chapter 6 marks of o show to be in stable condition, and

6-1

CHAPTER 6 ADVANTAGES OF CLARIFYING A PARTICLE CHARACTERISTICS TO THE BEHAVIOR OF AGGREGATE OF PARTICLES

6.1 INTRODUCTION In the designs of some structures on the ground, the followings procedure is performed. At the first, the ground is assumed as a simple and idealized model, and the constants of sub-layer in the ground are determined by the some information such as the field and laboratory test results. For examples, the failure criteria and the deformation coefficients of sub-layers in the model are prepared in the stability and deformation problems, respectively. Then, the external load to the ground is calculated. Of course, the dead load of structure is included in this external load. Adding the external load to the model, the response of model is obtained. The engineers must judge that the response is good or not. In general, the established standard and code are useful for the judgement of response. When the response passes the standard value, the design is accepted. When the response does not pass, the design is changed, and is again checked by the same way.

The ground is composed of soil, and is aggregate of particles. In the design, however, the ground is generally assumed as continuum. The gap between real ground and ideal model may cause some problems. If the detailed properties of ground can be clarified and the gap between ground and model is small reduced, the response of ground is thought to be predicted with high accuracy. This ground modeling including the constants of ground is important to get the prediction with high accuracy. Not only the calculation technique for obtaining the response but also the studies concerning with modeling are necessary.

Figure 6.1.1 Schematical relationship between stress condition and material characteristics

Figure 6.1.1 schematically shows the relationship

between stress condition of ground and crushing stress of particle as material characteristics on carbonate and silica sands under embankment and toe of pile. The

marks of O show to be in stable condition, and “ f ” is in unstable. Here, the crushing stress is defined as the peak force of the single particle compression test divided by square mean diameters (Kato, et al, 1999). The crushing stress of silica sand is much larger than that of carbonate one. In the carbonate ground, the ground is in stable under low embankment, but is in unstable under high embankment such as rockfill dam. In the silica sand ground, on the other hand, the ground is in stable under embankment, and the stratum of sand beneath pile is in unstable. As shown in the figure, the boundary divided into two groupes, stable and unstable regions can be drawn. Researching this boundary leads to the assessment of interaction between ground and structure and the development of design code.

Recently, new materials that made of fly ash, dredged clay, tire chip etc. have been developed. The background of this development is concerning with the environment problem. That is the use of by-product from construction projects and industrial products, and the reduction of disposal volume.

Such artificial material can control its strength by the change of volume of admixture stabilization. If the particle strength correlated closely with the behavior of its aggregate, the characteristics of new material can be determined. This is thought to lead to develop a new material effectively.

Figure 6.1.2 shows the relationship between consolidation yield stress, py and crushing stress, σf for silica sand (data: Nakata et al., 1999a; Kato et al., 1999) and shirasu (data: Katagiri et al., 1999).The σf and py relations are represent as regions due to their scattering. The plots shown in Figure 6.1.2 are thought to indicate the evaluation of ground behavior in considering with the characteristics of particles.

0.1

1

10

100

1000

0.1 1 10 100 1000py (MPa)

σ f (M

Pa) s ilica sand (after

Nakata et al.,1999 &Kato et al., 1999)

shirasu (after Katagiri et al., 1999)

Figure 6.1.2 Relationship between py and σf (Data: Nakata et al. 1999a, Kato et al., 1999 and Katagiri et al, 1999)

In this chapter, the studies for the interaction

between particle and aggregate properties are introduced in order to develop the current design methods and to investigate the evaluating method for new materials.

stress condition

mat

eria

l cha

ract

eris

tics

under em bankm ent beneath pilecarb

onat

e sa

ndsi

lica

sand

ff

f

stable

unstable

boundary

6-2

6.2 PILE END BEARING CAPACITY OF SAND RELATED TO SOIL COMPRESSIBILITY

6.2.1 INTRODUCTION In recent years offshore structures located on compressible carbonate sands have been shown to have unusually low pile bearing capacities in spite of the soils having relatively high friction angles. It has been recognized that as a consequence of the high compressibility and strongly contractile nature of these sands the values of end bearing capacity are likely to be much lower than for siliceous sands at the same relative density (e.g., Semple, 1988; Yasufuku and Hyde, 1995). It has become apparent therefore that pile end bearing capacities in sands are dependent on the soil's compressibility as well as its shear stiffness and strength. Compressibility varies widely for different soils, from relatively incompressible silica sands to highly compressible carbonate sands and also the compressibility becomes a key factor for better evaluating the pile end bearing capacity of sands (e.g., Yasufuku et al., 1994).

In this report, a simple method based on theoretical and experimental considerations is presented to predict the pile end bearing capacity and load-settlement curve in sands in relation to soil compressibility, which may strongly linked with soil crushability. The key to the method is in the assumption of a failure mode with a spherical cavity expansion pressure given as a function of the soil compressibility, shear stiffness and friction angle. Further, the pile tip settlement behaviour has also been discussed based on an empirical model incorporating the pile end bearing capacity from a cavity expansion analysis with a Kondner type hyperbolic function. A practical approach for determining the experimental parameters for improved predictions is also discussed. The overall usefulness of the approach is verified using data from model and in-situ pile load tests. 6.2.2 CHARACTERISTICS OF FAILURE MODE Ladanyi (1961) suggested that the deformation bulb beneath a loaded pile tip strongly resembles that for a spherical cavity expanded in an infinite medium. A similar observation was also made by Kishida et al. (1973) and Miura (1985). Figure 6.2.1 shows a typical failure mode below a pile tip for a typical carbonate sand at s/d = 1.0, which was obtained from model pile load tests performed by Yasufuku et al. (2001), where “s” and “d” are defined as pile settlement and diameter of pile. Similar model pile load tests were also conducted by Yasufuku and Hyde (1995). As indicated by Yasufuku and Hyde (1995) and Yasufuku and Kwag

(1999) it can be pointed out that although the compressibility and/or crushability under compression and shear of a typical carbonate sand is much larger than that of siliceous sand, the compressive failure zone for each sand is similarly shaped deformation bulb shown in Figure 6.2.1. This means that the effects of the compressibility on the shape of the failure mode are not significant. The corresponding relationships between applied pile stresses and settlements, s/d, normalized with respect to the pile diameter for these sands are shown in Figure 6.2.2. It is clear that despite having the same relative density, similar friction angles and shape of failure mode shown in Figure 6.2.1, the applied stress-normalized settlement curves of carbonate sands are markedly different from those of siliceous sand. Such a tendency suggests that the end bearing capacity may be affected not only by the

Figure 6.2.1 Pile tip failure mode for a typical carbonate sand

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Normalized settlement, s/d

Pile tip stress, qm (MPa)

Toyoura sandDr=80 %

Quiou sandDr=80 %

σv=400 kPaσh=200 kPa

K=0.5 :

φcv=31 °

φcv=36 °

Figure 6.2.2 Typical model pile test results for sands with different compressibility

6-3

strength of soils but also by characteristics such as shear stiffness and volumetric compressibility due to both shear and compression. The volumetric compressibility is simply described as compressibility in the following. 6.2.3 ANALYTICAL METHOD LINKED WITH SOIL COMPRESSIBILITY Considering the shape of failure modes in Figure 6.2.1, it seems that the spherical cavity expansion theory first proposed by Vesic (1972) may be a promising analytical method for the prediction of unit end-bearing capacities of piles in sands related to soil shear stiffness, compressibility and strength. Figure 6.2.3 shows the assumed failure mechanism for frictional soils linking the cavity expansion pressure pu to the ultimate end-bearing capacity qpcal. An important assumption in the use of cavity expansion theory in the context of pile end-bearing is that a rigid cone of soil exists beneath the pile tip with the angle ϕ which will be taken as ( )24 'φπ + , and outside of conical region a zone of soil under isotropic stress equal to the limit pressure for spherical cavity expansion approximately exists. In addition, active earth pressure conditions are considered to exist immediately beneath the pile tip, in which active earth pressure σv may be taken as

( ) ( ){ }'sin1sin1 ' φφ +−pcalq . Then, moment equilibrium

is considered about point B in Figure 6.2.3 for the cavity expansion pressure pu, ultimate end-bearing pressure qpcal and the active earth pressure σΑ. A simple equation relating pu to qpcal can be derived such that (Yasufuku and Hyde, 1995) ;

upcal pq 'sin11

φ−= (6.2.1)

where,

( )

vo

quK

Fp σ321+

= (6.2.2a)

( )[ ] ( )'sin13'sin4'

'sin3sin13 φ

φ

φφ

+

−+

= rrq IF (6.2.2b)

avr

rrr I

II∆+

=1

(6.2.2c)

( ) 'tan213

φσ vor K

GI+

= (6.2.2d)

in which Fq, Irr and Ir are called dimensionless spherical cavity expansion factor, reduced rigidity index and

rigidity index of soil, respectively, which are related to friction angle φ', shear stiffness G and average volumetric strain ∆av for a plastic zone around a cavity (see Fig. 6.2.3), together with the coefficient of earth pressure at rest K0 and overburden pressure σ’v. The rigidity index Ir gives a ratio of shear stiffness to strength, and the reduced rigidity index Irr is considered to be a parameter representing the soil compressibility, in which shear stiffness, shear strength and average volumetric strain are combined. It is important to note that when ∆av=0, Irr reduced to Ir. In order to rationally estimate the ultimate end- bearing capacity using Eqs. (6.2.1) and (6.2.2) from a practical point of view, it is needed to find out the well-balanced determination procedures for the parameters of K0, φ', G and ∆av. In general, it is requested that these parameters are simply determined from the conventional field and laboratory test data. The effect of these parameters on the end-bearing capacity is first clarified through Eqs. (6.2.2). The analytical results are shown in Figure 6.2.4. The Irr -∆av

τBC

CL

Plastic Zone

B

ψ

ψπ φ

= +4 2

Pile

Elastic Zone

ro

pu

qpcal

A

σA

C

σA = qpcal1− sinφ '

1+ sinφ '

τBC

CLCL

Plastic Zone

B

ψ

ψπ φ

= +4 2

PilePile

Elastic Zone

ro

pu

qpcalqpcal

A

σA

C

σA = qpcal1− sinφ '

1+ sinφ '

Figure 6.2.3 Failure mechanism assumed for frictional soils

1

10

100

1000

0 0.05 0.1 0.15

Reduced rigidity index, I rr

∆avAverage volumetric strain for a plastic zone,

Ir=500

100

25

5

(a)

Figure 6.2.4 Irr-∆av relationship with function of Ir

6-4

relationship is shown in Figure 6.2.4 as a function of Ir with semi-logarismic scale. It is recognized that the greater the Ir is, the more sensitive the effect of ∆av related to soil compressibility on the Irr values is. It means that the cavity expansion pressure in Eq. (6.2.2a) can remarkably decrease with the increase of soil compressibility. 6.2.4 ULTIMATE PILE END BEARING CAPACITY WITH SOIL COMPRESSIBILITY, It has been asserted that the critical state friction angle φ'cv will be effective and rational as a strength parameter in practical applications (Bolton, 1993; Yasufuku et al., 1997, 1998, 1999). Based on the definition of φ'cv -value, the friction angle can be regarded as a parameter to guarantee the minimum shear strength under the same initial condition and it is also considered to be uniquely determined, independent on soil density, initial fabric and confining pressure. In addition, it should be noted that φ'cv -value of sands is almost equal to the maximum friction angle under the high confining stress, which will be mobilized below the pile tip (Miura and Yamanouchi, 1977; Miura, 1985). Therefore, at least in practical application, φ'cv -value will be recommended in estimating the pile end-bearing capacity of sands. When φ'cv is used to calculate the pile end-bearing capacity, Eq. (6.2.2) can be rewritten as a closed form such that:

( )( )( )[ ] ( ) '0sin13

sin4

''

'

321

sin3sin1sin13 '

'

vrrcvcv

cvpcal

KIq cv

cv

σφφ

φφ

φ

⎟⎠

⎞⎜⎝

⎛ +

−−

+= +

(6.2.3) in which K0 is determined from '

0 sin1 cvK φ−= and Irr is evaluated from Eq.(6.2.2c). Thus, in order to concretely determine the qpcal value with parameter Irr, the evaluation of G and ∆av are still needed. Practical evaluation of shear stiffness In practical approach, the secant shear stiffness G is often correlated with the SPT blow count number named as N-value (e.g. Ohota et al., 1972). Based on theoretical considerations, Yamaguchi (1975) mentioned that the maximum shear strain corresponding to the shear stiffness used in the cavity expansion analysis was more or less in the order of 10-3. The G-values at shear strain level of 10-3 have been considered to be from one-second to one-third of the G-values obtained from the standard seismic velocity approach. This assertion seems to be supported by many experimental data (e.g. Tatsuoka and Kohata, 1994, Yamashita and Suzuki, 1999). Practical evaluation of soil compressibility ∆av

Based on the original Vesic approach, two or three isotropic and triaxial compression tests are needed to

determine the magnitude of ∆av which reflects the soil compressibility due to compression and shear. This manner may not be so simple in the practical applications, and thus the alternative way to simply determine the magnitude of ∆av is desired. For this purpose, the semi-analytical cavity expansion model which has already presented by Yasufuku and Hyde (1995) was used to make clear the characteristics of ∆av, where the manner of the numerical calculation is basically due to Baligh’s approach (1976). The resulting ∆av plotted against rigidity index Ir for various kinds of sands is shown in Figure 6.2.5. It is found that the ∆av.-Ir relationship is almost unique irrespective of the difference of the sort of sands and the relative density. Therefore, a following empirical equation is approximately presented to determine the ∆av.-value as a function of Ir. ( ) 8.150 −=∆ rav I (6.2.4) which means that ∆av is automatically determined from Ir in Eq. (6.2.2d). Introducing Eq. (6.2.2d) into Eq. (6.2.4), Eq. (6.2.4) is rewritten as a function of G, K0, σ'

v and φ'cv such that:

8.1''0 tan

321

50

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧⎟⎠

⎞⎜⎝

⎛ +

=∆G

Kcvv

av

φσ (6.2.5)

This equation indicates that the average volumetric strain ∆αv for a plastic zone around a cavity increases with the decreasing shear stiffness in the elastic zone and also with the increasing overburden pressure in the associated ground. Such tendency seems to be logical. Furthermore, introducing Eq. (6.2.5) into Eq. (6.2.3), a resulting equation for estimating the ultimate pile end-bearing capacity is given by

0

0.05

0.1

0.15

0 100 200 300 400

∆av

Rigidity Index, Ir

○: Dogs Bay sand (dense)□: Quiou sand◇: Aio sand△: Masado 1▽: Masado 2＋: Dogs Bay sand (loose)

Eq.(4)

Figure 6.2.5 Uniqueness of ∆av with rigidity index Ir

6-5

'8.0

'

'

'sin1 v

C

v

v

cvpcal

GDB

GAq σ

σ

σφ

⎪⎪⎪

⎭

⎪⎪⎪

⎬

⎫

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=

− (6.2.6a)

where,

( )

( ) ⎟⎠

⎞⎜⎝

⎛ +−+

=321

sin3sin13 0

'

' KA

cv

cv

φφ

(6.2.6b)

'0 tan321

cvK

B φ⎟⎠

⎞⎜⎝

⎛ += (6.2.6c)

( )'

'

sin13sin4

cv

cvCφ

φ+

= (6.2.6d)

( ) 8.1

'0 tan321

50⎭⎬⎫

⎩⎨⎧ +

= cvK

D φ (6.2.6e)

where, note that G-value is given as the value at shear

strain level of 10-3. Based on this equation, the ultimate pile end-bearing capacity qpcal for sandy ground with various soil compressibility is easily estimated as a function of four parameters, that is, σ'v, φ'

cv and G-value mentioned above. When considering the characteristics of Eq. (6.2.5) and Eq. (6.2.6), the effect of soil compressibility ∆av on the qpcal value is parametrically investigated. A typical relationship between qpcal and ∆av correlated with σ'v values are shown in Figure 6.2.6, where φ'cv are assumed as 35 degrees, respectively. It should be mentioned that ∆av has a strong influence for qpcal values especially at higher overburden pressures, namely, the ultimate pile end-bearing capacity qpcal decreases with the increasing soil compressibility, even if the friction angle and the overburden pressure were fixed. Practical manner for determining parameters needed The practical manner for determining each parameter is briefly shown in Table 6.2.1, which is related to the degree of the information from the soil investigations. The model presented here is also summarized in Table 6.2.2, together with the models of Vesic (1977), Yamaguchi (1975) and Prandtl (1921) for comparison, where the estimation of reduced rigidity index Irr and experimental parameters for Vesic model follows the approach presented here. The former three models are derived basically based on the cavity expansion approach, and Prandtl model is expressed as a function of an internal friction angle alone. It is noted that all the models can be expressed as qpcal = kσ'

v, and therefore the difference of each model reduces to the magnitude of the end bearing factor k. The relationship between the qm/qpcal and the measured normalized settlement sm/d for all the pile database (see Yasufuku et al., 2001) are shown in Figure 6.2.7, where qm and qpcal mean measured pile

0

5

10

15

20

25

30

0.0001 0.001 0.01 0.1 1 10

qpcal (MPa)

∆ av (%)

σv =50 kPa

300 kPa

σv =500 kPa

100 kPa

φcv=35 degrees

R=1.0

200 kPa

Figure 6.2.6 Effect of ∆av on qpcal values

Table 6.2.1 Practical procedure for determining three parameters needed Parameters needed

1.Method from laboratory testing 2.Method from in-situ test data (Case with poor soil data)

φ’cv

φ’-value at critical or characteristic state which determined from a triaxial compression test (e.g. JGS 0524-2000)

Determination from uniformity and angularity of soils in the corresponding pile tip ground (BS-code, 1994, see Table 1)

G

G-value at shear strain level of 10-3

which obtained from a triaxial or torsional tests with relatively small strain measurement.

G is determined from N-value which has already been presented by Yamaguchi (1975) such that : G=7.0N0.72 (MPa)

σ’v

σ’v is generally given as γ’

avz, where γ’

av :average value of submerged unit weight from the surface layer to pile tip depth z (e.g. JGS 0191–1990)

Determination from a code based on soil classification

6-6

stress and calculated value in Eq.(6.2.6), respectively. Three experimental parameters, σ'

v, G and φ'cv needed

for the calculation are determined by the manner in Table 6.2.1. Although the scatter can be found in the results, it is clear that the qm/qpcal tends to increase with the increasing sm/d, and the qm/qpcal gradually approaches from about 0.9 to 1.1. As far as the results are concerned, the calculated pile stress is associated with a physically ultimate end bearing capacity in practical applications. Figure 6.2.8 shows the typical measured and predicted model pile stresses for Omoi river sand in cases of dense state. The measured values roughly correspond to the applied pile stress at the pile settlement ratio s/d = 1.0, which are based on the data from Kishida and Takano (1977a, 1977b). The proposed model follows the trend for the results of model pile load tests in sands. For comparison, the theoretical curves predicted by the Vesic, Yamaguchi and Prandtl models are also depicted in this figure. Vesic model gives an optimistic tendency for both

sands. On the other hand, Yamaguchi model gives a conservative tendency for the sand, which confirms that as mentioned by Kishida and Takano (1977a, 1977b), the predicted values agree well with the model pile stress at sm/d = 0.2. Whether the tendency of the predicted straight line in Prandtl model is optimistic or conservative is not clear, because the model cannot evaluate the deformation properties of sands. 6.2.5 ESTIMATION OF LOAD-SETTLEMENT CURVES, The load-settlement curve is important to estimate the pile tip stress at an appointed settlement or realistic pile end bearing capacity in performance-based design related to the allowable deformation of the supporting ground. Kishida and Takano (1977a, 1977b), and Hirayama (1990) have already pointed out that the Kondner type hyperbolic curves are useful for predicting the load settlement curves of

Table 6.2.2 Comparison of four models for predicting pile end bearing capacity Basic equation

qpcal = kσ v

Proposed eq. (2001) ( )

C

v

v

v GDBGAk

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−= − 8.0'

csin1 σσ

φ

Vesic (1977)

( )

( )

C

v

v

v GDBGAek

vv

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−= −

−

8.0'c

tan2

sin1

'c

'c

σσ

φ

φφπ

Yamaguchi (1975)

( )( )

C

vv

v

KGAk

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+−

= 'c0

'c

sin21sin3

φσφ

Prandtl (1921)

'tan'2 )2(tan cvek cvφπφπ +=

( )( ) ⎟⎟

⎠

⎞⎜⎜⎝

⎛ +

−

+=

321

sin3sin13 0

'

' KA

cv

cv

φφ , '0 tan

321

cvKB φ⎟

⎠

⎞⎜⎝

⎛ +=

( )'

'

sin13sin4

cv

cvCφ

φ+

= , ( ) 8.1'0 tan

321

50⎭⎬⎫

⎩⎨⎧ +

= cvK

D φ

Experimental parameters :

zav'γσ = , ( ) RK cv

'0 sin1 φ−=

310−== γatGG 72.00.7 N≈ (MPa) (Yamaguchi, 1975) φ'cv: 30+∆φ'1+ ∆φ'2 (degs.) ∆φ'1=0-4; ∆φ'2=0-4 (BS code, 1994)

0

0.4

0.8

1.2

1.6

0 0.5 1 1.5 2

q m/q pcal

sm/d

Figure 6.2.7 Relationship between qm/qp,cal and normalized settlement sm/d for in-situ and model pile load tests

0

10

20

30

40

50

0 100 200 300 400 500 600

qpcal (MPa)

σ v (kPa)

Vesic eq.

Presented eq.

Yamaguchi eq.Prandtl eq.

sm/d=1.0

(b) Omoi river sand

emax=0.993 ; e

min=0.576

Dr=81-88 %

1.0

2.0

1.01.0

Figure 6.2.8 Measured and predicted model pile stress with over-burden pressure for Omoi river sand (Data given by Kishida and Takano, 1977)

6-7

non-displacement piles in vergin loading. In this report, a simple hyperbolic function is first assumed to be applicable for estimating the relationship between the applied pile tip stress, qcal, and the corresponding normalized pile tip settlement, s/d, and in addition, the normalized reference displacement (s/d)ref presented by Hirayama (1990) was introduced, which is defined as the normalized settlement s/d required to mobilize the half of the ultimate end bearing capacity qpcal. Note that (s/d)ref=0.25 is empirically derived based on many reliable loading test data for non-displacement piles in sands. When qpcal is assumed to be equivalent to the ultimate pile end bearing capacity, and introducing the hyperbolic curve with normalized reference displacement (s/d)ref given as 0.25, it is rewritten in the following form:

pcalcal q

ds

ds

q

⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛+

⎟⎠⎞

⎜⎝⎛

=25.0

(6.2.7)

The outline of the model is summarized in Figure 6.2.9. It should be emphasized that the applied pile tip stress at any pile tip settlement can be calculated by Eq. (6.2.7) using only three parameters needed for calculating the qpcal in Eq. (6.2.6), which present the effects of the overburden pressure, soil compressibility, shear stiffness and strength of soil. This means that a pile tip load-settlement curves can be easily estimated from a fundamental in-situ soil data shown in Table 6.2.1. For instance, when the pile tip stress at s/d = 0.1 is chosen as an allowable limit end bearing capacity in practical design, the calculated value of qcal, q0.1, is given by Eq.(6.2.7) such that:

pcalpcal qqq 29.01.025.0

1.01.0 =

+= (6.2.8)

This equation asserts that the allowable limit end bearing capacity calculated should be roughly 30% of qpcal in Eq. (6.2.7). It is important to point out that the limit end bearing capacity directly reflects the soil characteristics given by the estimating qpcal, and also that three parameters for estimating the qpcal are only needed to define the relationship between the pile tip stress and the normalized settlement. 6.2.6 VERIFICATION OF THE MODEL The applicability of the model presented by Eq. (6.2.8) is verified comparing with the database of pile load tests. The detail data have been reported by Yasufuku et al., (2001). Figure 6.2.10 shows the calculated and measured results in the relationship between the pile tip stress and the corresponding normalized pile settlement. The representative results of in-situ pile load tests for non-displacement piles in sandy soils by BCP committee (1971) and KR committee (Amori river site, 1995) are compared with the calculated ones. As mentioned above, three parameters, σ'

v, G and φ'cv

needed for the calculation are mostly determined from the soil classification and fundamental soil data (see Table 6.2.1). It can be seen from these figures that although the measured maximum normalized settlements and pile tip stresses of two piles differ from each other in the magnitude, the calculated results of each site have a good agreement with the measured

Pile tip stress, q

Nor

mal

ized

settl

emen

t, s m

/d

qpcal

0.25

(sref)

qcal =

sd

s d( )ref

qpcal+

s d( )qpcal

=s d( )

0.25 + s d( )qpcal

qpcal = kσ v

k =A

1− sinφcv

G σv

B + D G σ v( )−0.8

⎧ ⎨ ⎩

⎫ ⎬ ⎭

C

Pile tip stress, q

Nor

mal

ized

settl

emen

t, s m

/d

qpcal

0.25

(sref)

qcal =

sd

s d( )ref

qpcal+

s d( )qpcal

=s d( )

0.25 + s d( )qpcal

qpcal = kσ v

k =A

1− sinφcv

G σv

B + D G σ v( )−0.8

⎧ ⎨ ⎩

⎫ ⎬ ⎭

C

qcal =

sd

s d( )ref

qpcal+

s d( )qpcal

=s d( )

0.25 + s d( )qpcal

qcal =

sd

s d( )ref

qpcal+

s d( )qpcal

=s d( )

0.25 + s d( )qpcal

qpcal = kσ v

k =A

1− sinφcv

G σv

B + D G σ v( )−0.8

⎧ ⎨ ⎩

⎫ ⎬ ⎭

C

Figure 6.2.9 Outline of model for evaluating pile tip stress with normalized settlement at virgin loading of non-displacement pile

0

0.5

1

1.5

2

2.5

0 2 4 6 8

S m/d

qm (MPa)

(a) BCP-1B(No.1)σv=60 kPaφ cv,av =35 degsN,av=20

qp,cal=5.93 (MPa)

Predicted

Measured

(sm/d)

max > 2. 0

0

0.02

0.04

0.06

0.08

0.1

0 2 4 6 8

s m/d

qm (MPa)

(b) Amori site (1997) σv=280 kPa (41 m)

φcv=38 degs

N,av=18

(s/d)max=0.09

(G=56.1 MPa)

Predicted

Measured

qp,cal=16.2(MPa)

Figure 6.2.10 Comparison of calculated and measured results in q-sm/d relationship

6-8

ones. The ratios of measured pile tip stresses, qm to the

calculated ones, qcal plotted against the corresponding measured normalized settlements, sm/d for all the data are shown in Figure 6.2.11, comparing with the data calculated from N-values, that is, qcal = 15N which is .a typical Japanese Code. Considering that when the value of qm/qcal is closer to 1.0, the applicability of the model becomes better, the estimation method is suggested to be a valid one. The results obtained from N values seem to include an essential scatter related to the normalized settlement. The calculated pile tip stresses of sands give a totally good precision for estimating the pile tip stresses at any settlements, irrespective of a sort of sands. It is therefore concluded that the method can represent the effect of internal friction angle, shear stiffness and soil compressibility on the pile tip load-settlement curves. 6.2.7 CONCLUSIONS A geotechnical method in practical application of estimating the ultimate end bearing capacity and load-settlement curve at virgin loading for non-displacement piles has been presented. Its usefulness has been verified using model pile load tests and database of in-situ pile load tests. The main conclusions are as follows:

1) The use of spherical cavity expansion method offers potential for a better prediction of ultimate end bearing capacities by taking account of failure mechanism with soil compressibility, shear stiffness and strength of soils. 2) An empirical equation presented to evaluate the soil compressibility plays an important role to practically calculate the ultimate pile end bearing capacity in sands. 3) A method of determining the pile tip stress at any settlements has been presented, combining the proposed pile end bearing capacity with Kondner type hyperbolic function, in which the function is related to the normalized reference displacement which requires to mobilize the half of the ultimate end bearing capacity. 4) The model is given by a closed form, therefore, the calculating procedure is quite simple. The practical advantage of the model is that the pile tip load-settlement curves, which directly reflect soil characteristics, can easily be estimated from some fundamental soil data without any realistic pile load tests. 5) The applicability of the proposed method was verified, comparing the predicted results with those from reliable model pile load tests and a database for in-situ pile load tests in sands.

0

1

2

3

4

0 0.5 1 1.5 2

q m/q

cal

sm/d

(a) qcal

(predicted)

qm (Measured)

0

1

2

3

4

0 0.5 1 1.5 2

q m/q

N

(qN=1

5Nav

)

sm/d

qN=15N

av(b)

Figure 6.2.11 Relationship between qm/qcal and normalized settlement sm/d for in-situ and model pile load tests

6-9

6.3 A DEFORMATION ANALYSIS OF A ROCKFILL DAM DURING CONSTRUCTION

6.3.1 INTRODUCTION

Large rockfill dams basically consist of three types

of materials: rock, filter and core. Rocks, materials of large diameters, some exceeding 1m, are compacted with vibratory rollers. During construction, they exhibit settlement larger than any other materials, as a matter of fact. Core materials, finest among the three, are usually compacted with tamping rollers. They exhibit the second largest consolidation settlement during and after construction. Filter materials, produced by blasting rocks, are the hardest among the three and exhibit the smallest settlement. Therefore, stresses tend to concentrate on the filter zone during and after construction.

In this study, methods proposed by Iseda and Mizuno (1971) and Ohta and Hata (1977) are used in modelling the fill materials. These methods enable to model the behaviour of in-situ compacted materials based on a series of laboratory tests. Similar to usual clays, the in-situ compacted materials exhibit a sharp kink on the consolidation curve of void ratio plotted against logarithm of consolidation pressure. The location of the kink depends, in case of compacted materials, on the water content and the degree of compaction effort. The stress at the point of kink is called the equivalent pre-consolidation pressure of the compacted materials. Filter materials are fine enough to undergo the usual laboratory tests, but the grain size of rock materials is too large. Therefore, it is necessary to eliminate large particles of rock when preparing the specimens for laboratory tests. However, test results of thus prepared specimens do not represent the in-situ behaviour of the rock materials unless some proper grain size correction is made to correct the influence of the grain size difference between tested and in-situ materials. Back-calculations of the behaviour of dam embankments monitored during construction suggest that the methods proposed by Marachi et al. (1969) and Miura et al. (1985) are suitable for the grain size correction.

It is not widely recognized that, although filter and rock materials look like typical elastic media, they actually behave in a fashion similar to elasto-plastic clay-like materials under high overburden pressure of large rockfill dams. Comparisons between the laboratory test results and the in-situ measurements reveal that filter and rock materials subjected to consolidation exhibit a straight line with a sharp kink on the graph of void ratio plotted against logarithm of the overburden pressures in the manner exactly same to typical over-consolidated soils.

In this paper, after modelling the mechanical characteristics of fill materials based on the above-mentioned method, the actual behaviour of the dam embankment monitored during construction is

numerically simulated. The behaviour is analysed by the soil/water coupled finite element method in which the constitutive equation proposed by Sekiguchi and Ohta (1977) is incorporated. As a result, it is found that the analysis method can well simulate the monitored dam behaviour. In conclusion, the procedure of material testing and the method of specifying the constitutive parameters of fill materials introduced in this paper seem to be primarily appropriate.

As above mentioned, this paper focuses the deformation characteristics of large rock particles under high earth stress and importance for estimating deformation of a dam body.

Figure 6.3.1 Modelling of strength-deformation characteristics for compacted soil

6.3.2 PROCEDURES OF MATERIAL TESTING AND PARAMETER DETERMINATION

Strength-deformation characteristics of compacted soil

Fig. 6.3.1 shows the shear strengths of a sandy silt statically compressed in a shear box under certain consolidation pressures σv0' and sheared under conditions of constant volume. The e-log σv0' curves spread in the upper half of Fig. 6.3.1 depending on the initial water content, while the Su-log σv0' plots form a single curve regardless of the water content as seen in the lower half of Fig. 6.3.1. When the soil with water content of 12.5% is compacted by a heavy compaction equipment in the field, the shear strength of the compacted soil is predicted by the following procedure. First plot Point C, which is specified by the water content and the void ratio after compaction, and then follow a path of C→F→I. In case that the water content is 15.9 % (Point B) or 7.7 % (Point D), the predicted shear strength is given by Point H or Point J.

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

void ratio e

w=7.5% w=7.7%w=10.0% w=11.0%w=12.5% w=13.7%w=14.5% w=15.9%w=18.3% w=21.7%

0

50

100

150

200

250

300

1 10 100 1000equivalent pre-consolidation pressure

σvo'(kPa)

constant volume shear strength

Su (kPa)

Low water

content

High water

content

σvo'～Su relationship for

statically compacted soil

compactedground

B

D

E

K

J

I

H

G

FM

NO

0

sandy silt(Dmax=2.0mmD50=0.58mm)

A

C

L

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

void ratio e

w=7.5% w=7.7%w=10.0% w=11.0%w=12.5% w=13.7%w=14.5% w=15.9%w=18.3% w=21.7%

0

50

100

150

200

250

300


σvo'(kPa)


Su (kPa)

Low water

content

Low water

content

High water

content

High water

content



compactedground

B

D

E

K

J

I

H

G

FM

NO

0

sandy silt(Dmax=2.0mmD50=0.58mm)

A

C

L

6-10

This is the concept proposed by Ohta and Hata (1977). After the compaction equipment passed a point in the field, the in-situ compacted material experiences a change from Point C to Point A. When the embankment becomes higher and the own weight of the fill gradually increases, the material experiences a change from Point A to Point C and then to Point L. The settlement sharply increases after passing Point C and the shear strength increases from F to N (from I to O). The path A→C→L with a sharp kink at Point C resembles the consolidation curve for over-consolidated clays. Here, let us define the gradient of the curve A→C as the swelling index Cs (κ); the gradient of the curve C→L which appears after Point C as the compression index Cc (λ). Then the deformation behaviour of in-situ roller-compacted ground under high overburden pressure of a large rockfill dam may be modelled in the manner same as the behaviour of an over-consolidated soil by using these parameters. When the combination of the void ratio and water content during compaction changes, the characteristic parameter such as σv0' changes accordingly. Therefore, if the results of a series of laboratory tests (as shown on the upper half of Fig.1) and field data of the compacted ground (such as the void ratio and water content) are available, parameters (i.e. λ, κ, and σv0') needed in the analysis can be easily determined.

Strength-deformation characteristics of core material of Kami-Hikawa Dam

Kami-Hikawa Dam, as shown in Fig. 6.3.2, is a zoned rock fill dam with an impermeable center core. Using the same method shown in Fig. 6.3.1, the core materials of this dam are tested. The results are shown in Fig. 6.3.3 where we see the tendency similar to Fig. 6.3.1; the shear strengths of core materials can be estimated in the same manner as mentioned above and the deformation behaviour of compacted ground resembles that of an over-consolidated soil. Along with those tests, the deformation of Kami-Hikawa Dam is carefully monitored. Fig. 6.3.4 shows the changes in the void ratio of actual dam embankment during construction, which are measured using the differential settlement gauge (cross-arm) installed in the core zone. The values on the horizontal axis of Fig. 6.3.4, i.e. the overburden pressure, are calculated from the FEM analysis that is explained later. Each of the curves in Fig. 6.3.4 which corresponds to the compression curve of the actual dam embankment, has a kink at σv0' of about 300 to 500 kPa. The results of one-dimensional compression tests on the core materials of Kami-Hikawa Dam are also plotted in Fig. 6.3.4 by ○ and ●. The specimens are prepared in a way that their void ratio and the water content are exactly the same as those of in-situ compacted ground. Those laboratory test results resemble the compression curves of the actual dam embankment. This also indicates that the deformation parameters of core materials can be

directly estimated from laboratory tests on the materials sampled from the site. The stress paths of the core materials, obtained from large-scaled constant volume tri-axial compression tests, are shown in Fig. 5. The shearing behaviour, such as the change in the dilatancy characteristics with the increase in the confining pressure, also resembles that of over-consolidated soils. The theoretical stress paths obtained from the elasto-plastic model proposed by Sekiguchi and Ohta (1977) are also shown in Fig. 6.3.5 for reference. The test results are in relatively good agreement with the theoretical stress paths indicating that the elasto-plastic model works reasonably well in representing the mechanical behaviour of compacted soils.

Figure 6.3.2 Typical cross section and fill materials of Kami-Hikawa Dam

0

100

200

300

400

500


σv0' (kPa)


Su (kPa)

0.4

0.6

0.8

1.0

1.2

void ratio e

w=23%w=20%

w=17%

w=14%

w=11%

Core material (Kami-Hikawa Dam)Constant-volume shear test

In-situ large-scaleshear box test



Compcted withtamping rollers


Compactedwith bulldozers


●　no compaction▲　bulldozers■　tamping rollers

0

100

200

300

400

500


σv0' (kPa)


Su (kPa)

0.4

0.6

0.8

1.0

1.2

void ratio e

w=23%w=20%

w=17%

w=14%

w=11%

Core material (Kami-Hikawa Dam)Constant-volume shear test

In-situ large-scaleshear box test







●　no compaction▲　bulldozers■　tamping rollers

Figure 6.3.3 Strength-deformation characteristics of core material (Kami-Hikawa Dam)

L.W.L 1460

H.W.L 1481

1:2.7

1:2.0

core

Outer shell

filterInner shell

Inner shellOuter shell

EL. (m)

1380

1400

1420

1440

1460

1480

1500

Differential settlement gauge

PiezometerEarth pressure cell

0

20

40

60

80

100

0.1 1 10 100 1000

particle size　(mm)

Percent finer by

weight (%)

rock

core

filter

L.W.L 1460

H.W.L 1481

1:2.7

1:2.0

core

Outer shell

filterInner shell

Inner shellOuter shell

EL. (m)

1380

1400

1420

1440

1460

1480

1500





0

20

40

60

80

100

0.1 1 10 100 1000


Percent finer by

weight (%)

rock

core

filter

0

20

40

60

80

100

0.1 1 10 100 1000


Percent finer by

weight (%)

rock

core

filter

6-11

0

200

400

600

800

1000

0 200 400 600 800 1000

effective mean principal stress

p'=(σ1'+σ2'+σ3')/3　(kPa)

principal stress deviator q=σ1-σ3 (kPa)

failure point

theoretifal stresspath

Core materials (Kami-Hikawa Dam)Large-scale constant volume triaxial test

λ=0.106κ=0.013

σv0'=650kPa

e0=0.509

M=1.6

0.4

0.5

10 100 1000effective overburden pressure σv' (kPa)

　（σv'：calculated by FEM）

void ratio　e

laboratory test ①(w=17.2%)

laboratory test ②(w=15.0%)

Laboratory test

In-situ e-logσ'(measured bydifferential settlement gauge)

density,watercontent(field)

Walker-Holtz' correction

density,watercontent(laboratory)

0.4

0.5

10 100 1000effective overburden pressure σv' (kPa)

　（σv'：calculated by FEM）

void ratio　e

laboratory test ①(w=17.2%)

laboratory test ②(w=15.0%)

Laboratory test

In-situ e-logσ'(measured bydifferential settlement gauge)

density,watercontent(field)

Walker-Holtz' correction

density,watercontent(laboratory)

Figure 6.3.4 In-situ compression curves of dam embankment during construction compared with laboratory test results (Kami-Hikawa Dam ;core zone)

Figure 6.3.5 Large-scale constant volume triaxial compression tests for core materials (Kami-Hikawa Dam) Strength-deformation characteristics of rock material of Kami-Hikawa Dam

A comparison similar to Fig. 6.3.4 is made for the rock material that accounts for most of the volume of the rockfill dam. The results are shown in Fig. 6.3.6. Similar to the core materials, the compression curve for the in-situ rock zone consisting of large diameter rocks has a sharp kink at σv0' of about 400 to 500 kPa. Miura et al. (1985) explained this phenomenon as follows. Since the rock zone is formed with large diameter rocks, the overburden pressure is supported at a small number of contact points between rock particles. Large dams, which are exposed to high overburden pressures, could be subjected to plastic deformation due to crushing of rock particles at contact points and ensued rearrangement of rock particles, caused by the considerably high interparticle stresses at the contact points. A study by Miura et al. (1985) revealed that, like the case for core materials shown in Fig. 6.3.5, the behaviour of rock materials during shear under high Figure 6.3.6 In-situ compression curves of dam embankment during construction compared with laboratory test results

(Kami-Hikawa Dam ; rock zone)

Figure 6.3.7 Method of estimating the deformation

characteristics of in-situ rock zone by grain size correction

confining pressure can be described by the Cam clay type of elasto-plastic constitutive model. Similar to Fig. 6.3.4, the results for large-scaled one-dimensional laboratory compression tests on the rock materials are shown in Fig. 6.3.6 by ●. The curve for the results of the laboratory test also has a sharp kink. However, with respect to the gradients of the compression curve, which correspond to the swelling and compression indices, the gradients of in-situ actual compression curves are of values considerably larger than the laboratory tests, unlike the case of core materials. For laboratory tests, rock materials sampled from the construction site cannot be used as specimens without eliminating large particles because of the testing equipment which is not large enough. For this reason, specimens with small grain size must be used in laboratory tests. The use of such specimens, however, increases the number of contact points between rock grains, resulting in the inter-particle stresses at the contact points much smaller than in-situ condition for the same overburden pressure. This is the reason why the compressibility obtained from the laboratory tests is smaller than that measured in the actual dam embankment. This means that the deformation characteristics of in-situ rock materials cannot be

0.2

0.3

1 10 100 1000 10000effective overburden pressure σv' (kPa)

（σv'：calculated by FEM）

void ratio e

Laboratory tests

In-situ e-logσ'(measured byDifferential settlement gauge)

λfield

log σv'

e

field

laboratory

κfield

κlab

λlab

0.2

0.3

1 10 100 1000 10000effective overburden pressure σv' (kPa)

（σv'：calculated by FEM）

void ratio e

Laboratory testsLaboratory tests

In-situ e-logσ'(measured byDifferential settlement gauge)In-situ e-logσ'(measured byDifferential settlement gauge)

λfield

log σv'

e

field

laboratory

κfield

κlab

λlab

0

0.02

0.04

0.06

0.08

0.1

0 20 40 60 80 100

mean grain D50 (mm)

compression indexλ,swelling index κ

λfield

κfield

λlab

κlab 0

20

40

60

80

100

0.1 1 10 100 1000

grain size　(mm)percent finer by

weight(%)

D50lab

in-situgrain size

D50field

laboratorygrain size

D50lab D50fieldmean grain D50 (mm)

e


κlab

κfieldλlab

λfield

σv' (logarithmic scale）

in-situgrain size

Miura et.al (1985)

Miura et.al(1985)

Miura et.al (1985)

0

0.02

0.04

0.06

0.08

0.1

0 20 40 60 80 100

mean grain D50 (mm)

compression indexλ,swelling index κ

λfield

κfield

λlab

κlab 0

20

40

60

80

100

0.1 1 10 100 1000

grain size　(mm)percent finer by

weight(%)

D50lab

in-situgrain size

D50field


D50lab D50fieldmean grain D50 (mm)

e


κlab

κfieldλlab

λfield

σv' (logarithmic scale）

in-situgrain size

Miura et.al (1985)

Miura et.al(1985)

Miura et.al (1985)

Miura et.al (1985)

Miura et.al(1985)

Miura et.al (1985)

6-12

directly obtained from the laboratory tests, unless proper grain size correction is made. For this, the authors carry out data arrangement such as shown in Fig. 6.3.7. The swelling index (κlab, κfield) and compression index (λlab, λfield) are first calculated from the gradients of the compression curves in Fig. 6.3.6, which are obtained from both in-situ measurements and laboratory tests. The compression index obtained from in-situ measurements is larger than those from laboratory tests. They are then plotted on a graph with the swelling and compression indices on the vertical axis and the average grain size D50 of specimens (for both laboratory specimens and in-situ materials) on the horizontal axis. The trend shown in Fig. 6.3.7 by ■→■ corresponds to the difference between laboratory and in-situ conditions.

Miura et al. (1985) arranged the test results obtained by Marachi et al. (1969) in the similar way. Their plots are also shown in Fig. 6.3.7. The tendency of the increase in λ and κ with the increase in the average grain size is similar to that for Kami-Hikawa Dam. This indicates that the parameters for the in-situ rock materials can be estimated by extrapolating the correction method of Miura et al. (1985).

6.3.3 SIMULATION OF KAMI-HIKAWA DAM DURING CONSTRUCTION

The deformation behaviour of Kami-Hika Dam

The deformation and stresses of Kami-Hikawa Dam during construction are simulated by using a soil/water coupled FEM. A finite element model is prepared for

the typical cross section shown in Fig. 6.3.2. The finite element model and boundary conditions for the major measurement section of Kami-hikawa Dam are shown in Fig. 6.3.8. The embankment elements are added according to the actual construction sequence. The elasto-plastic model, which is used in Fig. 6.3.5, is adopted as the constitutive equation for the fill materials. Constitutive parameters are determined based on the results of field quality control tests (void ratio and water content) and the laboratory tests. The parameters of the rock zone are estimated in the same way as in Fig. 6.3.7 using the average grain size (D50) of in-situ rock materials and laboratory specimens. The comparison of measured and calculated settlements during construction is shown in Fig. 6.3.9. Monitored depth-wise distributions of settlement and their changes with time in the core and rock zones are in good agreement with the computer simulation. In figures for the rock zone, the results computed using the parameters obtained from laboratory tests without applying the grain size correction are also plotted for

Figure 6.3.9 Comparison of measured and calculated settlements of dam embankment during construction (Kami-Hikawa Dam)

Core zoneFilter zone

Rock zone

Undrained condition and fixed edge

Hydrostatic pressure and vertical roller

0

500

1000

1500

95/7/20 96/5/15 97/3/11

calculated

measuredＣ

0

500

1000

1500measured

Ｂ

1400

1450

1500

calculated

0

500

1000

1500measured

Ａ calculated

Ｃ

ＢＡ

0 500 1000 1500

settlement（mm）

Downstream rock

calculated①

calculated② measured

Ｃ

Ｂ

Ａ

0 500 1000 1500

settlement（mm）

measured

Core

calculated①

Ｃ

Ｂ

Ａ

0 500 1000 1500

settlement（mm）

Upstream rock

calculated①

calculated②

measured

1390

1410

1430

1450

1470

1490

E.L. (m)

　 measured 　 calculated① （correctedλ）　 calculated② （laboratoryλ）

elevation of

embankment (m)

settlement (mm)

0

500

1000

1500calculated① measured

calculated②

Ａ

0

500

1000

1500

95/7/20 96/5/15 97/3/11

calculated①

measured

Ｃ

calculated②

0

500

1000

1500calculated①

measured

calculated②

Ｂ

1400

1450

1500

0

500

1000

1500 calculated① measured

Ｂ

calculated②

0

500

1000

1500

95/7/20 96/5/15 97/3/11

calculated① measured

Ｃ

calculated②

0

500

1000


Ａ

calculated②

1400

1450

1500

0

500

1000

1500

95/7/20 96/5/15 97/3/11

calculated

measuredＣ

0

500

1000

1500measured

Ｂ

1400

1450

1500

calculated

0

500

1000

1500measured

Ａ calculated

Ｃ

ＢＡ

0 500 1000 1500

settlement（mm）

Downstream rock

calculated①

calculated② measured

Ｃ

Ｂ

Ａ

0 500 1000 1500

settlement（mm）

measured

Core

calculated①

Ｃ

Ｂ

Ａ

0 500 1000 1500

settlement（mm）

Upstream rock

calculated①

calculated②

measured

1390

1410

1430

1450

1470

1490

E.L. (m)

　 measured 　 calculated① （correctedλ）　 calculated② （laboratoryλ）

elevation of

embankment (m)

settlement (mm)

0

500

1000


calculated②

Ａ

0

500

1000

1500

95/7/20 96/5/15 97/3/11

calculated①

measured

Ｃ

calculated②

0

500

1000

1500calculated①

measured

calculated②

Ｂ

1400

1450

1500

0

500

1000

1500 calculated① measured

Ｂ

calculated②

0

500

1000

1500

95/7/20 96/5/15 97/3/11

calculated① measured

Ｃ

calculated②

0

500

1000


Ａ

calculated②

1400

1450

1500

Figure 6.3.8 Analytical and boundary conditon

6-13

reference. In this case, the calculated settlements are considerably smaller than the actual monitored values. This indicates that grain size correction is essentially needed for rock materials. The stress behaviour of Kami-Hika Dam

The comparisons between calculated and monitored values of pore-water pressure in the core zone and the earth pressures in the dam embankment are shown in Fig. 6.3.10. The figure shows that the analysis can well simulate the actual consolidation process in the core zone, in which the generation of pore-water pressures during construction and their dissipation during the winter interruption of execution are cyclically repeated. The analysis successfully simulate the tendency of earth pressures measured in the dam embankment, i.e. the increase in earth pressures during construction and the concentration of earth pressures on the filter zone. These results indicate that the modelling methods for the fill materials are reasonable and that the procedure to determine the constitutive parameters employed in this study is also reasonable as well.

6.3.4 CONCLUSION

Large dams, which are exposed to high overburden pressures, could be subjected to plastic deformation due to crushing of rock particles at contact points and ensued rearrangement of rock particles, caused by the considerably high stresses at the contact points. The specimens of laboratory tests, eliminating large particles, increases the number of contact points between rock particles, resulting in the inter-particle stresses at the contact points much smaller than in-situ

condition. This is the reason why the compressibility obtained from the laboratory tests is smaller than that measured in the actual dam embankment. The practical way of determining parameters of the rock zone using the average grain size (D50) of in-situ rock materials is presented by Authors. The comparison of measured and calculated settlements adopting this method shows that the grain size correction is quite satisfactory.

A B C

EL=1460m

0

200

400

600

800

overburden

pressure

σv (kPa)

core zonemeasured

Acalculated

0200400

600800

overburden

pressure

σv (kPa)

filter zonemeasured

B

calculated

0

200

400

600

800

1996/5/15 1996/8/23 1996/12/1 1997/3/11 1997/6/19overburden

pressure

σv (kPa)

rock zone

C

measuredcalculated

1400

1420

1440

1460

1480

1500

elevation of

embankment (m)

0

100

200

300

400

500

pore water

pressure U (kPa)

calculated

measuredP271996.9.12

0

100

200

300

400

500

1995/4/11 1995/8/29 1996/1/16 1996/6/4 1996/10/22 1997/3/11

pore water

pressure U (kPa)

P18 1996.9.12

measured

calculated

0

100

200

300

400

500

pore water

pressure U (kPa)

P30

1996.9.12

measuredcalculated

contoir of pore water pressure(1996.9.12)

0

200

400

600

800

1000

0 10 20 30distance from the center of core zone (m)

overburden

pressureσv(kPa)

●： measured （at completion of construction）

corefinefilter

coarsefilter

AB

C

rock

calculated（at completion of construction）

A B C

EL=1460m

0

200

400

600

800

overburden

pressure

σv (kPa)

core zonemeasured

Acalculated

0200400

600800

overburden

pressure

σv (kPa)

filter zonemeasured

B

calculated

0

200

400

600

800

1996/5/15 1996/8/23 1996/12/1 1997/3/11 1997/6/19overburden

pressure

σv (kPa)

rock zone

C

measuredcalculated

1400

1420

1440

1460

1480

1500

elevation of

embankment (m)

0

100

200

300

400

500

pore water

pressure U (kPa)

calculated

measuredP271996.9.12

0

100

200

300

400

500

1995/4/11 1995/8/29 1996/1/16 1996/6/4 1996/10/22 1997/3/11

pore water

pressure U (kPa)

P18 1996.9.12

measured

calculated

0

100

200

300

400

500

1995/4/11 1995/8/29 1996/1/16 1996/6/4 1996/10/22 1997/3/11

pore water

pressure U (kPa)

P18 1996.9.12

measured

calculated

0

100

200

300

400

500

pore water

pressure U (kPa)

P30

1996.9.12

measuredcalculated

0

100

200

300

400

500

pore water

pressure U (kPa)

P30

1996.9.12

measuredcalculated

contoir of pore water pressure(1996.9.12)

0

200

400

600

800

1000

0 10 20 30distance from the center of core zone (m)

overburden

pressureσv(kPa)

●： measured （at completion of construction）

corefinefilter

coarsefilter

AB

C

rock

calculated（at completion of construction）

Figure 6.3.10 Comparison of measured and calculated pore water pressures and earth pressures during construction (Kami-Hikawa Dam)

(a) pore water pressures (b) vertical earthe pressures

6-14

6.4 ANALYTICAL ESTIMATION OF SEABED DEFORMATION IN METHANE HYDRATE PRODUCTION

6.4.1 INTRODUCTION Methane hydrate is currently being eagerly examined as a next-generation energy resource in Japan to replace oil and natural gas. The Research Consortium for Methane Hydrate Resources in Japan was established to undertake research in accordance with “Japan’s Methane Hydrate Exploitation Program” prepared by the Ministry of Economy, Trade and Industry. In this Consortium the Engineering Advancement Association of Japan is doing research on Environment Impact. In the Research Group for Environment Impact we are investigating if the deformation of seabed ground occurs in production of methane gas from methane hydrate. Methane hydrate is dissociated by heating or reduction of pressure etc. So the volume change or pressure change occurs in the methane hydrate layer. And then it is possible that such change of the methane hydrate layer has an effect on the above seabed ground and the deformation of the seabed ground occurs. So in this study the analyses by finite element method were performed in order to grasp the effect of various parameters, for example, depth of ground, soil property, mechanical constants etc. on the deformation of the seabed ground. 6.4.2 ANALYTICAL METHOD In analyses the region of analysis includes from surface of seabed to upper surface of methane hydrate layer and the change of methane hydrate layer is modeled as the displacement on the upper surface of methane hydrate layer, that is on the bottom of the region of analysis. The constitutive law of ground used in analyses is elasto-perfect plastic model and axisymmetric condition is assumed. 6.4.3 ANALYTICAL CONDITION Parameters The parameters considered in analyses were composition of ground, depth of ground, kind of soil, coefficient of strength, magnitude of applied displacement and width of applied displacement. Its outline is shown in Fig. 6.4.1. In setting up the parameters Nankai Trough was kept in mind as an assumed ground and the typical values of data obtained in MITI Nankai Trough Well (Tezuka, Miyairi, Uchida and Akihisa, 2002; Hato and Inamori, 2002) were set as the standard values. The value of each parameter is indicated as following. (1) Composition of Ground Two kind of ground were assumed. One is a one layer ground. Another is a two layer ground. And two cases

were assumed as a two layer ground. Those are the case that upper layer is sandy soil, lower layer is cohesive soil and the case that upper layer is cohesive soil, lower layer is sandy soil. (2) Depth of Ground A seafloor exists about 945 meters under the sea surface and an upper surface of methane hydrate layer exists about 1153 meter under the sea surface in Nankai Trough. Therefore a depth of ground from seafloor to upper surface of methane hydrate layer is about 200 meter. So a standard value of depth of ground was set up 200 meter and three values were assumed as following. Small : 100 m, Standard : 200 m, Large : 400 m (3) Coefficient of Strength The soil property of seabed ground at Nankai Trough is classified a sand containing fine grain (Nishio, Ogisako and Denda, 2003). So coefficients of strength were set as following assuming average values of sand and normally consolidated clay. Sandy soil : Cohesion c’=0 Angle of internal friction φ’ = 30 degree (Small), 38 degree (Standard), 45 degree (Large) Cohesive soil : Cohesion c’ = 0 Angle of internal friction φ’ = 25 degree (Small), 30 degree (Standard), 35 degree (Large) (4) Elastic Modulus Elastic modulus was also set as following assuming average values of sand and normally consolidated clay. Sandy soil : 100 MPa (Small), 300 MPa (Standard), 600 MPa (Large) Cohesive soil : 10 MPa (Small), 500 MPa (Standard), 100 MPa (Large) (5) Magnitude of Applied Displacement The total depth of methane hydrate layer is about 16 meter, porosity ratio of methane hydrate layer is about 40 percent and methane hydrate saturation ratio in pore is maximum 80 percent in Nankai Trough. So, maximum compression after dissociation of methane hydrate is calculated as following. It is about 1 meter.

Compression = depth of layer (16 m) × porosity ratio (0.4) × methane hydrate saturation ratio (0.8) × volume decrease ratio after dissociation (0.2) = 1 m

Therefore magnitude of applied displacement was set as following. Small : 0.5 m, Standard : 1 m, Large : 2 m (6) Width of Applied Displacement The size of production area is not made clear at this stage. So width of applied displacement was assumed as following. Small : 50 m, Standard : 100 m, Large : 200 m

6-15

(7)Others The others were assumed as following. Poisson’s ratio : 0.3 Unit weight in water : Sandy soil : 9 kN/m3, Cohesive soil : 8 kN/m3

Analysis Case 24 cases indicated in Table 6.4.1 were investigated on the basis of parameters abovementioned. Analysis Model An example of analysis model is shown in Fig. 6.4.2. The left side in this figure indicates a center of axisymmetric model. An area in vertical direction is

Width of Displacement : B

Depth of Ground : H(Region of Analysis)

Surface of Seabed

Upper Surface of Methane Hydrate Layer

Magnitude of Displacement : δ

Seabed Ground

Coefficients of Strength : c', φ'

Elastic Modulus : E

Methane Hydrate Layer

No. Composition

of Ground

Depth ofGroundH(m)

Kind of SoilAngle of

Internal Frictionφ'（°）

ElasticModulusE(MPa)

Magnitude ofApplied

Displacementδ(m)

Width ofApplied

DisplacementB(m)

1 Sandy Soil 38 300 1 1002 Cohesive Soil 30 50 1 1003 45 300 1 1004 600 1 1005 2 1006 2007 1008 509 0.5 10010 100 1 10011 30 300 1 10012 35 50 1 10013 100 1 10014 2 10015 20016 10017 5018 0.5 10019 10 1 10020 25 50 1 10021 Sandy Soil 38 300 1 10022 Cohesive Soil 30 50 1 100

23 Upper : Sandy Soil Lower : Cohesive Soil

3830

30050 1 100

24 Upper : Cohesive Soil Lower : Sandy Soil

3038

50300 1 100

2002 Layer

400

200

100

1 Layer

38

30

Sandy Soil

Cohesive Soil

1

1

300

50

Table 6.4.1. Cases of analyses

Figure 6.4.1. Parameters considered in analyses

6-16

from sea floor to upper surface of methane hydrate layer. An area in lateral direction is from a center of model to lateral boundary which locates at distance four times as long as depth of ground. As boundary condition a side is assumed to be free in vertical direction, fixed in lateral direction. And a bottom which displacement is not applied is assumed to be fixed in vertical direction, free in lateral direction and a bottom which displacement is applied is assumed to be displaced in vertical direction, fixed in lateral direction. 6.4.3 RESULTS OF ANALYSES AND DISCUSSION Case of One Layer (1)Effect of Width of Applied Displacement Fig. 6.4.3 shows the relationship between width of applied displacement and settlement of seabed surface. The contours of vertical displacement and region of plasticity in the case that the width of applied displacement is 200 m, 100 m and 50 m respectively in sandy soil are shown in Fig. 6.4.4 and Fig. 6.4.5. A magnitude of displacement and region which displacement occurs become larger as width of applied displacement becomes larger as seen in Fig. 6.4.4. And this tendency is almost same in both of sandy soil and cohesive soil as seen in Fig. 6.4.3. However an increase of settlement corresponding to an increase of width of applied displacement is almost linear in cohesive soil, on the other hand is quadratic in sandy soil. Therefore it is supposed that the effect of width of applied displacement on settlement is more remarkable in sandy soil. The reason seems that the region of plasticity expands as width of applied displacement becomes larger and then elastic modulus is reduced in sandy soil as seen in Fig. 6.4.5. (2)Effect of Magnitude of Applied Displacement Fig. 6.4.6 shows the relationship between magnitude of applied displacement and settlement of seabed surface. A magnitude of settlement increases linearly as magnitude of applied displacement becomes larger in both of sandy soil and cohesive soil. But in sandy soil its rate of increase is small, on the other hand in cohesive soil it is large. (3)Effect of Depth of Ground Fig. 6.4.7 shows the relationship between depth of

ground and settlement of seabed surface. A magnitude of settlement decreases as depth of ground becomes larger. A decrease of settlement corresponding to an increase of depth of ground is almost quadratic in both of sandy soil and cohesive soil. But the rate of decrease in cohesive soil is larger than that in sandy soil. And settlement in cohesive soil is about twice as large as that in sandy soil in the cases of H = 100 m and H = 200 m but both is almost equal in the case of H = 400 m. So it is supposed that difference of settlement between sandy soil and cohesive soil becomes smaller as depth of ground becomes larger.

X

0. 50. 100. 150. 200. 250. 300. 350. 400. 450. 500. 550. 600. 650. 700. 750. 800.

Y

0.

50.

100.

150.

200.

(m)

(m)

Figure 6.4.2. Analysis model

0

10

20

30

40

50

60

0 50 100 150 200 250

Sandy soilCohesive soil

Width of Applied Displacement B (m)Se

ttlem

ent o

f Sea

bed

Surf

ace

(cm

)

Figure 6.4.3.Relationship between width of applied displacement and settlement of seabed surface

(m)

X

0. 50. 100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.

Y

0.

50.

100.

150.

200.

0.-0.05-0.1

-0.15-0.2

-0.25-0.3

-0.35-0.4

-0.45-0.5

-0.55-0.6

-0.65-0.7

-0.75-0.8

-0.85-0.9

-0.95-1.

X

0. 50. 100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.

Y

0.

50.

100.

150.

200.

X

0. 50. 100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.

Y

0.

50.

100.

150.

200.

(1) B=200m

(3) B=50m

(2) B=100m

Figure 6.4.4. Contours of vertical displacement in the case of sandy soil

6-17

(4)Effect of Elastic Modulus Fig. 6.4.8 shows the relationship between elastic modulus and settlement of seabed surface. There is some different tendency between sandy soil and cohesive soil in a change of settlement corresponding to a change of elastic modulus. In the case of sandy soil a magnitude of settlement decreases as elastic modulus becomes larger. On the other hand, in the case of

cohesive soil a magnitude of settlement almost levels off although elastic modulus becomes larger and a change of settlement for a change of elastic modulus is small. (5)Effect of Coefficient of Strength Fig. 6.4.9 shows the relationship between angle of internal friction and settlement of seabed surface. A magnitude of settlement decreases as angle of internal friction becomes larger in both of sandy soil and cohesive soil. The rate of decrease is also similar in both cases. Comparison between One Layer Ground and Two Layer Ground The result of comparison between one layer ground and two layer ground on settlement of seabed surface is shown in Table 6.4.2 to investigate effect of composition of ground. The settlement of two layer ground exists between settlement of one layer sandy soil ground and one layer cohesive soil ground and is

X

0. 50. 100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.

Y

0.

50.

100.

150.

200.

X

0. 50. 100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.

Y

0.

50.

100.

150.

200.

X

0. 50. 100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.

Y

0.

50.

100.

150.

200.

(1) B=200m

(3) B=50m

(2) B=100m

Elastic

Plastic

Figure 6.4.5 Region of plasticity in the case of sandy soil

0

10

20

30

40

50

60

0.0 0.5 1.0 1.5 2.0 2.5


Magnitude of Applied Displacement δ (m)

Settl

emen

t of S

eabe

d Su

rfac

e (c

m)

Figure 6.4.6 relationship between magnitude of applied displacement and settlement of seabed surface

0

10

20

30

40

50

60

50 100 150 200 250 300 350 400 450


Depth of Ground H (m)

Settl

emen

t of S

eabe

d Su

rfac

e (c

m)

Figure 6.4.7 Relationship between depth of ground and settlement of seabed surface

0

10

20

30

40

50

60

0 100 200 300 400 500 600 700

Sandy soil

Elastic Modulus E (MPa)

Settl

emen

t of S

eabe

d Su

rfac

e (c

m)

10

20

30

40

50

60

0 20 40 60 80 100 120

Cohesive soil

Settl

emen

t of S

eabe

d Su

rfac

e (c

m)

Elastic Modulus E (MPa)

Figure 6.4.8 Relationship between elastic modulus and settlement of seabed surface

0

10

20

30

40

50

60

20 25 30 35 40 45 50


Angle of Internal Friction φ' (degree)

Settl

emen

t of S

eabe

d Su

rfac

e (c

m)

Figure 6.4.9 Relationship between angle of internal friction and settlement of seabed surface

6-18

close to settlement of one layer sandy soil ground. And there is hardly any difference between the case that upper layer is sandy soil, lower layer is cohesive soil and the case that upper layer is cohesive soil, lower layer is sandy soil. Settlement is similar in both cases. 6.4.4 CONCLUSIONS The analyses to estimate the deformation of seabed ground in production of methane gas from methane hydrate layer were performed and the effect of various parameters on the deformation of the seabed ground were investigated. From the results of analyses the following are summarized. (1) A magnitude of displacement which occurs in seabed ground is larger as width of applied displacement becomes larger in both of sandy soil and cohesive soil. (2) A magnitude of settlement at seabed surface increases linearly as magnitude of applied displacement becomes larger in both of sandy soil and cohesive soil. But in sandy soil its rate of increase is small, on the other hand in cohesive soil it is large. (3) A magnitude of settlement at seabed surface decreases as depth of ground becomes larger. The rate of decrease in cohesive soil is larger than that in sandy soil. (4) A magnitude of settlement at seabed surface decreases in sandy soil but almost levels off in cohesive soil as elastic modulus of ground becomes larger. (5) A magnitude of settlement at seabed surface decreases as coefficient of strength of ground becomes larger in both of sandy soil and cohesive soil.

6.5 EFFECT OF SOIL COMPRESSIBILITY AND CRUSHABILITY ON MONOTONIC AND CYCLIC UNDRAINED SHEAR STRENGTH OF SOILS

6.5.1 INTRODUCTION In 1995 during the great Hanshin earthquake serious damage occurred to port and harbour facilities and coastal defences in areas such as the Kobe Port Island and Rokko Island. Both of these land areas were reclaimed from the sea using a local decomposed granite soil, Masado as a fill material. Masado is a residual granite soil widely distributed in the western part of Japan and is regarded as a high quality fill material. Since the Niigata earthquake liquefaction studies have concentrated on hard grained sands found in coastal and estuarine areas. However in many cities and industrial areas decomposed granite soils have been used as fill materials and now it seems they could be problematical under earthquake conditions.

Failure of volcanic soils due to earthquakes is common in Japan (Ishihara and Harada, 1996; Miura and Yagi, 1995) and in particular failures are known to have occured in Shirasu which is commonly found in large areas of Southern Kyushu (Yamanouchi, 1968). This material is also often used as a fill (Umehara et al, 1975). Both of the above mentioned soils are crushable materials and it is important to extend the scope of liquefaction research to study the characteristics of crushable soils.

Previously crushable soils have been shown to give unusually low pile bearing capacities and when problems occurred with offshore piled foundations in the 1980's many research programmes commenced to investigate the properties of crushable carbonate sands including their behaviour under cyclic loads (Golightly and Hyde, 1988; Houlsby et. al, 1988; Semple, 1988; Coop 1990).

The authors have conducted monotonic and cyclic triaxial tests on three types of crushable soil: carbonate sand (Hyodo, Hyde and Konami, 1994; Hyodo et al., 1996), Masado and Shirasu. The test results have been compared with those for a less crushable standard silica sand, Toyoura sand. The effect of both confining pressure and relative density on the shearing properties of these soils has been considered. The research presented here was performed in order to understand the effect of soil compressibility and crushability on the monotonic and cyclic undrained shear strength of soils. In addition an attempt has been made to relate monotonic and cyclic shear strengths. 6.5.2 MATERIALS AND EXPERIMENTAL

METHODS Physical Properties of Materials In this study three crushable soils Masado, Shirasu and Dogs Bay sand were used to investigate the correlation

between shearing properties and other mechanical characteristics. The Masado soil was taken from two locations, an area east of Hiroshima and Ube. They are both geologically similar, being weathered granite from the Hiroshima facies and they are referred to here

Grain size (mm)

Per

cen

t fi

ner

by

wei

ght

(%

)

0.001 0.01 0.1 1.0 100

20

40

60

80

100Dog's BayCarbonate sand

Toyoura sand

Shirasu

UbeMasado

Hiroshima Masado

Fig.6.5.1 Particle size distribution curnes Table 6.5.1 Physical properties of materials Gs emax emin Uc Li;(%)Ube Masado 2.615 1.243 0.728 4.772 2.690 Hiroshima Masado 2.610 1.394 0.784 5.819 3.731 Shirasu 2.489 1.494 0.775 29.50 － Dog’s Bay sand 2.723 2.451 1.621 1.92 － Toyoura sand 2.643 0.973 0.635 1.200 － as Ube Masado and Hiroshima Masado. The Shirasu, a volcanic soil, was sampled from a weathered deposit at Airagun in Kagoshima prefecture. Dogs Bay sand is a shelly algal sand sampled from a beach deposit on the west coast of Ireland (Golightly and Hyde 1988). Finally for comparison purposes Toyoura Japanese standard sand was also tested.

The particle size distributions are shown in Fig 6.5.1. The coefficient of uniformity (Table 6.5.1) for both the Masado soils and Shirasu is greater than for the Dogs bay and Toyoura sand. The fines content of the Shirasu (<074 mm) was about 35% but was non-plastic, containing the same minerals as the parent material (Okabayashi et al., 1994, Hyodo et al. 1980). Particles larger than 2 mm were removed. The Masado on the other hand was washed and passed through a 2 mm sieve, thus having a particle size range 0.074 - 2 mm.

The physical properties for each soil are shown in Table 6.5.1. The specific gravity of the individual pumice grains of Shirasu is very low due to intraparticle occluded voids. The maximum and minimum void ratios for both the Masado soils and Shirasu was greater than that for Toyoura sand. This was particularly so for the maximum void ratio. Masado has various degrees of weathering leading to a variation in mechanical properties. The degree of weathering can be shown by the ignition loss Li% in Table 6.5.1 which increases with the degree of weathering (Murata et al. 1987). On this basis the Hiroshima Masado is more weathered than the Ube Masado.

6-19

Experimental Methods All the triaxial specimen were 50 mm in diameter and 110 mm height. The initial void ratios of the Masado, Shirasu and Toyoura sand were in the range 0.8 to 1.15 (Fig. 6.5.2). However, the Dogs Bay sand had much higher initial void ratio (>1.9) because of the combined effects of the materials angularity and intraparticle voids.

Masado specimens were air pluviated from the same height producing an initial relative density Dri of 60 % for Hiroshima Masado and 50 % for Ube Masado. However because Shirasu has a high fines content and varying specific gravity of individual grains neither air nor water pluviation was used. Instead the required mass of material was weighed out and a loose sample was prepared by gently rodding the material into the mould. Following this the required relative density was achieved by tapping the mould until the volume had reduced to the required value. Two relative densities of 50% (loose) and 90% (dense) were tested for this material. In order to produce full saturation, the samples which had been prepared under dry conditions were first flooded with CO2 gas which was then displaced by de-aired water and a back pressure of 100kPa was applied to produce a B value greater than 0.96.

The samples of Dogs Bay carbonate sand required a rigorous de-airing process because of the intraparticle voids. In this case therefore samples were saturated with de-aired water and kept under a vacuum for 24 hours to eliminate air. Following this the triaxial cell base was de-aired and the mould filled with de-aired water. The sample was then carefully spooned into the mould and tapped to a pre-determined height to achieve a given relative density. Dogs bay sand was tested at relative densities of 60 % and 80 %.

After the application of the required cell pressure, monotonic and cyclic undrained triaxial tests were performed. Monotonic triaxial tests were performed in both compression and extension under constant cell pressure conditions and an axial strain rate of 0.1 % per minute. Cyclic tests were performed under stress controlled conditions with a sinusoidal load being applied by a pneumatic actuator at a frequency of 0.1Hz. Polished stainless steel end platens with a diameter of 60 mm together with silicone grease and a membrane were used to reduce end friction. The top and bottom platens each had a 5 mm diameter porous stone at the centre for drainage and pore water pressure measurement. 6.5.3 ISOTROPIC COMPRESSION CHARACTERISTICS The results for drained isotropic compression tests carried out on each of the sands are shown in Fig. 6.5.2 as continuous lines. Superimposed on these lines are the points representing the initial states of the samples tested under undrained monotonic triaxial shearing conditions, In the case of the Dogs Bay sand at a

0.01 0.1 1.0 100.6

0.7

0.8

0.9

1.0

1.1

1.7～～

1.8

1.9

2.0Dog's Bay sand(Dri=60%)

(Dri=80%)

Shirasu (Dri=50%)

Masado

(Dri=95%)Shirasu

(Dri=90%)

Vo

id r

ati

o e

M e a n e f f e c t i v e p r i n c i p a l s t r e s s p ' ( M P a )

: Ube Masado (Dri=50%): Hiroshima Masado (Dri=60%): Shirasu (Dri=50%): Shirasu (Dri=90%): Dog's Bay Carbonate sand (Dri=60%): Dog's Bay Carbonate sand (Dri=80%)

Fig.6.5.2 Triaxial monotonic test sample initial states relative to isotropic compression lines relative density Dri = 80 % and Shirasu at Dr. = 90 % there were no drained isotropic compression data, and dashed lines have been drawn through the data for the initial states of the undrained test samples. The isotropic compression data for each of the Masado sands were very similar and an average line was drawn for the two materials. For the stress range used in the triaxial tests it can be seen that the Toyoura sand, even when loose (Dri = 40 %), is relatively incompressible and the curved portion of the compression line lies well to the right of the crushable soils. This suggests one reason why in previous studies, such as those by lshihara et al. (1983) and Yunoki et al．（1982），the nomalized liquefaction resistance σd／2σc’ of Toyoura sand was not apparently affected by the confining pressure. 6.5.4 UNDRAINED MONOTONIC SHEAR PROPERTIES Undrained monotonic compression and extension tests were performed at various cell pressures. The cell pressures used were: 50 and 100 kPa for Hiroshima Masado; 50, 100, 200 kPa for Ube Masado; 50, 100, 300 kPa for loose and dense Shirasu; and 100, 300, 500kPa for Dogs Bay sand.

The initial consolidation stress σc’ is frequently used as a normalizing parameter in liquefaction studies (Ishihara, 1994). Therefore, in order to clarify the effect of this parameter on sample behaviour the deviator stress was normalised with respect to the effective consolidation pressure σc'. These typical normalised relationships are shown in figures 6.5.3 and 6.5.4 for Shirasu. For all the strain hardening materials, the normalisation process tended to bring the phase transformation points closer together, particularly with

6-20

Axial strain εa (%)

Dev

iato

r st

ress

rat

io

q/σ

c’

S h i r a s u ( L o o s e )

P h a s et ra n s f o r m a t i o np o i n t s( C o m p re s s i o n )

P h a s et r a n s f o rm a t i o np o i n t s ( E x t e n s i o n )

-18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2Dri=50%

σc’ (kPa): 50: 100: 300

Effective mean principal stress ratio p'/σc'

Dev

iato

r st

ress

rat

io

q/σ

c’

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

Dri=50%σc’ (kPa)

: 50: 100: 300


P T L

P T L

Fig.6.5.3 (a) Normalized Stress-strain curves and (b) normalized effective stress paths for Shirasu (loose) respect to the deviator stress ratio, suggesting that for these the effective consolidation pressure is a major determinant of the phase transformation strength. The exception to this was the loose Shirasu with marked strain softening behaviour at the lower confining pressures. In this case, although the phase transformation stress ratio q/p' remained constant, there was considerable variation in the normalized phase transformation strength. Comparison of the phase transformation stess ratios q/p' for the loose and dense Shirasu and the dense suggests that this ratio is independent of relative density and that the phase transformation stress ratio q/p' is constant for a given soil.Figures 6.5.3 and 6.5.4 show the behaviour for loose and dense Shirasu. At a low confining pressure the loose material demonstrates highly contractive behaviour with considerable strain softening after the peak deviator stress. This changes to more dilative and hardening behaviour as the effective consolidation pressure σc' increases. This is the opposite of normally

-20 -15 -10 -5 0 5 10 15 20-5

0

5

10

15

20

25


Dev

iato

r st

ress

rat

io

q/σ

c’

S h i r a s u ( D e n s e )

P h a s et ra n s f o r m a t i o np o i n t s

Dri=90%σc’(kPa)

: 50: 100: 300

(a)

0 2 4 6 8 10 12-5

0

5

10

15

20

25

Effective mean principal stress ratio p/σc’

Dev

iato

r st

ress

rat

io

q/σ

c’


P T L

P T L

Dri=90%

σc’(kPa): 50: 100: 300

Fig. 6.5.4 (a) Normalized Stress-strain curves and (b) normalized effective stress paths for Shirasu (dense)

(b) (b)

expected behaviour for sands. It can also be seen that the normalised deviator stress ratio for phase transformation and steady state points increased with increasing cell pressure.In Fig. 6.5.4 for dense Shirasu the deviator stress ratio at the phase transformation was the same but the steady state deviator stress ratio decreased with increasing confining pressure. This is the opposite of the behaviour for the loose Shirasu and the directions of the trends are the same as for the Masado and Dogs Bay sand. As the relative density for Shirasu was increased from 50 % to 90 % the strength increased by an order of magnitude and the material became extremely dilatant in behaviour. 6.5.5UNDRAINED CYCLIC SHEAR

CHARACTERISTICS

(a) Undrained cyclic shear tests were performed on Masado, Shirasu and Dogs Bay at the same confining pressures as for the monotonic tests. Figs. 6.5.5 and 6.5.6 show typical cyclic stress strain plots for Shirasu tested at100 kPa. For the purposes of this paper two

6-21

-20 -15 -10 -5 0 5 10 15 20-40

-30

-20

-10

0

10

20

30

40


Dev

iato

r st

ress

q (

kPa)


Dri=51.7%

f=0.1Hz

σc’=100kPa

σd/2σc’=0.134

0 20 40 60 80 100 12-40

-30

-20

-10

0

10

20

30

40

0

Effective mean principal stress p (kPa)

Dev

iato

r st

ress

q (

kPa)

S h i r a s u ( L o o s e )P T L

P T L

Dri=51.7%f=0.1Hz

σc’=100kPa

σd/2σc’=0.134

Fig.6.5.5 (a) Typical cyclic stress-strain curves and (b) cyclic effective stress paths for Shirasu (loose) kinds of cyclic end conditions are defined. The first is liquefaction, where the effective mean principal stress cycles through zero and axial strains accelerate to failure (eg. Fig. 6.5.5(a), (b)). The second is cyclic mobility, where the stress path cycles through or close to zero p' conditions but the cyclic axial strain increases at a steady rate to large values (eg. Fig. 6.5.6 (a), (b)). Liquefaction was observed to occur for the Masado, loose Shirasu and loose Dogs Bay sand, while the other materials demonstrated cyclic mobility.

In Figure 6.5.5 for the loose Shirasu, once again large axial strains only developed after the phase transformation point was reached. In this case however, large symmetrical strains developed very rapidly. Compared with Masado, the initial state condition for this material is situated further to the right of the steady state line leading to the expectation of more marked flow deformation behaviour under cyclic loading. The dense Shirasu whose initial states were to the left of the steady state, developed an assymetric cyclic mobility with large extension strains (Fig. 6.5.6 (a)). Similar behaviour was also observed for the Dogs Bay carbonate sand, with the loose material undergoing liquefaction and the dense achieving a state of cyclic mobility. In this case, both loose and dense developed

-9 -6 -3 0 3 6 9-60

-40

-20

0

20

40

60


Dev

iato

r st

ress

q (

kPa)


Dri=89.7%

f=0.1Hz

σc’=100kPa

σd/2σc’=0.182

(a) (a)

0 20 40 60 80 100 120-60

-40

-20

0

20

40

60

Effective mean principal stress p' (kPa)

Dev

iato

r st

ress

q (

kPa)

S h i r a s u ( D e n s e )P T L

P T L

Dri=89.7%

f=0.1Hz

σc’=100kPa

σd/2σc’=0.182

Fig.6.5.6 (a) Typical cyclic stress-strain curves and (b) cyclic effective stress paths for Shirasu (dense)

(b) (b)

assymetric behaviour with larger extension strains. It was observed that the initial states for the loose material crossed the steady state line while the dense states were to the left of this line.

For hard grained silica sands an initial state to the right of the steady state line representing a very loose sand would be quite unusual. However for crushable soils which are often also angular this kind of initial state is easily achieved. The corresponding stress paths for each of the materials are shown in Figs. 6.5.5 and 6.5.6 (b). Figs. 6.5.5 (b) for Masado and loose Shirasu show the development of liquefaction for these materials after very few cycles when the effective confining pressure becomes zero. On the other hand dense Shirasu exhibits typical cyclic mobility behaviour where the mean principal effective stress does not quite become zero.

Examination of Fig. 6.5.5 show that as p' loop decreases. On the other hand in Fig. 6.5.6 it can be seen that during the final cyclic mobility phase of the behaviour a residual p' remains and hence the slope of the cyclic stress strain curves although decreasing slightly remains at a higher value.

Researchers have traditionally defined liquefaction failure as a double amplitude strain DA = 5% (Ishihara,

6-22

Cyc

lic

dev

iato

r st

ress

rat

io σ

d/2σ

c’

Number of cycles N0.1 1 10 100 1000

Dri=50%

Dri=70%

Masado

Dri=90%

Toyoura sand

0

0.1

0.2

0.3

0.4

0.5 Ube Masado

HiroshimaMasado

Dri=50% Dri=60%σc’ (kPa) σc’ (kPa)

: 50 : 50: 100 : 100 : 200

Fig.6.5.7 Cyclic strength curves for double-strain amplitude DA=5%, for Masado

Cyc

lic

dev

iato

r st

ress

rat

io σ

d/2σ

c’


Dri=50%

Dri=70%

Dri=90%Toyoura sand

Shirasuσc’(kPa)50 100 300

0

0.1

0.2

0.3

0.4

0.5Shirasu

Dri=50%σc’ (kPa)

: 50: 100 : 300

Fig.6.5.8 Cyclic strength curves for double-strain amplitude DA=5%, for Shirasu (loose)

Cyc

lic

dev

iato

r st

ress

rat

io σ

d/2σ

c’


Dri=50%

Dri=70%Dri=90%

Toyoura sandShirasuσc’(kPa)50

100 300

0

0.1

0.2

0.3

0.4

0.5

ShirasuDri=90%

σc’ (kPa): 50: 100 : 300

Fig.6.5.9 Cyclic strength curves for double-strain amplitude DA=5%, for Shirasu (dense)

Cyc

lic

dev

iato

r st

ress

rat

io σ

d/2σ

c’


0

0.1

0.2

0.3

0.4

0.5

Dog's BayCarbonatesandσc’(kPa)

300500

100

Toyoura sandDri=90%

Dri=70%Toyoura sand Dri=50%

Dog's BayCarbonatesand

Dri=60%DA=5%σc’ (kPa)

: 100: 300: 500

Fig.6.5.10 Cyclic strength curves for double-strain amplitude DA=5%, for Dogs Bay sand (loose) 1994). This definition allows the inclusion of both cyclic mobility (Fig. 6.5.6) and classical liquefaction failures (Fig. 6.5.5). Cyclic strength is defined as the normalised cyclic deviator stress σd/2σc' required to cause failure after a given number of cycles.

Cyc

lic

dev

iato

r st

ress

rat

io σ

d/2σ

c’



σc’(kPa)100300500

Toyoura sand Dri=50%Dri=70%

Dri=90%

0

0.1

0.2

0.3

0.4

0.5


Dri=80%DA=5%σc’(kPa)

: 100: 300: 500

Fig. 6.5.11 Cyclic strength curves for double-strain amplitude DA=5%, for Dogs Bay sand (medium dense)

Figures 6.5.7 - 6.5.11 show the plots of stress ratio σd/2σc' against number of cycles N to cause liquefaction failure. The figures show data for the crushable soils over a range of confining pressures and for comparison purposes include the data for Toyoura sand at relative densities of 50 %, 70 % and 90 % (Hyodo et al., 1991; Hyodo et al. 1994). These latter lines are for a single approaches zero the average slope of the stress strain confining pressure of 100 kPa, however it has been shown that there is no effect due to confining pressure on silica sand over this range of relative densities (Ishihara et al., 1983; Yuki et al. 1982).

In these figures the cyclic strength of Hiroshima Masado is slightly greater than that for Ube Masado due to it's higher relative density but neither was affected by confining pressure. It can also be seen that the corresponding monotonic normalised stress paths in Fig. 6.5.7 are similar as are the phase transformation strengths for different cell pressures. On the other hand for loose and dense Shirasu as shown in Figs. 6.5.8 and 6.5.9 there appears to be a confining pressure dependence. The cyclic strength of loose Shirasu increased with increasing confining pressure while for the dense material the opposite tendency is observed, although in the case of dense Shirasu the nature of the confining pressure dependency is unclear and the data points for σc' equal to 100 kPa and 300 kPa are very close. Similarly opposite tendencies were also observed in the normalised monotonic stress paths in Figs. 6.5.5 – 6.5.6. Once again it is felt that for the loose Shirasu the densification occurring under higher confining pressures has an overriding influence on the behaviour. The Dogs Bay sand, Figs 6.5.10 – 6.5.11, has a marginally higher cyclic strength than Toyoura sand at an equivalent relative density. There also appears to be a dependence on confining pressure for the dense material but for the loose material, the results for σc = 100kPa are anomalous, giving a lower cyclic strength than the lines for 500 and 300kPa.

6-23

-20 -15 -10 -5 0 5 10 15 20-80

-60

-40

-20

0

20

40

60

80

Shirasu (Loose)

Monotonic

Monotonic

Cyclic


Dev

iato

r st

ress

q (

kPa)

Dri=51.7%f=0.1Hzσc’=100kPa

σd/2σc’=0.134

0 20 40 60 80 100 120-80

-60

-40

-20

0

20

40

60

80

Shirasu (Loose)

Monotonic

Monotonic

Cyclic


CSRP.T.L

Dev

iato

r st

ress

q (

kPa)

Dri=51.7%f=0.1Hzσc’=100kPaσd/2σc’=0.134

Fig. 6.5.12 Comparison of monotonic and cyclic curves for Shirasu (loose) (a) stress-strain curves (b) effective stress curves

Examination of the state lines in Figures 6.5.3 – 6.5.4 suggests that where the initial states are to the right of the steady state line the cyclic strength tends to be lower than that of the silica sand at an equivalent relative density and conversely where the initial states are to the left of the steady state line the reverse tends to be true. The latter trend can be seen in particular for the dense Shirasu. 6.5.6 CORRESPONDENCE BETWEEN CYCLIC

AND MONOTONIC LOADING Given the apparent correspondence between the phase transformation point in monotonic tests and the cyclic strength, it seems worth investigating the link between the two types of test a little further. The relationship between cyclic and monotonic loading tests can be illustrated by examining the cyclic stress path shown in Fig. 6.5.12, in relation to the monotonic stress path and the phase transformation and critical stress ratio lines, for loose Shirasu with σr’ = 100 kPa. When the cyclic stress path on the extension side reached the critical stress ratio line as defined previously, flow occurred as the pore pressures rapidly increased. Following this the

-8 -6 -4 -2 0 2 4 6 8-500

-400

-300

-200

-100

0

100

200

300

400

500Dog's BayCarbonate sand(Medium dense)


Dev

iato

r st

ress

q (

kPa)

M onotonic

M onoton ic

Cyclic

Dri=81.1%f=0.1Hz

σc’=500kPaσd/2σc’=0.299

(a) (a)

0 100 200 300 400 500 600-500

-400

-300

-200

-100

0

100

200

300

400

500Dog's BayCarbonate sand(Medium dense)


Dev

iato

r st

ress

q (

kPa)

CyclicM onotonic

M onotonic

P.T.L

Dri=81.1%f=0.1Hzσc’=500kPaσd/2σc’=0.299

Fig. 6.5.13 Comparison of monotonic and cyclic curves for Dogs Bay sand (medium dense) (a) stress-strain curves (b) effective stress curves

(b) (b)

cyclic stress path formed a closed loop on the phase transformation line and liquefaction occurred.

However, for most of the soils tested it was difficult to define a CSR line, but a clear phase transformation line (PTL) existed for each sand, with extension being weaker than compression. The liquefaction characteristics are therefore assumed to be governed by the PTL on the extension side. This is typically illustrated in Fig. 6.5.13 for the medium dense carbonate sand consolidated to 500 kPa, where liquefaction occurred after the cyclic stress path reached the PTL. The cyclic strength data has therefore been normalized by the deviator stress at the phase transformation qPT for all materials and confining pressures and is shown in Fig. 6.5.14. Although there is some scatter there appears to be a relationship for the data shown. In earthquakes, liquefaction occurs after only a few cycles of loading. A useful way of defining the susceptibility of a soil to liquefaction failure, therefore, is to define a single point strength as the cyclic deviator stress ratio required to cause failure after 20 cycles. Given the foregoing evidence of a relationship between the phase transformation strength and liquefaction

6-24

behaviour, the normalized deviator stress required to cause liquefaction failure after 20 cycles (σd/2σc’)20 has been plotted against the normalized phase transformation strength qPT /2σc’ (Fig. 6.5.15). Data are plotted not only for the crushable soils under consideration but also for Toyoura sand at 50 % and 70 % relative densities. There is a unique relationship for the cyclic strength plotted against the phase transformation strength, regardless of effective initial confining pressure, relative density and type of material, such σσ σ

d

c

PT

c

q2

0 03 0 63220′

⎛

⎝⎜

⎞

⎠⎟ = +

′

⎛

⎝⎜

⎞

⎠⎟. .

It would appear that the cyclic strength of a soil can

be uniquely determined from the monotonic phase transformation strength.

As mentioned previously, Ishihara et al. (1996) estimated cyclic deviator stress ratios σd/2σc’ of 0.5 to 0.7 to have occurred at shallow depths in the 1995 Hyogo-ken Nambu earthquake. These values are well in excess of the strengths shown in Fig. 15 for any of the materials. It is clear, therefore, that under severe earthquake conditions angular crushable soils are as susceptible to liquefaction damage as other harder-grained silica sands. 6.5.7 CONCLUSIONS This study has examined the cyclic behaviour of soils of varying crushability characteristics in relation to basic parameters determined from isotropic compression and monotonic undrained stress paths. The conclusions can be summarised as follows:

The slope of the isotropic compression line in the working stress zone for Toyoura sand was very small on the other hand the Masado and Shirasu soils exhibited grain crushing and yielding behaviour and hence a much steeper compression line in the same stress range.

Monotonic undrained shear behaviour of loose Shirasu changed from strain softening to strain hardening with increasing confining stress. The normalised phase transformation and steady state strengths increased with increasing confining pressure. This is the opposite of what is normally expected. Dense Shirasu under monotonic undrained shear dilated at every cell pressure and finally ended on the steady state line in a dilative state.

For undrained cyclic shear behaviour of Masado and loose Shirasu, liquefaction occurred suddenly after the phase transformation point was reached in extension. On the other hand for dense Shirasu cyclic strains gradually increased until a state of cyclic mobility was achieved.

Both Hiroshima and Ube Masados had cyclic strength curves independent of confining pressure. In loose Shirasu the cyclic strength increased with

Hiroshima MasadoDA=5%

σc’ (kPa) σc’ (kPa)

: 50: 100

Ube Masado

: 50: 100: 200

ShirasuDog's BayCarbonate sand

Dri50 90

: 50: 100: 300

Dri60 80

: 100: 300: 500

Cyc

lic

dev

iato

r st

ress

rat

ioσ

d/2σ

c’

｜q

PT｜

/2σ

cNumber of cycles N

0.1 1 10 100 10000

0.4

0.8

1.2

1.6

2.0

Fig. 6.5.14 Cyclic strength normalized to phase transformation strength

: Ube Masado (Dri=50%): Hiroshima Masado (Dri=60%): Shirasu (Dri=50%): Shirasu (Dri=90%): Dog's Bay Carbonate sand

(Dri=60%): Dog's Bay Carbonate sand

(Dri=80%): Toyoura sand (Dri=50,70%)

0 0.1 0.2 0.3 0.4 0.50

0.1

0.2

0.3

0.4

0.5

｜q P T｜/ 2σ c’

Cyc

lic

dev

iato

r st

ress

rat

io (σ

d/2σ

c’) 2

0

(σd/2σc’)2 0

=0.03＋0.63(｜qPT｜/2σc’)

Fig.6.5.15 Relationship between cyclic stress ratio required to cause failure after 20 cycles and phase transformation strength increasing confining pressure while for dense Shirasu the opposite was true.

There is a relationship between the cyclic deviator stress to cause failure after 20 cycles and the phase transformation strength determined from monotonic testing.

6-25

6-26

6.6 STABLITY OF HIGTH EMBANKMENT 6.6.1 INTRODUCTION In recent years, superhighways are constructed on high embankments to make use of excavated soil for their construction and reduce waste, and abutments are constructed on high embankments to reduce the construction costs of bridges. Although there were no cases of collapse of embankments of superhighways during earthquakes in the past, it is necessary to evaluate the influence of the deformation of embankments upon foundations and superstructures if foundations are to be constructed in embankments. With the application of the limited-state design method to the foundations of structures, it is necessary to evaluate the deformation of embankments during earthquakes accurately.

In this study, an on-line seismic-response test on an actual high embankment was carried out by using the actual banking soil to analyze its behavior in earthquakes. Based on the results of the experiment, deformation modes of embankments and deformation mechanism of elements were studied. Then, a response analysis was performed by giving actual seismic waves and a sine wave to the embankment and study was made for an appropriate design seismic coefficient. Besides, the relation between the safety factor of each element and the shearing strain and the relation between the deformation of the embankment and the shear strain were ascertained by defining the strength of banking soil at each level of shearing strain. Then, study was made for a simple method of estimating the horizontal displacement of the top of an embankment continuously during an earthquake by using the safety factor calculated by stability analysis. 6.6.2 OUTLINE OF ON-LINE SEISMIC RESPONSE TEST Fig. 6.6.1 shows the principles of on-line seismic response test. This system was developed by Kusakabe et al. (1990). The algorithm of on-line test is as follows. First, a model of an embankment to be analyzed is made in a mass system and earthquake motion is inputted through the base surface of the model. Then, the oscillation equation of the mass system is solved by a computer to calculate the response displacement of each mass point. Next, shear strain equivalent to the calculated response displacement is given to test pieces under the control by a computer. At that time, restoring force is automatically measured, which is used to calculate the response displacement of the next step. These steps are repeated during earthquake motion. In other words, the ever-changing nonlinear restoring force of the ground is found directly from test pieces for element tests and inputted on-line into response analysis to simulate the behavior of the ground during an earthquake. This technique enables seismic response

analysis wherein the actual behavior of soil is estimated without relying on complex constitutive equations of soil. Fig. 6.6.1 Concept of On-Line Seismic Response test 6.6.3 ESTIMATION OF BEHAVIOR OF HIGH EMBANKMENT BY ON-LINE SEISMIC RESPONSE EXPERIMENT Fig. 6.6.2 shows the cross section of the high embankment with the height of 20 m analyzed in the present study.

Fig. 6.6.2 Model for Analysis A model of the section passing through the top of a slope was made in a one-dimensional mass system for the response analysis. The top three layers S1, S2, and S3 whose nonlinearity was prominent were considered to be on-line layers and their on-line seismic response test was made through element tests. The on-line seismic response test of the other layers was made by using a modified R-O model. Although the section is two-dimensional, the subject of the on-line test was the one-dimensional model connecting the five mass points “m1” to “m5” shown in Fig. 6.6.2. The response experiment was made after giving the initial shear stress calculated in advance by FEM analysis to each test piece and each element. The test piece was considered to be in the so-called shake down mode (Tanaka and Sekiguchi, 1996) wherein the test piece allows itself to deform laterally and vertically with a constant volume in an undrained state while vibration is being applied to it. The simple direct shearing tester developed by Kusakabe et al. (1988) was used. The same soil, that was used for the construction of the high embankment, was put through a sieve of 2 mm, given an optimum water content, and compacted into test pieces.

MX+CX+F=-MLAccg

Accg

Response analys is

Computer

Control and measurement

・・・・

X1～N ⇒ γ1～N

F 1～N 　 τ1～N

⇒

γ1 γN1 N

γ γ

τ1 τN

τ τ

C=0

.. .

Numerical model

Numerical model

On-line tseting

Base

Layer　n

Layer　1

Layer　i

Layer　i+1

Layer　i+2

･･･

･･･

5m

5m

5m

4.75m

5.25m

：On-line layers（S1～S3）：Analysis layers（S4,5）（Nonlinear model）

S1 layerm1

m2

m3

m4

m5S4 layer

S2 layer

S3 layer

S5 layer

6-27

6.6.4 BEHAVIOR OF HIGH EMBANKMENT DURING EARTHQUAKE MOTION OF VARIOUS WAVEFORMS Three irregular waves observed around the epicenters during an inland earthquake (type-II earthquake motion), one irregular wave observed during a large-scale earthquake with a focus at the boundary between two plates (type-I earthquake motion), and a sine wave were used in the seismic response analysis. Fig. 6.6.3 shows the time history of response acceleration of each mass obtained by the on-line seismic response experiment. Fig. 6.6.3 (a) shows the inputted acceleration [N-S component observed at JR (Japan Railways) Takatori Station during the Hyogo-Ken Nanbu Earthquake] and the response acceleration of each layer. Fig. 6.6.3 (b) shows the input acceleration (a sine wave with maximum acceleration α max of 600 gals) and the response acceleration of each layer. As shown in Fig. 6.6.3 (a), the input acceleration attenuated when it moved from the bottom layer S5 to the upper layers and is amplified at the top layer S1. Besides, the period of the inputted acceleration became longer as it moved from the bottom layer S5 to the top layer S1. (a) Irregular wave (N-S component at JR Takatori)

Fig. 6.6.3 Time Histories of Inputted Acceleration and Response Acceleration

(b) Sine wave Fig. 6.6.3 Time Histories of Inputted Acceleration and

Response Acceleration The same tendency was observed with the other waveforms. Fig. 6.6.4 shows the time history of horizontal response displacement of the top of the embankment when the N-S component observed at JR Takatori Station during the Hyogo-Ken Nanbu Earthquake was inputted. As shown in Fig. 6.6.4, horizontal displacement of about 60 cm at the maximum occurred at the mass point “m1” during the application of earthquake motion and residual displacement of about 30 cm in the direction of initial shear stress occurred at the mass point “m1” after the application of earthquake motion. Fig. 6.6.5 shows the relation between the shear stress and shear strain of the third layer S3 and Fig. 6 shows the relation between the shear stress and vertical strain of the same layer. As shown in Figs. 6.6.5 and 6.6.6, the residual shear strain is in the direction of the initial shear stress and the vertical strain accumulated as the shear was repeated. Fig. 6.6.4 Time History of Horizontal Response Displacement of Top of Embankment

-800

0

800

0 2 4 6 8 10

-800

0

800

-800

0

800

-800

0

800

-800

0

800

-800

0

800

Acc

eler

atio

n α

(G

al)

Time t (s)

αm ax=500 Gal

αm ax=569.91 Gal

αm ax=-532.88 Gal

αm ax=358.85 Gal

αm ax=-401.53 Gal

αm ax=-658.12 Gal

Inputted acceleration

Mass 4(Analysis)

Mass 4(Analysis)

Mass 3(On-line)

Mass 2(On-line)

Mass 1(On-line)

-800

0

800

0 2 4 6 8 10

-800

0

800

-800

0

800

-800

0

800

-800

0

800

-800

0

800

Acc

eler

atio

n α

(G

al)

Time t (s)

αm ax=687.00 Gal

αm ax=673.27 Gal

αm ax=475.53 Gal

αm ax=450.21 Gal

αm ax=466.19 Gal

αm ax=-614.79 Gal

Inputted acceleration

Mass 5(Analysis)

Mass 4(Analysis)

Mass 3(On-line)

Mass 2(On-line)

Mass 1(On-line)

-200

204060

0 2 4 6 8 10 Hor

izon

tal

Res

pons

e D

ispl

acem

ent

(cm

)

Time t_(s)

26 .07cm

Hm a x=59.53cm

6-28

Fig. 6.6.5 Relation between Shear Stress and Shear Strain Fig. 6.6.6 Relation between Shear Stress and Vertical Strain 6.6.5 EQUIVALENT SEISMIC COEFFICIENT (1)Method of calculating Equivalent Seismic Coefficient The equivalent seismic coefficient is the proportional constant between the external force during an earthquake and the static external force equivalent to the external force during the earthquake. Problems awaiting solution in calculating the equivalent seismic coefficient are as follows. 1) Irregularity of Earthquake Motion The direction and magnitude of earthquake motion changes irregularly and repeatedly in a short time; accordingly, if the maximum amplitude of the irregular acceleration waveform of earthquake motion is simply converted into a seismic coefficient, it is overestimation of the earthquake motion. It is reasonable to take the irregularity of earthquake motion into account in estimating an effective seismic coefficient. For this purpose, an equalizing coefficient Cr was devised . Distribution of Response Acceleration in Sliding Block If we are to handle the external force acting on an embankment during an earthquake statically as a seismic coefficient and calculate the stability of the embankment against a slide, we will assume that the external force acts on a sliding block evenly and in one direction. However, the acceleration to be inputted through the base of an embankment during an

earthquake has phase differences in both the horizontal and vertical directions and the maximum values of acceleration differ. Thus, needed is a factor (response factor β) which considers the distribution of response acceleration against the acceleration inputted through the base of the embankment. After the above two corrections, the equivalent seismic coefficient is finally given by the equation below.

gCk req

maxαβ=

(6.6.1) Fig. 6.6.7 shows the flow of calculation of the equivalent seismic coefficient. Fig. 6.6.7 shows the concept of response when a regular wave and an irregular wave are inputted. The definitions of the equalizing coefficient Cr and the response factor β are as follows. When the horizontal response displacement of the top of slope caused by a regular wave is equal to that of the same top caused by an irregular wave, equalizing coefficient Cr is find by dividing the inputted acceleration of the regular wave by the maximum acceleration of the irregular wave. While a regular wave is being inputted, the response factor β is find by dividing the average acceleration of mass points in the slope by the inputted acceleration when the response acceleration of the top of slope becomes maximum. Fig. 6.6.7 Flow of Calculation of Equivalent Seismic Coefficient (2) Equivalent Seismic Coefficient Table 6.6.1 shows equivalent seismic coefficients calculated from equalizing coefficients and response factors. As shown in Table 6.6.1, the values of equivalent seismic coefficients can be classified by the types of earthquake motion and those of the types I and II are about 0.2 and about 0.25, respectively.

0 1 2 3 4 5-150

-75

0

75

150

Vertical strainεver (%)

She

ar S

tres

sτ (

kPa)

-5 -2.5 0 2.5 5

-150

-75

0

75

150

Shrar strain γ (%)

She

ar s

tres

sτ (

kPa) S3 layer (On-line)

α α

αα

β= =

αe q

α re s

αave αave

αeq Cr・αmax

αm a x

Sin wave

These horizontal response displacements of the tops are equal to each other.

Irregular wave

Response factor Foundation Ground Foundation Ground

Embankment Embankment

Equalizing coefficient

Input motion入力

ｔｔ

ｔｔ Cr=αeq

αmax

6-29

Table 6.6.1 Calculation of Equivalent Seismic Coefficients

6.6.5 STRENGTH USED FOR ESTIMATION OF STABILITY OF EMBANKMENTS DURING EARTHQUAKES A cyclic shear test with constant stress amplitude and a monotonous loading test were carried out to find the strength to be used for the estimation of the stabilities of high embankments. These tests were made by using the same loading apparatus and under the same boundary conditions as the on-line seismic response experiment. The monotonous loading test was made at the rate of 1%/min of strain. The cyclic shear test was made at about 0.02 Hz.

Fig. 6.6.8 shows the relation between the shear stress (initial shear stress τs + cyclic shear stress τd) and the maximum shear strain when the number of times of repetition is 10 in the cyclic shear test. Fig. 6.6.8 shows the relation between the shear stress and the shear strain obtained by the monotonic loading test, too. Although the strength found by the cyclic shearing test is slightly larger that the strength found by the monotonic loading test, there is no significant difference between them. The strength find by the monotonic loading test was considered to be enough as the strength to be used for stability analysis during earthquakes and the strength parameters of c = 15 kPa and φ = 33° were adopted. The shear stress at the time of shear strain of 5% was adopted as the shear stress at the time of failure for the following reason. When the horizontal displacement of the top of the high embankment exceeds 60 cm, the bridge on the embankment is jeopardized because of the relative displacement between the embankment and the abutment of the bridge. Accordingly, the horizontal displacement, 60 cm, of the top of the high embankment was considered the allowable displacement and the shearing strain equivalent to the allowable displacement was considered breaking strain in the present study.

Fig. 6.6.9 shows the relation between the horizontal displacement of the top of the embankment and the maximum shear strain in the on-line seismic response experiment when the sine waveform was inputted. As shown in Fig. 6.6.9, there is a univocal relation between the horizontal displacement of the top of the model embankment and the maximum shear strain.

maxmax 6.12 γ=H (cm) (6.6.2)

Accordingly, the maximum shearing strain

equivalent to the horizontal displacement of 60 cm is about 5 %; therefore, the shearing stress at the time of shear strain of 5 % was considered to be the shear stress at the time of failure τf. Fig. 6.6.8 Comparison of Results of Monotonic Loading Test and Cyclic Shear Test Fig. 6.6.9 Relation between Shear Strain and Maximum Horizontal Response Displacement 6.6.7 ESTIMATION OF MAXIMUM HORIZONTAL RESPONSE DISPLACEMENT OF TOP OF EMBANKMENT DURING EARTHQUAKE The allowable displacement of embankments varies depending on the kinds of structures to be constructed on them and the degrees of importance of the structures. However, if the strength is changed every time the allowable displacement changes, it is troublesome. Accordingly, devised in this study was a method of fixing the strength to be used and estimating the deformation from the safety factor to be calculated. As shown in Fig. 6.6.8, there is a univocal relation between the shearing stress and the shear strain. If the shear stress at the time of the shearing strain of 5 % is regarded as the reference failure stress τf, there is a univocal relation between the safety factor (the ratio of

Type αmax C r β keq

O saka G as II 736 0 .645 0 .507 0 .246

JR Takatori N -S II 687 0 .672 0 .533 0 .251

JR Takatori E -W II 672 0 .539 0 .696 0 .257

O n’nenu ma O ha shi I 365 0 .613 0 .913 0 .208

0 5 10 15 200

20

40

60

80

100

She

ar s

tres

s　τ

s+τ

d(kP

a)Shear strain　γ(%)

N=10cycles

K=0.4,σ v '=100kPaτ s =15kPa

(τ s =15k Pa)Mon oto nic load test

0 2 4 6 8 100

20

40

60

80

100

Shear strain γ (%)

Hma x=12.6γ

Max

imum

hor

izon

tal

res

pons

e di

spla

cem

ent

H

max

(cm

)

6-30

τf to τs +τd) and the shear strain, which is shown in Fig. 6.6.10 and represented by the following equation.

3.3max 5 −= sFγ (%) (6.6.3)

In addition to the checkup of stability by the

safety factor, the stability can roughly be checked by the horizontal displacement of the top of the embankment if we use the equation (6.6.2) as well as the shear strain calculated with the equation (6.6.3). Fig. 6.6.10 Relation between Safety Factor and Shear Strain 6.6.8 STABILITY ANALYSIS AND CALCULATION OF DISPLACEMENT OF TOP OF EMBANKMENT

The stability of the embankment was estimated by using the equivalent seismic coefficients of Table 6.6.1. The calculation of circular slip was made by using a simple circular arc method. Table 6.6.2 shows the calculated safety factors and horizontal displacement of the top of the embankment during the earthquakes. Fig. 6.6.11 is the comparison between the maximum horizontal displacement of the top of the embankment calculated from safety factors by the proposed method and the same obtained by the on-line seismic response experiment. As shown in Table 6.6.2 and Fig. 6.6.11, the embankment has a safety factor close to 1.0 and maximum horizontal displacement of 50 – 60 cm, considerably close to the allowable displacement, under the type-II earthquake motion, whereas it has a relatively high safety factor and relatively small displacement under the type-I earthquake motion.

Table 6.6.2 Calculated Safety factors and Horizontal Displacement

Thus, the safety factor of the embankment and the horizontal displacement of the top of the embankment calculated from the equivalent seismic coefficients check approximately with the results of the on-line seismic response experiment, proving their validity. 6.6.9 CONCLUSIONS

Findings in the present study are as follows.

The equalizing coefficient Cr taking the irregularity of seismic waves into account was about 0.6 under the earthquake motion of both the types I and II and the response factor β indicating the distribution of response acceleration in the sliding block was 0.9 under the type-I earthquake motion and 0.6 under the type-II earthquake motion, rendering the equivalent seismic coefficient about 0.2 under the type-I earthquake motion and about 0.25 under the type-II earthquake motion.

The horizontal displacement of the top of an embankment during an earthquake can continuously be estimated by using the safety factor of the embankment to be obtained from stability analysis.

Type keq Fs Hmax

(cm)

Osaka Gas II 0.246 1.08 49

JR Takatori N-S II 0.251 1.06 52

JR Takatori E-W II 0.257 1.07 50

On’nenuma

Ohashi

I 0.208 1.20 34

0.0 0.4 0.8 1.2 1.60

2

4

6

8

She

ar s

trai

n　γ

(%)

τ f/(τs+τd)= Fs

γ=5･Fs -3.3

6-31

6.7 EFFECT EVALUATION OF PARTICLE SHAPE ON CYCLIC DEFORMATION OF RAILROAD BALLAST

6.7.1 INTRODUCTION At ballasted track structures composed of rails, sleepers, railroad ballast and roadbed as shown in Figure 6.7.1, “track deterioration” which has serious consequences on the safety of train operation is usually observed. The track deterioration is a phenomenon such that the rail level becomes irregular by degrees due to repeated train passages. Accordingly, the irregularity of rail level should be kept at an appropriate level required from the viewpoint of riding quality and safety through periodic maintenance activities. Since nearly 80 percent of Japanese railway tracks are ballasted tracks, enormous amounts of maintenance costs and work force are needed every year to maintain the irregularities at a satisfactory level. In general, a dominant factor of track deterioration is supposed to be the differential settlement of railroad ballast due to the cumulative irreversible (plastic) deformation caused by cyclic train loads. Therefore, in order to reduce maintenance costs and work force at ballasted tracks, therefore, it is essential to examine the deformation characteristics of railroad ballast in detail.

Figure 6.7.1 Ballasted track structure

The railroad ballast component in which sleepers

are embedded is a pile of well-compacted crushed stones called “ballast.” Traditionally, angular, crushed, hard stones and rocks, uniformly graded and free of dust and dirt, have been considered good ballast materials. The reason is that such materials have high durability and bearing capacity against high contact pressures from the adjacent ballast particles at train passages. However, cyclic wheel loading causes the deterioration (abrasion, breakage, etc.) of ballast particles, and as the result rounded ballast particles lose high bearing capacity against contact pressure between particles. Moreover, when ballast particles are rounded off, railroad ballast is easy to induce the differential settlement due to the high mobility of ballast particles. So far, the shape of a constituent

particle, even though strongly influences the mechanical behaviour of railroad ballast as an assemblage of ballast particles, has been given much less consideration.

Furthermore, when the ballast particles deteriorate, ballast renewal work is performed and waste ballast is discarded as industrial waste. Recently, from the viewpoint of cost reduction and effective utilization of resources, the recycle of waste ballast has been attempted. In order to recycle the waste ballast, it is needed to adjust the grain size distribution according to the standard (Sato and Umehara, 1987a), since waste ballast contains fine grains in quantities. However, even though the grain size distribution of waste ballast satisfies the standard, rounded railroad ballast does not necessarily have the stiffness or deformation properties similar to those of new ballast because the particles of waste ballast are abraded and/or fractured under cyclic train loads. Although studies have been made in the past on the strength and deformation properties of railroad ballast (Kohata et al. 1999), there are few studies focused on the relationship between the abrasion of particle and the strength - deformation characteristics, and the subject how the material properties of ballast affect mechanical properties of railroad ballast has not been investigated satisfactorily.

This section describes a fundamental study to inspect the significance of numerical modelling which takes the particle properties such as particle shape and rock material into account, and to justify the use of the modelled grains in further geotechnical engineering applications. First, in this study, two types of methods to evaluate the shape of ballast particles qualitatively were proposed. Next, a series of large triaxial tests and cyclic loading tests with a full-scale model track were performed for three types of ballasts which differ in the degree of abrasion of ballast particles. Based on the test results, the following assignments are discussed; ・ Proposal of an evaluation index of particle shape

by focusing on the abrasion process of ballast particles under cyclic train loads.

・ Correlation of the particle properties such as particle shape and rock material with the strength - deformation characteristics of granular materials.

・ Influence of the degree of abrasion of ballast particles and the shape properties by the proposed shape function on the settlement characteristics of geotechnical structures made of granular materials like railroad ballast.

6.6.2 TEST PROCEDURE Test materials Three types of test samples which differ from each other in the degree of abrasion of ballast particles were employed in this paper. The railroad ballast is usually composed of single-grained crushed andesite stone in

6-32

Japan, and new ballast is angular crushed hard stone. In this study, new ballast was abraded by force using the Los Angels test apparatus in order to simulate the abrasion process of ballast particles under cyclic train loads. The amount of ballast put into the Los Angels test apparatus was 15 kg, and the speed of rotation was 33 rpm. The abrading time represents the degree of abrasion. Here, the term “abrasion level 0” is used to refer to the ballast whose abrading time is 0 minute, the term “abrasion level A” 10 minutes and the term “abrasion level B” 35 minutes. The gradation curves for test samples are shown in Figure 6.7.2, together with the proper grading of railroad ballast provided by the Japanese railway specification. The grain sizes of railroad ballast falls in the 10 to 60 mm range.

10 1000 20 40 60 80

100

20 40 60 80

○：Abrasion 0 （Uc 1.39）

△：Abrasion A （Uc 1.49）

□：Abrason B （Uc 1.45）

Pas

sing

per

cent（

%）

Particle size (mm)

Range of standard

Figure 6.7.2 Grain size distribution of ballast blocks Testing methods (1)Evaluation for the particle shape of ballast The particle shape of ballast was evaluated by an analytical method to use an argument function and radius function after converting the cross section shot with a digital camera into the X-Y coordinate value. The argument function is a function of the tangential line at Px, which is the point advanced X from the reference point S, and the angle of reference line θ(x) as shown in Figure 6.7.3. If the full length of the closed curve is L, the argument function is normalized as shown in Equation (1) since θ(x+L)=θ(x)+2π.

( ) ( ) ( )LxxxN πθθ 2−= (6.7.1) Since the normalized argument function θN(x) is a

periodic function of period L, it can be developed to a Fourier series shown in Equation (6.7.2). The k-th amplitude spectrum can be expressed by Equation (6.7.3).

( ) { }∑∞

=++=

10 /)2cos()/2sin(2

kkkxN LkxbLkxab ππθ (6.7.2)

( )22kkk baC += (6.7.3)

where ak and bk are :

( )∫+

=Lx

xk dxLkxxfLa 0

0)2sin()(2 π k=1,2,…

( )∫+

=Lx

xk dxLkxxfLb 0

0)2cos()(2 π k=0,1,2,…

∑=

=20

3fv )(NA aluefunction vargument normalized The

kkC (6.7.4)

Kono et al. (1999) reported that the sum of the 3rd

to 20th amplitude spectra shown in Equation (6.7.4) indicates the degree of angularity of particle. Then, the angularity of abraded ballast particle was summarized by using the NAfv obtained from Equation (6.7.4). The radius function is a function of length r(α) of the straight line that connects a certain point Pα on the contour and the centre of gravity O as shown in Figure 6.7.3. It is expressed by Equation (6.7.5). The k-th amplitude spectrum is expressed by Equation (6.7.6).

( ) { }∑∞

=++=

10 )cos()sin(2

kkk kbkabr ααα

(6.7.5)

( )22kkk baC += (6.7.6)

where ak and bk are :

( ) ( ) ( ) αααππα

αdkrak sin1

20

0∫

+= k=1,2,…

( ) ( ) ( ) αααππα

αdkrbk cos1

20

0∫

+= k=0,1,2,…

Kono et al. (1999) reported that the ratio of the 2nd and zero order amplitude spectrum shown in Equation (6.7.7) indicates the degree of aspect ratio of particle. Then, the variation of aspect ratio was summarized by using the radius function value obtained from Equation (6.7.7).

02fv /)(R aluefunction v radius The CC= (6.7.7)

Argument function θ(x)

x

Px

Reference line of argument function

Reference point S

Radius function Pα

α

r(α) Reference line of radius function O

Figure 6.7.3 Conceptual figure of argument and radius function (2)Large triaxial tests A series of monotonic loading triaxial compression tests were performed for three types of test samples in order to examine their strength and deformation characteristics. Figure 6.7.4 shows a schematic view of a large size triaxial apparatus. The specimen dimensions are 60 cm in height and 30 cm in diameter. The specimens were prepared by tamping with a wooden rammer and vibrator-compaction with constant energy at each layer of 60 mm in height into a cylindrical mould. The densities of specimen with the

6-33

abrasion 0, A and B are 1.632, 1.679 and 1.681 g/cm3, respectively. The specimens were kept under air-dried and drained conditions throughout the tests.

②

①

③

④

⑤

Top cap

Vacuum

Pedestal

①Load cell ②External Deformation Transducer ③Local Deformation Transducer (LDT) ④Proximeter for Axial Deformation ⑤Proximeter for Lateral Deformation

30cm LDT

Cylindrical Specimen

60cm

④

⑤

Figure 6.7.4 Large triaxial test apparatus

The axial stress (σa) was measured by a loadcell installed on the top cap, and the axial strain (εa) was measured by an external transducer, proximity transducers and local deformation transducers (LDTs) (Goto et al., 1991). The lateral strains (εr) were measured by proximity transducers positioned diagonally opposite each other around the specimen diameter. The loading process was performed as follows. After isotropic consolidation of a specimen under the low effective confining pressure (σc´) of 19.6 kN/m2 by vacuuming, an axial deviator stress (q) was applied at the constant axial strain rate of 0.01 %/min while keeping the confining pressure constant. Unload / reload cycles at about 49.1, 98.1 and 147.2 kN/m2 were applied during monotonic axial loading. (3)Cyclic loading tests with full-scale model track A series of cyclic loading tests with a full-scale model track were performed for three types of test samples. The general test arrangement of fixed-place cyclic loading test is shown in Figure 6.7.5. The model track, which simulates a transverse section of real ballasted track, is in the plane strain state assuming the transverse section to be infinitely continued. The model track was constructed on the asphalt roadbed in a large pit, 7.0 m long, 3.5 m wide and 2.5m deep, consisting of PC sleepers, short rails and railroad ballast. The railroad ballast of model track was kept air-dried conditions throughout the tests, and it was compacted with a vibration roller so that the density of railroad ballast was close to that of triaxial test specimens. In this study, asphalt roadbed was selected so that ballast particles may not penetrate into roadbed and the settlement of roadbed may not arise.

Repeated vertical loads with constant amplitude were directly applied to the sleeper by using a large loading apparatus with two electro-pneumatic actuators. A sinusoidal loading waveform was employed because this waveform is said to approximate the loading pulse applied to sleepers under actual field conditions

(Raymond, 1987). Pulsating compression vertical loads (Pr) ranged from 9.8 to 68.6 kN/(one rail) were cyclically applied up to 300,000 cycles. The applied load value was determined by the weights of vehicle and passenger, the load distribution ratio and other factors. The loading frequency of 11 Hz was selected by assuming running speed of train as about 100 km/h. To check the response of model track, the vertical load (Pr) was measured by a load cell installed on each rail, and the vertical displacement (y) was measured by a proximity transducer likewise.

Subgrade (Gravely sand)

7000mm

2500

mm

300mm

Sleeper Rail

Roadbed

Load2400mm

Figure 6.7.5 Schematic figure of full-scale track model

6.7.3 TEST RESULTS Evaluation for the particle shape of ballast Figure 6.7.6 shows photographs of the particle shape of abraded ballast at the abrasion levels of 0, A, and B. The normalized argument function waveform obtained from Figure 6.7.6 is shown in Figure 6.7.7. The amplitude decreases as abrasion progresses. The waveform tends to become an obtuse angle. For ballast particles at each abrasion level, about 100 particles were shot in three directions and the distribution of NAfv obtained from the normal argument function waveform were summarized as shown in Figure 6.7.8. The frequency distribution is normalized by the percentage to the total, since the numbers of analyzed ballast particles are different in each case. The distribution of NAfv is similar to the normal distribution. As abrasion progresses, the NAfv at the peak frequency value, the peak frequency value, mean value and standard deviation all decrease. That is, the NAfv becomes smaller, as the particle becomes roundish.

Abrasion 0 Abrasion A Abrasion B Figure 6.7.6 Example of photographs of abraded ballast particles

6-34

-60

θn(

x)

Distance from reference point x0 200 400 600 800 1000

-30 0

30 60 80 Abrasion 0

Abrasion A Abrasion B

Figure 6.7.7 Example of argument function waveform

0 20 40 60 80 100 120 1400.0

0.1

0.2

0.3

0.4Abrasion BMean value : 51.1Standard deviation:8.5

Abrasion 0 Mean value : 73.7 Standard deviation : 11.2

Abrasion AMean value : 59.1Standard deviation:10.9

Nor

mal

ized

fre

quen

cy

Normalized argument function value, NAfv Figure 6.7.8 Frequency distribution of argument function value

0 50 100 150 200 250 300 350

125

150

175

200 Abrasion 0 Abrasion A Abrasion B

Rad

ius f

unct

ion,

r (α

)

Angle from reference line, α Figure 6.7.9 Example of radius function

0.0 0.1 0.2 0.3 0.40.00

0.05

0.10

0.15

0.20

0.25

0.30

Abrasion BMean value : 0.113Standard deviation : 0.068

Abrasion A Mean value : 0.117 Standard deviation : 0.069

Abrasion 0Mean value : 0.130Standard deviation : 0.067

Nor

mal

ized

fre

quen

cy

Radius function value, Rfv Figure 6.7.10 Frequency distribution of waveform radius function value

An example of radius function waveform is shown in Figure 6.7.9. As abrasion progresses, the amplitude of the radius function waveform decreases and the

waveform tends to become an obtuse angle. Similar to the NAfv, the values of Rfv obtained from about 100 ballast particles at each abrasion level were summarized. The frequency distribution normalized by the percentage to the total is shown in Figure 6.7.10. The frequency distributions of Rfv have some peak values at each abrasion level. The mean tends to decrease as abrasion progresses. The effect of abrasion on the standard deviation is not seen clearly.

0 2 4 6 8 10 12 140

100

200

300

Abrasion 0 Abrasion A Abrasion BD

evia

tor s

tress

, q

(kN

/m2 )

Axial strain, εa (%) Figure 6.7.11 CD TC test results

0 50 100 150 200 250 300-50

050

100150200250300

Abrasion 0

Tang

ent Y

oung

's m

odul

us,

Eta

n (MN

/m2 )

Deviator stress, q (kN/m2)

Initial load 1st reload 2nd reload 3rd reload

(a) Abrasion 0

0 50 100 150 200 250 300-50

050

100150200250300

Abrasion A Initial load 1st reload 2nd reload 3rd reload

Tang

ent Y

oung

's m

odul

us,

E tan (M

N/m

2 )


(b) Abrasion A

0 50 100 150 200 250 300-50

050

100150200250300

Abrasion B

Tang

ent Y

oung

's m

odul

us,

E ta

n (MN

/m2 )


Initial load 1st reload 2nd reload

(c) Abrasion B Figure 6.7.12 Relationships between Etan and q obtained from CD TC tests

6-35

Large triaxial tests The relation between deviator stress q and axial strain εa at each abrasion level is shown in Figure 6.7.11. As abrasion progresses, the maximum deviator stress qmax becomes small. Figure 6.7.12 shows the relationship between q and tangent Young’s modulus Etan for each abrasion level. The values of Etan of abrasion levels 0 and A decrease suddenly at the initial potion of loading in initial loading and are constant as shear progresses. After that, it decreases again.

Etan at the abrasion level B decreases constantly from the initial potion of loading with shear. On the other hand, in the case of reloading, Etan at abrasion levels 0 and A increase from the initial potion of loading with shear. After a peak has emerged, it decreases and reaches the value of Etan in initial loading. Etan at the abrasion level B decreases constantly from the initial potion of loading with shear in the same way as in initial loading. In the case of reloading, the abrasion level A shows larger Etan than the abrasion level 0, presumably because the abrasion became adequate and the placement of particles in the specimen was improved. At the abrasion level B, it is considered that Etan decreased since the effect of the progress of abrasion is larger than the effect of the placement of particles.

0.0 0.5 1.0 1.5 2.0-2.0

-1.5

-1.0

-0.5

0.0

Abrasion BAbrasion A

ν=1.0

ν=1.75

Late

ral s

train

, ε r (%

)

Axial strain, εa (%)

Abrasion 0

Figure 6.7.13 Relationships between εr and εa

The lateral strain εr as well as the axial strainεa is

important to discuss the strength and deformation properties of materials under the triaxial condition. The relationship between axial and lateral strain is shown in Figure 6.7.13. It plots up to 1.5 %, and the lines of Poisson’s ratio ν=1.0 and 1.75 were also indicated in this Figure. In the range of εa to 1.5 % for each abrasion level, εr is lager than εa. It seems that ν is between 1.0 and 1.75. However, in the range of εa to about 0.2 %, εa is lager than εr. It is seen that the amount of axial and lateral strain becomes opposite to each other. Figure 14 shows the relation between εa and ν. In the range of εa to about 0.5 %, ν increases as εa increasing. It has already become in the yield state at εa larger than 0.5 % for each abrasion level as shown in Figure 6.7.13. In the range of εa to about 0.1 %, ν

is large in the order of abrasion levels A, 0 and B. This order is the same as the order of the value of Etan at q less than 100 kN/m2. However, at εa larger than 0.1 %, ν is large in the order of abrasion levels 0, A, and B. As mentioned above, it was seen that the effect of ν on the strength and deformation properties of ballast is large.

0.0 0.5 1.0 1.5 2.00.0

0.5

1.0

1.5

2.0 Abrasion B

Abrasion 0

Poss

on's

ratio

, ν

Axial strain, εa (%)

Abrasion A

Figure 6.7.14 Relationships between ν and εa Cyclic loading tests with full-scale model track The relation between the number of cycles and residual settlement of sleeper is shown in Figure 6.7.15. The residual settlements progress suddenly at the initial potion of loading for each abrasion level. After that, it tends to increase linearly at the number of cycles larger than 100,000 times. In order to quantitatively evaluate the trend of residual settlement by cyclic loading, a curve based on the empirical Equation (6.7.8) (Sato and Umehara, 1987b) used for ballast settlement by cyclic loading is also indicated in this Figure. The indexes β and γ in Equation (6.7.8) show the rate of progressive settlement and settlement at the initial poison of loading. It is seen that both values become large as abrasion progresses.

( ) xey x βγ α +−⋅= −1 (6.7.8) where y: residual settlement, x: number of cycles, α: index, β: rate of progressive settlement, γ: settlement at the initial poison. Relationship between the particle shape and the strength and deformation properties In order to discuss the relationship between the particle shapes, the strength and deformation properties of railroad ballasts and the settlement of track, the results of shape evaluation of ballast particles, large triaxial tests and cyclic loading tests with a full-scale model track were summarized.

The relations between the qmax, Etan from large triaxial tests and β, γ from cyclic loading tests with a full-scale model track are shown in Figure 6.7.16. Etan is obtained at the stress (about 160 kN/m2) that divided cyclic load amplitude in a full-scale model track test by the bottom area of sleeper. This stress is equal to the value of q at a reloading in the large

6-36

triaxial test. The reason adopting the stress at the reloading is that the full-scale model track test is the cyclic loading test. In this Figure, β and γ tend to decrease as qmax and Etan increase. And it is indicated that the settlement of track decreases as the strength and stiffness of railroad ballast increase.

10

8

6

4

2

00 5 10 15 20 25 30

γ (mm) β (mm/times): Abrasion 0 3.788 8.733 x 10-6

: Abrasion A 4.098 1.000 x 10-5

: Abrasion B 4.781 1.000 x 10-5

Number of cycles (x104)

Res

idua

l set

tlem

ent

(mm

)

Figure 6.7.15 Relationships between residual settlement and number of cycles obtained from large-scale track model test

0 100 200 300 4003.0

4.0

5.0

6.0

7.0

0.7

0.8

0.9

1.0

1.10 15 30 45 60

Initi

al se

ttlem

ent,

γ (m

m)

Maximum deviator stress, qmax (kN/m2)

Rate

of p

rogr

essiv

e se

ttlem

ent,

β

(x1

0-5 m

m/ti

mes

)

Tangent Young's modulus, Etan (MN/m2)

γ β

White symbol : qmax

Black symbol : Etan

○，●： △，▲：

Figure 6.7.16 Relationships between qmax, Etan, β and γ

The relations between the NAfv on the degree of angularity of particle, Rfv on the degree of aspect ratio of particle, qmax and Etan in the large triaxial tests are shown in Figure 6.7.17. The qmax and Etan decrease linearly as the NAfv and Rfv decrease. Kono et al. (1999) reported that Rfv is 0 when the aspect ratio of circum-scribed rectangle on the silhouette of ballast particle is 1 and nearly 10 when the aspect ratio is 1.5. Therefore, it is considered that the variation of qmax and Etan by the variation of Rfv shown in Figure 6.7.17 is mainly caused by the variation of NAfv.

The effect of abrasion of particle is shown in the results of full-scale model track test. It seems from Figure 6.7.18 that the NAfv and Rfv increase, that is, β and γ decrease as the abrasion of particle progresses.

40 50 60 70 800

100

200

300

400

0

15

30

45

600.10 0.11 0.12 0.13 0.14 0.15

Tang

ent Y

oung

's m

odul

us, E

tan (M

N/m

2 )

Max

imum

dev

iato

r stre

ss, q

max

(kN

/m2 )

Normalized argument function value, NAfv

△，▲：

qmax

Etan

○，●：

White symbol : NAfv

Black symbol : Rfv

Radius function value, Rfv (kN/m2)

Figure 6.7.17 Relationships between NAfv, Rfv, qmax and Etan

50 60 70 803

4

5

6

7

0.7

0.8

0.9

1.0

1.10.10 0.11 0.12 0.13 0.14 0.15

Initi

al se

ttlem

ent,

γ (m

m)

Normalized argument function value, NAfv

Radius function value, Rfv (kN/m2)

Rat

e of

pro

gres

sive

settl

emen

t,

β

(x1

0-5 m

m/ti

mes

)

△，▲：

White symbol : NAfv

Block symbol : Rfv

○，●：γβ

Figure 6.7.18 Relationships between NAfv, Rfv, β and γ 6.6.4 CONCLUSION The following conclusions can be derived from the results of shape evaluation of particles, large triaxial tests and cyclic loading tests with a full-scale model track on abraded ballast; (1) The values of β and γ obtained from cyclic loading

tests with a full-scale model track decrease as qmax and Etan of railroad ballast obtained from large triaxial tests increase.

(2) When NAfv of ballast particle becomes small, qmax and Etan decrease, and β and γ increase. This means that, while the angularity of ballast particle is lost by abrasion, the strength and stiffness decrease and settlement increases on railroad ballast.

(3) When Rfv of ballast particle becomes small, qmax and Etan decrease and β and γ increase. However, since the variation of Rfv is small though the degree of abrasion of ballast particle is different, the decrease of qmax and Etan and increase of β and γ are mainly caused by the decrease of NAfv. That is, it

6-37

is due to the lack of angularity of ballast particle. From what has been mentioned above, it becomes

clear that the newly proposed shape evaluation analysis with the normalized argument function is effective as a method to evaluate the change in particle shape of ballast particles under the abrasion process by cyclic train loads, and to examine how the particle properties of ballast affect the mechanical behaviour of railroad ballast. The conventional designing standard does not prescribe a relationship between the particle properties of ballast and the differential settlement of railroad ballast definitely, though it has regulations about grain size distribution and rock material. If further investigation reveals the relationships between the properties of a constituent particle and the strength - deformation characteristics of the grain assemblage in detail, it is likely that a new standard suitable for performance-based design of railroad ballast can be exhibited by evaluating the particle properties (rock material, particle shape, grain size, crushability, etc.) quantatively. In addition, the evaluation method may promote the efficient reutilization of waste ballast and contribute to the development of new granular materials substitutive for ballast. ACKNOWLEDGEMENTS This section is a conflation, revision, and expansion of two earlier studies, (Kohata et al., 1999) and (Sekine and Kohata, 2003). The author would like to thank Dr. Etsuo Sekine, Railway Technical Research Institute for permission to use the figures and data.

6-38

6.8 PROPERTIES OF FILTER-PRESSED CLAY LUMP AND ITS AGGREGATE

6.8.1 INTRODUCTION As the navigation channels and anchorage areas are important infrastructure for the ship traffic, the dredged projects to improve and to maintain their function will continue. However, it is difficult to construct a new disposal pond for dredged soils and therefore the long use of existing disposal pond has become an important and urgent technical issue.

The means for the long use of existing disposal pond are separated into two. One is the increase of capacity of pond by means of raising of embankment as shown in Figure 6.8.1. In this case, the widening of embankment is constructed for the stability of revetment. The volume of increasing capacity has to cut down the volume of widening of embankment when the widening is constructed with hill-cut materials. The other means is the reduction of disposal volume. If the dredged marine clay can be used for widening, the capacity of pond increases.

Replacement sand Existing sea bottom

Revetment

dredged clay

Raising of embankment

Sea

widening ofembankment

Figure 6.8.1 Outline of raising of embankment for increase in capacity of disposal pond

Murayama et al. (2004) reported the mechanical characteristics of dewatered clay lumps made of dredged marine clay. The objective of their report was whether the dewatered clay lumps could be used as the materials for widening of embankment. In this section, the characteristics of clay lump and aggregate of clay lumps that were reported by Murayama et al. (2004) are introduced. Moreover, the relationship between strength of dewatered clay lump and consolidation yield stress of aggregate of lumps is compared with that of silica sand and Shirasu. 6.8.2 MECHANICAL PROPERTIES OF DEWATERED CLAY LUMP (MURAYAMA ET AL., 2004) Properties of clay used

The original clay was sampled from the No.3 area of the Shin-Mojioki disposal pond. The physical properties of clay used were ρs = 2.627 – 2.683 g/cm3, wL = 52.5 – 76.0 %, Fs = 6.1 – 10.1 % and Ip = 25.7 – 44.1. The water content of clay before the dewatering was treated around 300 %.

Making method of dewatered clay lump: Filter-press method

The clay slurry with water content of around 300 % was pumped into the chambers covered by filter cloth. While pumping continued the hydraulic consolidation continued. Figure 6.8.2 shows the schematic time-behavior of supplied pressure and accumulated filtrate (Murayama, et all., 2004). Finally, the chambers were opened and dewatered clay lumps were released. The maximum pump pressure was 4 MPa. They was produced the filter-pressed clay lumps with 1 and 4 MPa of supplied pressures to investigae the characteristics of clay lump and its aggregate.

Time

Supplying pressure

Designed pressure

Time

Accumulated filtrate

(a) Time - supplying pressure relation

(b) Accumulation of filtrate with time

end ofconsolidation

stop of supplying

Figure 6.8.2 Dewatering behavoir of filter-pressed clay lump (Murayama et al., 2004)

As shown in Figure 6.8.2, the pumping of

clay-slurry was usually stopped before the hydraulic consolidation of clay in the chamber was not finished. Therefore, the water content and effective stress in the clay lump distributed.

Although the filter chamber had much larger size, the dewatered clay was broken into pieces when it was dropped on to a belt conveyer. The maximum diameter of a lump was about 100 mm and the thickness of the lump was approximately 23 mm.

Compression properties of dewatered clay lump

Figure 6.8.3 shows the e – log p relations of clay lumps with filter-press pressures of 1 and 4 MPa (Murayama, et al., 2004). The arrow in this figure indicates the consolidation yield stress determined by the consolidation tests. The average of compression index Cc was 0.65, and the distribution was from 0.58 to 0.73.

The consolidation yield stress was smaller than that the supplying pressure. The ratio for 1 MPa material was 60 % of supplying pressure, and that for 4 MPa was 40 %. This reason was that the dewatered lump was generated by the hydraulic consolidation and the pumping was stopped during consolidation, as mentioned earlier.

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Figure 6.8.4 shows the cv – p relation of clay lumps with supplying pressure of 1 and 4 MPa (Murayama, et al., 2004). The arrow was also the consolidation yield stress by consolidation tests. In the normally consolidated condition, cv was almost 250 cm2/day, that in the overconsolidated condition was 10 times larger.

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

10 100 1000 10000 100000p （kPa）

e

1MPa-11MPa-24MPa-14MPa-2

pc(kP

Cc

566.6594.3

1470.51720.7

0.7320.6860.5830.606

consolidation yield

Figure 6.8.3 e – log p relations of dewatered clay lumps with pumping pressures of 1 and 4 MPa (Murayama et al., 2004)

100

1000

10000

100000

10 100 1000 10000 100000p （kPa）

c v （

cm2 /d

ay）

1MPa-11MPa-24MPa-14MPa-2

consolidation yield

Figure 6.8.4 log cv – log p relations of dewatered clay lumps with pumping pressures of 1 and 4 MPa (Murayama et al., 2004)

0

500

1000

1500

2000

0 1000 2000 3000 4000σv （kPa）

τ f （

kPa）

1MPa4MPa

pc =1600 kPa

pc =580 kPa NC

OCOC

OC NC ccu(kPa) φcu(°) ccu(kPa) φcu(°)

140.3 10.7 291.7 14.1 0.0 23.5

Figure 6.8.5 Failure criteria of dewatered clay lumps with pumping pressures of 1 and 4 MPa (Murayama et al., 2004) Box shear strength of dewatered clay lump Figure 6.8.5 shows the failure criteria of dewatered

clay lumps with pumping pressures of 1 and 4 MPa (Murayama, et al., 2004). The lines in the normally consolidated condition are approximately piled up. The arrow shows the consolidation yield stress from the consolidation tests. The left hand side from this arrow was regarded as the overconsolidated condition. In this OC, the failure lines are drawn to be parallel. The magnitudes of shear stress at normal stress of zero in the 1 and 4 MPa materials are 140 and 290 kPa, respectively. These magnitudes are equivalent to 20 – 25 % of consolidation yield stresses of dewatered clay clumps. 6.8.3 MECHANICAL PROPERTIES OF AGGREGETE OF DEWATERED CLAY LUMPS Definition of true void ratio of aggregate In the case of highly dewatered lumps such by filter-press, the clay lump has a sufficient strength to form a particulate structure when dumped into the pond. Figure 6.8.6 shows the void ratio of the aggregate of clay lumps to understand the true void ratio (Murayama, et al., 2004). The clay lump itself consists of solid and void space in it. The aggregate is composed of clay lumps and void space between clay lumps. The true void ratio, etrue is defined as (Vagg – Vsoild) / Vsolid in Figure 6.8.6. The apparent void ratio, eagg is defined as (Vagg – Vlump) / Vlump.

Void of claylum ps

Void am ongaggregate of clay

lum ps

Solid 1

elump 1

1

etrue

eagg

Vsolid

Vagg

Vlump

Figure 6.8.6 Definition of true void ratio of aggregate of dewatered clay lumps (Murayama et al., 2004) Table 6.8.1 True and apparent void ratios of aggregate of clay lumps Material True void ratio Apparent void ratio

1 MPa material 2.78 – 2.97 0.49 – 0.58

4 MPa material 2.20 – 2.35 0.45 – 0.55 Table 6.8.1 is summalized the true and apparent void ratios of specimens for box shear tests conducted by Murayama et al. (2004). The true void ratio of aggregate of 1 MPa material is a little larger than that of 4 MPa. The apparent void ratios of both the materials are almost the same, and are like the value of sandy materials. The reason is the void ratio of clay lumps is different.

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Compression properties of aggregate Figure 6.8.7 shows the relationship between true void ratio and consolidation pressure of two aggregates of filter-pressed clay lumps with supplying pressures of 1 and 4 MPa (Murayama, et al., 2004). The compressibility of both the materials can be drawn as the bilinear relation. The interaction point in the relation is defined as apparent consolidation yield stress, and is dependent on the supplying pressure. The compression index of aggregate of clay lumps, that is defined as the slope of true void ratio – consolidation pressure relation, is also influenced by the property of clay lump.

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

1 10 100 p (kPa)

e tur

e

1 MPa lump aggregate

4 MPa lump aggregate

0

apparent consolidationyield stress

apparent consolidationyield stress

Figure 6.8.7 Void ratio – consolidation pressure of aggregate of clay lumps (Murayama et al., 2004) Figure 6.8.8 is the relationship between apparent consolidation yield stress of aggregate and consolidation yield stress of clay lump. Considering that a clay lump is equivalent to a particle, the apparent consolidation yield stress of aggregate is regarded as consolidation yield stress of ground shown in Figure 6.1.2 and the consolidation yield stress of clay lump is equivalent to the crushing stress of particle. Therefore, the relations of silica sand and Shirasu shown in Figure 6.1.2 are also drawn in the same figure. The relations of four kinds of geo-materials are thought to be linear, and the ratio of particle property to aggregate characteristics is almost the same in spite of the kind of geo-materials. Figure 6.8.9 shows the relationship between coefficient of consolidation and consolidation pressure on the aggregate of clay lumps (Murayama, et al., 2004). In this case, the same relations for clay-water mixture and clay lump in the normally consolidated stress range are also drawn. The coefficient of consolidation of aggregate of clay lumps is much larger, and settlement behavior is practically regarded as the immediate settlement. Shear strength and deformation characteristics of aggregate of clay lumps

Due to the maximum size of 100 mm, a large cell with the size of 800*800*500 mm was used for the box shear test on the aggregate of dewatered clay lumps. The clay lumps were loosely packed into the cell by a

procedure similar to the test method for determining the minimum density of sand in order to simulate the dumping into the sea. The void ratio of specimen was summlized in Table 6.8.1. At the consolidation stage, the specimens under consolidation pressure consolidated to satisfy the compressibility shown in Figure 6.8.7.

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000py (MPa)

σ f (M

Pa)

s ilica sand (afterNakata et al.,1999 &Kato et al., 1999)

shirasu (after Katagiriet al., 1999)

4 MPa m aterial(after Murayam aet al., 2004)

1 MPa

Figure 6.8.8 Relationship between particle property and aggregate charateristics

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

10 100 1000 10000 100000

　p (kPa)

cv (

cm

2/da

y)

4 MPa lump

clay mixture （w 0 = 3w L）

4 MPa material aggregate

1 MPa materialaggregate

1 MPa lump

Figure 6.8.9 Coefficient of consolidation and consolidation pressure relation of clay lump and its aggregate (Murayama et al., 2004)

Figure 6.8.10 shows the horizontal deformation and shear stress curves for two types of aggregates of dewatered clay lumps (Murayama, et al., 2004). Figure 6.8.10 (a) is the 1 MPa material, and (b) is the 4 MPa. In the 1 MPa material, the horizontal deformation and shear stress curve is dependent on the consolidation pressure, and horizontal deformation and volume change is independent on the consolidation pressure. In the 4 MPa, on the other hand, the horizontal deformation and volume change curves are separated into two types, one is shrinkage, and another is from shrinkage to expansion. The former is the drained shear behavior of clay, but the later is the normal drained characteristics of sandy material. The boundary of those behaviors is thought to exist the consolidation pressure of around 20 kPa.

As mentioned earlier, the apparent consolidation

6-41

yield stress was approximately 20 kPa in Figure 6.8.7. Considering this apparent yield stress as boundary between normally consolidated condition and overconsolidated condition, that is, true yield stress, the consolidation behavior is consist with the shear behavior. The mechanical behavior of this material depends on the consolidation pressure.

In the 1 MPa material, the consolidation pressures were set at 24, 48, and 98 kPa in shown in Figure 6.8.10 (a). The apparent consolidation yield stress determined by the consolidation tests on the aggregate of clay lumps was not clear, but was guessed at 8 kPa in Figure 6.8.7. If the shear test under less than 8 kPa was performed, the volume change of specimen would represent the shrinkage to expansion.

Shear behavior of aggregate of dewatered clay lumps depends on the clay lump property caused by supplying pressure.

-60

-40

-20

0

20

40

60

80

100

0 20 40 60 80 100 120 140δ (m m )

τ (k

Pa)

-30

-20

-10

0

10

20

30

40

50h

(mm

)

σv

①：24kPa②：48kPa③：95kPa

①

②

②

①

③

③

shear s tress

shrinkag

expansion

volume change

1 MPa material

(a) 1 MPa material

-60

-40

-20

0

20

40

60

80

100

0 20 40 60 80 100 120 140δ (m m )

τ (k

Pa)

-30

-20

-10

0

10

20

30

40

50

h (m

m)

σv

①：24 kPa②：48 kPa③：95 kPa

①

②

②

①

③

③

4 MPa material

σv

④：12 kPa⑤： 6 kPa

④

④

⑤⑤

(b) 4 MPa material

Figure 6.8.10 Shear resistance and volume change during shearing of aggregate of dewatered clay lumps (Murayama et al., 2004)

Figure 6.8.11 shows the failure criteria of aggregate of clay lumps (Murayama, et al., 2004). Here, each plot is consolidation pressure and maximum shear stress. Both the criteria are indicated as single lines in spite of consolidation pressure. The slope of 4 MPa material is 36.5 degrees, and is larger than that of 1 MPa material. The criteria of aggregate of clay lumps depend on the lump property caused by supplying pressure in production process.

0

50

100

0 50 100 150σv (kPa)

τ f (k

Pa)

4 MPa material1 MPa material

φ = 23.6°c = 9.4 kPa

φ = 36.5°c = 5.1 kPa

Figure 6.8.11 Failure criteria of aggregate of clay lumps (Murayama et al., 2004)

6.8.4 CONCLUSIONS In this section, the characteristics of aggregate of clay lumps and property of clay lump are introduced. The shear strength of clay lump and apparent consolidation yield stress were compared. The ratios of apparent consolidation yield stress to shear strength in both the cases are around 15, and are almost the same as those of Shirasu and silica sand. The behaviour of aggregate depends on the characteristics of clay lump. Therefore, the study on the particle properties leads to understand the behavior of ground.

6-42

6.9 APPLICABILITY AS A SANDY GEOMATERIAL OF GRANULATION COAL ASH

6.9.1 INTRODUCTION In Japan, based on "the law about promotion of usage of renewable resource" (resources recycling law) enforced in 1991, the coal ashes generated from a thermal power plant are specified as by-product of electric industry and there is a duty to promote their effective usage (Environmental technology association (2000)). Moreover, in the 1999 fiscal year, 7.6 million ton per year of coal-ashes was generated, and this quantity tends to increase every year. At the present, about 80% of the coal-ashes are used effectively and the most is used as blended material in cement, such as in civil engineering field. Since a large quantity can be utilized at once in this field of application, it is expected civil engineering usage can be as an acceptance place of the predicted increasing coal-ashes. As the usage of the coal-ashes in civil engineering field, reclamation, backfill material, sub-grade material, and soil improvement material, are reported.

As a part of coal-ashes recycling, mainly the electric power companies are doing research on granulated coal-ashes, i.e., cement is mixed with coal-ashes to make grained sand. The advantages of granulated size are: (i) enable to control the outflow of a heavy-metallic component, and (ii) compared to the powdered ashes, it is easier to manage its storage.

On the other hand, beach and river sand which are a good material as cement aggregate and reclamation material are in a deficiency state, and have become a serious problem in recent years. Especially, in the Seto-uchi coast area, extraction of beach sand is forbidden. Therefore, developments of alternative materials instead of natural sand are urgently needs, e.g., research on the possibility of application of granulated coal-ashes. In order to use such artificially granulated materials as geo-material, it is necessary to grasp their mechanical properties, such as, settlement, bearing capacity, and compressibility of the material.

It is reported that influence of particle crushing cannot be simply neglected in dealing with compressive deformation of geo-material (Yamamuro et al.(1996), Nakata et al.(2001a)). When particle crushing occurs, the volume will decrease due to the voids are buried by crushed tiny particle. Especially, compressive deformation caused by particle crushing remarkably occurs at brittle crushable soils, such as, underneath fill-dam and around pile foundation tip under high pressure.

Furthermore, single particle crushing test as an examination to understand simply the crushing properties of a single particle has been also reported (Nakata et al. (1999b), Kato et al. (2001)). It was investigated that the particle strength obtained from single particle crushing test could express the crushing

property of material and it has correlation with one-dimensional compressive yielding stress, (Nakata et al. (2001b), Kato et al. (2002)), i.e., the information obtained from single particle crushing test can be considered as an effective index to evaluate compressibility of geo-material. Moreover, the strength of the granulated material can be controlled by changing the added cement quantity. Therefore, if the compressibility evaluation based on the particle strength of material can be attained, it will retrieve significant contribution in evaluation of granulated material application and its development as well.

In this research, single particle crushing properties of granulated coal-ashes and their compressibility are investigated. Furthermore, evaluation of their applicability as geo-material is also discussed. 6.9.2 MECHANICAL PROPERTIES Material used In this research, four kinds of sand-size granulated coal-ashes were used. The compositions of coal-ashes and cement additive differ from No.1 to No.3, respectively. The composition of No.4 was the same as of No.1, but they were manufactured in different method. The composition of each granulated coal-ashes and the types of granulating machine are shown in Table 6.9.1. The physical properties of each granulated coal-ashes are shown in Table 6.9.2. Table 6.9.1 Composition and granulation method

composition (%) Sample fly ash cement addition type ofmachine

spin speed

No.1 76 5 19 Mortar mixer

low- middle


low- middle


low- middle

No.4 76 5 19 Eirich mixer high

Table 6.9.2 Physical properties

Sample Gs emax emin d50(mm) Uc No.1 2.38 1.98 1.57 1.275 2.35No.2 2.35 2.06 1.65 1.120 3.45No.3 2.42 2.22 1.8 1.160 2.10No.4 2.38 1.68 1.38 1.340 2.82

Single particle crushing testMaterial used The test was carried out by placing a particle on the lower plate in a most stable direction and then moving the upper plate at a constant rate of displacement to crush the particle. Since those plates are flat, the loads during test are applied from two points in the vertical direction. Force and displacement were measured during test. The load measuring capacity was 4.91×102N with a resolution of 9.81× 10-3N. And the displacement was measured by un-contacted type with

6-43

measuring capacity of 2.00mm in a resolution of 1.00×10-3mm. Displacement rate of 0.1mm/minute was applied. Single particle crushing test was carried out on d50 size particle of each granulated coal ash. Crushing strength σf is defined as equation (6.9.1).

20

ff d

F=σ (6.9.1)

where, Ff is the maximum load, d0 is the initial height of particle. The average value of each crushing strength σf in the same conditions is defined as the single particle crushing strength σfm.

Since granulated coal-ashes’ properties are influences by cement contents, and their self-hardening characteristics, and it is considered that their strengths are the functions of mixture age, therefore, the single particle crushing test schedule was divided into 4 steps. Figure 6.9.1 shows the relationship between σfm and age. Each single particle crushing test was carried out on 10 - 30 particles on each step.

It can be seen from the figure that although crushing strengths change in the early ages, increase linearly in logarithm scale after 40 days and do not converge even after 200 days. In the comparison among their single particle crushing strengths, it was found that No.3 with the most cement content has higher strengths than No.1 and No.2, respectively. Moreover, although No.4 has equivalent cement content with No.1, but since it was manufactured in a different granulation method, it is shown that No.4 has about 5-times strength of No.1 and even it performs higher strength than No.3 with more quantity of cement. In the future, by performing accumulation of data, it is considered that the strength of single particle can arranged by controlling cement content and granulating method.

The strength of a particle is sharply changed due to particle size, shape, mineral composition, and internal crack of a particle. (Nakata et al. (1999), Fukumoto and Hara (1998)). Therefore, it is important to investigate the representative value of the particle crushing strength and their variances as well. Authors (2002) divided the variances of particle strength into two independent factors, i.e., variance influenced by particle size V(X), and variance influenced by the other factor V(Y). And the variance of crushing strength for all the particles contained in the sample is defined as V(X+Y)=V(X)+V(Y). Furthermore, the following Weibull function is applied and the Weibull modulus m shows the variation index of particle crushing strength.

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

m

Pfm

fs exp

σσ (6.9.2)

where, σf/σfm is a normalized crushing strength, m is the Weibull modulus in which larger value of m shows

smaller variance of single particle crushing strength. The relationship between the age and the Weibull

modulus m is shown in Figure 6.9.2. In this figure, it is found that the Weibull modulus m does not respect to the age of each granulated coal-ashes. Therefore, it can be said that the influence of the age to the variance in particle strength is small.

10 1000.1

1

10

100

age (days)300

Me

an

cru

shin

g s

tre

ss σ

fm (M

Pa

) No.1

No.2

No.3

No.4

Figure 6.9.1 Relationship between σfm and age

10 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

age (days)300

We

ibu

ll m

od

ulu

s m

No.1

No.2

No.3

No.4

Figure 6.9.2 Relationship between Weibull modulus m and age One dimensional compression test In order to evaluate compressibility of the granulated coal ashes, one-dimensional compression test was carried out on the 200 days sample. Compression tests were carried out on dry sand samples in diameter of 50mm and height of 10mm at a constant deformation rate of 0.1mm/min. Figure 6.9.3 shows the change of the void ratio to the increase in vertical stress. In this figure, the result of silica sands is also shown. For granulated coal-ashes, compared to silica sand, decrease of a remarkable void ratio is observed from a low stress region. Since single particle crushing strength of granulated coal ash is smaller than that of silica sand, it is considered that void ratio decreases due to particle crushing begins from a low stress region.

Here, by using tangent slope in an arbitrary stress on an e-logσv curve, Cc' is defined as the following

6-44

equation.

vc log'

σ∆∆eC = (6.9.3)

Furthermore, it can be said Cc' becomes the

parameter which shows the compressibility of the material under compressive stress. The relationship between compression index Cc' and vertical stress is shown in Figure 6.9.4. Compression index Cc' of each granulated coal-ashes shows higher value from low stress region. And the value of Cc' become about 0.7 ～ 0.8 at σv=90MPa. It is higher than the value of silica sands 0.5.

0.01 0.1 1 10 1000.0

0.5

1.0

1.5

2.0

No.1　203No.2　205No.3　203No.4 203

age(d)

Silica0.18 -2 .0

loose

Silica0.18 -2 .0

dense

dense

Vertical stress σv (MPa)

Vo

id r

ati

o e

Figure 6.9.3 e-logσv curve

0.01 0.1 1 10 1000.01

0.1

1

Silica0.18 -2 .0

loose

Silica0.18 -2 .0

dense

dense

Co

mp

ress

ion

in

de

x C

c'


No.1　203No.2　205No.3　203No.4 203

age(d)

Figure 6.9.4 Variation of compression index during one-dimensional compression Authors (2002) defined the vertical stress at Cc'=0.3 as one-dimensional compression yield stress (σv)Cc'=0.3, and defined R' in an equation (6.9.4) as the parameter of curvature of e-logσv curve.

( )( ) ⎥

⎦

⎤⎢⎣

⎡=

=

=

1.0'v

3.0'vlog'Cc

CcRσσ (6.9.4)

The relationship between single particle crushing strength and one-dimensional compression yield stress is shown in figure 6.9.5. In this figure, the result of natural sand is also shown. Irrespective of granulated

coal-ashes to natural sand, an ascending straight is obtained, and it is shown that one-dimensional compression yield stress can be predicted from single particle crushing strength. Since granulated coal-ashes has low single particle crushing strength, it can be said that its yield stress is lower than of natural sand. The relationship between Weibull modulus m and the curvature of e-logσv curve R' is shown in figure 6.9.6. In this figure, the natural sand result is also shown. It is shown that the result of granulated coal-ashes is located on the line obtained to natural sand, and can match the curvature of a compression curve from the variance in single particle crushing strength. From the above result, it is shown that the information from a single particle crushing test can be considered as an effective index to investigate the compression characteristic of granulated coal-ashes.

10-1 1 101 102 10310-1

1

101

102

103

Mean crushing stress σfm (MPa)

Ver

tica

l st

ress

(σ

v)C

c'=

0.3

(M

Pa

)

Silica0.18 -2 .0

Silica-2 .0

ChiibishiQuiouShirasuShirasuc ut

MasadoGlassToyoura0.106-0.25

Silica sands

Crushable soils

Natural sands Dr0=100% (Kato et al.2002)

No.4

No.1 No.3

No.2dense (age:200days)

Figure 6.9.5 Relationship between single particle crushing strength and one-dimensional compression yield stress (σv)Cc'=0.3

0.1 1 10

0.1

1

R '= 0.6m-1.2

Weibull modulus m

dense (age:200days)

No.4

No.1

No.3

No.2

R' (

=lo

g{(σ

v)C

c'=

0.3

/(σ

v)C

c'=

0.1

})

Silica0.18 -2 .0

Silica-2 .0

ChiibishiQuiouShirasuShirasuc ut

MasadoGlassToyoura0.106-0.25

Silica1.4 -1 .7

Silica0.6 -0 .71

Silica0.25 -0 .3

Aglass0.85 -1 .0

Masado1.4-1 .7

Aio0.85 -2 .0

Natural sands Dr0=100% (Kato et al.2002)

Figure 6.9.6 Relationship between Weibull modulus m and the curvature of e-logσv curve R' 6.9.3 APPLICABILITY OF GRANULATED COAL-ASHES AS A SANDY GEOMATERIAL From the result of single particle crushing test and one-dimensional compression test, it is confirmed that the granulated coal-ashes behave as brittle particles, therefore, they have low yield stress and can perform as high compressibility material. As a geo-material

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application, to obtain higher density, it is necessary to compact by a certain method. It is expected by increasing density, enable to make their yield stress and shear strength become higher. Figure 6.9.7 is a schematic diagram of higher yield stress by increasing density. It is considered to obtain the same effect to the preloading method to the normally consolidated clay, i.e., by decreasing initial void ratio, follow e-logσv behavior ideally changes by inclination of Cs until it reaches normally compression curve. Then, when the compaction energy is taken into account, if the required energy for a certain yield stress can be grasped, it will direct to a reliable and economical design. In that case, the relationship between the energy E (input energy) required to make density increase, and the work W actually spent on change of volume is shown as follows.

Normal compression lineE:compaction energy

E = αWW =∫σvδεv (J/cm3)

⊿e∽⊿γd = f (E)

Cc

1

σvy0

e0

e

σvy

Vertical stress σv

Vo

id r

ati

o e

Cs1

Figure 6.9.7 Schematic diagram of the increase in the yield stress by the increase in density

WE α= (6.9.5)

where α is an index depend on compaction method and/or material.

On one-dimensional compression test, the work W, which is spent in the change of specimen volume, is defined by following equation.

vvδεσ∫=W (6.9.6)

where, σv is the vertical stress (MPa), εv is the vertical strain.

The relationship between vertical stress σv and the work W is shown in Figure 6.9.8. In this figure, it is found that the value of vertical stress σv in one-dimensional compression test can be calculated when certain W is known. And the σv shows the new yield stress σvy in an e-logσv curve. It is shown that the work W required to obtain the yield stress beyond a certain design load, the compaction energy E (input energy) for a known α, can be predicted. Furthermore, the volume strain εv in equation (6.9.5) can be calculated from the change of the void ratio e by the following equation.

ee+

=1δ

vε (6.9.7)

The work W is given by a vertical stress σv and a void ratio e, so the W-logσv relationship can be obtained from an e-logσv curve in Figure 6.9.3. And an e-logσv curve is predicted by single particle crushing strength and its variance. From the above result, it is confirmed that the information obtained from single particle crushing test of granulated coal-ashes becomes effective and important in case of the application as a geo-material.

0.1 1 10-0.2

0.0

0.2

0.4

0.6

0.8

1.0

No.1　203No.2　205No.3　203No.4 203

age(d)

Silica0 .18-2 .0


Vo

rk W

(J/

cm3)

Figure 6.9.8 Relationship between σv and W 6.9.4 CONCLUSION The applicability of the developed granulated coal-ashes as geo-material, as part of the coal ashes recycling was investigated. The single particle crushing test was carried out for granulated coal-ashes. Particle strength and its variance were considered. Moreover, one-dimensional compression test was performed to investigate the compressibility of granulated coal-ashes. From this research, it become clear that single particle crushing strength of granulated coal ashes continues increasing with age, and changes with cement contents and granulation method, and does not converge although at 200th days. Furthermore, compared to natural sand, yield stress of granulated coal-ashes is lower and compressibility was higher than that of natural sands. A close correlation was found between the single particle crushing strength or its variance and one-dimensional compression properties. Accordingly, it is confirmed that the information from a single particle crushing test enable to serve as an effective index to investigate compression characteristic of granulated coal-ashes.

These results showed that the compressibility of the granulated coal-ashes as geo-material was governed by cement content and granulation method. In the other words, it is possible to manufacture geo-material with properly expected compressibility properties. Furthermore, it is concluded that in the application of granulated coal-ashes as geo-material, it is necessary to conduct compaction appropriately. In this research, a simple equation is proposed to calculate the required compaction energy from single particle strength.

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Yasufuku Aramaki Katagiri nishio ishikawa Fujiyama Nakata Fujii

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chapter 6 marks of o show to be in stable condition, and

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