ar to the one which have been

used by other researchers， for example， ISHIMOTO & IIDA (1937)， HARDIN & RICHART (1963)， etc.

The details of resonance column method have been reported elsewhere hy NAKA-

GAWA (1975)， however the receiver pick up has been improved from the velocity type of electro-magnetic transducer to the displacement type transducer.

SchematIe diagram of the resonance columll test system is， showm ill Fig，. ] .

The range of frequency in measur~ment is about 100 KHz for ultrasonic pulse

transmission method， and 100-400 Hz for the resonance column method and for shear pulse method.

•

""-=・

Elastic moduli 01 clayey sediments under undrained state 3

Chem.ical analysis

An10ng many chemical factors， we thought that the cation exchangeable capacity and the composition of exchangeable cation hardly related to surface activity of the fine

particle aggregate. Then， these analyses were rnade to examine this relation. The exchangeable cation were determined by the Peech method (FUNABIKI & AOMINE，

1957). The sample of 10 g of dry powder was leached by 100 ml of ammonium acetate

solution. After filtration of leaching solution， the filtrate was used for the analysis of each cation. Then， the exchangeable capacity was determined by the distrillation of the absorbed ammonium in the sample. .

O'rganic carbon was determined by the wet oxidation by chrornic acid and by titration

(JAKCSON， 1958). The method of fractionating humus is based on the extraction of organic matter

from soil with caustic alkali and the futher subdivision of the extracted material by partial

precipitation with mineral acid (BLACK， t965). And， humic carbon was determined by acid oxydation method using p0tasiurn permanganate solution.

Specimen

Undisturbed specimen

Specirnens used for this study are mainly Pleistocene and Recent sedimentary clay

in Osaka.IlThe specimens were obtained frorn the outcrop or boring cored sample， and

N

-As

Osaka Bay

Osaka City

-Ab

Sakai City

~Ki

Kishiwada City

。.Tu

Ko •

5 10 Km I I

Fig. 2. Localities of sampling points.

4 Kaicbi NAKAGAW A ana Tsum..e0 OKUD;A

trimmed in cylindrical share with diameter of .abo;ut 5 cm and le~gth of about 10 cm for

application to the reson.ance co[umn method. The range of the coll1oidal fraction. of

using secliments is frQNl 10 %をo50 %. Loca]ities of sampling points are shown in Fig.. 2.

Remolded specimen

Remolded sp@cimens were p戸re叩pareωdaωs tおuUows. The specimen waωs' kmeaded s印ufι-t五ficientI砂yb)i hi埼:ghspe~d mix:er with add~mg d~おおfSi⑤釣~叫t

pressed in the mo】制duωSi加nga s叩peeia[t旬aflilpe釘fwith diameter 0f .5..0 'cm. The filter paper

and two porous were used iJn. ofrder to make a11 3!i'ound drainage. mn most cases， primary consolidation was completed at t50-20(() minutes. Total con:solidatiQJn period of the

remolded s;pecimen was 23 hours. The extr~ded specimens of c]ay were cut into about

10 cm length. Samples for the analysis of exehangeable cati0fl and organIlc IJlatter were air四 dried，

，gliound to pass a 120 mesmes sieve， and thoroughly. mi.xed.

Experinteatal results

Rigidity iD" n.atural state and! the results of chemircal analysis

The measur吋 parameters@f tbe speeim.ens sueh as void ratI!Q，，rigidity， li'quid Hmit and plastic limit or v;arious. s'edimentary elays' in Osaka are lIlsted in Table]. The

rig，idities within a smaU strain Fange， a;bgqt )0:-6， were measured umder the atmospheric press:t)re and the MmdrallOed conditionふ

The results. of ，ebemical aoa[ysis， of the specimens， ar.e l~sted in 'Tabfe 2.

Effect of 'Straia a~pli仇Ide 、

It is experimental1y' weU known fact tha~ e!astic moduli ol sedimeats clecrease with

increase of strain.

Fig. 3 shows the typieal relatroft be1tween the rigidity 3!sd tbe shear strain which is

meaJsll~ed by reSQnaliilCe ~ethod :for tae sedむmeAtaryc~ay in Osaka Groupl.

As C3!O be s'een from Fig. 3'，. it appears， tkat t}t@re erists. some critica~ leVre~ of strain

at whi.ch the fIJgidity starts to ，decrease. H(i)wever，. I!t should be noted tl¥at the magßlit~de ot ttbe eritIrcal .shear strain dぽeJswith each clay speci.mem.

F or the purpose of the cQ1mparison of rigirditites' of various sedim.emts， ftot oruy the initial rigidity under sma]l strain level but also stllain effects on. the rigiditけysぬh.ouldbe

taken into acoount.

Effec~， Df an.iSQtropy

GeneraUy， tae mecbanicat properti:es 0f tlile sedim.eated materials allie coRs-idered to slbow anisot，op，y， in-oons'eqlJence of p間 fet:)redoriIentation of the clay patrticles'，. sowever， Fig. 4. ぬ-owsthe change of va;1111岱 ofmechanical com.staots ot tbe P~eistocene marine

Elastic moduli of clayey sediments under undrained state 5

Table 1. Rigidities， void ratios， liquid limit and plastic limit of various sedimentary clays in Pleiはoceneand Recent strata.

(*); Samtpled from boring oore.

+』

qdn

n・1

・101

p

pゐ制円。 Depth Horizon Void Ratio

Rigidity LL PL

(m) (dyn/cm2 )

Y

+」e・1

bAnLV

.ェ田・L

oa

yk

ma

os

k

-10 Ma 1 Ko l 1.327 1.27 X 109 ーー、

Taishi目 bashiOsaka City

~17 Ma 6 Mo 6 1.845 8.51 X 108

134 40

Ma 10

As 40

As 4.2

As 81

As 83

2.027

2.055

1.531

1.285

3.01 X 108

7.04 X 108

1.18 X 109

1.31 X 109

ーー、‘.，，*

f

rt+」SL

so

aa

yo

--c .n s

A

-40

...42

.，..81，

-83

Ma 12 ーー

92 33

国

Kishiwada Ma 4

Ki 38

Ki 39

Ki 59

Ki 78

Ki 91

Ki 92

Ki 109

Ki 129

K土ヱ30

Ki 142

Ki 173

Ki 193

1.807

1.960

1.367

1.940

1.327

1.488

0.706

0.843

0.934

1.245

1.970

1.536

a

o

A

6

6

0

a

o

a

o

a

o

a

o

a

o

a

O

A

3

A

宮

内

宮

n

u

n

u

n

u

n

u

n

u

n

u

n

υ

n

u

n

υ

n

u

n

u

n

u

-

-

-

1

1

1

1

1

1

1

1

z

l

×

×

×

×

×

×

×

×

×

×

×

×

nonu

司

ム

司

3

nフ

胃

ム

q，h

n

y

且uzroauIEJ

n司J8U1

£J

必uI

守，

r。、

よ

弓

Jnυ

司

3

凋品

1

r

o

•••••••••••• 必噌

晶

品

I

A句

、

ム

守

，

RJ

『

I

司4

r

O

胃

ム

司

ム

噌

ム

89

67

23

28

City

-38

-39

-59

-78

-91

-92

-109

-129

-130

-142

-173

司 193

Ma 8

(*)

Kishiki-cho

ーMa 6

ny

弓

3

凋品

I

E

J

勺

JnwJnO

必

U1

no

守

r

E

J

噌ム

『

J

司

3

司

3

q

，-:Ma 3

ーーMa 2

75

117

97

司

，

白

咋

，

司

3

司3

司4

司3

Ma 2 ?

Ma 1

Ma 0 ーー

Nariai Kumatori

Town surface

10wer Osaka Group

Tu 2 0.845 8.99 X 108 68 26

Y

+」-l c

a

ok

na

es

ぬ。

-16 Ma 8 Ab 8 2.699 3.28 X 108 128 39

C1ay

Am 1

Am 2

Am 3

Am 4

Am 5

Am 6

Am 7

Am 8

且m 9

Am 10

Am 11

Am 12

Am 13

Am 14

Am 15

Am 16

Am 17

Am 18

1.819

2.122

2.163

2.073

2.117

1.946

2.102

1.823

1.914

1.933

1.713

1.441

1.188

1.357

1.594

1.506

0.691

0.862

6.45 X 107

6.99 X 107

6.65 X 107

9.48 X 107

1.10 X 109

7.31 X 107

9.95 X 107

9.66 X 107

8.63 X 107

8.66 X 107

1.01 x 108

7.81 X 107

7.64 x 107

8.41 X 107

7.76 X 107

8.66 X 107

2.49 X 107

6.46 X 107

向

フ

司

ム

コ

J

R

J

n

ヨ

τム

n

O

Tム

n

o

q

J

n

u

yム

QU

弓3

ζ

u

n

u

o

u

r

o

7

0

0

9

9

9

9

8

8

8

8

6

5

6

7

6

2

3

1

1

auz

胃ム

ny

にJ

8品Z

A

U

吋，h

n『

JAUEJnυ

守，

ronwJ

且

品

宮

司

ム

マ

'

nフ

弓3

』

uz

司3

司3

司J

q

J

『

J

q，

白

弓

3

弓3

『

J

q

4

司，

h

q

L

司3

「

J

司

ム

司

ム

Ci七y

- 9.9

-11.4

-11.5

-13.5

-14.3

-15.4

-16.5

-17.1

-18.5

-18.9

-19.6

-21.1

-21.7

-22.5

-22.7

-23.7

-24.4

-25.9

A11uvia1

Samondo -

River

Amagasaki

6 Koiehi NAKAG戸'AWA and Tsuneo， OKUDA

Table 2. Cation exehangeable capacities， exchangeable 'cations， total organic carbons and humie carbons of variQus sedi，ments

r

噌4

h

u

p-m

訓

恥

‘‘a'

eyg

qto

nn・1

0

0ac-

-1ha--

七

cpe

axam

円

tvR“nuv

，、

Mg* Ca * Na + c

・1-n

、，

、Anoa'

aa一b

(

tqx

ora

T

O

C

Humic

Carbon e*

(me/100g)

+ K

(毛)

Ko l.

'Mo 6

As 4'0

As 42

As 81

As 83

Ki 38

Ki 39

Ki 59

K:f 718

Ki 91

Ki 912

Ki 1'09

Ki 129

Ki 13:0

Ki 142

Ki 161

Ki 173

Ki 193

Ki 222

Tu 2

Ab 8

On 7

Am 1

Am 2

Am 3

tiln 4

Am 5

.Am '6

Am 7

Alro 8

如n' 9

Am 10

Am 1正

Am 12

Am 13

Am 14

Am 15

Am 16

Am 17

Am 18

ヱ7.1323.'68

24;88

26.'916

23.53

22.34

1，8.9，1

18.04

工5.0，5

19.6'5

21.64

18.D1

9.4''5

13.08

1'5.12

24.02

2'0.45

17.44

2'0.9，0

10.4'5

2'0'.30

23.73

2'9.IO，(i)

2'2.'54

25.73

2'$.9'8

2，4' .'07

2 '~. 38

1，8.67

25.13

21.81

25.78

25.07

23.，87

2ヱ.05

18.04

22.26

37.8'9

22.16

8，.44'

12.46

13.06

18.74

9.77

10'.5，8

11. $，9

11.77

8，.5，1

8.61

9，.09

19.19

13.53

8.50

4.160

5.46

6.，27

11.94

12.71

7.819

9.66

4.67

7.8，3

8.94

16.94

11.36

15.34

14.25

13.37

13.09

10.0'4

14.14

11.88

1.4.生4

13.33

12.4'3

10.0'5

7.83

9.515

1l.7 • 4'3

1~)' O，s

3，.8:4

$ .'63

4.92

'8.4，6

34.41

3'2.19

1，0.32

9. 8:9

2101.9)9

3，6.83

6.9'8

9.41

14.42

4'.31$

:3 .，84

4.86

5.64

12.65

2.67

9.，，0，1

9.94

5，.51

9.612

14.61

9.014

9.13

29'@ 42

3;5.5，4

38.24

3'1.6'6

3.5，. '8，8

28.22

12.46

1-0. 3，9

10.78

10.13

7.14

3.3'8

3.8:t

9.22

4'.416

1.62

2.57

0.08

3.35

5.22

3.1:9

0.9'3

0.7'7

1.06

1.11

o.ヲ0(i)'.312

0.45

01.5'4

D'.33

01.41

0，.3¥9

0.62

0.58

0.4'4

0.66

0'.20

01 • $，4

0.76

8'.26

4.2'6

8.99

1，0'.6'8

エ0.74

12.04

5.2'6

1].99

ヲ.3，8

9，.83

8'.30

7.014

8. '5~3

5.37

7.9'5

9.21

5.70

4.56

5.22

0.09

0.18

2.63

2.，'819

2.26

2.07

2.27'

2.28

1.44

o • 0'5 o.正王Oト.04

0..61Q

0.73

01. 810

エ.540.11

0.814

0，.93

0.56

.0.66

1.12

2.23

3.，12

4.10

3.97

3.82

4.Q9

2.7'8

3.36

2.38

3，:27

3.10

2.97

2.8:2

1.96

2，.10

1.68

0:.'96

01.6，4

0.90

1.02

1.37

1.09

10216

6.66

0'.，6，3

0.8，)

0.89

o • 9'1 1.35

0.'91

0.93

0.24

0.35

0.'51

0.59

1.23

0.'53

(i). 74

0.15

0.43

1.38

3.'00

1.52

1.59

1.51

1.33

1.32

91.92

1.18

1.05

1.19

1.23

].17

1.01

1.1..4

1.78

4.84

4.25

(L49

0.98

，0，.043

0.11

0.18

01'.21

0.046

0.02'9

01.13

01 • ヱ2

0.048

D.19

6.10

0.13

0.008

0.024

O~. 0，47

0.042

0.067

o • 0'8:0 0.14

O.D04

0.811

0.28

O.8'0

0.17

0.20

0.1，9

0.13

0~28

D.Jl.8

0.12

D.12

0.13

O.エ3

0.13

0，.12

0.21

01.35

0.96

1.52

0.11

0.24

1.598

2.155

2.155

2.2，87

1.7'92

1.745

2.061

2.192

1.6，66

2.084

2.DSO

1.8'01

0.930

0.996

1.254

2.'0ヲ8

1.810

ヱ.'94[0 2.49'0

0.9O4

1.3'04

2.611

2'.367 、-ー--ー

-ー

-圃.

--ー

ー

ー

ー

ー

-圃.

--由

Elastic moduli 01 clayey sediments under undrained state 7

2

K 1 193< (N)

e、aE ^ υ10" ‘h C 〉、

刀

KI 91 (N)

K1130 (N) 18

句

ω 、.41

Z16 E 。、.0 仏

i一一・ぐ i /i VS 10-J ¥ .//

• -- ¥一〉同 A b 8

1

Koichi NAKAGAWA and Tsuneo OKUDA

τ ττ7 I τ τ 1

---

• 寸10'0← 8

"".1" ヘ @ト唯旬、通項哲治ー償制F

2 3 1

。島。 Bul k Modulus

• 4‘ • Rlgtdity

10'0

5

10"

5

NEυ~ch刀

• ー

• 109

二コ旬。芝

ー

ー

LL L 。。。

。。。

宅

も。8

P.l

4 •

109ド

108←

NEυ~ch司

U 1 t rαsonic Pulse Trarnsmlsslon Method

• 、万一-一

ー。Resonance Col umn

Method

。107ト

可コ a

•

，-、・b'‘

i，

2 ・ー• •

• -5

U一一宇的ロ}凶

。。。。。

Righ Power SR Wαve Generatlon Method

。

106ト

。、

-ーα

•• • • .. 、.A... .-2、#: 108

ー

。

。

5

l' ...L 3.0

' 」2.0

• L '-0

l' 内

υ

Eg nu

aE

・・ 3.0 2.0

R a t i 0 1.0

Void

。R a t i 0 V-0 i d

Relation of bulk modulus and rigidity with void ratio for Osaka clay， calcu-lated from P and S wave velocities. The solid line is calculated from the equation (1). 1; Pleistoncene sedi-ments 2; Recent sediments 3・

remolded specimens.

Fig. 6. Relation between rigidity and void ratio of remolded specimen obtained from Pleisto-ceme marine c~ay， Ma 6. U]trasonic pulse and SH Wave transmission method have been carried out for eonsolidated specirnens at the end of primary consolidation. Reso-nance column method were applied to specimens about 1300 minutes after end of primary consolidation.

Fig. 5.

、、.，，4EA

，，EE

、

• • • • • • • • • • • • • • • 1 . e 一一一Kg

. Kw 1+e Ks

:' bulk modulus of soils as solid and water Ks where， b叫kmod叫USoa bost rock (Kg=3.87x 1011 dynfcm2)

:b叫kmodulus of water (Kw=2.40x 10J.0 dynfcm2)

-• Kg k匁)

: void ratio. e

The value of Kg is of Rokko granite which is supposed to be main host rock in Osaka

clay. The equation (1) is known as Wood equation (Woon， 1930) and rigorously derived by ISHIHARA (1968). Therefore， this experimental results show that bulk modulus of

Quaternary sediments in Osaka is mostly independent of their structures such as grain

size， shape of grain， etc.， except for the composition which relates to the void ratio， the degree of saturation and kind of the.forming minera1. The rigidity of sediment， however，

can not be related directly to tbe voIld ratio and compositi∞.

•

Relationship between rigidity and vord~ ratio

Using the resonance method， HARDIN & RICHART (1963) studied the effects of void

9

Their em-

Elastic moduli of clayey sediments under undarined state

ratio and hydrostatic confining pressure on the S wave velocity of sands.

pirical1y obtained equations are expressed by ，eq. (2) and (3).

For round-grained sands

…・・…(2)G = 697 _{2.17-e)2UFO-5 1+e ..，

For angular-grained sands

-…………( 3 ) G = 32612.96-e)2 b 0・51十e '"

where， G c: hydrostatic confining pressure. HUMPHRIES & W AHLS (1968) and HARDIN & BLACK (1969) examined the applicability

of the above relations to clay. One of the common results drawn from two investigations

implys that the rigidity of clay with high surface activity is much complicated and

different from those of sand. The effect of consolidation pressure of several Quaternary

As shown in the figure， there is an important difference sediments is shown in Fig. 7. between sandy and clayey sediment.

Several experimental results of sediment' s rigidities with void ratio are plotted for

remolded state as well as natural state shown in Fig. 8. Slopes of the lines between the

log rigidity and the void ratio in remolded state are found to vary widely with types of

1012

5and 109

Natural

' --e a

Granite Rokko

10" e‘ E u -c 〉、.。

Ma 8

:トk cley ヘ ¥と吋

AM 8

Clay

制

Eυ~ch刀

〉、

‘ ....

刀 109

σ、

広‘. 、、

‘.

，、、、、、、・、、

、

，、4ぬu'

，‘EE-

-

¥1・

、、

、、、、

、、、、

、、、、

、¥

¥

、、

05

〉、 108

司....

て3

01

α: 108 、、、

•• ••• 、Study

。¥、 Plot ot Hardin's Equatlon

、.....Present

107

30 2.0

R a t i 0 1.0

Void nv

句，nu ---2.5

¥

0.5 2.0 1.5

R a t i 0

1.0

Vo i d

E玄amplesfor the relation between

rigidity and void ratio for several

specimens. The arrows show the

reduction of rigidity for remolding.

Fig. 8. Relation between rigidity and void ratio

under drained and confined state for vari-

ous specimens. The arabic numerals

beside the solid line show the confining

pressure (kgfcm2).

. Fig. 7.


Fig. 9. Relation between rigidity and efe* for

remolded specimens.

Fig. 10. Relation between e* and cation ex・changeable capacity.

sediments. As shown in the figure， their straight lines appear to be concentrate at a certain point when the void ratio is nearly zero. lt seems that the slopes in the figure

depend upon interparticle characteristics in sediment. The higher steepness of the

slope is found to correspond to the lower rigidity of the sediment with the same void ratio.

To understand more easily this relation， for the sake of convenience， a special void ratio， e*， is defined as void ratio at which the specimen shows the rigidity of 108 dynfcm2

in remolded state. Therefore， relative magnitude of the rigidity， i.e.， the interparticle bdnding forces among the various kind of clay， can be compared using the e*.

The values of rigidity and of eJe* for each specimen are plotted in Fig. 9. This stra-ight line is formulized by least squares method and it is expressed as follows;

Log Grz10.385-2.3754 e-"

where， Gr: rig，idity of remolded specimen.

Rigidity and chemical property

. . . .……(4)

Because of the e* may be used as an index of the relative activity of clayey sediment as above mentioned， the results of chemical analysis were compared with e* for the various kinds of clayey sediments to investigate the relationship between e* and physicochemical propertles.

The relation between e* and cation exchangeable capacity is almost positive linear， as shown in Fig. 10.

RASHID & BROWN (1975) pointed out that the organic matter especially humic acid， plays an important role for the mechanical properties of sediments from their investi-

gation for compression test of several kinds of sediments.

However， the exchangeable capacity of organic matter was hardly analyzed by using

•


the ammonium acetate as in the Peech method. Because of the extreme high value of

exchangeable capacity of humic acid compared with that of other component of organic

matter， exchangeable capacity of organic matter is governed and determined by the quantity of humic acid in organic matter ..

The content of humic acid is usually estimated from humic carbon content based on

the following relation，

HA=RwxHC

Eventually，

CEC= Ceυ×ム+Cec，hx型100' ， 100

……………( 5 )

where， CEC : total cation exchangeable capacity of sediment (mej100 g) Cec， i : cation exchangeable capacity of inorganic part (mej100 g)

乙:percentage of inorganic part in the sample (%) Cec， h : cation exchangeable capacity of humic acid (200-400 mej100 g) HA : humic acid (%)

Rw : weight ratio (キ1.7)of humic acid to humic carbon (JACKSON， 1958) HC : humic carbon (%)

Fig. 11 shows the relation between CEC and e*.. The coe伍cientsof correlation

for data plots in. Fig. 10 ar吋 Fig.11 are 0.79 and 0.85 respectively. 1n this figure， it should be noted that the data contain wide range of specimen material from fat clay of

montmolli1onite to silt of crushed granite.

The relation between e* and total cation exchangeable capacity shown in Fig. 111 may

be expressed as follows from least squares method.

1..0

3.0

2.0ト

e持

。。

• •

/.・-y •

ー/三..

，

10 20 30

Total Cation Exchangeable Capacity mell00 9

Fig. 11. Relation between e* and total cation exchangeable capacity.

A plot in right-up-wards coordinate is Na-montmollilonite

benthonite.


* e O.0767x CEC+O.226 ………・(6 ) The equation shows the strong linear relationship between CEC and e*. The value

of the CEC is thus considered as one of the factors to control

bonding force of the particle. * e"-， and consequently the

No consistent direct correlation was found between the value of e* and the compo圃sition of exchangeable cation.

. . . . . • • • • • ・.. . ・.. ・・.• • • • .

• • • • .

:-P:・:-:-:-:--.

Fig. 12.

External J="orce

Van der Waals

At tractive

Force

yノ

Bonding Material

旬、fgroミil)

Doable Layer

Repulsive

Force

Crystal

Partic/e

• 。

聞.".・.・・・.・・.・・・.. . . .... .'.~ - 00" ー.一一 . :.. . .一.一.'_'.o・・・.・・・・・・.・・-・今'.. . . . .一一一・.・..・・一・・.. . ・..... .

• • • • • • • • • • • • • • • • • • • • • • • • • • • • . .・

Cσtion

Anion

Amorphous Matter

Highly Oriented

Moleculσr Zone

Linked Zone with Molereular Cha /('1

Liquid Phase

Microstructural model of clayey sediment. (after NAKAGAWA et al.， 1977)

•


争骨e

3.0

2.0

'.0

。。

Fig. 13.

•

/

50

Liqt;Jid

•

ー・・/・•

100

Li m i t

•

150

Relation between e* and liquid limit.

7 一τ 7 1 I 1

'.0ト.'.. 、ヘ‘。崎.a d. 00 ". ~。 ... Jロ• . t.. Q ，、一

〉、..... 勺

m z

ト

0.9← 勺QI

N

U

E ‘-。

ト

z 0.8←

ト

Fig. 14.

・. .ロ..- .. ‘・ 4‘.

よ-10・6

• K I 130 ・KI 92 A K I 109 ・KI 129 o KI 91 I

U-Ab-L'

ーよ-10-5

Shear

• 4‘ •

•

Strain

• -. 0 0向。.・。0_• Vo

" ・・ O~d .. 哩ロ・ロ。

• 4‘ a

- ・・。ー1. ._・。

• 4‘

a‘ 4‘

」

t. ... 0

‘-.. ロ・。

4‘

。 . .l ・. - -• ‘ d a ・‘ ..

a

ロ

•

• 0 • • .

一

よー.10・4 10・3

Example for the relation between normal-ized rigidity， GJGo and shear strain for typical specimens.

with the specific surface Further discussion will be necessary on the relationship

area of material or the electrolyte concentration of water solution.

From these experimental results， the microstructural model was suggested by NAKA-GAWA et al. (1977) as edge-to-surface contact structure shown in Fig. 12. The relation

between the rigidity and the cation concentration will be reported in detail at a later date.

Fig. 13 shows the relation between liquid Iimit (LL) and e*， and that e* is nearly proportional to LL. This relation is expressed as follows with some scattering.

e*=0.022xLL -・・・・………(7)

From a relation e* and Atterberg liquid limit， the both indices are considered to denote the material characteristics with common physical base.

Effect of strain amplitude

Generally， the rigidity of granular substance decreases with increase of shear strain leve1. As shown in Fig. 3， the rigidity is almost constant， if the strain is smaller than a certain criticaI Ieve1.

Fig. 14 shows the relation between GjGo and shear strain. Where， Go is rigidity at a small strain. The point at which the rigidity starts to decrease depends upon a kind of

sediments. But it seems that the shape of decreasing curve of rigidity is independent of

the difference of specimens. And the shapes obtained in present study agree approximately

with the data of sand of HARDIN & DRNEVICH (1972).

'rhe experimental relatIon between Go and the critical strain To・9 are plotted for

several specimens shown in Fig. 15. 'The critical strain To・9 is de:fined by the shear

strain at which the rigidity becomes 90 % of Go• As it seems that r 0.9 is proportional to Go in the same kind of specimen with different void ratio and its slope is a function of

the value of e*， we shall estimate some constants graphically as following eq.uation，

Koichi NAKAGAWA and Tsuneo OKUDA 14

。Ab 8 ・KI 193 A K I 91

・KI 130 V KI 129 ロ KI 109

../ ./

今/

/. ，rF

15 舎、‘

E υ 旬、.C 〉、

て3tD

o

10

5

(ω・0l

z一ω)。ο

o Jlb 8 e・・260 ・"1 193 0・・2 49 A KL 91 e".l 81 ・K1 130 0..1 73 v Kl 129 o'・o99 ロ Kl 109 e'-O 93

‘50ma 5tando¥d ~anι 。唱11tySond

d /

5 。dE υ ‘、.C 〉、

てコ

109

〉、司俳d

てコロ、

広108

5

5

10 20

Critical Shear Stram

30 10・4

。。10-2 5 5 10・3Shear Strain

10・4

Critical 5

the value， critical shear

Relation between

Go{げー0.5)and straln， r 0.9・

Fig. 16. Relation between rigidity at smal1 strain

level and critical shear stram， r 0・9Fig. 15.

……( 8 ) γ0・9e*-0.5

Go = 0.50 X 1012

Go(e*-0.5) and γ0・9are shown in Fig. 16 with the scatter in

We get an experimental equation as folIows，

The relation between

a reasonable range.

……・(9) ro・9= 2Go(e*ー 0.5)X 10-12

be expressed convenient form as， Accordingly， it can

-……(10) 2=1ー αr1.5

where，αis constant depending Q，n the kind of sediment. The equation (10) is valid within the strain range under which the rigidity decrease to 70 %.

From the equations (9) and (10)，

、Ea''

噌

EA

4

・A，，EE

、

• • • • • • • • • • • • • • • 1.5 X 1016 γ Go(e*-0.5)

三=1-3.535 x G。

Rearrangement by substitution of the equation (7) into (11)， G/Go is expressed as follows，

、EE，，

ヴ'M

4EA

rsE

、• • • • • • • 1・5X1017

、EE，，今

、u向

Jヲ“ヮ“γ一一L

L

，，目、、G

三=t-4.503 x G。

'Fhis equation suggests that the strain effect on the value of rigidity may be obtained

simply from the data of liquid limit and initial rigidity.

Conelusion'

•

1n the present study， the dynamic rigidity at lower strain level of the Pleistocene and Recent elayey sediment distributed in! .Osaka anq its vicinity was described. 'The chemi-


cal analysis of the sediments was also made for the investigation of physicochemical

factors influencing mechanical characteristics. An important problem of physicochemical

mechanism of interparticle bonding in clayey sediments has been left unsolved.

The conclusions obtained in this study are shown as follows;

(1) The results from measurement of the rigidity of undisturbed clayey sediment at

lower strain and the chemical analysis are listed in Table 1 and Table 2.

(2) Anisotropy of tbe m.echanical properties such as the velocities of longitudinal and

shear waves and its damping factor have not been found so far as the material tested.

(3) The relation between the bulk modulus obtained from wave velocity and the void

ratio for soft sediment can be given as following equation，

ー一必 l+e

1 ， e 一一一Kg . Kw

where， the parameters of Ks， Kg and Kw are the bulk modulus of bulk structure of sedi-ment， granite and respectively water， and e is void ratio. For the relation between the rigidity and the v:oid ratio， no simple relation as above can be found in various kinds of sediment. ln remolded state of clayey material， the relation between the rigidity and the void ratio is found to show following simple form over the wide range，

Log G = a-be

where， a and b are constants and depend on the physicochemical properties of the clay. 'Fhis equation appears to be valid for various kinds of remolded specimen.

(4) The relation between the cation exchangeable capacity and the value of e* is obtained

as following empirical equation，

e* = 0.0767x CEC+0.226

where， e* defined as void ratio at which the specimen shows the rigidity of 108 dyn/cm2

in remolded state.

The relation between the e* and the liquid limit LL is given as，

e* = 0.022xLL

(5) The rigidity of sediment is generally affected remarkably by the strain level. But， the rigidity is almost constant in the very smal1 strain region. The magnitude of the critical

strain differs with each specimen. The empirical equations of rigidity related to the

strain level are obtained as follows，

G = Go-3.535 x附 xGバJ¥15¥e*-O.5 G = Go-4.503 X 10

17 X GõO•5(γ5 、LL-22コ3where， r is shear strain， LL is liquid limit and Go is the rigidity in small strain level.

16 Koichi NAGAGAWA and Tsuneo OKUDA

References

AFIFI， 8.S. & F.E. RICHART (1973): Stress history effects on shear modulus of soils. Soil and FoundationsJ ]SSMFEJ 13， No. 1， p. 77-95.

BLACK， C.A. (1965): Methods of soil analysis. American Society of Agronomy， Inc.， Wisconsin~ p. 1409.

BOLT， G.H. (1956): Physico-chemical analysis of the compressibility of pure clay. Geotechnique，

6， No. 2， p. 8“6一-913DUFFY丸， J. & R.D.恥MINDLI江I悶N (1957): Stress-strain relation of a granular mediurn. ]our. Appl.

Mech.， Trans. ASCEJ Pec.， 1'. 585-593. FUNABIKI， S. & S. AOMINE (1957): Soil analysis (in Japanese). Yokendo， To~yo， p. 147. GASSMANN， F. (1951): Elastic waves through a packing of spheres. GeophysicsJ 15， p. 673'-685. GRIM， R.E. (1962): Applied clay mineralogy. McGraw-Hill， New York. HARDIN， B.O. & W.L. BLACK (1968): Vibration modulus of normally consolidated clay. ]our.

Soil. Mech. and Found. Div'J Proc. ASCEJ 94， SM 2， p. 353=-369. HARDIN， B.O. & V.P. DRNEVICI王 (1972): Shear modulus and damping in soils; Measurement

and paraaeter efFeets. ]omに Soil.Mech. and Found. Div'J Proc. ASCEJ 98， 'SM 6， t'. 603-624.

HARDIIN， B.O. & F.E. RICHAR1' (1963): Elastic wave velocities in granular soUs. ]OU!f. So，仏 Mech.and Found. Div'J Proc. ASCEJ 89， SM 1， p. 33-65.

HUMPHRIES， W.K. & H.E. WAHLS (1968): Stress history effects on dynamic modulus of clay. ]our. Soil. Mech. and Found. Div.J Proc. ASCEJ 94， SM 2， p. 371-389.

ISHIHARA， K. (1968): Propagation of compressional waves in a saturated soi1. Proc. of the Interna・tional Symp. of Wave Propagation and Dynamic Properties of Earth MaterialJ Univ. df New

お1:exicoPress.

lSHIMOTO， M. & K. IIDA (1937): DeterminatIon ，o'f elas，tlIc constafl~S of soils by means of vibration method. Part 11. Modulus of rigidity and Poisson's ratio. Bull. Earthq. Res. Inst'J Tokyo Univ.， 15， p. 67-86.

ITo， T. & T. MATSUI (1975): Plastic flow mechanism of clays (in Japanese). Proc. ]SCEJ No. 236. JACKSON， M.L. (1958): Soil chemical analysis.， Prentice-Hall， New Jersey， p. 211. MITCHELL， J.K.， A. SINGH & R.G. C'AMPANELLA (1969): Bonding， effective stresses and strength of

soils. ]our. Soil. Mech. and Found. Div'J Proc. ASCEJ 95， SM 5， p. 1219-1246. MURAYAMA， S. & T. SHfBATA (1'958): On the rh.eological characteristics of clays. Part 1， Bull.

Disast. Prev. Inst.， Kyoto Univ.， No. 26. NAKAGAWA， K. (t975): Measurement of shear wave velocity ~n soi1s，. JOU!f. Geosci.， Osaka City

Univ.， 19， p. 139-147. NAKAGAWA， K.， Y.T. IWASAKI， T~ OKUDA & M. TSURlJMAKI (1977): Elastic moduli of un-

drained clayey 80iis based on clay-water-electrolyte system. Constitutive Equations of SoilsJ IX

lnternatiQnal Conference on Soil Mechanics and Foundation EngineeringJ TokyoJ p. 207-211.

OLPHEN， V.H. (1'963): An introduction to olay colloid chemistry. Interscience， New York. RASHID， M.A. & J.D. BROWN (1975): Influence of marine organic compounds on the engineering

properties of a remolded sedim.ent号、 Eng.Geol.， 9， p. 14t-154. SEED， H.B. & I.M. IDRISS (1970): Soil moduli and damping factors for dynamic response analyses.

Earthq. Eng. Res. CenterJ Coll. of Eng.， Univ. oJ Cali.J Rep. No. EERC 70-10.， p. 1-15 TAKAHASHI， T: & Y. SATO (1949): On the theory of elastic waves in granular substance. Bull.

Earthq. Res. Ins.， Tokyo Univ・， 27， p. 11-16. WHITE， W.A. (1958): Water sorption properties of homoionic elay minerals. Rep. Investz"gation，

208， Illinois state Geol. Surv.， p. 7-46. WOOD， A.s. (1930.): A te:;ctbook of sound. G. BeI1 & Sons， London.

可.

experimenta.1 study on elastic moclul:i of c:layey sediments under. undrained'...

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