Experimenta.1 Study on Elastic Moclul:i of C:layey Sediments under. Undrained'...
Transcript of Experimenta.1 Study on Elastic Moclul:i of C:layey Sediments under. Undrained'...
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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
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』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.
•
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""-=・
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.
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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
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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
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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.
-
10 Koichi NAKAGAWA and Tsuneo OKUDA
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
•
-
Elastic moduli of clayey sediments under undrained state 11
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.
-
12 Koichi NAKAGAWA and Tsuneo OKUDA
* 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)
•
-
Elastic moduli of clayey sediments under undrained state 13
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-
-
Elastic moduli of clayey sediments under undrained state 15
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
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可.