Comprehensive tests on a clean sand were performed to evaluate the effects of the methods of sample preparations on shear moduli and hysteretic damping ratios of sands with use of a resonant-column apparatus and a static torsional shear device. All of the tests were conducted under the fully drained condition. Specimens for resonant-column tests were solid cylindrical and those for torsional shear tests were hollow cylindrical. These specimens were sheared torsionally and cyclically. It was found that for a wide range of shear strain the shear modulus and the hysteretic damping ratio of the sand tested by cyclic drained shear tests are quite insensitive to the methods of sample preparations adopted in this investigation. These include the different methods of pouring, compacting, moistening, saturating, unsaturating or so.
Recent advances in geotechnical engineering have shown that mechanical properties of sands are not determined necessarily only by density or void ratio. It has also been pointed out that structures or fabrics of sands and strain or stress histories can affect considerably mechanical properties of sands. Oda (1972, a) has demonstrated by performing a comprehensive series of static triaxial compression test on specimens of clean sands prepared by different methods that among mechanical properties of sands, stress-strain relationship and internal friction angle at failure are considerably affected by methods of sample preparation. At the same time, Oda (1972, a) showed that samples are, in general, stiffer in the vertical direction of deposition than in the horizontal direction. Oda (1972, b) also showed that these variation in mechanical properties of sands with different methods of sample preparation are due to the variations in internal structures of fabrics in sand sample. These findings were also confirmed by Arthur and Menzies (1972) and these
* Associate Professor, Institute of Industrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo.
** Chief, Ground Vibration Section, Works Research Institute, Ministry of Construction, No. 1, Ohwaza-Asahi, Toyosato-machi, Tsukuba-gun, Ibaragi.
*** Assistant Researcher, do.
**** Graduate Student, University of Tokyo.
***** Japan Association for Building Research Promotion.
Written discussions on this paper should be submitted before January 1, 1980.
TA TSUOKA ET AL.
properties of sand were termed as "inherent anisotropy". In the field of soil dynamics, Ladd (1974) has shown that cyclic undrained strengths of reconstituted sands determined by dynamic triaxial tests are strongly affected by the various sample preparation methods. Mulilis, Chan and Seed (1975), Silver et al. (1976), Silver and Park (1976) and Ladd (1976) have also confirmed these results. It was shown by their investigations that for both medium dense and dense specimens of sand, the specimens prepared by compacting moist sand have significantly greater resistance to cyclic undrained shear than those compacted in the dry condition, the difference being as much as 110 percent. It is to be noted that the sands tested by them involve both of clean sands and non-clean sands which include fine particles less than 74 µ and/or being well graded.
On the other hand, Ishihara, Tatsuoka and Yasuda (1975) have shown that liquefaction potentials of sand are closely related to the dilatancy performances of sands. The sand which has the strong tendency of the decrease in volume under fully drained condition or the increase in excessive pore pressure under undrained condition when sheared statically has small resistance to cyclic undrained shear. Tatsuoka and Yoshiwara (1973) have shown that the tendency of the decrease in volume under static loading is also decreased considerably by overconsolidating specimens. Ishihara and Sodekawa (1973), and Ishihara and Okada (1978) have also demonstrated that overconsolidated specimens of clean sands and silty sands have greater resistance to cyclic undrained shear than normally consolidated specimen for the equal density. It was also demonstrated by Mulilis, Mori, Seed and Chan (1977) that long time consolidation increases cyclic undrained strength considerably for both of clean sands and silty sands.
Finn, Bransby and Pickering (1970) have shown that cyclic undrained shear strength of clean sand can decrease drastically due to large shear strain histories. These may be due to induced anisotropy in the structures of samples. Tatsuoka (1968) have shown, on the other hand, that small shear strain history may increase cyclic undrained strength of sand sample.
In summary, it has been clarified by many investigations that liquefaction potentials or dilatancy performances are rather sensitive to structures or fabrics of sands and stress or strain histories.
On the other hand, Afifi and Richart (1973) have shown by performing resonant-column tests that overconsolidations do not affect the shear modulus of uniform dry soils which had a grainsize, D 50 larger than 0. 04mm. For finer soils, it was found that the considerable increase in shear modulus is caused by overconsolidation, but this is primarily due to a reduction of the void ratio of the sample not by overconsolidation history itself. At the same time, it was revealed by them that the increases in shear moduli of uniform dry soils whose D50 are larger than 0. 04 mm during long time consolidation are insignificant. But it was found that for finer soils having D50 <0. 04 mm the time dependent increase in shear modulus can be significant and must be evaluated.
Anderson and Woods (1977) examined the effects of sample compaction techniques on shear moduli of a silty clay and a fat clay at r<I0- 6 using a Hardin-type resonant-column device. They concluded that the compaction method influenced the shear moduli of the silty clay and the fat clay tested noticeably, and the effects seemed to be more significant at lower pressure levels.
These findings described above can be summarized as in Table 1. It can be seen from Table 1 that cyclic undrained strength of sands are more sens1t1ve to several factors than shear modulus at very small strain level. It is also seen from this table that there are still many unknown factors which can or do not affect shear moduli and dampings of clean sand or silty sand when cyclically sheared under the fully drained condition.
Therefore, it has been required to clarify whether various sample preparation methods
Table 1. Factors relating to structures of sands which can affect dynamic properties of sands I Causes I
o Specimen Preparation
o Shear Strain History
o Over Consolidation
o Long Time Consolidation
o. Others
Dynamic Properties I
j Macro Factors I I Micro Factors I
.o Inherent Anisotropy
o Stress System Induced Anisotropy
o Heterogeneity
o Dilatancy Performance
o Others
o Cyclic Undrained Strength
o Rigidity at Cyclic Drained Shearing
o Damping at Cyclic Drained Shearing
o Others
Researches Relating to Above Faetors
o Number of Interparticle Contact
o Grain Orientation
o Interparticle Orientation
o Interparticle Stress Distribution
o Void Distribution 'W'ithin Specimens
o Others
Ladd (1974)
Mulilis et al. (1975)
Silver and Park (1975)
Silver et al. (1976)
Ladd (1976)
Ishihara et al. (1973)
Ishihara and Okada (1978)
Finn, Bransby and Pickering (1970)
Tatsuoka and Yoshiwara (1973)
Afifi and Richart (1973)
Anderson and Woods (1977)
Clean Sands Different specimen preparations can vary cyclic undrained strength.
Clean Sands Large shear strain histories decrease cyclic undrained strength.
Clean Sands Small shear strain histories can increase cyclic undrained strength.
Clean Sands Overconsolidation histories and long time consolidation do not increase Silty Sands significantly shear modulus at shear strain level of l0-4 or less.
a silty clay The compaction method influences the shear modules at y< lo-6 noticeably, and a fat clay and the effects seem to be more significant at lower pressure level.
can or do not affect shear moduli and dampings of sands for a wide range of strain amplitude. These knowledges are quite important to utilize the test data of reconstituted sands for design purposes. These sample preparation effects are also necessary to be clarified in order to correlate the data by different organizations.
Presented herein are the results of resonant-column testings and torsional shear testings on one clean sand, adopting various methods of sample preparation. For each test, a specimen was reconstituted by a different method. The results clearly demonstrate that when cyclically sheared under the fully drained condition, shear modulus and damping of this clean sand are relatively insensitive to the method of reconstitution of samples adopted in this investigation for a wide range of shear strain amplitude.
TEST PROCEDURES
In this test program, Toyoura Sand was utilized. The physical properties of this sand are : Gs=2. 64, D10=0. 12 mm, D50=0. 162 mm, Uc= 1. 46, the content of fine particles (<74 µ) =0. 0%, emax and emin by the Yoshimi and Tohno method (Yoshimi and Tohno, 1972) are 0. 96 and 0. 64, respectively, and the grain shape is angular. The resonant-column apparatus used in this investigation was another one than that used in the previous studies (Iwasaki and Tatsuoka, 1977 ; Iwasaki, Tatsuoka and Takagi, 1978). But, the principal of testing is identical to that of the previous apparatus. Solid cylindrical samples were used for resonant-column tests in this investigation. Sample dimensions are lOcm in height and 7 cm in diameter. The total rotational inertia of the top mass is 0. 019 kgf-cm-sec2• The spring constant varies slightly with the amplitude with being 85 kgf-cm-sec2 at the amplitude of 3X10-4 radians. Shear strains for solid cylindrical samples were defined as those at two third of the radius from the center of the sample. In resonant-column tests, reconstituted sand samples were firstly isotropically confined by the pressure of 0. 2 kgf/cm2
TATSUOKA ET AL.
(about 20kN/m2). Then, resonant-frequencies were measured at several shear strain amplitudes ranging from 10-6 to 10-4 in single amplitude. All of the tests on air-dry, moist and saturated samples were performed under the fully drained condition. After the measurements at the confining pressure of 0. 2 kgf/cm2 were completed, the confining pressure was increased to 0. 5 kgf/cm2 (about 50 kN/m2) and the measurements described above were repeated. Such measurements were also repeated at the confining pressures of 1. 0, 2. 0 and 4. 0 kgf/cm2• From the relationships between shear modulus and single strain amlitude r for the confining pressures of 0. 2, 0. 5, 1. 0, 2. 0 and 4. 0 kgf/cm2 (about 20, 50, 100, 200 and 400 kN/m2), the shear moduli at the shear strain amplitudes of 10-6, 10-5 and 10-4 were read off and used in the following analyses.
In order to obtain shear moduli and hysteretic damping ratios for the shear strain amplitude larger than about 10-4, a torsional shear device was utilized. In these tests, hollow cylindrical samples were used, the dimensions of which are 10 cm in height, 10 cm in outer diameter and 6 cm in inner diameter. All of the samples in this test were isotropically consolidated at the confining pressure of 1. 0 kgf/cm2 (about 100 kN/m2). No initial torsional shear stresses were applied to the sample before cyclic torsional stresses were applied. Cyclic shear tests were performed by controlling the amplitude of torsional shear stress. First, ten times of cyclic shear tests were conducted for a sample at the shear strain amplitude of about 5X10-5 under the fully drained condition. Then, with a larger cyclic shear stress amplitude producing around a doubled shear strain amplitude as in the previous cyclic shearing, the second stage with ten times of cyclic shearings was done. With increasing shear stress amplitude, such stages as above were repeated until the sample were torsionally failed. As it was found that the stress-strain hysteresis loops in the first cyclic loadings at the second or further stages were affected by the previous cyclic loadings, those in the second and tenth loadings were used to analyse shear moduli and dampings in the following. In each test of both resonant-column and torsional shear tests, fresh sand was used. The details of test procedures were described in the previous papers (Iwasaki and Tatsuoka, 1977 ; Iwasaki, Tatsuoka and Takagi, 1978).
SAMPLE PREPARATION
It has been pointed out by Mulilis et al. (1975) and Ladd (1976) that both the molding water content at sample preparations and the method of sample preparation can be the primary causes for variations in cyclic undrained strength. Therefore, in this investigation, for each sample preparation method, several values of water content at sample preparation were adopted. In total, twenty one different methods of sample preparation were adopted. These are illustrated in Fig. 1 and listed in Tables 2 and 3.
At the time of pouring of sand, three different moist conditions were adopted ; air-dry, moist and saturated. For air-dry samples, air-dry sand was poured into a mold by two methods. In the dry-pluviation method, air-dry sand is poured into a mold through a small hole with the rate of flowing out being 50 g per minute. The position of the hole was always kept 10 cm high above the surface of sample. No compaction procedures were followed in this case. In the other dry pouring methods, air-dry sand was poured into a mold with a spoon and then compacted by various methods. Saturated sand was firstly poured with a spoon into a mold fulfilled with de-aired water for all the specimens. Besides the saturated-spooning method, all the specimens were compacted by various methods. Moist sand was poured with a spoon and then compacted by various methods.
For compacting specimens, five different methods were adopted. In the tapping method for air-dry and saturated specimens, the mold was tapped with a small wooden hammer twenty times for each of five layers from all directions. In the tamping method, at one
Table 2. Sample preparation methods adopted for resonant-column tests
Nt: Number of tamping for each layer of five layers.
Spooning Method on Saturated Samples
TA TSUOKA ET AL.
Spoon
Vibrator
Vibration Method on Air-Dry Samples and Saturated Samples (Frequency of Vibration 1s around 120 Hz )
Tamping Rod
0 = 3.5 cm for IOcm Hx 7cm D Mold and ¢ = 1.8 cm for 10cmH x
10cm0.D. x 6cm ID. Mold
Tamping Method
an Air-·Dry Samples, Moist Samples and Saturated Samples
:: 10cm
Pluviation Method on Air - Dry Samples
Tapping Method on Air- Dry Samples and Saturated Samples
Rod fJ = 0.6 cm and 0 = 1.5 cm
Rodding Method on Air- Dry Samples. Moist Samples and Saturated Samples
Fig. 1. Specimen preparation methods adopted in this investigation
time one fifth of sand of the total inner volume of the mold was poured with a spoon and tamped with a tamping rod twenty times for air-dry specimens, ten or twenty or fourty times for moist and saturated specimens. The compaction properties of this sand for various water contents are shown in Fig. 2. Several water contents were adopted for moist specimens as shown in Tables 2 and 3. The diameters of the foot of the tamping rod are 3. 5 cm for the samples of resonant-column tests of 10 cm Hx7 cm D and 1. 8 cm for the samples of torsional shear tests of 10 cm Hx 10 cm ODX 6 cm ID. The weight of the tamping rod was 1. 8 kg and the weight of the falling weight was 0. 7kg. The falling height was 10 cm. In the rodding method (I) for air-dry, moist and saturated specimens, a rod of 0. 6 cm in diameter was plunged one hundred times uniformly into each of five layers. In the rodding method (II) for air-dry, moist and saturated specimens, a rod of 0.15 cm in diameter was plunged two hundred times uniformly into each of five layers. In the vibration method, a handy vibrator was utilized to compact air-dry or saturated specimens. The frequency of the vibrator was around 120 Hz. The vibrator was pushed to the mold to give horizontal vibrations for one minute for each of five layers.
The water contents of several specimens were changed before shearing tests. Several air-dry specimens for resonant-column tests were moistened by flowing water into the
Test No.
SHEAR MODULUS AND DAMPING
Table 3. Sample preparation methods for torsional shear tests
Method of Sample Preparation
Dry-Tapping
Dry-Pluviating
Saturated-Spooning
Saturated-Tapping
Dry-Tamping
Dry-Rodding I
Dry-Rodding II
Dry-Vibration
Saturated-Tamping
Saturated-Rodding I
Saturated-Rodding II
Saturated-Vibration
Moist-Tamping
Moist-Tamping, Freezing and Saturating
Fig. 2. Compaction properties of
Note
Iwasaki, Tatsuoka and Takagi (1978)
Number of Tamping for Each of Five Layers Nt=40 Rod; 0.6cmj> Rod; Nt=lD
Nt=40 Rod; 0.6cm<f> Rod; 0.15cm4'
Nt=40
Nt=lO
Nt=40
Saturated Nt=20, by Flowing Water into Sample
TATSUOKA ET AL.
specimens from the bottom of the specimen. And several saturated specimens were made unsaturated for resonant-column tests by two different methods. In the unsaturation method (I), saturated specimens were made unsaturated by flowing air into the specimens from the bottom of the specimen. In the unsaturation method (II), water was sucked from the inside of a specimen by vacuum pressure from the top of the specimen. The water contents of these specimens at shearing tests were listed in Tables 2 and 3.
Several samples made by the tamping method at moist conditions were frozen. After stored in a refrigerator for several weeks, these specimens were set in triaxial cells and thawed with being sucked by the vacuum pressure of -0. 2 kgf/cm2• After thawed, these specimens were confined by the air pressure of 0. 2 kgf/cm2 (about 20 kN/m2) for resonantcolumn tests and of 1. 0 kgf/cm2 (about 100 kN/m2) for torsional shear tests and then saturated by flowing water into the specimens from the bottom. The test conditions of these specimens were listed in the bottoms of Tables 2 and 3.
Toyoura Sand obtainted by resonant-column tests for the confining pressure p ranging from 0. 2 to 4. 0 kgf/cm2 (about 20 to 400 kN/m2) at the single amplitude shear strains of 10-s, 10-5 and 10-4• It can be seen from Fig. 3 that the shear modulus of air-dry Toyoura Sand for the ranges of p and r shown in this figure is insensitive to the reconstitution methods adopted in this investigations. It was found, however, that shear moduli of moist and saturated specimens of Toyoura Sand were slightly less than those of air-dry specimens. This is shown in Fig. 4 where shear moduli for r of 10-6, 10-5 and 10-4 and for p of 0. 5, 1. 0 and 2. Okgf/ cm2 are shown. In this figure, shear moduli are divided by (2.17-e) 2/(l+e) to eliminate the effects of void ratio on measured shear moduli. Iwasaki, Tatsuoka and Takagi (1978) have already shown that this procedure is reasonable for Toyoura Sand. The solid line and the broken line in this figure indicate the average shear moduli of air-dry specimens divided by (2.17-e) 2/(l+e) ; Gn/ (2.17-e) 2/(l+e) which was obtained from Fig. 3 and 0. 8XGn/(2.17-e) 2/(l+e), respectively. It can also be seen from Fig. 4 that while the shear modulus of Toyoura Sand decreases slightly with the increase in the degree of saturation Sr the shear modulus is rather insensitive to the method of
Fig. 3. Relationship between G/(2.17-e) 2/(l+e) and p of air-dry Toyoura Sand by resonant-column tests
sample preparations which include the procedures of pouring, compacting, moistening, unsaturating, saturating, freezing and thaw-
Fig. 4. Relationship between G/(2.17-e) 2/(l+e) and the degree of saturation of Toyoura Sand by resonant--column tests
ing. Note again that shear moduli shown in Fig. 4 were measured under the fully drained conditions.
SHEAR MODULI BY TORSIONAL SHEAR TESTS
Measured shear moduli for P= I. 0 kgf/cm2 which were obtained by torsional shear tests on specimens reconstituted by several methods are shown in Fig. 5 for the second cyclic loading and in Fig. 6 for the tenth cyclic loading. The shear moduli shown in this paper are the equivalent secant moduli defined in Fig. 5. In these figures, measured shear moduli are divided by
(2.17-e)2 o.s
P (1)
m which G* is shear modulus in kgf/cm2, e is measured void ratio and p is confining pressure in kgf/cm2• Eq. (1) was originally proposed by Hardin and Richart (1963) for round-grained Ottawa Sands and for r of 10-4 or less. To eliminate the effects of variations in e and p, which actually differed slightly from 1. 0 kgf/cm2 in some cases, on G, measured G was divided by G*. The solid curves and the hatched bands in Figs. 5 and 6 indicate the average and the range of the scatter of measured shear moduli of the specimens reconstituted by the first four methods listed from the top in Table 3, respectively. These tests were performed by Iwasaki, Tatsuoka and Takagi (1978) and it was shown by them that the shear modulus and the hysteretic damping of Toyoura Sand by cyclic torsional shear tests are not strongly affected by those four methods. It can be seen from Figs. 5 and 6 that while some scatterings can be observed among the data, the shear modulus of Toyoura Sand by torsional shear tests is also insensitive to the other methods of reconstitution adopted in this investigation for the shear strain am-
Torsional Shear Tests , Toyoura Sand
Average of Data by Iwasaki, Tatsuoka and Takagi ( 1978 l
Fig. 5. Relationship between G/G* and r for the second cyclic loading of Toyoura Sand by torsional shear tests
• Torsional Shear Tests, Toyoura Sand
Average of Data by Iwasaki, Tatsuoka and Takagi (1978 l P = 1.0 kgf/cm 2 (100kN/m 2) 0-a I 0-r = t. 0
Range of Data Iwasaki et al.
Average of Doto by
l I wo soki, Totsuoko and Takagi ( 1978) \t:lf-
(a) Y = 10 4 , P =1.0 kgf/cm2 • N =10 { 100 kN/m2 l See Tobie 3 for Legend.
Table 3 for Legend
Single Ar:nplitude Shear Strain Y
Fig. 6. Relationship between G/G*:..and r for the tenth cyclic loading of Toyoura Sand by torsional shear tests
Fig. 7. Relationship between G/(2.17-e) 2/(l+e) and the degree of saturation for the tenth cyclic loading of Toyoura Sand by torsional shear tests
50 TATSUOKA ET AL.
plitude ranging from 5X10- 5 to 10- 2 • To examine the effects of the degree of saturation Sr on shear moduli, measured shear moduli divided by (2.17-e) 2/(l+e) for the tenth cyclic loading at several shear strain amplitudes were plotted against Sr as in Fig. 7. It can be seen from Fig. 7 that the shear modulus of Toyoura Sand is not affected considerably by the degree of saturation. From the test results by resonant-column tests and torsional shear tests, it can be concluded that the shear modulus of Toyoura Sand for the shear strain amplitude ranging from 10-6 to 10-2 is quite insensitive to the methods of sample preparation employed in this investigation. Furthermore, it can be derived that the shear modulus of Toyoura Sand decreases slightly with the increase in the degree of saturation, but the degree of decreasing is not noticeable.
HYSTERETIC DAMPING RATIOS IN TORSIONAL SHEAR TESTS
Measured hysteretic damping ratios r; of Toyoura Sand by torsional shear tests on reconstituted specimens are shown in Fig. 8 for the second cyclic loading and in Fig. 9 for the tenth cyclic loading. The definition of r; is illustrated in Fig. 8. The solid curves and the hatched bands indicate the average and the range of the scatter of the data of the specimens prepared by the first four methods listed in Table 3. The original data are shown in the paper by Tatsuoka, Iwasaki and Takagi (1978). It can be seen from these ;figures that while more scatterings than in shear moduli can be observed among the data there is not a trend showing that the hysteretic damping ratio of Toyoura Sand by torsional shear tests is noticeably affected by the methods of sample preparation. It can be also indicated in Figs. 8 and 9 that r; is also insensitive to the change in moist conditions. Figs. 10 and 11 show the relationship between r; and G/{G}r=l0-6 by torsional shear tests for the second cyclic loading and for the tenth cyclic loading, respectively. The value 0.3
Torsional Shear Tests
Toyoura Sand
P = 1.0 kgf/cm 2 ( 100 kN/m 2 ) 0-a/ur = 1.0 , N = 2 0
Average of Data by Tatsuoka , Iwasaki and Takagi ( 1978)
See Table 3
Range of Data by Tatsuoka et at ¢ w 2 T 17=-l_M _ 2TT W Legend
2 5 104 2 5
2 5 10-2 Single Amplitude Shear Strain 6
Fig. 8. Relationship between 7J and r for the second cyclic loading of Toyoura Sand by torsional shear tests
Torsional Shear ·Tests
Toyouro Sand
? .= 1 0 kgf/crn2 ( 100 kN/m 2 )
0-a I CTr = 1. 0 , N = 10
Average of Data by Tatsuoka , Iwasaki _(!_Q
Range of Data Ta tsuoka et
See Table 3 for Legend by aL
Fig. 9. Relationship between 'Tl and r for the tenth cyclic loading of Toyoura Sand by torsional shear tests
0.5 .-----..l---.....1---+---
Torsional Shear Tests. Toyouro Sand
0.41'" b
Average of Data for N = 2 and 'P = 0.25 20 k9f'cm2 (25,,,200 kN/m 2)
:31: by Tatsuoka, Iwasaki and
Takagi ( 1978
N = 2
See Table 3 for Legend
Fig. 10. Relationship between 'Tl and G/ {G} r=10-6 for the second cyclic loading of Toyoura Sand by torsional shear tests
of G/{G}r=l0- 6 for each sample was obtained by dividing measure values of G/G* by 1.4 which is the average value of G/G* at r=l0- 6 of Toyoura Sand (Iwasaki, Tatsuoka and Takagi, 1978). This is because the equal value of 1. 4 was considered reasonable as the value at r=l0- 6 for any sample tested. The solid curves in Figs. 10 and 11 are the average curves of the data of the specimens prepared by the first four methods in Table 3 by Tatsuoka, Iwasaki and Takagi (1978). These curves can be utilized to evaluate 1J from
Torsional Shear Tests , Toyoura Sand
Average of Data for N = 10 &. 11 *
3:13: 0.3 'ii &<l + -& 0 and 1l = 0.25 2.0 k<Wcm2 (25"'200kN/m2l by Ta1suoka, Iwasaki and To.kagi ( 1978)
Fig. 11. Relationship between 71 and G/ {G}r=io-s for the tenth cyclic loading of Toyoura Sand by torsional shear tests
the value of G/{G}r=l0- 6 • The data shown in Figs. 10 and 11 indicate that the r;-G/ {G} r= 10-5 relationship is also insensitive to the methods of sample preparations adopted in this investigation.
DISCUSSION
It is indicated in the above that the equivalent secant shear modulus and the hysteretic damping ratio of Toyoura Sand for the second cyclic loading or more under the fully drained condition are quite insensitive to the methods of sample preparation adopted in this investigation for a wide range of shear strain amplitude. The variety of the methods of sample preparation adopted in this investigation can be considered sufficient for the data by this investigation to be compared with the data by the previous studies. Therefore, these observations are, apparently, contrary to the fact that cyclic undrained strength of sands considerably depends on the methods of sample preparation. It is likely that there are some reasons for that difference. Firstly, the cyclic undrained strengths affected by the sample preparation methods reported by Ladd (1974) and others were obtained by cyclic triaxial tests. On the other hand, shear moduli and hysteretic damping ratios reported in this paper were obtained by torsional shear tests. At present, it has not been clarified whether undrained cyclic strengths of hollow cylindrical specimens by torsional shearing are less sensitive to the sample preparation methods than those of solid cylindrical specimens by cyclic triaxial tests or not. Therefore, further investigations are necessary to clarify this point. It seems, however, that the differences in the shape of specimen and the mechanism of shearing are not main causes for the different responses to cyclic loadings. It is likely that the different responses, the small or negligible effects of the sample preparation methods on the drained cyclic stress strain properties of sand and the considerable effects on the undrained cyclic strength, can be explained as follows. In undrained cyclic triaxial tests, excessive pore pressures accumulate due to the tendency of volume decrease of sand by cyclic loadings. The cumulative effect of excessive pore pressure induces failure or significant deformation. Therefore, small differences in each cyclic loading easily result in great differences in cyclic undrained strength which reflect the accumulation of excessive pore pressure. The amount of the increase in the excessive pore pressure can be considered to be related to dilatancy performance at virgin monotoneous loading which can be quite
SHEAR MODULUS AND DAMPING
different among the specimens prepared by the different methods of sample preparation. Therefore, the sample preparation method can easily affect undrained cyclic strength. On the other hand, equivalent shear moduli and hysteretic damping ratios under the fully drained condition depend only on the present condition of the specimens, not on the re· spouses to the previous cyclic loadings. Therefore, it is likely that while stress-strain rela· tionships of sands at the first monotoneous loading can be greatly affected by the sample preparation method or the stress-strain histories, the stress-strain relationships at the second cyclic loading or more under the fully drained condition can be insensitive to the sample preparation methods. Furthermore, the mechanism of the increase in the excessive pore pressure in undrained cyclic tests is closely related to dilatancy performances of sands. It can be envisioned that the cyclic dilatancy performances of sands can be considered more sensitive to fabrics or structures of sands than the rigidity or the damping capacity of sands under the fully drained condition. Further investigations are necessary to clarify the reasons for those differences described as above.
Lastly, Drnevich and Richart (1970) has reported that in resonant-column tests on a clean dry sand at constant confining pressure, prestraining at r= 10-4........,6X10-4 produces significant increases in the shear modulus and the damping property at shear strains less than those during prestrain, although void ratio is not significantly changed. They postulated interparticle contact wear as the cause of the effects of prestraining. As the samples were prepared at no or negligible confining pressure in this study, it is reasonable that such effects by wear at interparticle contacts as above can not be expected in this study.
CONCLUSIONS
To examine the effects of the methods of sample preparation on the shear modulus and the hysteretic damping ratio under the fully drained condition, resonant-column tests and torsional shear tests on Toyoura Sand were performed. Twenty one different methods for sample preparation were adopted. On the basis of the test results, the followings were found.
( i ) The shear modulus of Toyoura Sand for the shear strain amplitude ranging from 10-6 to 10-4 by drained resonant-column tests decreases slightly with the increase in the degree of saturation.
(ii) the shear modulus and the hysteretic damping ratio of Toyoura Sand at the second cyclic loading or more by drained torsional shear tests are not affected considerably by the change in the degree of saturation for the shear strain amplitude ranging from 5X10-5 to 10-2, and
(iii) the shear modulus and the hysteretic damping ratio of Toyoura Sand, a clean angular sand, at the second cyclic loading or more under the fully drained condition are insensitive to the methods of sample preparation including pouring, compacting, saturating, unsaturating, moistening, freezing and thawing.
To clarify whether shear moduli and hysteretic damping ratios of non-clean sands includ· ing finer soils less than 74 µ to some extent are affected by the sample preparation methods or not, further investigations are necessary.
ACKNOWLEDGEMENT
The authors wish to express their appreciations to Mr. Yutaka Itoh of Toa Harbour Works Co. for his helpful cooperations in conducting experiments, and to Miss Michie Torimitsu of Institute of Industrial Science, University of Tokyo for laborious work of typing.
NOTATION
e =void ratio 1
P = 3 (O' a+ 2 O' r) ; mean principal stress
w=water content (%)
G=equivalent secant shear modulus
N=number of cyclic loadings
Sr= degree of saturation (%)
r =single amplitude shear strain h . d . . 1 .dW 7J= ysteret1c ampmg rat10= 2 7t W--
{G}r=10-s=G at r=l0-6 o a• or= axial and radial stresses
Gn=average value of G for air-dry sand
G*=700 (2.17-e)2 o.s l+e P
(G* and p are in kgf/cm2)
REFERENCES
1) Afifi, S.S. and Richart, F. E. Jr. (1973): "Stress-history effects on shear modulus of soils," Soils and Foundations, Vol. 13, No. 1, pp. 77-95.
2) Anderson, A. M. and Woods, R. D. (1977): "Discussion," J. GED, Proc. ASCE, Vol. 103, No. GT 10, pp. 1200-1202.
3) Drnevich, V. P. and Richart, F. E. Jr. (1970): "Dynamic prestraining of dry sand," Jour. of SMF Div., ASCE, Vol. 96, No. SM 2, Mar., pp. 453-469.
4) Finn, W. D. L., Bransby, P. L. and Pickering, D. J. (1970): "Effect of strain history on liquefaction of sand," J. SMFD, Proc. ASCE, Vol. 96, No. SM 6, pp.1917-1934.
5) Ishihara, K. and Sodekawa, M. (1973): "Liquefaction of saturated sand including fine contents," Proc. of the 8th Ann..;al Meeting of JSSMFE, pp. 323-326 (in Japanese).
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7) Ishihara, K. and Okada, S. (1978): "Yielding of overconsolidated sand and liquefaction model under cyclic Soils and Foundations, Vol. 18, No. 1, pp. 57-72.
8) Iwasaki, T. and Tatsuoka, F. (1977): "Effects of grain size and grading on dynamic shear moduli of sands," Soils and Foundations, Vol. 17, No. 3, pp.19-35.
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12) Mulilis, J.P., Chan, C. K. and Seed, H.B. (1975): "The effects of method of sample preparation on the cyclic stress-strain behavior of sands," Report No. EERC 75-18, Univ. of California.
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14) Oda, M. (1972 b): "The mechanism of fabric changes during compressional deformation of granular material," Soils and Foundations, Vol. 12, No. 2, pp.17-36.
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17) Tatsuoka, F. and Yoshiwara, M. (1974): "On the yielding characteristics of sand in triaxial compression," Proc. of the 9th Annual Meeting of JSSMFE, pp. 211-214 (in Japanese).
18) Tatsuoka, F., Iwasaki, T. and Takagi, Y. (1978): "Hysteretic damping of sands under cyclic loading and its relation to shear modulus," Soils and Foundations, Vol. 18, No. 2, pp. 25-40. (Received May 10, 1978)
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the best of herself, because she was a woman of spirit who, on entering a room, made an impression. There was in Callendar a strange sort of vanity which demanded satisfaction, a vanity which was, perhaps, another and a masculine manifestation of his mother’s passionate sense of property. It would have been impossible for him to have married a woman, no matter how pretty she might have been, who was simply commonplace, sweet and insipid. He demanded in his wife an element of the spectacular. He had devoted himself to the tawny Lorna Vale, to the black and glittering Mrs. Sigourney, and to that strange, uncivilized musician from the middle west. About them all, there had been a spectacular quality, an undercurrent of fierce vitality, of outward distinction from the mob which appeared to have fascinated him.
She did not flatter herself that he had married her through desire; yet from the moment of their marriage he had been passionate after a fashion which shocked her. It was confusing to find that a man who was so polite and indifferent, so free from the little tendernesses which, to be honest, she had never expected, could at times display a passion so fierce and unexpected. It was as if in some way, love, passion, desire—she could not in his case define it precisely—were isolated, a thing apart.
There were reasons enough why she had married him. He was a great match; women would have desired him even if he had not been rich. And, she reflected with astonishing coldness, to have won him in the face of so much competition was a triumph worth paying for with much unhappiness. It was a victory over women who hated her and had sought with all the bag of their nasty feminine tricks to outwit her. She had married him too because she had come very nearly to the conclusion that she could never fall passionately in love with any man and that, therefore, it was far better to choose an interesting husband than a dull one. It was impossible, she felt, for love to survive such a passion as hers for dissection and analysis; love could not stand being pinned down and pulled apart. She did not then expect great love, and for the rest of it, Callendar had fascinated her as no other man had ever done, because he had always eluded her, just as he was eluding her now that he was her husband. In a sense, he offered her material vigorous enough to last a lifetime.
More than once in the midst of such reflections there returned to her the memory of the night when the raw young creature, whom she now thought of as “that musician,” had fainted. She remembered how, on this occasion, she had regarded Callendar minutely as he stood, his hands clenching the back of a chair, watching the naked Burmese dancer swaying to the insidious rhythm of tom-tom and flageolet. She remembered how the dancer and the barbaric music had shocked her a little as being wildly out of place in the big stuffy drawing-room. It was music which to her meant very little save that it was mildly exciting. Upon Callendar and his mother it had produced the most astonishing effect. Could it be that in this lay the clue alike to his fascination and to her failure to fathom that obscure thing which people called his soul? Though he had been her husband, even her lover, for a long time, she knew him no better than she had known him on the night of his mother’s absurd soirée.
And lying in that preposterous boudoir that had once belonged to the mistress of Wolff, she found herself admitting that slowly and certainly he was gaining complete possession of her imagination. It troubled her because she valued above all else in the world her own aloofness; so long as she did not lose her sense of being a spectator, no one could hurt her, not even her own husband. It troubled her too because she could not be certain whether this new interest had any relation to love or whether it had its roots in a sort of perverse attraction, fundamentally intellectual in quality ... an attraction which carried an element of the sensual hitherto entirely foreign to her nature. Day after day she found herself smiling over the thought that this sensual attraction should have been a little shocking and was not. In one sense he had overwhelmed her. He was a cruel, a passionate lover. If she had been less intelligent, more innocent, more sentimental, he might have wounded her very soul; but the curse which made romantic love impossible also saved her. Never, for more than a passing moment, had he been able to dissipate her awful awareness.
He had come to her, after all, from Lorna Vale, from Mrs. Sigourney, perhaps even from that American girl (though of this she could not be certain) and, doubtless, from many other women. So much experience, she understood, made him dangerous to any woman possessed of curiosity.
During those first weeks in Paris, it amazed Sabine to find that her husband knew so few of his own countrymen; he told her that most Americans who chose to live in Paris were either silly or depraved and so revealed for the first time the fact that he did not consider himself American. He became sulky when she asked him to dine with a school friend of hers whose husband chose to live in Paris.
“I know her husband,” he answered in contempt. “He is an ass who tries to live like the French. He’s not a Frenchman. His money comes out of a New England shoe factory.”
But he went all the same, perhaps because she managed to convey to him without saying it, that he was neglecting her. During the day she spent a great deal of time with friends and acquaintances, mostly women who had married foreigners of one sort or another. In their company she went from shop to shop buying an endless number of clothes. The same taste which caused her to shudder at the monstrous house in the Avenue du Bois led her to love clothes passionately. She knew too that beautiful clothes satisfied the strain of vanity in her husband which demanded a wife who was dressed with taste and distinction. She had begun already to plan how she might attract and keep him.
One evening, while they were dressing for the Opera, he said to her as she came out of the boudoir and faced him, “It is true what Jacques said at the club to-day. It takes the Parisian to make the clothes and the American to wear them. The Americans are the best dressed women in the world.”
And he looked at her in such a way that she grew warm suddenly in the knowledge that her figure was superb, that her shoulders were marvelously white and beautiful, and that her clothes were perfect. Until lately she had dressed, like most American women, for the sake of other women; now she understood that, without knowing it, she had been dressing of late to please a man, because she had found one who understood the beauty and importance of clothes. There was, despite all her other doubts, great satisfaction in that.
She discovered too that his friends were not among the Americans and the English but among the French and the Russians. She found herself, night after night, at dinners watching him as he stood, straight, dark and handsome, his queer gray eyes wrinkled a little with laughter, talking to some friend who was a foreigner, and at such moments she was aware of his
great difference from her own people. He was, in some obscure fashion, linked with that preposterous boudoir and its florid decorations. Perhaps, secretly, he really liked the awful house as much as his mother liked it.
She saw too, with the green eyes which took in everything, that the women about her were intensely conscious of him, and she knew then that she had been at the same time lucky and tragically unlucky. It would be so easy for him ... a man of so much intelligence and a beauty like that of a fine animal.
Toward the end of the first winter, a day or two after she had made certain that she was to have a baby, she interrupted her shopping long enough to have lunch at the Ritz. She had a table, alone, in one corner of the big room and, having no one to talk with her, she fell to observing the types at the other tables and reflecting upon the vulgarity and self-conscious glitter which marked the patrons of such hotels the world over. So she was startled when she found that the personality of some one who entered the room at that moment had the power of distracting her.
Two women came in together and stood for a time surveying the room. The one (it was she who was disturbing) was tall, slender and handsome, dressed smartly in a black suit with a black fur. The other, plainly a Jewess (who understood perfectly the manipulation of head-waiters) was small, with a ferrety, good-natured face and an energetic, chattering manner. They took a table at a little distance so that Sabine was able to watch them.
In the beginning, as she realized that there was some reason for her having noticed the pair, she became aware of a sense of familiarity in the taller woman. Then, as she watched them, the reason became quite clear. It was the American girl ... the musician, in Paris and in the Ritz of all places, and no longer dowdy but handsomely dressed!
By long established precedent, Sabine made no move toward approaching the newcomer. It was her habit to avoid involving herself with too many people; such a course made life far too tiresome and complicated. She had known the girl well enough, but there was no point now in renewing the acquaintance; indeed, it seemed idiotic even to consider the idea. Vaguely, she reflected, it was a good idea to leave what was well enough alone.
But the old, insatiable curiosity had been aroused; she found herself puzzled as to the presence of Ellen ... (Tolliver, that was her name) ... in Paris. She had been poor. She had been, she told Sabine during those stark conversations in the house on Murray Hill, hindered by a hundred obstacles. Yet here she was, in Paris, dressed handsomely in clothes which the appraising eye of Sabine told her had come from one of the best establishments, probably Worth or Chanel. Sabine was curious too regarding the whereabouts of the husband ... the husband whom she had once mistaken very stupidly for the girl’s lover. And slowly, in the midst of the noisy room filled with a fantastic assortment of people, there rose in her memory a picture of that vulgar apartment the Babylon Arms, and a glimpse as they opened the door of the tiny top floor flat, of a mild little man in shirt sleeves. What had become of him?
She remembered too the confidences which she had exchanged with her mother-in-law in the days when the young musician seemed so near to upsetting their carefully laid plans. Mrs. Callendar had mentioned the mild little man, saying, “I’m certain the girl doesn’t care a fig for him. She’s tied to him by pity. That’s all. But we can be thankful for him. He stands between her and Richard.”
Where was the little man to whom she was tied by pity?
Any one noticing Sabine as she made ready to leave the dining room might easily have taken her for an adventuress. She drew her veil over her face and holding her fur almost up to her eyes, she hastened out, taking care on the way that her back was toward the tall girl and the busy little Jewess. In the battle between an overwhelming curiosity and a vague instinct of fear, it was fear which, unaccountably, won the victory.
As her motor, very small and very expensive, sped away along the Rue de Rivoli and across the white spaces of the Place de la Concorde into the Avenue des Champs Elysées, Sabine succumbed to an inexplicable sense of depression. It occurred to her that she did not really know whether the girl had ever been the mistress of her husband. She could not even be certain that Callendar had ever asked Ellen Tolliver to be his wife. Thérèse Callendar had the word of the girl that there had been nothing; yet with Callendar, it was impossible to know. If he had asked her to marry him, it must have been but a step toward seducing her from her husband, the mild
little man. It did not occur to Sabine that with two women a man might be two quite different persons.
The motor sped smoothly along the asphalt past the Elysée Palace, around the Arc de Triomphe and on toward the huge house in the Avenue du Bois.
It might be, she thought, that Callendar himself knew the girl was in Paris. It might even be that he had arranged it for her to be there.
And again Sabine reflected that in her good fortune there was a tragic element of bad luck.
Callendar came in late for tea. She heard the footman speaking to him as he came through the vast hall across the tesselated floor. She waited for him, sitting behind the silver tea things in the small sitting room at the back of the house, and as he entered she was seized again by the disturbing fear of losing herself. He kissed her, casually, and said, “Well, have you had a busy day?”
“Nothing.... I went shopping with Madeleine and lunched alone at the Ritz.”
She might easily have added, “And whom do you think I saw there?” But she did not. On the contrary, she said, “It’s a funny show ... the Ritz.... And you?... What have you done?”
She did not hear his answer, because her attention was swallowed up by a sharp sense of his presence ... a vivid image of the dark face and the fine, muscular hand as he raised his silk kerchief in a familiar gesture to stroke his mustaches. In the back of her mind a small voice told her that it was perilous and awful to have such emotions.
She poured his tea but he did not drink it.
“I’ll have a glass of port,” was his reply. And then, “I had luck to-day. I won eleven thousand francs at baccarat ... playing with Henri and Posselt, the Russian.”
“Good,” was her reply, and again it was not what she might have said. This gambling worried her. It was not that he would bring them to poverty by it; that was almost impossible. But there was in her mind a feeling of disgust at the picture of men spending five hours of daylight in gambling. She tried to reproach herself by the thought that the idea was American and provincial. But she understood why his mother sometimes reproached him
for not thinking more of his business. (Always he retorted that she liked business and he did not.)
There was silence and presently Sabine said, “I wonder, Dick, if we can’t do something about this house ... either take one of our own or clear out some of this rubbish.”
“It’s very comfortable.... There’s every luxury.”
She laughed. “Too much luxury.... I feel at times like a kept woman. Wolff had it for his mistress.... I’m sure he did.”
Callendar smiled. “That’s true,” he replied. “Some of it is very bad, but can’t we stick it out until spring? We’ll go to the country then or to England for a time.”
She had spoken of the matter before and the answer had always been the same. She now revived the discussion without hoping for any solution; she wanted to know whether he really liked it, whether he was really linked in some way to the extravagance of that awful boudoir. Watching him as she spoke, she believed that he did.
For a time they smoked in silence and then Sabine, crushing out the ash of her cigarette, observed with a magnificent air of indifference, “I wonder what has become of that American girl ... the musician. You remember, ‘Miss Tolliver’ was her name.”
She saw that he looked at her sharply and then, disarmed by her indifference, that his face assumed an expression which matched her own.
“I don’t know. I suppose she’s still in New York. She was very talented.”
“She planned to come to Paris some day. If she does, it would be a nice thing to do to look her up.”
Her husband smiled before he answered her, a quiet amused smile such as he used to display when he caught his mother in some intricate feminine plot.
“I don’t see why we should. She probably wouldn’t like it. After all, it wouldn’t be the same, would it?”
From this she could make nothing. All that he had said might mean anything at all. It seemed to her that the more she talked, the more confusing, the less clear everything became.
“I simply happened to think of her. She’s a remarkable girl. She’s had a struggle from the beginning.”
“A damned fine lot,” was his comment. “You’ll hear from her some day.”
She must have understood that all her slyness was of no use, that methods such as this brought her nowhere, for she fell silent after this until Dick rose and said, “Shall we go up? My nerves are on edge from playing all afternoon. I think I’ll sleep a bit.”
Then while she watched him, as from a great distance, it occurred to her that all this was scarcely the behavior of a bridegroom on his honeymoon; it was, on the contrary, as if already they had been married for years.
As she rose to go with him, a sudden decision crossed her mind. Without thinking why she was employing it, she used the one stake which she had at hand.
“Dick,” she said abruptly, “I am going to have a baby.”
He turned, and into his face came an expression of pleasure the like of which she had not seen there before. He smiled and, moving toward her, took her gently into his arms.
“That’s fine,” he said softly. “That’s wonderful.” And she felt him kiss her gently after a fashion that was new and disarming. It was neither a casual kiss, nor a passionate one; those two moods she knew very well. This was something new. She felt almost that she were an animal, a pet for whom he had a great affection and a strong desire to protect.
“Your mother will be pleased,” she said, frightened again by the old dread of losing herself. (She was ashamed too that he should feel her tremble so.)
“She will be delighted. She wants an heir. She thinks I’m not much good at taking care of all her money.” And he kissed her again in the same tender fashion.
“But it might be a girl.”
He laughed a little. “No, I’m lucky.... Think of my eleven thousand francs!”
But she saw that he wanted a boy, desperately, that he was not in the least interested in a girl. It was very foreign of him ... that desire for some one to carry on the name, to inherit all the fortune.
After they had gone up the stairs with the rail of red plush, he came into the sitting room again to kiss her gently and to ask if she were feeling well, and when he had gone Sabine, as she lay in the darkness among the gaudy pillows of the chaise longue, understood clearly and bitterly for the first time the change which their marriage had brought about. He was being gentle and loving not because she was a woman or because he loved her, but because she had become now by the course of nature an institution, a wife, a prospective mother. He was being tender not toward her but toward an idea. He placed her a little apart, so that the old sense of companionship was no longer possible. She was a symbol now ... the wife and mother who was the rock and foundation, the one who produced sons to carry on name and property, but not by any chance the one who was loved because she was a woman.
