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CHAPTER 7. PHYSICAL PROPERTIES OF ALLOPHANE SOILS

CHAPTER 7. PHYSICAL PROPERTIES OF ALLOPHANE SOILS

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230



T. MAEDA ET AL.



could have been used. The reader should interpret “allophane” in this less

specific sense.

The concept of allophane is changing as more becomes known about the

material. Imogolite is now distinguished from allophane, but is included in our

use of the term “allophane soils.” Imogolite, with its thread-shaped particles, has

long-range order in one direction. It has a characteristic form in electron

micrographs and has an identifiable X-ray diffraction pattern. Allophane, as the

term is now used, has only short-range crystalline order, but does have an

identifiable spherule form in electron micrographs. There are “amorphous materials” in soils which do not have this spherule form. It is likely that some of

these materials are of pyroclastic origin.

Possibly the term “andept” or “andosol” would have been a better choice to

describe these soils. However, for the nonspecialist, the term “allophane soil”

will probably best bring to mind the soils which we will be describing here. While

these soils are dominated by allophanic properties, other minerals are often

present in addition to allophane and imogolite. There are soils which contain

small amounts of imogolite and/or allophane which would not be considered

allophane soils here because they do not possess the physical properties associated with allophane.

Allophane soils are widely distributed. They occur frequently in the Caribbean and Andean lands, as well as in the Pacific areas of Indonesia, Japan, New

Zealand, and the United States. More studies on physical properties have been

carried out in Japan than in any other country. One of the purposes of this

review is to make the results of the published Japanese studies more readily

available to readers of the English language. The references cited are mostly in

Japanese, but usually have summaries in English. The more recent articles often

have legends for figures and tables in English. Some of the papers are written in

English.

The justification for a review on physical properties of allophane soils is that

they have distinctive properties which distinguish them from other soils. Soils

can be divided into three groups on the basis of physical properties. In the first

group, void characteristics determine physical properties, and void volume

changes little with changes in water content. These soils, with sands as the

example, can be treated as rigid, porous media. In the second group, the nature

and extent of surfaces determines physical properties. Volume changes accompany water content changes; these changes are reversible even though they show

hysteresis. Physical-chemical descriptions of behavior are often more useful than

mechanical descriptions. Swelling clays are examples of soils in this group. In the

allophane soils, of the third group, void characteristics rather than surface area

determine physical properties. There are volume changes accompanying water

content changes, but the effects are largely irreversible. The matrix changes on

drying, and the dried soil can be considered a different material.



PHYSICAL PROPERTIES OF ALLOPHANE SOILS



23 1



Much of this review will, therefore, be in the form of comparing physical

properties of allophane soils with the properties measured for soils with crystalline clay minerals. It is assumed that most readers will be familiar with the latter.



B. GENERAL NATURE OF PHYSICAL PROPERTIES OF ALLOPHANE



The measured values of physical properties of allophane soils, in summary,

show: they have low natural bulk density, high 15-bar water content, and high

natural water content; that medium to low amounts of water are available to

plants; they have high liquid limit and low plasticity index; they are difficult t o

disperse; and that there are irreversible changes in all these properties on drying.

Several good general summary descriptions of physical properties of allophane soils have been published. Swindale (1964) lists the following features:



. . .deep



soil profiles, usually with distinct depositional stratification, and normally

friable in the upper part; topsoils as thick as one metre, and dark brown to black in

color, containing humic compounds which are comparatively resistant to microbial

decomposition; prominent yellowish brown to reddish brown subsoil colors with a

smeary feel when the soil is wet; very light and porous profiles with a low bulk density

and high water-holding capacity; rather weak structural aggregation, with easily destroyed porous peds lacking in cutans, and lack of horizontal differentiation in the

subsoil except for the occurrence of duripans in some soils;. .. Smeary consistencies

are marked only in soils in very humid or per-humid climates. The soils which form in

per-humid climates tend to dry irreversibly when they are allowed to dry out in road

cuts or banks. This feature of irreversible drying is a useful classification criteria,

although the soils in the field never become dry enough to exhibit the property to any

significant extent.



.



Fieldes and Claridge (1975) have summarized the early studies by Fieldes and

his co-workers on New Zealand allophane soils:



. . . allophane in its early stages of formation could be visualized as gel-like fragments of

random aluminosilicate held together by cross-linking at a relatively small number of

sites. The fragments have an open internal structure, which originally, in the hydrogel

state, enclosed much water. Until the water is removed, rearrangements of materials

with more ordered structure cannot occur, and the moist clay has a weak “waxy”

consistence. When the water is removed by drying, the structure collapses and further

cross-linking takes place so that the process cannot be reversed; and the resultant

material has considerable mechanical strength. Thus, it is not possible to reconstitute the

moist hydrogel structure by rewetting, although the more compact xerogel is still open

enough to have a strong affinity for water..



..



Allophane soils generally have a friable surface soil and massive structure in the

subsoil, which however has a relatively high permeability. The friable structure

of the surface soil is partly due t o effects of drying. Often allophane soils have

several layers with very different physical properties which affect water movement and water available for plant use.



232



T. MAEDA ET AL.



Many properties, such as volume or water retention which decrease on drying,

show an irreversible decrease beyond 10- to 15-bar suction.

Physical properties of allophane soils do not show the dependence upon

exchangeable cation which is prominent in soils with crystalline minerals. For

example, Kubota (1971) showed that there was no difference in glycerol

adsorbed on allophane with different exchangeable cations Mg, Ca, Sr, and Ba,

and only about 4% lower adsorption with K as compared with Li. For bentonite

there is a 20% difference for the divalent ions and nearly a 100%difference for

the monovalent ions. Water vapor adsorption showed a similar pattern.

I I. Index Properties



A. GRAIN SIZE DISTRIBUTION



The grain size distribution, also called particle size distribution or mechanical

analysis, of a soil is the most widely used index property for physical properties

of soils. Much effort has been spent in soil science on grain size measurements.

For soils with crystalline clay minerals, especially in glaciated areas, and for clay

contents less than 30%, one can predict many soil properties from the grain size

distribution (Warkentin, 1972). However, for allophane soils the grain size is not

an adequate index property.

The index properties used for allophane soils include water retention (Flach,

1964; Colmet-Daage et al., 1967) and plasticity (Warkentin, 1972). Packard

(1957) used surface area as a measure of clay content, as did Birrell (1966).

Flach (1964) recommends using the 15-bar water retention to estimate clay

content.

The difficulty in obtaining dispersion, against both chemical and physical

forces, and the uncertainty of what is the unit particle of an allophane soil, are

the reasons for the limited usefulness of grain size in predicting physical

properties of allophane soils. Chemical deflocculation is the problem with wet

allophane subsoils, while in surface soils which have been dried the problem is

cementing to form larger particles. These cementing bonds can be broken to

different degrees. There is a considerable literature on the problems of dispersion

of allophane soils (Gautheyrou et al., 1976). It is not possible from most of the

studies to separate the effects of chemical deflocculation from physical dispersion. Therefore, the general term “dispersion” is used here.

The difficulty of dispersing allophane soils has been noted by many people.

Davies (1933) was one of the first to study the problem and recommended using

0.002 N HCl for dispersion. Kanno (1961) used 0.002 N HCl as a dispersant for

Japanese allophane soils. Optimum pH for good dispersion of Kanto loam, both

surface and subsoil, is in the pH range 2.5-3.5 (Tada and Yamazaki, 1963).



PHYSICAL PROPERTIES OF ALLOPHANE SOILS



233



AUophane soils flocculate in sodium silicate solutions, but polyphosphates can

sometimes be used as dispersants. Sodium pyrophosphate was a better dispersant

than sodium metaphosphate for Indonesian soils (van Schuylenborgh, 1953).

Low pH or calgon were used for Japanese soils (Kobo and Oba, 1964); the

former works better for subsoils and the latter for surface soils with organic

matter. Sherman et al. (1964) emphasized that the usual dispersing agents could

not be used for allophane soils. Ultrasonic vibration was found to increase

dispersion (Kobo and Oba, 1964), and is now generally used for allophane soils.

Oba and Kobo (1965) found that ultrasonic dispersion released clay size grains

from aggregates. A number of papers describe the use of this method (Gautheyrou et al., 1976). Espinoza et al. (1975) found that ultrasonic treatment still

gave much lower values for clay content than did the estimate from the 15-bar

water content, i.e., clay = FBP X 2.5.

Ahmad and Prashad (1970) have taken a different approach t o dispersion of

allophane soils. They found good dispersion by reversing the charge with

zirconium to get a positively charged particle.

Drying the sample decreases the measured clay content. This can be attributed

to the cementing on drying. The phenomenon has been described by many

workers, e.g., Sherman (1957), Birrell (1966), Wesley (1973). The magnitude of

the effect varies with the particular allophane soil. Kubota (1972) measured the

approximate soil suction at which irreversible bonding of clay into sand-size

grains occurs on drying. The clay and silt contents began to decrease when the

pF exceeded 3.5; fine sand-size grains were formed. Increases in coarse sand-size

grains were not measured until about pF 5, at which time the clay and silt-size

grains were at a minimum. The fine sand grains were then being bonded to coarse

sand-size grains. No further changes in grain size distribution occurred at suctions above pF 5.5.

Particles of pumice break down on stirring, and sand-size particles settle more

slowly than expected because of internal pores (Youngberg and Dyrness, 1964).

They also have a long wetting time because of entrapped air.

Kobo (1 964) has summarized the Japanese studies on dispersion of allophane

soils, and Colmet-Daage et al. (1972) report on an extensive series of tests of

dispersion of allophane soils of the Antilles and Latin America. Their results are

summarized as follows. There is no one best method which can be recommended. Surface and subsoils react differently, as do allophane soils containing

different components such as gibbsite or halloysite. Both flocculation and

incomplete physical dispersion occur. Undried samples always disperse more

completely than air-dried or oven-dried samples, the difference being much

larger for subsoils than for surface soils. Surface soil samples generally disperse

better at high pH of 10 or 11 with ammonium or sodium hydroxide (the Kanto

loam is an exception), while subsoils generally disperse better at pH 3 with HCl.

Subsoils generally flocculate at high pH. Sodium pyrophosphate is an effective



234



T. MAEDA ET AL.



dispersant for surface soils, but metaphosphate is not. AUophane soils containing

gibbsite are difficult to disperse in acid or basic suspensions. With small amounts

of gibbsite, dispersion appears to be better at pH 3; with larger amounts the best

dispersion is obtained at high pH. Soils with halloysite disperse at high pH, but

not at low pH. Ultrasonic vibration is recommended for dispersion. Birrell and

Fieldes (1952) had also noted that the presence of gibbsite makes allophane soils

more difficult to disperse.

Dispersion of surface soils at low pH might be attempted when solubilization

or organic matter at high pH would interfere with subsequent measurements.

The use of pyrophosphates might also interfere with other measurements on

separated soil fractions.

Control of pH is critical for dispersion at low pH, but not at high pH.

The results given by Kubota (1972) are representative of the effect of different

treatments on hydrandepts. On a B horizon sample the clay contents measured

were as follows: 1Okc-300W sonic dispersion, 56%; standard shaking on moist

sample, 31%; on air-dry sample, 5%; and on an oven-dry sample, 1%.

Baba (1971) was able to disperse allophane soils in an alkaline medium only

when ultrasonic treatment was used. Under these conditions sodium silicate was

a more effective dispersant than sodium polymetaphosphate.

While it is generally preferable to work with undried samples, this is not always

possible. Undried samples may not be desirable if the soil contains predominantly sand and gravel because of the difficulty in obtaining a representative

subsample of a wet soil.

Grain size analysis, therefore, has a limited usefulness in characterizing allophane soils. The measurement should be done on field-moist samples (e.g.,

Schalscha et al., 1965) and the details of the method should be given. Since

different allophanes react differently to dispersion treatments, some experimentation is necessary to obtain maximum dispersion (Colmet-Daage et al., 1972).

The method most generally used for dispersion is ultrasonic vibration and low

PH.

B. PLASTICITY



The plasticity is one of the physical properties which distinguish allophane

from crystalline materials. The name “allophane” comes from the striking

change on drying of allophane clays. Glassy when wet, the allophanes become

earthy on drying (Grim, 1953). The wet material is plastic, and the dry earthy

material is nonplastic.

Many papers have documented the plasticity limits, or Atterberg limits, and

their change on drying (Birrell, 1951; Gradwell and Birrell, 1954; van Schuylenborgh, 1953; Yamazaki and Takenaka, 1965; Wesley, 1973; Warkentin and



PHYSICAL PROPERTIES OF ALLOPHANE SOILS



235



Maeda, 1974; Kodani ef al., 1976; and others). Wet allophane soils have a high

liquid limit, but also a high plastic limit, and hence a low range of water content

over which they are plastic. As the samples are gradually dried, the liquid limit

decreases more rapidly than the plastic limit. Highly allophanic soils become

nonplastic before they reach the air-dry water content. The nonplastic state is

where the plastic limit cannot be measured, or where its measured value equals

or exceeds the liquid limit.

Since the samples are completely rewetted during the determination of plasticity limits, the decreases in liquid and plastic limits on drying indicate an

irreversible decrease in hydration of the allophane surfaces. The nature of these

irreversible changes is discussed in Section 111, A.

The values of plasticity limits are shown on a Cassagrande plot in Fig. 1.

Crystalline clays have plasticity values which fall near the “A” line. The allophane samples fall far from the line, with the most allophanic samples having the

highest liquid limit and the lowest plasticity index. This has suggested the use of

plasticity values in classification of allophane soils (van Schuylenborgh, 1953;

Gradwell and Birrell, 1954; Warkentin, 1972; Warkentin and Maeda, 1974). The

measurement of plasticity is r e a d y made, while other measures of allophane are

difficult to make. The intensity of allophanic characteristics would be highest

for samples with high liquid limit and low plasticity index, and lowest for values

approaching the A line. Samples which remain plastic on air-drying or oven-drying would have low allophanic characteristics.

The difficulty in using plasticity values for classification is that the measured

values depend upon degree of previous drying and upon content of organic

matter. Since the drying history of surface soil samples is usually not known,

air-dry samples may have to be used. The method might be more suitable for

subsoils.



120



c



Liouid Limit



FIG. 1. Cassagrande plasticity chart with values for Japanese allophane soils (from

Yamazaki and Takenaka, 1965). 0, Fresh soil; 0 , air-dried soil.



236



T. MAEDA ET AL.



Organic matter contributes t o the water held at the liquid limit (Kodani et aZ.,

1976), an effect which decreases irreversibly on drying. Maeda et al. (1976) have

shown the separate contributions of organic matter and mineral matter to the

liquid limit of allophane soils (Table I). The liquid limit is increased from 1.5 t o

3% for each 1% organic matter in the samples they used. Their results indicate

that not all the organic matter in a soil sample contributed to the liquid limit.

Bonfils and Moinereau (1971) found that both liquid limit (L.L.) and plastic

limit (P.L.) were strongly related to organic matter content (O.M.); the equations were: L.L. = 2.7 O.M. + 41 and P.L. = 2.7 O.M. + 34. The plasticity index

was not correlated with organic content.

The activity values (ratio of plasticity index to clay content) measured for

allophanes are variable. Northey (1966) gives values of 1.2 t o 1.5, Wesley (1973)

gives value below 0.6. The meaning of these values is uncertain because the

measurement of clay content is difficult.

The measurement of plasticity is more difficult for allophane samples than for

crystalline clays, and the precision is lower. This results from the low range of

water content over which the samples are plastic. The slope of the liquid limit

determination (water content versus log number of blows) is also more variable

for allophane clays than for crystalline clays. The one-point liquid limit method

(Sowers, 1965) cannot be recommended for allophanes. The degree of remolding

and working of the soil with water affects the liquid limit, especially of subsoils

(Ikegami and Tachiiri, 1966).

Measurements of liquid limit by Soma and Maeda (1974) on soils which were

gradually dried show a sharp break at a specific water content where irreversible

changes occur (Fig. 2). Drying does not produce irreversible change for the soil

shown until the water content falls below 100%. The shrinkage limit also occurs

at this water content.

TABLE I

Effect of Organic Matter on Liquid Limit of Allophane Soil'

Water content

at liquid limit

Organic

Soil content (%)

A



29



B



20

20

17

23

11



C



D

E

F



Natural water

content (%)

142

116

119

133

108

44



'From Maeda etul. (1976).



Decrease in liquid limit

on air-drying



Whole Organic matter Due to organic

Due to

soil (%) removed (%)

matter (%)

allophane (%)

180

164

147



151

172

62



83

72

72

107

107

42



33

28

36

8

52

2



36

21

15

40

5

3



PHYSICAL PROPERTIES OF ALLOPHANE SOILS



237



180



.=E 160

._



-I 140

v

.S



.F 120

-I



Q



.-



,,

1.4-



I00

I



*.-*



2b



40



60 80 IiO IhO I40 I60

Initial Water Content



FIG. 2. Decrease of liquid limit and volume of allophane soil o n gradual drying (from

Soma and Maeda, 1974).



Freeze-drying produces less particle bonding than air-drying, and results in

higher measured plasticity (Warkentin and Maeda, 1974). Ultrasonic vibration

increases the measured liquid limit (Soma and Maeda, 1974) because it causes

some dispersion.

There is little change in liquid limit with different exchangeable cations. For

some samples the Na-soil has a slightly higher liquid limit than the Ca-soil, for

others it is reversed (Yazawa, 1976). The flow index (slope of the water content

versus number of blows curve in the determination of liquid limit) is also not

consistently different for Na or Ca allophane soils (Yazawa, 1976).



C. SURFACE AREA AND HEAT O F WETTING



Measurements of surface area for allophane soils have been reviewed recently

by Wada and Harward (1974). This literature will not be reviewed in detail here.

The surface area values are high, in the range of 300-600 mZg-’, but some of

this surface is not accessible to large molecules. This is not equivalent t o the

internal and external surfaces of swelling clays, but is due to small size of voids

and small necks leading to voids. The heats of adsorption indicate that physical

adsorption rather than chemical adsorption is dominant (Fieldes and Claridge,

1975).

Total surface area is often calculated from the amount of ethylene glycol

adsorbed, and external surface is measured from nitrogen adsorption; internal

surface area is estimated from the difference. Aomine and Egashira (1970) found

ratios of total to internal surface from 2.3 t o 3.0, while Fieldes and Claridge

(1975) report ratios of 1.8 to 2.6 when the nitrogen surface was measured after

heating to 600°C. Egashira and Aomine (1974) found that total surface area

measured on samples vacuum-dried over P2 O5 was higher than for oven-dried

samples.



23 8



T.MAEDA ET AL.



Aomine and Egashira (1970) measured the heat of immersion of allophane

soils in comparison with soils containing crystalline minerals. They found that

for equal surface areas, allophane soils had heats of immersion about twice as

large as montmorillonite soils. The ratio of heat of immersion to surface area

for allophane and from 0.023 to 0.029 for

ranged from 0.047 to 0.056 cal

montmorillonite soils. The exchangeable cation had only a small effect on heat

of immersion of allophane soils. For montmorillonite soils, hydration of exchangeable cations is a more important part of total heat of immersion. Water

molecules are bonded more strongly on allophane surfaces than on montmorillonite surfaces. When the heat of immersion was plotted against initial

water content of the allophane soils, the oven-dry samples fell below the smooth

curve joining the vacuum-dried and moist samples. This indicated to the authors

that oven drying had altered the nature of the allophane surface.

Maeda er al. (1976) measured heat of wetting values for an allophane soil

ranging from 7.3 cal g-' at 4% organic matter to 11.2 cal g-' at 26% organic

matter.

D. MINERAL DENSITY



Some measured values of mineral density, or specific gravity, of wet allophanes

are low, in the range of 1.8-1.9 g cm-3 (Fieldes and Claridge, 1975). These

values had been accepted in earlier studies. However, other measurements show

values of 2.7 or higher. Forsythe etal. (1964) quote values of 2.7-2.9 g ~ m - ~ .

Wada and Wada (1975) measured values of 2.72 to 2.78. They took special

precautions to remove entrapped air from the samples. If the unit particle of

allophane is accepted to be a hollow spherule of 50 A outside diameter and

about 30 A inside diameter, water movement into and out of this sphere would

be difficult and could account for the low mineral density sometimes measured.

Bonfils and Moinereau (1971) measured values of 2.32 to 2.70, the lower

values being for horizons with large amounts of organic matter-about 25%.

E. THERMAL CONDUCTIVITY



The thermal conductivity of a soil depends upon the conductivities of the

components-mineral, organic, water, and air. Because the path of heat transfer

from one component to another cannot be easily specified, the conductivity of a

soil cannot be readily calculated from the conductivities of the Components.

Models exist for some heat flow paths, but in general the preceding statement is

true. However, soil thermal conductivities vary in a predictable way with

properties of the components. On this basis allophane soils would be expected t o



PHYSICAL PROPERTIES OF ALLOPHANE SOILS



239



have thermal conductivity and thermal diffusivity values which are lower than

the corresponding values for soils with crystalline clay minerals. Diffusivity is the

ratio of conductivity to heat capacity and is the constant which relates temperature changes in the soil to the temperature gradient.

The conductivity of glass is lower than that of clay minerals or quartz

(Cochran et al., 1967). Allophane soils have a lower bulk density than soils with

crystalline minerals; this should result in lower thermal conductivity. The higher

water content would give a higher heat capacity and hence lower thermal

diffusivity.

Some of the results obtained are summarized in Table 11.

Yakuwa (1 943) made extensive measurements on soil temperature and thermal

properties of different soils in Japan, including allophane soils.

Higashi (1951) measured a value of 0.32 cal g-' O C - ' for specific heat of dry

allophane soil. Thermal diffusivities were calculated from amplitude ratios and

phase differences of temperature waves; the phase differences gave more consistent results. While the dense packing seems to give higher values of diffusivity,

the scatter was such that no conclusions could be drawn on effect of bulk

density (Table 11). The maximum in the diffusivity curve occurred at 50% water

on a weight basis or about 0.25 on a volumetric basis. Thermal conductivity,

calculated from specific heat and diffusivity, was higher at high bulk density.

~ ; dense packing

The loose packing had a bulk density of around 0.5 g ~ m - the

varied from 1.0 at 0% water to 0.7 g cm-3 at 50% water. Higashi (1952) also

measured thermal properties of frozen allophane soils. The thermal diffusivity is

similar for frozen and unfrozen soils below a water content of about 30%, but at

higher water contents the diffusivity of frozen soils increases very quickly.

Cochran et al. (1967), using a line heat source probe, found that thermal

conductivity of a pumice material was very low, only 'slightly higher than for a

peat soil (Table 11). They used this to explain low night temperature and the

high incidence of frost in pumice soil areas of Oregon. The maximum in the

diffusivity-water content curve occurred at a low volumetric water content of

0.04 for the C horizons of the soil.

Maeda (1968) measured temperature gradients in soils near Sapporo, Japan. He

calculated thermal diffusivities from amplitude ratios and phase differences. The

diffusivity of fine pumice was higher than for an alluvial soil, and the allophane

soil was the lowest (Table 11).

Kasubuchi (1975a) found that the specific heat of allophane clay (0.229 cal

g-' "C-') was higher than bentonite (0.209), kaolin (0.201), or quartz (0.170).

Kasubuchi (1 975b) measured thermal conductivity of different soils using a line

heat source probe. The values again show conductivity and diffusivity values for

allophane which are 20 to 35% of those for soils with crystalline minerals. The

higher heat capacity and lower heat conductivity of allophane soils results in

slower temperature changes.



TABLE I1

Measured Thermal Properties of Allophane Soils



Material



Bulk

density

(g cm--' )



Water

content

(w, %)



1.15

Loose

Loose

Dense

Dense



11

0

50

0



Heat

Thermal

capacity

conductivity

(cal ~ r n - ~ ~ c - ' )(mcal cm-' sec-' "C'

)

~



Pumice soil

Allophane soil



Crown glass

Pumice



0

40%

0

40



0.15

0.55

0.30

0.70



-



0.76



Clay soil

Allophane soil

Alluvial soil

Fine pumice

Allophane

Alluvial soil

Diliivial soil

Black andosol

Brown andosol



50



0.32

0.20

0.39

0.29

0.53



0.2-0.3

0.5

0.5

0.77

0.72



40

40

40

40

40



Reference



~~



1.1

0.22

0.81

0.32

1.23

2.3

0.37

I .25

0.60

3.80

-



-



Thermal

diffusivity

[cm2sec-' (X



0.5-0.7

2.0-2.5

3-4



0.6

0.8



3.4

1.13

-



2.34

-



2.6

2. I

2.4

3.5

6.6

1.5-1.7

3.74.0

4.5-5.5

1.5

1.7



Yakuwa (1943)

Higashi (1951)

Higashi (1951)

Higashi (1951)

Higashi (1951)

Cochran et al. (1967)

Cochran ef a!. (1967)

Cochran et nl. (1967)

Cochran et al. (1967)

Cochran et al. (1967)

Maeda (196 8)

Maeda (1968)

Maeda (1968)

Kasubuchi (1975b)

Kasubuchi (1975b)

Kasubuchi (1 975b)

Miyazawa and Konno (1976)

Miyazawa and Konno (1976)



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