CYCLIC RESISTANCE OF SANDS SUBJECTED TO INITIAL STATIC SHEAR Siva Sivathayalan, Department of Civil & Environmental Engineering, Carleton University, Ottawa, Canada Da Ha, Department of Civil & Environmental Engineering, Rensselaer Polytechnic Institute, New York, USA ABSTRACT The effect of initial static shear stresses on the cyclic simple shear response of two soils is presented. One of the sands tested strain softens over a range of initial states, and the other strain hardens even at the loosest deposited state. It is shown that the Kα correction factor is dependent on the type of the soil, and the loading mode. Presence of static shear stresses seriously degrades the cyclic resistance of contractive sands regardless of the density states. Smaller Kα values were obtained under simple shear loading than under triaxial conditions. Even though the current empirical static shear correction factors underestimate the cyclic resistance of dilative sands by a wide margin, they may overestimate the liquefaction resistance of contractive strain softening sands, and hence lead to unsafe designs. RÉSUMÉ L'effet des efforts de cisaillement statiques initiaux sur la réponse simple cyclique de cisaillement de deux sols est présenté. Un de la contrainte testée par sables se ramollit sur une gamme des états initiaux. L'autre contrainte de sable durcit même à l'état déposé le plus lâche. On lui montre que le Kα le facteur de correction dépend du type du sol, et du mode de chargement. La présence des efforts de cisaillement statiques réduit la résistance cyclique des sables contractive indépendamment des états de densité. Un Plus petit Kα des valeurs ont été obtenues sous le chargement simple de cisaillement que dans des conditions à trois axes. Les facteurs statiques empiriques courants de correction de cisaillement sous-estiment la résistance cyclique des sables dilative par une marge large. Mais, ils peuvent surestimer la résistance de liquéfaction des sables se ramollissants de contrainte contractive. 1. INTRODUCTION

Cyclic resistance of sands is dependent on the initial effective stress state, which is normally characterized by the confining, and the static shear stress levels. Under simple shear loading mode the confining stress is generally represented by the vertical effective stress, and the static shear is represented by the shear stress on the horizontal plane. Liquefaction resistance is characterized by the cyclic resistance ratio (CRR), which is defined as the ratio of the cyclic shear stress, τcy causing liquefaction in a specified number of load cycles (typically 10 or 15 cycles) to the effective confining stress, σ'vc. At a given density, the CRR of a hydrostatically consolidated sand decreases with increasing confining stress level. This reduction in cyclic resistance due to increasing confining stresses is accounted for by using the correcting factor Kσ (Seed 1983). Extensive research has been carried out on the effect of initial confining stress level on cyclic resistance, and the Kσ correction factors proposed in the literature have been well established, and are considered reliable (Vaid and Thomas 1995; Haynes and Olsen 1999; Boulanger 2003a). The presence of static shear stress has been recognized to influence the cyclic resistance of the soils, and several attempts have been made over the years to quantify the cyclic resistance of soils subjected to initial shear stresses. The role of initial static shear on liquefaction resistance, however, has not been fully understood yet. Lee and Seed (1967) pioneered testing of soils under initial static shear (using anisotropically consolidated

triaxial specimens), and Seed (1983) proposed a correction factor Kα (which is defined as the ratio of the cyclic resistance with static shear stress to that without static shear stress) to account for the effects of initial static shear on cyclic resistance. However, significant uncertainties still exist in the Kα correction factors proposed in the literature. An increase in static shear may either increase or decrease the cyclic resistance depending on the density, and the levels of confining and static shear stresses. The empirical data presented by Seed and Harder (1990) shows significant reductions in the cyclic resistance of loose sands with increasing static shear stress, but indicates that cyclic resistance of medium dense to dense sands increases with increasing static shear stress. In contrast, experimental data (Vaid et al. 2001) shows that the cyclic resistance of loosest deposited sand increases with increasing static shear up to moderate levels of static shear. The summary report of a National Center for Earthquake Engineering Research (NCEER) workshop published in 2001 concluded that the published Kα values “should not be used by non-

specialists in geotechnical earthquake engineering or in

routine engineering practice” (Youd et al. 2001), possibly on account of these uncertainties. Undrained behaviour of sands is stress path dependent (Vaid et al. 1990). Under identical initial conditions a sand may strain harden under a given loading mode (e.g. triaxial compression), but strain soften and be highly susceptible to liquefaction under another (e.g. triaxial extension). Therefore, the most credible assessment of liquefaction susceptibility would be obtained if the soil

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element in the laboratory would be loaded along the stress path anticipated in the field. The cyclic simple shear device simulates the stress conditions in soil elements in-situ due to vertically propagating shear waves. Even though cyclic simple shear is a more realistic representation of sand behaviour under earthquake loading, liquefaction resistance in the laboratory is often determined using cyclic triaxial tests. The measured cyclic triaxial resistance is then corrected using empirical correction factors to obtain equivalent simple shear, or in-situ response. The influence of state variables on cyclic resistance has also been obtained from the measured cyclic triaxial response. The effect of loading mode, if any, on the Kα correction factor has not been addressed in the literature. 2. EXPERIMENTAL ASPECTS

All tests were carried out in the geotechnical research laboratory at Carleton University. The NGI type device (Bjerrum & Landva 1966) that was used to carry out the simple shear tests is shown in Figure 1. The test specimen was about 70mm in diameter and 20mm in height, and was confined using a steel-wire reinforced membrane. The specimen was consolidated to the desired effective stress state, and the cyclic shear stress was applied under constant volume conditions. The pore pressure in constant volume simple shear tests is always atmospheric, and thus the change in total vertical stress during shear equals the excess pore pressure generated in an equivalent undrained test (Dyvik et al. 1987). All tests were carried out under stress controlled loading mode. Cyclic simple shear tests were carried out on a sub-rounded Silica sand, which conforms to ASTM C-109 specifications, and is quite similar to the widely used Ottawa sand. The sand is very poorly graded, and the average particle size D50 of the sand is 0.42mm. The maximum and minimum void ratios determined according to ASTM standard tests methods (ASTM D-4253; ASTM D-4254) of the sand are 0.723 and 0.478 respectively, and the specific gravity of the sand is 2.66. A limited number of tests were also carried out on Fraser Delta sand. This semi-angular sand was dredged near Abbortsford, British Columbia. The natural material was processed to remove the fine particles passing #200 sieve and those retained in #20 sieve. This provides a fairly uniform sand with a mean diameter of 0.30mm, and uniformity coefficient of 2.9. Such uniform material is essential for fundamental laboratory studies that require several repeatable, homogeneous specimens be reconstituted in the laboratory. Similar material has been used in several past studies reported in the literature (Vaid and Thomas, 1995; Vaid and Sivathayalan, 1996; Wijewicreme et al., 2005). The maximum and minimum void ratio of this batch of Fraser River sand determined according to the ASTM standard test methods is 0.806 and 0.509 respectively. While the mineral composition of this sand is similar to the various batches of Fraser River

sand discussed in the literature the differences in the gradation, and the geographical origin cause fairly significant changes in the maximum and minimum void ratio. Such changes between different batches of Fraser Delta sands have been reported previously as well. Simple shear specimens were reconstituted using the dry pluviation technique, which yields uniform and repeatable specimens. Specimens were reconstituted at the loosest state, and higher densities, when needed were obtained by applying low-energy, high frequency vertical vibrations under a small seating load. Void ratio of the specimens were confidently determined using the volume of the cavity and mass of the solids. Cyclic shear stresses were applied by an electro-pneumatic transducer at a frequency of 0.1 Hz, and the data recorded using a high-resolution A/D card at a rate of 64 data points per cycle. This permits an examination of the mechanism responsible for the development of strains within the loading cycle. All stresses were measured with resolutions of better than 0.2 kPa and strains with resolutions of better than 10–4. 3. TEST RESULTS AND DISCUSSION

Monotonic, and cyclic simple shear tests were carried out at different confining stress levels (σ’

vc = 100, 200 & 400 kPa), densities, and at various levels of initial static shear. The level of initial static shear is characterized by the static shear stress ratio α that is defined in simple shear as the ratio of the initial shear stress on the horizontal plane to the initial vertical effective consolidation stress. α=0 corresponds to zero shear stress on the horizontal plane, and hence a traditional simple shear test with no static shear. The cyclic shear stress ratio, CSR defined as the ratio of the cyclic shear stress amplitude to that of the initial vertical effective confining stress is used to quantify the level of the cyclic loading. A series of such specimens were loaded with a given value of cyclic shear stress (CSR) amplitude until liquefaction. The cyclic resistance

Figure 1. NGI type simple shear device at Carleton University

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ratio CRR of the sand at a given density, confining stress, and static shear stress was then obtained from the data. The term liquefaction is used herein to refer to all forms of large deformation without regard to the actual strain development mechanism. Simple shear specimens were deemed to have liquefied when the single amplitude shear strain exceeded 3.75%. (NRC 1985). The cyclic resistance ratio CRR reported in this paper therefore corresponds to the uniform cyclic stress ratio that caused the shear strain to exceed 3.75% in ten stress cycles. 3.1 Undrained monotonic behaviour

Monotonic response of the sands is assessed to provide a baseline for evaluating the characteristics of the cyclic response. The loosest deposited Silica sand exhibited significant strain softening regardless of the initial effective stress state. It exhibited marginal strain softening at denser states depending on the initial stress state. Typical monotonic response of the Silica sand subjected to initial static shear stresses is shown in Figure 2. Shear loading has been applied both in the direction of the static shear, and in the opposing direction. The modified brittleness index, which is defined as the

ratio of the difference between the peak and minimum strength to the difference between the peak and static shear stress is often used to characterize the degree of brittleness. The variation of the modified brittleness index for Silica sand at various initial stress and density states is shown in Figure 3. It can be seen that sand strain softened over a range of initial states, and that increasing static shear increased the brittleness of the material. At identical initial states, the material is less brittle when the monotonic shear loading reversed the initial static shear.

The static behaviour of Fraser River sands has been well established in the literature (Vaid and Thomas 1995, Vaid and Sivathayalan 1996, Vaid et al 2001). Unlike the tested Silica sand, Fraser Delta sand is only marginally strain softening at the loosest state in simple shear loading, and is dilative at higher initial densities. Reported values of the brittleness index of Fraser River sand in simple shear loading have been smaller than 0.2, which clearly indicates that strength degradation is fairly small in Fraser Delta sands even if they strain soften. In comparison, brittleness index values of up to about 1.1 can be noted in the data presented in Figure 3. 3.2 Undrained cyclic behaviour

Different mechanisms of strain development have been found to be responsible for the triggering of liquefaction under cyclic loading (Vaid and Chern 1985). The initial stress and density state, and the relative values of the static, and cyclic shear stress amplitudes dictated the mechanism responsible for strain development. Strain softening was generally responsible for strain development in Silica sand, but Fraser River sand exhibited only marginal strain softening even at the loosest state. Typical stress-strain, and stress path of Silica sand under cyclic loading is shown in Figure 4. Negligible levels of strains develop until the sixth cycle when the effective stress state reaches the critical stress ratio line. Sudden flow deformation associated with strain softening ensues at this state, and very large strains develop. The excess pore pressure does not reach a Figure 2. Monotonic undrained behaviour of Silica sand

Figure 3. Effect of initial density and static shear stress on the degree of strain softening

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state of zero effective stress. It should be noted that shear stress reversal is a pre-requisite for the development of 100% excess pore pressure, and therefore specimens with an α value higher than the CSR cannot realize a state of zero effective stress. Given the definition of liquefaction adopted herein following the NRC (1985) recommendation, this specimen was deemed to have liquefied in six cycles. Several such tests were carried out at different density and cyclic stress ratio levels to yield a void ratio vs number of cycles to liquefaction plot at constant cyclic stress ratio contours (Ha, 2004). Figure 5 shows the cyclic resistance of Silica sand consolidated to an effective confining stress of 100 kPa, and a static shear stress of 20 kPa in the form of void ratio ec vs number of cycles to liquefaction. Each contour in the Figure represents a constant amplitude of cyclic stress ratio. Strain development in specimens with relative density less than about 60% was due to contractive strain softening for this initial condition, and the corresponding data points in the Figure are marked with the letter C. The initial static shear stress amplitude is larger than the cyclic shear stress amplitude for all the tests shown in

Figure 5, and hence cyclic mobility without transient states of zero effective stress was responsible for strain development in other cases. It should also be noted that the sand could be liquefied by subjecting it to fairly small levels of cyclic shear stresses (CSR = 0.02) at loose states. Such small undrained perturbations from the initial state trigger strain softening deformation at loose density states. This occurs because the highly contractive sand is already subjected to a relatively large static shear under drained conditions during consolidation, and when undrained conditions were imposed the strength of the material is smaller than the initial static shear. 3.3 Kα Correction Factor

The data shown in Figure 5 is used to estimate the void ratio at which the sand would liquefy in 10 cycles of loading for a specified cyclic stress ratio. This would relate the relative density and cyclic resistance ratio CRR of the sand for liquefaction induced in 10 cycles to the specific α value. Contours similar to that in Figure 5, but at other α and confining stress values were also established. This permitted the generation of the cyclic resistance curves of the sand, and the determination of the Kα correction factor at various levels of confining stress, density and α (Ha 2004). The variation of Kα correction factor with α is shown in Figure 6 at different density levels for samples consolidated to 100 kPa. Significant reduction in the cyclic resistance of the Silica sand can be noted at looser density states. At the loosest deposited state, the sand consolidated to α = 0.20 possesses only about 20% of the cyclic resistance compared to the sand that is not subjected to any static shear stresses. The reduction in Kα factor is less pronounced at higher consolidated density states, but the presence of static shear almost always decreases the cyclic resistance in this sand regardless of the density and the level of static shear. Similar plots obtained for consolidation stress levels of 200 and 400 kPa show that Kα factor at a given density and α level decreases with increasing confining stress level. At any given confining

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Figure 4. Cyclic response of strain softening sand

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Figure 5. Cyclic resistance of Silica sand consolidated to 100 kPa confining stress with a = 0.20

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stress level, CRR vs. Dr relationship is profoundly influenced by the level of static shear. The measured Kα is marginally larger than one, only for the densest state at the lowest confining stress level. Similar tests were carried out on Fraser Delta sands under simple shear loading mode at 100 kPa effective consolidation stress and at three different density levels. The Kα values obtained for Fraser Delta sands were generally much higher than those obtained for the Silica sand under similar initial states. The Kα values in Fraser Delta sands were often larger than one, which indicates that the presence of initial static shear increases the cyclic resistance of Fraser delta sands, especially at medium-dense or dense states. Similar response of Fraser Delta sands, where Kα values close to, or exceeding one have been reported by Vaid et al. (2001) based on cyclic triaxial tests. The variation of Kα in Silica, and Fraser Delta sands (consolidated to the same stress level) is compared in Figure 7. Drastic differences can be seen in the Kα values determined for the two sands. Presence of initial static shear stress significantly reduces the cyclic resistance in Silica sand at all density states shown. On the other hand, the presence of static shear only marginally decreases the cyclic resistance of the loosest deposited Fraser Delta sand. Further, initial static shear increases the cyclic resistance by as much as 50% at denser states in Fraser River sand. These results clearly indicate that the role played by the initial static shear stresses on cyclic resistance is dependent on the material itself, in addition to density and confining stress levels. It appears that contractive soils would see a significant reduction in cyclic strength and dilative soils would see a marginal reduction or an increase in cyclic resistance depending on the density level. Therefore attempts to quantify Kα should not relate it to the relative density, but rather to the type of the response of the soil at the given relative density. Boulanger (2003b) suggests relating Kα to the relative state parameter index.

All data discussed previously were obtained from cyclic simple shear tests. While this loading mode represents the stress conditions of a soil element in-situ under vertically propagating seismic waves very well, the simple shear device is not commonly available. As a result, extensive research has been carried out using cyclic triaxial tests to determine the Kα values. Figure 8 compares the Kα values obtained using simple shear tests on Fraser Delta sand to those obtained using cyclic triaxial tests by Vaid et al. (2001). All specimens were consolidated to 100 kPa effective confining stress. Initial static shear under triaxial loading conditions is obtained by subjecting the specimen to an anisotropic initial consolidation stress. Under triaxial loading conditions α is defined as the ratio of the maximum shear stress to the normal stress on the plane of maximum shear stress during consolidation. The loading mode influences the determined Kα values regardless of the density or static shear stress levels. The variations are the largest at α = 0.1. 4. SUMMARY AND CONCLUSIONS

Experimental results of a series of cyclic simple shear tests on a Silica sand, and Fraser River sand have been presented. Cyclic resistance of the sands has been assessed over a range of initial density and stress states to obtain the Kα correction factors. Kα values are rarely greater than one in the strain softening Silica sand, but are almost always greater than one in the strain hardening Fraser River sand. Drastically different Kα values are obtained at the same relative density in both sands. The results suggest that relative density should not be used to characterize the variation of Kα. In addition, significant differences have been noted in the measured Kα values depending on the type of the cyclic test (triaxial vs simple shear). This clearly indicates that Kα values are dependent on the loading mode.

Figure 6. The variation of Kα factor with α in Silica sand consolidated to 100 kPa effective confining stress

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Figure 7. Kα values determined for Silica sand vs Fraser River sand

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Estimation of Kα value in practice should not be based on the relative density of the sand, but on the anticipated deformation characteristics (strain softening vs strain hardening) of the sand. The use of Kα factors determined from cyclic triaxial tests might lead to unsafe designs, especially at the loose density states. The large scatter in the reported Kα values are a reflection of the effects of other parameters on the cyclic resistance of soil under initial static shear. The effect of increasing static shear is much serious compared to that of increasing confining stress at liquefaction prone strain softening sands. 5. ACKNOWLEDGEMENTS

This research reported herein has been supported by grants from the Natural Sciences and Engineering Research Council of Canada, Canada Foundation for Innovation, and the Ontario Innovation Trust. Financial assistance provided to the second author by Carleton University, and the technical assistance of Ken McMartin, Stanley Conley, Jim Whitehorne, and Maya Esparoni-Evans are gratefully acknowledged. 6. REFERENCES

ASTM D-4253-00, 2001, Standard Test Methods for Maximum Index Density and Unit Weight of Soils Using a Vibratory Table, American society for testing

and materials, Vol 04.08 ASTM D-4254-00, 2001, Standard Test Methods for

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testing and materials, Vol 04.08 Bjerrum, L. and Landva, A., 1966, Direct simple-shear

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Earth Dams and Caverns, ASCE, New York, 41–64. Seed, R. B. and Harder, L. F., 1990, SPT-based analysis

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Vaid, Y. P. and Sivathayalan, S., 1996, Static and cyclic liquefaction potential of Fraser Delta sand in simple shear and triaxial tests, Canadian Geotechnical

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Journal, 27(1): 1-7 Vaid, Y. P., Stedman, J. D., and Sivathayalan, S., 2001,

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Wijewickreme, D., Sriskandakumar, S. and Byrne, P., (2005), “Cyclic loading response of loose air-pluviated Fraser River sand for validation of numerical models simulating centrifuge tests”, Canadian Geotechnical

Journal, 42(2): 550-561. Youd, T. L., Idriss, I. M. , Andrus, R. D., Arango, I.,

Castro, G., Christian, J. T., Dobry, R., Finn, W. D.L., Harder Jr, L. F., Hynes, M. E., Ishihara, K., Koester, J.

0 0.1 0.2 0.3 0.4α

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Figure 8. Dependence of Kα on the loading mode

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P., Liao, S. C., Marcuson III, W. F., Martin, G. R., Mitchell, J. K., Moriwaki, Y., Power,M. S., Robertson, P. K., Seed, R. B., and Stokoe II, K. H., 2001, Liquefaction Resistance of Soils: Summary Report from the 1996 NCEER and 1998 NCEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils, Journal of Geotechnical and

Geoenvironmental Engineering, 127(10): 817-833

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