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Effects of Initial and Induced Anisotropy on Initial Stiffness of Sand by Triaxial and Bender Elements Tests

著者 Yamashita Satoshi, Hori Tomohito, Suzuki Teruyuki 著者別名 山下 聡, 鈴木 輝之 journal or Geomechanics: Testing, Modeling, and publication title Simulation volume GSP143 page range 350-369 year 2005-05 URL http://id.nii.ac.jp/1450/00008021/ doi: http://dx.doi.org/10.1061/40797(172)20

EFFECTS OF INITIAL AND INDUCED ANISOTROPY ON INITIAL STIFFNESS OF SAND BY TRIAXIAL AND BENDER ELEMENTS TESTS

Satoshi Yamashita1, Member, JGS, Tomohito Hori2, Member, JGS and Teruyuki Suzuki3, Member, JGS

ABSTRACT: In this study, to examine the effects of the fabric anisotropy of sand specimen and the anisotropic consolidation stress on the small strain stiffness, the bender elements test and the cyclic and monotonic triaxial tests were performed on several kinds of reconstituted and undisturbed sand samples. These laboratory test results were compared to the results of in-situ seismic surveys. Test results showed that the shear wave velocity estimated from the Young’s modulus on triaxial test is lower than those from bender elements and in-situ tests. In particular, it was remarkably recognized in the sample including coarse materials. Therefore, in the case of a comparison of initial stiffness between the laboratory and in-situ tests, the shear wave velocity should be measured in the laboratory test in the same way as the in-situ test.

INTRODUCTION Shear modulus G is an indispensable parameter on the deformation or seismic response analyses of the ground. To assess the in-situ initial (small strain) stiffness, laboratory tests on samples retrieved from the site or in-situ tests have been performed. One laboratory technique widely adopted in the last decade has been the propagation of seismic waves by means of piezoelectric transducers, called simply “bender elements”, housed in a triaxial apparatus (e.g. Dyvik and Madshus 1985). In this method, the shear wave velocity propagated vertically VVH has been commonly measured. In addition, the samples are generally isotropically consolidated under the in-situ effective overburden pressure. On the other hand, in in-situ seismic surveys, the down-hole or suspension technique measures VVH, whereas VHH or VHV is measured by the cross-hole technique. Note that the first and second sub-scripts for V

1 Associate Professor, Kitami Institute of Technology, 165 Koen-cho, Kitami, 090-8507, Japan, [email protected] 2 Graduate Student, Kitami Institute of Technology, 165 Koen-cho, Kitami, 090-8507, Japan 3 Professor, Kitami Institute of Technology, 165 Koen-cho, Kitami, 090-8507, Japan

1/20 S.Yamashita et al. denote the directions of shear wave propagation and polarization, respectively. In addition, the in-situ stress conditions may be mostly anisotropic, and in-situ subsoil has an anisotropic fabric. In respect to the effects of anisotropic fabric on the initial stiffness, it has been recognized that the initial stiffness obtained from laboratory tests depends on the type of test devices, because of the difference in the mode of shear deformation (e.g. triaxial vs. torsional shear). In addition, it has been pointed out that the shear 2 modulus estimated by shear wave velocity (G = ρVS ) differs with the propagating direction of the shear wave. In the literature, the GHH is found as slightly higher than the GVH and GHV even in isotropically consolidated soils, and the ratio of GHH to GVH or GHV increases as the K0-value increases (Lo Presti and O’Neil 1991; Stokoe et al. 1995; Bellotti et al. 1996; Fioravante 2000; Yamashita and Suzuki 2001a). On the other hand, in respect to the effect of stress anisotropy on the initial stiffness, it is well known that the shear wave velocity is independent of the magnitude of normal stress on the plane through which the shear body wave propagates (Roesler 1979; Yu and Richart 1984; Stokoe et al. 1995). It is also possible to express the dependence of the small strain shear modulus Gij on the current state of a soil by means of the following empirical equation (e.g. Jamiolkowski et al. 1995); n n G  σ '  i  σ '  j ij  i   j  = SijF(e)    (1) p r  p r   p r  where Sij = nondimensional material constant of given soil that also reflects its fabric; F(e) = void ratio function; σi' = effective principal stress along the direction of wave propagation; σj' = effective principal stress in the direction of particle motion; pr = reference stress; and ni, nj = empirical exponents. Moreover, Hardin and Bladford (1989) suggested that the Young’s modulus for elastic compressive strain increments in a certain direction is a unique function of the normal stress in the corresponding direction. Therefore, the small strain Young’s modulus Ei on isotropic or anisotropic stress condition may be expressed as: n E  σ '  i  i  = Si F(e)  (2) pr  pr  Accordingly, it would seem that the initial stiffness obtained from laboratory tests on isotropic consolidated samples differs from in-situ initial stiffness relevant to anisotropic consolidation state due to the differences of stress conditions, shear mode and propagating direction of shear wave, etc. Moreover, most of above results are based on the laboratory test results for reconstituted or remolded samples. In this paper, to clarify the effect of the propagating and vibrating directions of shear wave relative to the bedding plane of specimen and the anisotropic consolidation stress on the initial stiffness, the bender element test and the cyclic triaxial test were performed on several kinds of reconstituted and undisturbed sand samples. In addition, these laboratory test results were compared to the results of in-situ seismic surveys.

2/20 S.Yamashita et al.

Kitami

Natori River (Holocene ground)

Tokyo Edo River (Pleistocene ground) Osaka Higashi-Ohgishima (man-made island) Yodo River (Holocene ground)

FIG. 1. Sampling Sites of In-Situ Freezing Samples

TABLE 1. Physical Properties of Sands Sample Sample Sampling σ ' ρ Fc*** v in-situ s e e Uc** name type* depth (m) (kPa) (g/cm3) max min (%) TO RE - - 2.645 0.966 0.608 1.22 0 KU RE - - 2.562 1.973 1.253 4.46 0 HO UN RE 9.25 - 9.30 97.1 2.727 1.036 0.654 2.54 1.89 NR UN RE 7.45 - 7.60 77.3 2.637 0.921 0.592 3.13 0.06 YR UN RE 9.70 - 9.85 95.5 2.631 1.005 0.590 3.67 0.16 ER UN RE 15.15 - 15.30 150.2 2.701 - - 2.87 0.02 * UN: undisturbed sample; RE: reconstituted sample ** Uc: coefficient of uniformity (D60/D10) *** Fc: fine fraction content (≤ 75µm)

TEST PROGRAM Test Materials The tested materials are Toyoura (TO) sand, Kussharo (KU) volcanic ash sand and four kinds of undisturbed sand samples. Toyoura sand has been widely used for laboratory stress-strain tests in Japan. Kussharo sand is volcanic ash sand taken from the suburbs of Kitami, Japan. Kussharo sand used was graded with cut off particles more than 2 mm and less than 0.075 mm in size. The undisturbed sand samples were retrieved by the in-situ freezing method at four sites in Japan as shown in Figure 1. The sampling sites are Higashi-Ohgishima (HO) man-made island (Yamashita et al. 1997), Natori River (NR), Yodo River (YR) (PWRI and JGCA 1998) and Edo River (ER). Natori and Yodo River samples were retrieved from Holocene deposits, and Edo River samples were retrieved from a Pleistocene deposit. The physical properties, the particle shapes and the grain size distribution curves of these sands are shown in Table 1, Photo 1 and Figure 2.

3/20 S.Yamashita et al.

Toyoura Kussharo

0 0.5 1.0 (mm) 0 0.5 (mm) 1.0 (a) Toyoura sand (b) Kussharo volcanic ash sand

Higashi-Ohgishima Natori River

0 0.5 1.0 (mm) 0 0.5 1.0 (mm) (c) Higashi-Ohgishima sand (d) Natori River sand

Yodo River Edo River

0 0.5 1.0 (mm) 0 0.5 1.0 (mm) (e) Yodo River sand (f) Edo River sand

PHOTO 1. Particle Shape of Tested Sands

4/20 S.Yamashita et al. 100 Higashi–Ohgishima 80 Toyoura 60 Edo river Yodo river Natori river 40

Percent passing (%) 20 Kusshro

0 0.05 0.1 0.2 1 2 10 20 Grain size (mm)

FIG. 2. Grain Size Distribution Curves of Tested Sands

DIMENSION OF SAND CONTAINER (mm)

Hopper

10 Porous stone 1 170 Nozzle water supply SATURATION 280 220

Sieve

0 20

30 DEWATERING (-5kPa) V, D, H-specimen

V D H

PLUVIATION OF SAND FREEZING (-25ºC) CUTTING

FIG. 3. Preparation Procedure of MSP-F Specimen

Sample Preparation Method In this study, two kinds of sample preparation methods were employed for reconstituted specimens. The first one was the dry-vibration (DV) method. In this method, after the air-dry sand was pluviated into a mold from the nozzle of a tube, the specimen was compacted by vibrating the mold using an electric vibrator until a desired density was attained. The second method was the MSP-F method for Toyoura and Kussharo specimens. In this method, the air-dry sand was pluviated into a container from a multiple sieving pluviation (MSP) apparatus, as shown in Figure 3. The sand deposited in the container was permeated by water and thereafter

5/20 S.Yamashita et al. unsaturated at suction induced by no volume expansion due to freezing. For facilitation of specimen forming, the sand deposited in the container was frozen in a freezer. Specimens with an angle between the axial direction of the triaxial specimen and the pluviation direction of 0° (V-specimen), 45° (D-specimen) and 90° (H-specimen) were cut from the frozen sand blocks. The diameter and height of Toyoura and Kussharo specimens are 70 mm and 70 or 150 mm, respectively. Specimens of 70 mm in diameter and 150 mm in height were reconstituted by the DV method, whereas those of 70 mm in diameter and 70 mm in height were reconstituted by the MSP-F method. Toyoura sand specimens were reconstituted to a relative density Dr ranging from 40 % to 80 %. For Kussharo sand specimens, the Dr ranged from 60 % to 100 %. Moreover, the diameter and height of undisturbed and its reconstituted specimens (HO, NR, YR, ER) are 50 mm and 100 mm, respectively. The reconstituted samples with same density to undisturbed samples were prepared by the DV method, using soil from undisturbed specimens recycled after testing.

Test Procedures After each dry reconstituted specimen was set up in the cell, or after each frozen specimen was subject to thawing under an isotropic negative pressure of 30 kPa, the cell pressure was raised to 30 kPa, and carbon dioxide was percolated through the specimen. Subsequently, deaired water was permeated through the specimen. Back pressure of 98 kPa was, thereafter, applied for about one hour. All specimens were isotropically and/or anisotropically (K = σh'/σv' = 0.5) consolidated to σv' = 392 kPa. The stress path at consolidation is shown in Figure 4. The shear wave velocities in three different directions were measured by bender elements (BE) method on each consolidation state (solid circle mark in Fig. 4). In addition, the undrained equivalent Young’s modulus at small strain (0.001 %) was measured by cyclic triaxial (CTX) loading on same consolidation states. In each state, the specimen was subjected to eleven undrained loading cycles performed by applying uniform triangle cyclic axial displacement with a frequency of 0.1 Hz. The axial stress and the axial strain were measured by a load cell and one pair of proximity transducers placed inside the cell, respectively. The equivalent Young’s modulus Eeq is defined by the average value of those at 2nd to 10th cycles. In BE test, one pair of bender elements was attached to the top cap and the pedestal. Two pairs of bender elements were attached to the lateral surface of specimen after specimen set up. The lateral BE was composed of a metallic plate (aluminum plate) glued with one end of a BE (Fioravante 2000). The plate was glued to the internal surface of the membrane with buttonhole. The BE was glued on a metal plate using quick-drying glue after the complete preparation of the specimen as shown in Figure 5 and Photo 2. This method does not give disturbance to the specimen, because the BE does not penetrate into the specimen, and adapts well to testing for granular soil including coarse materials. However, the shear wave velocity of vertical direction (VH-wave) of some undisturbed specimens has not been measured, because it was difficult to penetrate the BEs attached cap and pedestal into the frozen specimen, especially in the sample including gravel such as Edo River sample (see Fig. 2 and Photo 1f).

6/20 S.Yamashita et al. 450

400 K = 0.5

350 ' (kPa) v 300 σ

250 K = 1.0

200

150

Effective vertical stress, 100

50

0 0 50 100 150 200 250 300 Effective horizontal stress, σh' (kPa)

FIG. 4. Stress Path at Consolidation

Specimen

Membrane

Aluminum plate

Araldite coating Bender Element

Araldite

FIG. 5. Lateral Bender Element

PHOTO 2. Set up of Lateral Bender Elements

The transmitting element was driven by ±10V amplitude waves from a generator with a single sinusoidal wave of different frequency. The effective propagating distance and the arrival time of the shear wave were defined by the distance from tip-to-tip of the bender elements and the starting points of the input and received waves, respectively (Yamashita and Suzuki 2001b). The shear wave velocity used was the average of those measured using sinusoidal waves of 10, 15 and 20 kHz.

7/20 S.Yamashita et al. 20 40 60 80100 200 400 20 40 60 80100 200 400 500 500 Toyoura sand Kussharo v.ash sand 400 (a) 400 DV method DV method n dry specimen dry specimen 300 n 300 (b) D = 40 % r : VVH (n=0.18) : VVH (n=0.26) 200 : VHH (n=0.22) 200 : VHH (n=0.30) : VHV (n=0.22) Dr = 60 % : VHV (n=0.29) 500 500 2 Dr = 60 % F(e)=(2.17–e) /(1+e) 400 D = 80 % 400 (m/s) (m/s) r 0.5 0.5 300 300

/ F(e) : VVH (n=0.20) / F(e) : VVH (n=0.28) s s

V : VHH (n=0.23) 200 V : VHH (n=0.28) 200 : VHV (n=0.22) : VHV (n=0.26) 500 500

400 Dr = 80 % 400 Dr = 100 % F(e) = e–2 300 300

: VVH (n=0.23) : VVH (n=0.27) 200 : VHH (n=0.22) 200 : VHH (n=0.28) : VHV (n=0.22) : VHV (n=0.29)

20 40 60 80100 200 400 20 40 60 80100 200 400 σ'c (kPa) σ'c (kPa)

FIG. 6. Effect of Propagating Direction of Shear Wave (DV Method); (a) Toyoura Sand, (b) Kussharo Sand

TEST RESULTS Effect of Propagating Direction of Shear Waves Figures 6a and 6b show the shear wave velocity VS versus the effective confining pressure σc', plotted on a logarithmic scale, for three different propagation directions of shear waves on isotropic consolidated Toyoura and Kussharo dry specimens reconstituted by the DV-method. In order to eliminate the effect of the difference in density on test results in these figures, the shear wave velocity was normalized by dividing it by the square root of the following void ratio functions: Toyoura sand F(e) = (2.17-e)2/(1+e) (Iwasaki et al. 1978), and Kussharo sand F(e) = e-2 (Hoshi et al. 2000). It can be seen that in Toyoura sand, the effect of the propagating direction of the shear wave is relatively small, and the VHH is slightly higher than the VVH. On the other hand, in Kussharo sand the VHH is higher than the VVH and the VHV. This trend agrees with results that measured the shear wave velocity in three directions in the calibration chamber (Stokoe et al. 1995) and on the triaxial specimen (Fioravante 2000). It is considered that this is due to the effect of the fabric anisotropy of the specimen. In addition, the effect of the propagating direction on the shear wave velocity for the Kussharo specimen is larger than that for the Toyoura specimen. It would seem that this is because Kussharo sand particles are flatter than those of Toyoura sand, as shown in Photos 1a and 1b.

8/20 S.Yamashita et al. VH-wave

HV-wave HH-wave Bedding plane V-specimen H1-specimen H2-specimen

: VVH* : VHH* : VHV*

FIG. 7. Relations between Propagating Direction and Bedding Plane

TABLE 2. Relations between Propagating Direction and Shear Wave Velocity Wave V-specimen H1-specimen H2-specimen VH-wave VVH* VHV* VHH* HH-wave VHH* VHV* VVH* HV-wave VHV* VVH* VHH*

Effect of Fabric Anisotropy of Specimen As mentioned above, it has been indicated that the shear wave velocity obtained from a HH-wave is higher than that from VH or HV-waves. It is considered that this is due to the effect of the fabric (inherent) anisotropy of the specimen. Thus, to further clarify the effect of the fabric anisotropy on the shear wave velocity, shear wave velocities in three different directions were measured for the specimens with an angle between the axial direction of the triaxial specimen and the pluviation direction of 0° (V-specimen) and 90° (H-specimen) cut from the frozen sand blocks (see Fig. 3). Figure 7 illustrates the relationships of the propagating direction of the shear wave to the bedding plane. There are two kinds of H-specimens due to the difference in attaching direction of the bender elements relative to the bedding plane. The following three kinds of shear wave velocities, which were defined by the relations of the propagating direction versus the bedding plane, were measured on these specimens (see Table 2) -VVH* = the propagating direction of the shear wave is normal and the vibrating direction of the particles is parallel relative to the bedding plane; -VHH* = the propagating direction of the shear wave and the vibrating direction of the particles are parallel relative to the bedding plane; and -VHV* = the propagating direction of the shear wave is parallel and the vibrating direction of the particles is normal relative to the bedding plane.

9/20 S.Yamashita et al. 20 40 60 80100 200 400 20 40 60 80100 200 400 500 500 : V * (V–specimen) Toyoura sand : V * (V–specimen) Toyoura sand 400 VH 400 VH : VHH* (H2–specimen) MSP–F method : VHH* (H2–specimen) MSP–F method 300 : VHV* (H1–specimen) 300 : VHV* (H1–specimen) VH–wave VH–wave 200 200 Dr = 40 % Dr = 60 % 500 500 : VVH* (H2–specimen) 400 : VVH* (H2–specimen) 400 (m/s) : VHH* (V–specimen) (m/s) : VHH* (V–specimen) 0.5 0.5 : VHV* (H1–specimen) 300 : VHV* (H1–specimen) 300

/ F(e) HH–wave / F(e) HH–wave s s

V 200 V 200 F(e)=(2.17–e)2/(1+e) F(e)=(2.17–e)2/(1+e) 500 500 400 : VVH* (H1–specimen) 400 : VVH* (H1–specimen) : VHH* (H2–specimen) : VHH* (H2–specimen) 300 : VHV* (V–specimen) 300 : VHV* (V–specimen) HV–wave HV–wave 200 (a) 200 (b)

20 40 60 80100 200 400 20 40 60 80100 200 400 σ'c (kPa) σ'c (kPa)

20 40 60 80100 200 400 20 40 60 80100 200 400 500 500 : V * (V–specimen) Toyoura sand : V * (V–specimen) 400 VH 400 VH : VHH* (H2–specimen) MSP–F method : VHH* (H2–specimen) 300 : VHV* (H1–specimen) 300 : VHV* (H1–specimen) VH–wave Kussharo v.ash sand 200 200 MSP–F method Dr = 80 % VH–wave Dr = 80 % 500 500 : VVH* (H2–specimen) 400 : VVH* (H2–specimen) 400 (m/s) : VHH* (V–specimen) (m/s) : VHH* (V–specimen) 0.5 0.5 : VHV* (H1–specimen) 300 : VHV* (H1–specimen) 300

/ F(e) HH–wave / F(e) s s

V 200 V 200 F(e)=(2.17–e)2/(1+e) HH–wave F(e)=e–2 500 500 400 : VVH* (H1–specimen) 400 : VVH* (H1–specimen) : VHH* (H2–specimen) : VHH* (H2–specimen) 300 : VHV* (V–specimen) 300 : VHV* (V–specimen) HV–wave 200 (c) 200 HV–wave (d)

20 40 60 80100 200 400 20 40 60 80100 200 400 σ'c (kPa) σ'c (kPa)

FIG. 8. Effect of Fabric Anisotropy on Shear Wave; (a) Toyoura (Dr=40%), (b) Toyoura (Dr=60%), (c) Toyoura (Dr=80%), (d) Kussharo (Dr=80%)

10/20 S.Yamashita et al. 400 500 Toyoura sand Kussharo v.ash sand MSP–F method MSP–F method (m/s) (m/s) VHH*/VVH* = 1.05 0.5 0.5 400

e) e) VHH*/VVH* = 1.13 ( 300 ( * / F * / F

HV HV 300

, V VHV*/VVH* = 0.99 , V VHV*/VVH* = 1.00 0.5 0.5 e) e)

( 200 ( : VHV* – VVH* : VHV* – VVH* : V * – V * 200

* / F HH VH * / F : VHH* – VVH* HH HH

V (a) V (b) 100 100 100 200 300 400 100 200 300 400 500 0.5 0.5 VVH* / F(e) (m/s) VVH* / F(e) (m/s)

FIG. 9. Relation of VHH* or VHV* to VVH*; (a) Toyoura Sand, (b) Kussharo Sand

Figures 8a to 8c show the shear wave velocity versus the effective confining pressure measured under the same propagating direction of the shear wave relative to the axial direction of the specimen with a different direction of bedding plane on Toyoura sand. When the propagating direction of the shear wave relative to the direction of bedding plane is the same, although the propagating direction of the shear wave relative to the axial direction of the specimen is different, the share wave velocities for propagating and vibrating parallel to the bedding plane VHH* are slightly higher than the VVH* and the VHV*. The VVH* is almost the same as the VHV*. Figure 8d shows the shear wave velocity versus the effective confining pressure on Kussharo sand. In the case of Kussharo sand, the VHH* is clearly higher than the VVH* and the VHV*, and the VVH* is the same as the VHV* as well as the Toyoura sand. From the above, it can be concluded that shear waves propagate faster in the plane parallel to the bedding plane than in the normal one. Figures 9a and 9b show the VHH* and the VHV* versus the VVH* on the MSP-F Toyoura and Kussharo specimens. It can be seen that the VHH* is higher than the VVH* with an average value of VHH*/(VVH* = VHV*) = 1.05 on Toyoura sand and 1.13 on Kussharo sand. The difference between Toyoura and Kussharo sand is the difference in inherent anisotropy due to the difference in particle form. Similar results were obtained from undisturbed and its reconstituted samples. Figures 10a and 10b show the relationships of the VHH and the VVH versus the VHV on four kinds of undisturbed and reconstituted samples consolidated isotropically. It is found that the VVH is almost the same to the VHV on both undisturbed and reconstituted samples, and the VHH is slightly larger than the VHV on reconstituted specimens. However, the VHH is not larger than the VHV in undisturbed samples. This difference may be the effect of fabric anisotropy on the shear wave velocity is lower than that of aging effect on undisturbed samples, since the initial stiffness increase by the ageing effect. However, further research will be necessary to clarify the difference of the results between undisturbed and reconstituted samples.

11/20 S.Yamashita et al. 600 600 : Higashi–Ohgishima : Higashi–Ohgishima : Natori river : Natori river 500 : Yodo river 500 : Yodo river : Edo river (a) : Edo river (b) V /V =1.05 400 400 HH HV (m/s) (m/s) HH HH

, V 300 , V 300 VH VH

V : VVH – VHV V : VVH – VHV 200 : VHH – VHV 200 : VHH – VHV Undisturbed sample Reconstituted sample 100 100 100 200 300 400 500 600 100 200 300 400 500 600 VHV (m/s) VHV (m/s)

FIG. 10. Relation of VHH or VVH to VHV; (a) Undisturbed Sample, (b) Reconstituted Sample

1.6 : Geophone : BE : Cyclic loading

VH 1.4 /G

HH 1.2

, G range of this study

V (reconstituted) 1.0 /M

H : Lo Prest & O'Neill (1991) : Stokoe et al. (1991) 0.8

, M : Bellotti et al. (1996)

V : Hoque & Tatsuoka (1998)

/E : Kuwano (1999) H 0.6

E : Fioravante (2000) : Yamashita & Suzuki (2001a) 0.4 E /E M /M G /G H V H V HH VH

FIG. 11. Relation of Vertical and Horizontal Moduli

Next, these results compare the results of other research. Figure 11 shows the relations between the horizontal and vertical stiffness at small strain measured by the geophone, BE and cyclic loading tests on sands. In the seismic wave tests such as geophone and BE tests, the horizontal moduli are larger than the vertical moduli. On the other hand, in the cyclic loading test, the horizontal Young’s modulus EH is lower than the vertical modulus EV. However, in this CTX test, the EH was not directly measured. Some assumptions (for example Poisson’s ratio) are required in evaluating the EH, because two principal stress changed under cyclic loading. On the other hand, in this study, the EH can be measured directly using H-specimen, because two principal stresses have not changed.

12/20 S.Yamashita et al. 350 0.35

300 Toyoura sand σc' = 98.1 kPa 0.30 Cyclic triaxial test f = 0.1 Hz

) 250 drained loading 10th cycle 0.25 200 0.20 h ) (MPa

e 150 0.15 : V–sample /F(

eq 100 : D–sample 0.10 E : H–sample 50 0.05 0 0.00 10–6 10–5 10–4 10–3 10–2 Single amplitude axial strain, (ε ) a SA

FIG. 12. Cyclic Triaxial Test Results for V, D, H-Specimens

350 500 –10 Toyoura sand Drained triaxial compression test 450 –9 300 Toyoura sand Triaxial compression test (b) draine loading 400 –8 350 –7 250 σc' = 98.1 kPa (%) v

ε = 0.5 %/min 300 –6 ε 200 a 250 –5 150 200 –4

/F(e) (MPa) (a) 150 –3 sec : V–specimen 100 σc' = 98.1 kPa E : D–specimen 100 : V–specimen (e=0.676) –2 Volumetric strain, 50 : H–specimen Deviator stress, q (kPa) 50 : D–specimen (e=0.676) –1 : H–specimen (e=0.672) 0 0 0 –6 –5 –4 –3 –2 10 10 10 10 10 1 Axial strain, ε 0 2 4 6 8 10121416 a Axial strain, εa (%)

FIG. 13. Monotonic Triaxial Test Results for V, D, H-Specimens; (a) Small to Medium Strains, (b) Medium to Large Strains

Figure 12 is the result of CTX test on the V, H, and D-specimens. When the EH is directly measured, the EH is slightly larger than the EV the same as seismic test results. A similar result was obtained from the Monotonic test (see Fig. 13). The EH is slightly larger than the EV at small strain. However, the EV became larger than the EH with the increase in strain level due to the dilatancy effect. Because the stiffness mainly depends on the slide friction at elastic range, the dilatancy effect increases at middle to large strain level. As a result, the EV became larger than the EH at middle to large strain levels.

Effect of Stress Conditions on Initial Stiffness Figures 14a and 14b show the relationships of the VVH versus the VHV on four kinds of undisturbed and reconstituted samples consolidated isotropically and anisotropically. It is found that the VVH is almost the same to the VHV on both undisturbed and reconstituted samples, irrespective of stress conditions imposed. This is because shear wave velocity depends on the stress of propagating and vibrating directions (e.g. Roesler 1979), even in undisturbed sand samples. In other words, the VVH and VHV depend on the vertical and horizontal stresses.

13/20 S.Yamashita et al. 600 600 K=1.0, 0.5 K=1.0, 0.5 : Higashi–Ohgishima : Higashi–Ohgishima 500 : Natori river 500 : Natori river : Yodo river : Yodo river : Edo river 400 400 (m/s) (m/s) VH

VH 300 300 V V (a) 200 200 Undisturbed sample Reconstituted sample (b) 100 100 100 200 300 400 500 600 100 200 300 400 500 600 VHV (m/s) VHV (m/s)

FIG. 14. Relationship between VVH and VHV; (a) Undisturbed, (b) Reconstituted

600 600 K=1.0, 0.5 K=1.0, 0.5 : Higashi–Ohgishima : Higashi–Ohgishima 500 : Natori river 500 : Natori river : Yodo river : Yodo river : Edo river : Edo river 400 400 VHH/VHV=1.05

(m/s) V /V =0.95 (m/s) HH HV VHH/VHV=0.95

HH 300 HH 300 V V (a) 200 200 (b) Undisturbed sample Reconstituted sample 100 100 100 200 300 400 500 600 100 200 300 400 500 600 VHV (m/s) VHV (m/s)

FIG. 15. Relationship between VHH and VHV; (a) Undisturbed, (b) Reconstituted

Figures 15a and 15b show the relationships of the VHH versus the VHV. It is found that the VHH is lower by about 5 % than the VHV on anisotropic stress conditions (K=0.5). This is because the VHH depends only on the horizontal stress, whereas the VHV depends on both vertical and horizontal stresses as mentioned above, bearing in mind that the vertical stress is higher than the horizontal stress at anisotropic consolidation. Figures 16a and 16b show the relationships between the vertical or horizontal stresses and the undrained equivalent Young’s modulus Eeq obtained from undrained CTX tests on undisturbed samples. It is found that the Eeq on isotropic stress conditions is the same to that on anisotropic stress conditions in the same vertical stress. On the other hand, in the case of same horizontal stress, the Eeq on isotropic stress conditions is lower than that on anisotropic stress conditions, because the

14/20 S.Yamashita et al. vertical stress at the isotropic stress condition is lower than that at the anisotropic stress condition. In other words, the Young’s modulus at small strain only depends on the stress in loading direction (e.g. Hardin and Bladford 1989), even in undisturbed sand samples.

700 700 500 Higashi–Ohgishima Natori river 500 Cyclic triaxial test 300 300

: K=1.0 (σv'=σh') 100 : K=0.5 (σ '>σ ') 100 80 v h 80 700 700 (MPa)

eq 500 Yodo river Edo river 500 E 300 300

100 Undisturbed sample (a) 100 80 80 40 60 80100 300 500 40 60 80100 300 500 σv' (kPa) 700 700 500 Higashi–Ohgishima Natori river 500 Cyclic triaxial test 300 300

: K=1.0 (σv'=σh') 100 : K=0.5 (σ '>σ ') 100 80 v h 80 700 700 (MPa)

eq 500 Yodo river Edo river 500 E 300 300

100 Undisturbed sample (b) 100 80 80 40 60 80100 300 500 40 60 80100 300 500 σh' (kPa)

FIG. 16. Relationship between Equivalent Young's Modulus and (a) Vertical Stress, (b) Horizontal Stress

Comparison of Laboratory and In-Situ Tests Figures 17a to 17d show the shear wave velocity VS profile with depth on undisturbed samples in this study together with CTX tests, in-situ seismic cone and PS logging tests data at different depth reported by PWRI and JGCA (1998) and Yamashita et al. (1997). In these figures, some data in CTX and BE tests under in-situ effective overburden pressures were estimated from those at different stress conditions shown in Figure 4.

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: Seismic cone (VVH) : PS logging (VVH) 2 : CTX test (K=1.0) 2 PWRI & JGCA (1998) 4 Yamashita et al. (1997) 4 6 6 8 8 10 10 Depth (m) Depth (m) 12 12 Yodo river (c) 14 Higashi–Ohgishima (a) 14 16 16 0 100 200 300 0 100 200 300 Shear wave velocity, V , V (m/s) Shear wave velocity, V , V (m/s) L in–situ L in–situ 0 0 Natori river This study 2 2 : CTX test (K=1.0) : PS logging (VVH) 4 : CTX test (K=1.0) 4 : CTX test (K=0.5) PWRI & JGCA (1998) : BE test VHV (K=1.0)

6 6 : BE test VHV (K=0.5) 8 8 Edo river 10 10 12 12 Depth (m) Depth (m) 14 14 16 This study 16 : CTX test (K=1.0) (b) 18 : CTX test (K=0.5) 18 : PS logging (VVH) : BE test VVH (K=1.0) (d) 20 20 : CTX test (K=1.0) : BE test VVH (K=0.5) PWRI & JGCA (1998) 22 22 100 150 200 250 300 100 200 300 400 500 Shear wave velocity, V , V (m/s) Shear wave velocity, V , V (m/s) L in–situ L in–situ

FIG. 17. Comparison of VS from Laboratory (VL) and In-Situ (Vin-situ) Tests; (a) Higashi-Ohgishima, (b) Natori River, (c) Yodo River, (d) Edo River

The VS(CTX) ( = E / 3ρ ) estimated from CTX tests in this study (circle mark) almost agree with reported CTX test data (double circle mark). On the other hand, the VS(BE) obtained from BE tests on isotropic stress conditions (open triangle mark) are slightly higher than those from in-situ tests. It would seem that this reasons is attributed to the difference of stress condition between the laboratory and in-situ tests, noting that in-situ subsoil was anisotropically consolidated. On the other hand, the VS obtained from BE tests on anisotropic stress conditions (solid triangle mark) are similar to those from in-situ tests.

16/20 S.Yamashita et al. Specimen Gravel

50mm

FIG. 18. Arrangement of Gravel to Specimen

20 1.0 sin wave (f=10kHz) 10 0.5 0 0.0 –10 –0.5 –2020 –1.01.0 sin wave (f=20kHz) 10 0.5 0 0.0 –10 : with gravel –0.5 : without gravel Input wave (V) –2020 –1.01.0 pulse wave Receved wave (mV) 10 0.5 0 0.0 –10 –0.5 first arrivals –20 –1.0 –0.1 0.0 0.1 0.2 0.3 0.4 Time (ms)

FIG. 19. Received Wave Records on Specimens with and without Gravel

In addition, in comparison of CTX test and in-situ test results, in the case of Edo River sample, the VS estimated from CTX tests are much lower than those from in-situ tests. It is also found that the VS obtained from BE tests is much higher than that from CTX tests when comparing with the other sands. It would seem that in case of the sample including coarse materials such as Edo River sample (see Fig. 2 and Photo 1f), the shear wave velocities have a tendency to be overestimated, since the shear wave has a tendency to transmit faster through stiff parts (gravel), as pointed out by Tanaka et al. (2000) and Anhdan et al. (2002). Then, to clear the VS from BE test is higher than that from CTX test in the sample including coarse materials, the BE test was performed on Edo River reconstituted sample. In this test, one tested specimen was prepared by Edo River sand less than 2 mm, another specimen was gravel put on a propagating route of shear wave, as shown in Figure 18. Figure 19 shows input and received wave records by two specimens. In the case of specimens including coarse materials on propagating route, the arrived time is about 40 % fast. Therefore, it is said that the shear wave velocities have a tendency to overestimate, in case of the sample including coarse materials.

17/20 S.Yamashita et al. 1.5 1.4 Cyclic triaxail test K=1.0 : Higashi–Ohgishima 1.3 : Natori river 1.2 : Edo river 1.1 : Yodo river in–situ 1.0 / V 0.9 CTX

V 0.8 0.7 : this study 0.6 : other study 0.5 0 100 200 300 400 500 Shear wave velocity from in–situ test, Vin–situ (m/s)

FIG. 20. Comparison of VS from CTX (VCTX) and In-Situ (Vin-situ) Tests

1.5 1.5 1.4 K=1.0 Higashi–Ohgishima 1.4 K=0.5 1.3 : VVH 1.3 : VVH Natori river : VHH Higashi–Ohgishima : VHH 1.2 : V 1.2 : V HV Natori river HV

1.1 in–situ 1.1 in–situ

/V 1.0 / V 1.0

BE 0.9 BE 0.9 V Yodo river Edo river V 0.8 0.8 0.7 0.7 Yodo river Edo river 0.6 (a) 0.6 (b) 0.5 0.5 0 100 200 300 400 500 0 100 200 300 400 500 Shear wave velocity from in–situ test, Vin–situ (m/s) Shear wave velocity from in–situ test, Vin–situ (m/s)

FIG. 21. Comparison of VS from BE (VBE) and In-Situ (Vin-situ) Tests; (a) K = 1.0, (b) K = 0.5

Figures 20 and 21 show the ratios of shear wave velocities in laboratory VCTX, VBE and in-situ tests versus the in-situ shear wave velocity Vin-situ. In CTX tests, the ratios of VCTX and Vin-situ become small with increase the Vin-situ irrespective of stress conditions, as shown in Figure 20. In BE tests, in the case of isotropic stress condition, the VBE is higher than the Vin-situ irrespective of the propagating direction of shear waves, as shown in Figure 21a. On the other hand, in anisotropic stress condition, the VBE is similar to the Vin-situ irrespective of the Vin-situ, as shown in Figure 21b. In particular, the VVH and VHV almost coincide with the Vin-situ. It must be pointed out that the propagating direction of shear wave in all in-situ tests coincide with the vertical direction, because in-situ test is suspension technique; i.e. Vin-situ is VVH. Accordingly, it is said that in the case of comparison of initial stiffness between the laboratory and in-situ tests, the shear wave velocity should be measured in the laboratory test in the same way as the in-situ test. In addition, the shear wave velocity of VH or HV-wave on anisotropic stress conditions should be measured in the

18/20 S.Yamashita et al. laboratory test on the similar stress condition to the in-situ stress condition. This method is also important to evaluate the quality of sample. For example, there is a fear that the Edo River sample is evaluated as disturbed a sample based on the CTX test result, because the elastic modulus is much lower than that from the in-situ test. However, for using design or analyses parameter, the VS or G from in-situ tests should not be use in case of the sample including coarse materials, because it is overestimated value. It would seem that the correct elastic modulus is average or a little larger than that from CTX test, because the CTX test result has some problems such as the bedding error, assumption of Poisson’s ratio, and so on.

CONCLUSIONS Based on the comparison with laboratory test results on undisturbed and reconstituted sand specimens and in-situ test results, the following conclusions were obtained; (1) The VVH is almost the same to the VHV on both undisturbed and reconstituted samples irrespective of the inherent anisotropy, the stress condition and the kinds of sands. On the other hand, the VHH is slightly higher than the VVH and VHV on reconstituted sample under isotropic consolidated state. (2) The EH at small strains is slightly larger than the EV on reconstituted sample under isotropic consolidated state. However, the EV became larger than the EH with the increase in strain level. (3) The shear wave velocity estimated from the EV on CTX test is lower than that from BE test. In particular, it was remarkably recognized in the sample including coarse materials. (4) In the case of a comparison of initial stiffness between the laboratory and in-situ tests, the shear wave velocity should be measured in the laboratory test in the same way as the in-situ test.

ACKNOWLEDGMENT The authors are grateful to Public Works Research Institute (PWRI) for providing the Natori, Yodo and Edo River samples.

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