Small-strain soil behavior parameters for site response analyses

Transcription

1 Small-strain soil behavior parameters for site response analyses G. Lanzo/') M. Vucetic^ ^ Department of Structural and Geotechnical Engin., University of Rome "La Sapienza ", Via A. Gramsci 53, 0097, Rome, Italy glanzo@dsg.uniromal.it ^ Civil and Environmental Engin. Department, University of California vucetic@ucla. edu Abstract Cyclic simple shear tests were conducted on specimens of reconstituted clean sand and undisturbed high-plasticity clay. The presentation is focused on the secant shear modulus and damping ratio in the small strain range. The variation of these parameters with confining pressure, cyclic shear strain amplitude, stress history and frequency of cyclic loading is investigated. Experimental data are presented in the format that can be utilized for seismic response analyses. Introduction The accurate knowledge of the stress-strain characteristics of soils under cyclic loading at small strains is of primary importance for the response of soil deposits to seismic excitation. For the calculation of the seismic site response the stressstrain characteristics of soils under cyclic loading are usually described by the following two main parameters, the secant shear modulus, Gs, and the damping ratio, X. Both GS and X, are nonlinear, that is they are strongly dependent on the cyclic shear strain amplitude, y^. At very small strain levels (yc<0.000%) the secant shear modulus G% approaches its maximum value, G^ax- As the shear strain level increases, the secant shear modulus Gs decreases while the damping ratio X increases. In current practice, it is customary to present the variation of GS and A. with y^ in terms of normalized shear modulus reduction curves, and damping ratio curves, X-yc.

2 354 Earthquake Resistant Engineering Structures Over the past two decades, there have been considerable advances in the determination of GJG^x-Jc and -y^ curves for various soils. It has been found that for different soils the curves are quite different. The determination of these curves with great accuracy is therefore essential for conducting reliable seismic response analyses. In the past the shear modulus and damping ratio of soils at small cyclic shear strains (yc= %) were measured in the laboratory mainly by means of high-frequency resonant column tests, while low-frequency cyclic tests (torsional shear, cyclic triaxial, simple shear tests) have been used to determine properties at larger strain levels. In the last decade, however, noticeable advances in laboratory testing and development of new apparatuses have increased the capability of performing reliable cyclic tests at small strains. In the study described in this paper, a recently developed cyclic simple shear device (Doroudian & Vucetic*) was used to investigate the cyclic properties of two soils at shear strains ranging from y<,=0.0004% to approximately y^.0%. The effect of the cyclic shear strain amplitude, YC, effective vertical consolidation stress, a'vc, overconsolidation ratio, OCR, and frequency of cyclic loading, f, were investigated and are presented. The implications of these effects for seismic site response analyses are discussed in some detail. 2 Soils tested, testing apparatus and testing procedure The tests were performed on a reconstituted sand called Toyoura sand and an undisturbed clay called Augusta clay. Toyoura sand is a well-known Japanese clean sand whose stress-strain characteristics have been thoroughly investigated by numerous researchers (Iwasaki & Tatsuoka^, Iwasaki et al^, Kokusho^, Teachavorasinskun et ap, Jamiolkowski et al*, Pallara^, Lo Presti et al^). It is a predominantly quartz fine sand having a mean size Dso=0.6 mm and the uniformity coefficient Uc=.52. The maximum (e^ax) and minimum (e^m) void ratios are and 0.605, respectively. Augusta clay is a marine pleistocene clay coming from a quite homogeneous deposit located at the Saline site in the city of Augusta (southeast of Sicily, Italy). The clay is medium stiff, overconsolidated and of high plasticity. Its natural water content is around 34%, liquid limit is 74.5, plastic limit is 30.8, and hence the plasticity index PI=43.7. More information on the Augusta clay deposit is given by Maugeri & Frenna^, Cavallaro^ and Lo Presti The testing apparatus used was the so-called double specimen direct simple shear device (DSDSS) developed by Doroudian & Vucetict The specimens were tested under the constant volume conditions, Toyoura sand in dry state and Augusta clay fully saturated. They were cylindrical, 6.6 cm in diameter and 2 cm high, prepared and tested following the original Norwegian Geotechnical Institute (NGI) constant-volume equivalent-undrained simple shear procedure (Bjerrum & Landva\ Dyvik et al*). Accordingly, the test results presented in the paper are representative of undrained conditions.

3 Earthquake Resistant Engineering Structures Testing program A total of 52 cyclic tests were performed on specimens of Toyoura sand and 90 cyclic tests on Augusta clay. The conditions prior and during the cyclic tests are listed in Table. For each condition, the specimens were subjected under the same initial vertical stress, a\c, and overconsolidation ratio, OCR^ to several consecutive cyclic strain-controlled tests with different levels of constant cyclic shear strain amplitude, YC, and different frequencies, f. No more than 20 cycles were applied in each cyclic test. Table. Summary of cyclic testing conditions Soil Toyoura sand Augusta clay Testing condition Vertical load sequence Unloading Unloading Unloading Unloading Reloading Reloading Cj'vc (kpa) e OCR Yc (%) f (Hz) Tests results 4. Reduction of secant shear modulus, G* The values of the GS are plotted versus YC for different a\c and OCR in Figs, la and Ib for Toyoura sand and Augusta clay, respectively. The curves are fitted manually through the data points with solid lines and extrapolated by broken lines to yc=0.000%. The extrapolation was performed to estimate the maximum shear modulus, G^ax For both soils G% decreases with y^ and increases with a'vc and OCR. 4.2 Evaluation of maximum shear modulus, G«,» The values of G^ax were approximated assuming that Gmax is equivalent to G% at Yc=0.000%. The values of Gmax approximated in this way are compared to those obtained by empirical correlations available in the literature. It is generally recognized that Gmax can be conveniently expressed by the following empirical equation (Harding:

4 356 Earthquake Resistant Engineering Structures Cyclic shear strain amplitude, j^ (%) Figure. Reduction of GS with y^ for: (a) Toyoura sand; (b) Augusta clay, d-n) () where F(e)=void ratio function, OCR=overconsoiidation ratio, k=factor which depends on the plasticity index PI, a'm=((?\+2a\)/3=mean effective confining stress where a\ and a\ are the vertical and horizontal effective consolidation stress respectively, Pa=atmospheric pressure and S and n=dimensionless parameters. Iwasaki & Tatsuoka from the results of resonant column tests on reconstituted clean sands found that G^ax can be expressed as: G nr&n (2-7 e), Q max- 900 ; (Tm Pa ( + e) (2) By comparing eqns. () and (2), it can be seen that they are equivalent if F(e) is taken as (2.7-ef/(l+e), S=900 and n=0.4. The reliability of eqn. (2) in predicting the maximum shear modulus has been actually confirmed from the results of resonant column and monotonic/cyclic torsional tests on Toyoura sand (Teachavorasinskun et ap, Jamiolkowski et al, Pallara^). The G^ax values divided by F(e)=(2.7-e)V(l+e) calculated with eqn. (2) are compared in Fig. 2a

5 Earthquake Resistant Engineering Structures 357 with those obtained by the extrapolation of the measured GS data in Fig.. It can be seen in Fig. 2a that the calculated Gmax/F(e) values are just slightly greater than those estimated from the DSDSS test results. Hardin & Black^ developed the following empirical equation from the results of resonant column tests on undisturbed clayey soils: = 323 (2.973-e ( + e) (3) By comparing eqns. () and (3), it can be seen that they are equivalent if F(e) is taken as (2.973-ef/(l+e), S=323 and n=0.5. The G^ax values calculated with eqn. (3) are compared in Fig. 2b with those obtained by the extrapolation of the measured GS data in Fig. Ib. It can be seen in Fig. 2b that the measured G^ax values are consistently smaller than those computed. Discrepancies between the Gmax values measured and those calculated with the Hardin & Black equation were also observed for different cohesive soils by Kim and Novak ^. The G^ax values of Augusta clay obtained by the extrapolation of the measured GS data (Fig. Ib) were also compared with those measured by Cavallaro^ using resonant column and cyclic torsional shear tests. The comparison is illustrated in Fig. 3 and is pretty good. T Is CD "S Computed G, /F(e) (MPa) Computed G^ax (MPa) Figure 2. Comparison between G^x (or Gmax/F(e)) estimated from test results and those computed for: (a) Toyoura sand, (b) Augusta clay (A _3 3 "O 0) _c (f) J i i i i This study DCavallaro(997). ^ 0 T i 0. 0 Mean effective confining stress, a'm (MPa) Figure 3. Variation of G^ax of Augusta clay with a'^ from two studies employing different laboratory tests 400

6 358 Earthquake Resistant Engineering Structures 4.3 Normalized shear modulus (GJG^^-Jc) and damping (X-yJ curves For Toyoura sand the variation of Gs/G^ax with y^ is illustrated in Fig. 4a. The data confirm previous findings (Iwasaki et af, Kokusho^), that the Gs/Gma*-Yc curves for sands are significantly affected by <?\c As a\c increases the ordinates of the Gs/Gmax'Tc curve increase, i.e. the curve plots higher. For comparison, the Gs/Gmax-Yc curves obtained from torsional shear tests on isotropically consolidated specimens of Toyoura sand by Iwasaki et al* are also plotted in Fig. 4a with dashed lines for a'^00 kpa and a'm=200 kpa. A good agreement between the two sets of curves can be recognized in Fig. 4a. Fig. 4a also shows that the experimental data fall above the average bound proposed by Seed & Idriss^ for sands. For Augusta clay the G«/Gmax-Yc curves are shown in Fig. 4b. It can be seen that the scatter between the various curves is relatively small, in spite of the large variation of a\c and OCR applied. This means that the effect of a\c and OCR on the position of the G/Gmax-Yc curves is relatively negligible. This trend is consistent with previous data published in the literature (Kokusho et al^, Lanzo et al^) which show that the effect of a\c and OCR become less significant as the PI of the soil increases. For comparison, the G/Gmax-Yc curve obtained by Cavallaro^ from the results of resonant column tests on isotropically consolidated specimen (a',n=398 kpa) of Augusta clay is plotted with dashed line. Furthermore, the Gs/Gmax-Yc curves proposed by Vucetic and Dobry^ for soils having different plasticity indices, PI, are also included for comparison purposes. The variation of damping ratio,, with y^ is presented in Figs. 5a and 5b for Toyoura sand and Augusta clay, respectively. The data correspond to the second cycle of loading. As can be seen in Fig. 5 a, X for Toyoura sand significantly decreases with increasing a\c, as reported previously (Tatsuoka et al^' ). The X-y^ data in Fig. 5a are compared with the X-y^ curve for Toyoura sand determined by Lo Presti et al^ from the results of cyclic torsional shear tests on isotropically consolidated specimens under a'm=00 kpa and at cycles Further, it can be noticed in Fig. 5a that some data points do not fall within the range proposed by Seed & Idriss^ for sands. For Augusta clay, it can be seen in Fig. 5b that the variation of X with a\c and OCR is relatively small, in spite of the large variation of cr\c and OCR applied. Again, this trend is consistent with previous data published in the literature (Kokusho et al*\ Vucetic et al**) which show that the effect of a\c and OCR on damping ratio X become less significant as the PI of the soil increases. The values obtained in this study are compared in Fig. 5b to those obtained by Cavallaro^ from resonant column and cyclic torsional shear tests. A very good agreement can be observed between X values obtained with DSDSS and torsional shear tests. However, X values from resonant column tests plot higher than those determined by DSDSS. In Fig. 5b the damping ratio curves proposed by Vucetic & Dobry^ are also plotted for comparison purposes.

7 Earthquake Resistant Engineering Structures 359 Iwasakietal. (978) Seed& ldriss(970) A 7 O 8 Q X Figure 4. Cavallaro(997) Vucetic&Dobry(99) Cyclic shear strain amplitude, ^ (%) x data for: (a) Toyoura sand; (b) Augusta clay Lo Presti et al. (997) Seed &ldriss (970) Cyclic shear strain amplitude, y^ (%) Figure 5. Damping ratio data for: (a) Toyoura sand; (b) Augusta clay

8 360 Earthquake Resistant Engineering Structures For seismic response analyses it is of interest to compare the damping ratio curves of sand and clay. This is done in Fig. 6 for approximately the same value of a'vc- From this plot is evident that at small yc<0.005%, damping ratio of sand is lower than that of clay, while at Yc>0.02% the opposite is true; at Yc around 0.0% the damping ratio curves of sand and clay intersect each other. This trend is consistent with previously published results (Vucetic et al^). ou - I II ^P cr- zb TOYOURA SAND ~~OOkPa << on \ x^ ^, 0 O <?vc=48kpa AUGUSTA CLAY I 5-0) \ 4r\ /-^ E o S I^/ A " (,,o ^ Cyclic shear strain amplitude,?c (%) Figure 6. Variation of with YC for Toyoura sand and Augusta clay 4.4 Effect of frequency on damping ratio, X The effect of frequency on damping ratio for Toyoura sand was found to be negligible for frequencies between 0.02 and.0 Hz. The effect of frequency on damping ratio has been examined for Augusta clay in the range of frequencies between approximately 0.0 Hz and Hz for three different levels of cyclic shear strain y^ Yc~0.005%, Yc~0.0% and Yc-0.05%. In Fig. 7 these values of are plotted as a function of frequency, f, for these three shear strain levels. It can be seen in Fig. 7 that attains a minimum value around 0. Hz, while below and above it increases. This trend is independent of the shear strain level and confining pressure. Furthermore, this trend is consistent with previously published data for Augusta clay (Cavallaro^) and some other clays (Shibuya et ap, d'onofrio^). c "Q. ro Q o - AUGUSTA CLAY 6 - D Yc~0.0% A A Yc=0.05% A A D - aflrt " ^^ Q Jl»ff"** " n Frequency, f (Hz) Figure 7. Variation of damping ratio,, with frequency, f, for Augusta clay 0

9 Earthquake Resistant Engineering Structures 36 5 Conclusions Cyclic strain-controlled tests on reconstituted clean sand and undisturbed clay were conducted in a direct simple shear device for small-strain testing. The effects of YC, a'vc, OCR and frequency on the secant shear modulus, G%. maximum shear modulus, G^x, and damping ratio,, were investigated. The test results show that there is a good agreement between the G^ax values obtained in this study and those measured with different laboratory tests. Moreover, it has been found that empirical formulae available in the literature for determining Gmax yield consistent result for clean sand while overestimate results for clay. Since G^ax is one of the main input parameters in site response analyses, a sitespecific investigation of G^ax is recommended. All of the expected trends of the normalized shear modulus reduction curve, G/Gmax-Yc, and damping ratio curve, -Yc, with a vc, OCR and the frequency of cyclic loading were obtained. These trends are in good agreement with published data obtained using different testing devices. The main conclusions from this investigation which are relevant for seismic response analyses are the following: - G/Gmax-Yc and -Yc curves are significantly affected by a vc, for sands; this means that the variation of G/Gmax-Yc and -Yc curves with depth has to be considered when performing seismic response analyses of a sandy deposit; - G/Gmax-Yc and X-YC curves are not significantly affected by cr vc and OCR for high-plasticity clays; - in general, at small strain levels (yc<0.00%) damping ratio for sands is lower than damping ratio of clays; at higher strain levels (Yc^O.0%) the opposite is true; at YC between 0.00% and 0.0% the damping ratio curves of sand and clay may intersect each other; - damping ratio depends on the frequency of cyclic loading and for a particular problem it should be determined at the frequency of interest; - soil-specific modulus reduction and damping curves and their variation with depth must be determined for accurate site-specific studies of site response; in the absence of detailed laboratory tests data, the Seed and Idriss curves for sands and the Vucetic and Dobry curves for clays are suitable for preliminary site response analyses. Acknowledgments Toyoura sand and Augusta clay were supplied by Prof. Lo Presti at the Politecnico di Torino. The testing was conducted at the University of California at Los Angeles (UCLA) and was supported from a Pacific Earthquake Engineering Research (PEER) Center grant. PEER Center is principally supported by the National Science Foundation (NSF) research grant CMS References. Bjerrum, L., & Landva, A., Direct Simple-Shear Test on a Norwegian Quick Clay,

10 362 Earthquake Resistant Engineering Structures Geotechnique, 6,, pp. -20, Cavallaro, A., Influenza della velocita di deformazione sul modulo di laglio e sullo smorzamento delle argille., PhD Thesis, Universita di Catania D'Onofrio, A., Comportamento meccanico deu'argilla di Vallericca in condizioni lontane dalla rottura, PhD Thesis, Universita di Napoli "Federico II", Doroudian, M., & Vucetic, M., A Direct Simple Shear Device for Measuring Small- Strain Behavior. Geotechnical Testing Journal, 8,, pp , Dyvik, R., Berre, T., Lacasse, S., & Raadim, S., Comparison of truly undrained and constant volume direct simple shear tests, Geotechnique, 37,, pp. 3-0, Hardin, B.O., The nature of stress-strain behaviour for soils. SOA, Proc. Geot. Eng. Div. Speciality Conf. on Earth. Eng. and Soil Dyn, ASCE, Pasadena, California, Hardin BO., & Black, W.L., Closure to "Vibration modulus of normally consolidated clay". Joz/ATM/ q/\w/mgca. awfoww. D/v., ASCE, 95(SM6), pp , Iwasaki, T., & Tatsuoka, F., Effect of grain size and grading on dynamic shear moduli of sands, Soils and Foundations, 7, 3, pp 9-35, Iwasaki, T., Tatsuoka, F., & Takagi, Y., Shear moduli of sands under cyclic torsional shear loading, Soils and Foundations, 8, l,pp 39-56, Jamiolkowski, M., Lancellotta, R.., Lo Presti, D.C.F., & Pallara, O., Stiffness of Toyoura sand at small and intermediate strain, Proc. XIIIICSMFE, New Delhi, pp , Kim, T. C., & Novak, M., Dynamic properties of some cohesive soils of Ontario, Can. Geotech. Journal, 8, pp , Kokusho, T., Cyclic triaxial test of dynamic soil properties for wide strain range, Soils and Foundations, 20, 2, pp 45-60, Kokusho, T, Yoshida, Y., & Esashi, Y., Dynamic properties of soft clay for wide strain range, Soils and Foundations, 22, 4, pp. 2-8, Lanzo, G., Vucetic, M, & Doroudian, M., Reduction of shear modulus at small strains in simple shear, Journal of Geotech. and Geoenv. Eng., 23,, pp , Lo Presti, D.C.F., Jamiolkowski, M., Pallara, O., & Cavallaro, A., Shear modulus and damping of soils, Geotechnique, 47, 3, pp , Lo Presti, D.C.F., Pallara, O., Maugeri, M., & Cavallaro, A., Shear modulus and damping of stiff marine clay from in situ and laboratory tests, Proc. First Int. Conf. On Site Characterization, Atlanta, Georgia, 2, pp , Maugeri, M., & Frenna, S.M., Soil-response analyses for the 990 South-East Sicily earthquake, Proc. Third Int. Conf. on Recent Adv. in Geotech. Earth. Eng. Soil Dynam., 2, pp , Pallara, O., Comportamento sforzi-deformazioni di due sabbie soggette a sollecitazioni monotone e cicliche, PhD thesis, Dept. Struct. Eng., Politecnico di Torino, Seed, KB., & Idriss, I.M., Soil moduli and damping factors for dynamic rtesponse analyses, EERC Rep. 70-0, Univ. of Calif., Berkeley. 20. Shibuya, S., Toshiyuki, T., Fukuda, F., & Degoshi, T., Strain Rate Effects on Shear Modulus and Damping of Normally Consolidated Clay, Geotechnical Testing JownW, 8, 3, pp , Tatsuoka, F., Iwasaki, T., & Takagi, Y., Hysteretic damping of sands under cyclic loading and its relation to shear modulus, Soils and Foundations, 8, 2, 25-40, Teachavorasinskun, S., Shibuya, S., & Tatsuoka, F., Stiffness of sands in monotonic and cyclic torsional simple shear, Proc. Geotech. Eng. Congr., 2, pp , Vucetic, M., & Dobry, R., Effect of Soil Plasticity on Cyclic Response. Journal of the GeotechnicalEngin. Div., ASCE, 7,, pp , Vucetic, M, Lanzo, G., & Doroudian, M., Damping at small strains in cyclic simple shear test, Journal of Geotech. and Geoenv. Eng., 24, 7, pp , 998.