Small-Strain Stiffness and Damping of Soils in a Direct Simple Shear Device

Transcription

1 Small-Strain Stiffness and Damping of Soils in a Direct Simple Shear Device B. D Elia, G. Lanzo & A. Pagliaroli Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma La Sapienza, Italy. ABSTRACT: Cyclic properties of reconstituted sand and clay were measured in a double specimen direct simple shear (DSDSS) device for small-strain testing, recently developed at the University of Rome La Sapienza. The original version of the DSDSS device was designed and built in 1994 at the University of California at Los Angeles (UCLA). The objective of the paper is twofold: to assess the repeatability of the testing technique with the new DSDSS device; to compare the results of simple shear testing obtained in the original and new DSDSS device. Typical results of the experimental investigation are presented in terms of stress-strain hysteresis loops as well as in terms of traditional cyclic parameters such as maximum shear modulus (G ), secant shear modulus ( ), normalised shear modulus ( /G ) and damping ratio (D). 1 INTRODUCTION It is well known that the cyclic behaviour of soils is nonlinear and hysteretic, and consequently stiffness and damping characteristics of soils are strain-dependent. This dependency is illustrated in Figure 1a, where an idealised cyclic stress-strain curve is plotted together with the various parameters commonly utilised to describe the cyclic behaviour of soils. In the figure, is the cyclic shear strain amplitude, τ c is the cyclic shear stress amplitude, G is the maximum shear modulus, is the secant shear modulus corresponding to τ c and, W is the area enclosed by the loop and D is the damping ratio. The nonlinear and hysteretic behaviour of soils is traditionally represented in a normalised form, such as depicted in Figure 1b. Figure 1b shows that, even in the small strain range, soil behaviour is nonlinear and hysteretic, with the normalised shear modulus, /G, decreasing and the damping ratio, D, increasing with the cyclic shear strain amplitude. Such behaviour requires accurate evaluation of the cyclic stress-strain properties in the range of small strains for the analysis of several geotechnical engineering problems involving cyclic loading. In the last ten years special efforts have been dedicated towards accurate measurements of cyclic properties of soils at small strains, either by improving existing laboratory testing techniques or by developing new devices. As a matter of fact, several cyclic apparatii (i.e. triaxial, torsional shear) equipped with small transducers are nowadays capable to accurately measure small-strain properties of soils and represent a valid alternative to dynamic tests (i.e. resonant column, bender elements). In this paper a recently developed simple shear device was employed to carry out a laboratory investigation for measuring small-strain stiffness and damping characteristics of two reconstituted soils. 2 EXPERIMENTAL APPARATUS The testing apparatus employed for this investigation is named the Double Specimen Direct Simple Shear (DSDSS) device. The original DSDSS device was designed and built at the University of California at Los Angeles (UCLA) and it is fully described in Doroudian & Vucetic (1995). A new version of the DSDSS apparatus was recently constructed at the University of Rome La Sapienza and was used for the investigation presented in this study. The basic concept and configuration of the Paper Number 111

2 original DSDSS device was maintained in developing the new version and only minor modifications have been made. For this reason only a brief description of the device is made hereafter. γ W D = 1 4π 1/2 τ c loading reloading τ G τ c 1 /G 1 γ /G, D D W τ c τ unloading in log scale Figure 1. Idealised cyclic stress-strain loop; typical format of normalised shear modulus, /G, and damping ratio, D, vs. cyclic shear strain amplitude. The simplified scheme of the DSDSS device is shown in Figure 2. Its peculiar feature is the twospecimens configuration, instead of the one-specimen configuration traditionally employed in direct simple shear and other geotechnical laboratory testing devices. This particular configuration enables almost complete elimination of problems associated with false deformations, system compliance and friction which are typical of a standard DSS direct simple shear device. The DSDSS device is capable of investigating, in a single test, the cyclic properties of soils in a very wide range of strain, from very small to very large. In fact, stiffness and damping characteristics of different soils have been successfully measured in the original DSDSS device in the range of strain varying between.4% to 3% (Lanzo et al. 1997, Vucetic et al. 1998, Lanzo et al. 1999). VERTICAL LOAD PROXIMITY TRANSDUCER TARGET SPECIMEN CYCLIC LOADING SPECIMEN LOAD CELL Figure 2. Schematic layout of the Double Specimen Direct Simple Shear (DSDSS) Device. 2.1 Testing on rubber specimens VERTICAL LOAD To assess the DSDSS device for system compliance, rubber specimens were used first. The specimens were made of liquid silicon casting rubber (RTV 11), which was poured in stainless steel rings of 6.6 cm in diameter and 2 cm in thickness and cured. The rubber specimens obtained in this way were then placed between the specimen caps, mounted in the DSDSS device and then tested. It was assumed that the rubber specimens should have zero damping and constant stiffness over a wide range of shear 2

3 strains, because of its essentially elastic behaviour. A typical hysteresis loop is shown in Figure 3a. The stress-strain curve is linear resulting in no damping, as expected. The variation in secant shear modulus,, with the cyclic shear strain amplitude,, is also plotted in Figure 3b. The secant shear modulus is independent of the cyclic shear strain amplitude, in the range between.4% to 1%. Therefore, shear modulus and damping can be properly measured in the DSDSS device over a wide range of cyclic shear strain amplitude without any compliance problem =.53 MPa D = σ' v c =25 kpa =.39 % Shear strain, γ Cyclic shear strain amplitude, Figure 3. Test results on rubber specimens: typical cyclic stress-strain curve; variation of secant shear modulus,, with cyclic shear strain amplitude,. Secant shear modulus, (MPa) =.52 MPa 3 SOILS TESTED, TESTING PROCEDURE AND TESTING PROGRAM Reconstituted Toyoura sand and Santa Barbara clay were used for the tests. Toyoura sand was extensively used in laboratory investigations for measuring dynamic properties of cohesionless soils since seventies (Iwasaki and Tatsuoka 1977, Iwasaki et al. 1978, Kokusho 198). It is a predominantly quartz fine to medium sand, having a specific gravity = 2.65, a mean grain size D 5 =.2 mm, a coefficient of uniformity U c =1.3; the maximum and minimum void ratio are, respectively, e max =.975 and e min =.561. Santa Barbara clay was obtained by utilising the clayey waste materials resulting from excavation in the Santa Barbara open-pit mine, in Central Italy (Milillo et al. 1999). The clay has specific gravity = 2.65, liquid limit w L = 47%, plasticity index PI = 17 and clay fraction CF = 34%. The Toyoura sand specimens were reconstituted by pouring dry sand with a spoon in five layers into the reinforced membrane and tamping each layer with a small wooden rod. The Santa Barbara clay specimens were prepared from slurry, mixing the clay with water so as to have the water content of the slurry to be about 1.5 the liquid limit. The slurry was consolidated in a mould under a consolidation pressure of about 3 kpa. The specimens were cylindrical, 6.6 cm in diameter and 2 cm high. The Toyoura sand specimens were tested in dry state with initial void ratio e =.59. The Santa Barbara clay specimens were tested fully saturated, with an initial water content w = 4% and initial void ratio e = 1.6. The specimens were tested following the original NGI constant-volume equivalent-undrained direct simple shear testing procedure (Bjerrum & Landva 1966). The accomplishment of the constant volume conditions was possible by keeping the height of the specimens constant. Since the specimens are confined laterally by the wire reinforced membranes, which restrict or almost completely prevent lateral deformations, maintaining constant height results in a constant volume test (Dyvik et al. 1987, Airey & Wood 1987). The program of the tests is listed in Table 1. In order to check the repeatability of testing with the new DSDSS device, two pairs of specimens of Toyoura sand (#1 and #2) and Santa Barbara clay (#1 and #2) were tested under the same vertical confining stresses, σ vc, and the results were compared. Toyoura sand was tested at three values of σ vc, i.e. 1, 2 and 4 kpa, while the clay was tested only at σ vc = 4 kpa. For each σ vc the specimens were subjected to several consecutive straincontrolled tests with different levels of constant. No more than 1 cycles were applied in each test. 3

4 Soil Table 1. Summary of cyclic testing conditions Vertical effective consolidation stress (kpa) Cyclic shear strain amplitude Frequency (Hz) Toyoura sand # Toyoura sand # Santa Barbara Clay # Santa Barbara Clay # TEST RESULTS 4.1 Toyoura sand In Figure 4 typical hysteresis loops of Toyoura sand obtained at σ vc = 2 kpa for six values of cyclic shear strain amplitudes, i.e. =.33%, =.15%, =.43%, =.1%, =.41% and =.12%, are presented. It is evident that the cyclic loops were clearly recorded even at very small strains and both secant shear modulus and damping ratio could be determined with confidence =.33% =12.2 MPa D % =96.1 MPa D = 1. % =65.1 MPa D = 8.8 % (c) =.43% =.41% (e) Shear strain, γ Figure 4. Cyclic stress-strain loops of Toyoura sand obtained at σ vc = 2 kpa for increasing levels of =99.9 MPa D % =89.1 MPa D = 2.1 % =35.8 MPa D = 18.8 % =.15% (d) =.1% (f) =.12% Shear strain, γ 4

5 4.1.1 Strain dependency of modulus and damping Figure 5 shows the strain dependency of the secant shear modulus,, for the two pairs of specimens (#1 and #2) under the three applied confining stresses (σ vc =1, 2 and 4 kpa). The clusters of the data points pertain to different cyclic strain-controlled stages and each data point in a cluster pertains to a single cyclic stress-strain loop recorded during the given stage. From the comparison, it can be seen that the values obtained in the two tests plot on top of each other, confirming an excellent repeatability of the testing technique. In Figure 5 the curves obtained on Toyoura sand in the original DSDSS device, at approximately the same vertical stresses and void ratios, are also shown by solid lines for comparison (Lanzo & Vucetic 1999). These curves are extrapolated at =.1% by dashed lines to determine the maximum shear modulus G. It can be seen that only minor differences do exist between the two sets of data which can probably attributed to the slight differences in confining stress and initial void ratio. Figure 5. Variation of secant shear modulus,, with cyclic shear strain amplitude,, for Toyoura sand specimens. The variations of /G and D with is illustrated for test #1 only in the Figures 6a and 6b, respectively. In Figure 6a each single data point represents an average of the cluster of the data points obtained for all cyclic stress-strain loops recorded at a given. In Figure 6b each single data point represents the damping ratio value obtained at the second cycle (N=2). In the Figures 6a and 6b the average /G values and the D values for N=2 obtained at approximately the same vertical stress and void ratio in the original DSDSS device are also reported for comparison. A very satisfactory agreement can be recognised between the two sets of data. Normalised modulus, /G Secant modulus, (MPa) Toyoura sand This study #1 σ'vc (kpa) Lanzo & Vucetic (1999) σ'vc (kpa) Cyclic shear strain amplitude, Toyoura sand 42 kpa 18 kpa Cyclic shear strain amplitude, Cyclic shear strain amplitude, Figure 6. Comparison between test results on Toyoura sand obtained in the original and in the new DSDSS device: normalised shear modulus, /G, vs. data points; damping ratio, D, vs. data points. Damping ratio, D 9 kpa Toyoura sand N=2 This study #1 #2 σ'vc (kpa) Lanzo & Vucetic (1999) 5

6 4.2 Santa Barbara clay Typical hysteresis loops of a series of cyclic tests on Santa Barbara clay are presented in Figure 7. The figure shows the stress-strain curves obtained at σ vc = 4 kpa for eight different values of cyclic shear strain amplitudes, i.e. =.38%, =.98%, =.38%, =.1%, =.39%, =.1%, =.28% and =.92%. As for Toyoura sand, it can be seen that cyclic loops were clearly recorded at strains as small as =.38% (Fig. 7a) up to very large strains of about 1% (Fig. 7h). Differently from sand, it can be noticed that at about =.4% damping ratio of clay attains a very small but finite value of damping =.38% =19.9 MPa 3-3 =55.4 MPa D = 1.6 % =54.5 MPa D = 1.9 % =44.1 MPa D = 4.8 % D = 14.7 % =.38% =.39% =.28% (c) (e) (g) Shear strain, γ =54.8 MPa D = 1.8 % =53.5 MPa D = 2.1 % =32.6 MPa D = 8.6 % =8.9 MPa D =19.1 % =.98% (d) =.1% =.1% =.92% (f) (h) Shear strain, γ Figure 7. Cyclic stress-strain loops of reconstituted Santa Barbara clay at σ vc = 4 kpa for increasing levels of. 6

7 4.2.1 Strain dependency of modulus and damping Figure 8 shows the reduction of with for the two pairs of clay specimens under the applied confining stress of 4 kpa. The clusters of the data points pertaining to the two cyclic straincontrolled stages overlap one each other, thus confirming an excellent repeatability of test results also for the clay specimens. For each test, the data points are connected through solid lines to obtain the versus relationship. In addition to that, to estimate the value of G, the versus relationship was extrapolated to =.1% by a dashed line. Figure 8. Results of tests #1 and #2 on reconstituted Santa Barbara clay: variation of secant shear modulus,, with cyclic shear strain amplitude. The variation of the normalised shear modulus, /G and the damping ratio, D, with cyclic shear strain amplitude,, is illustrated for the two pairs of specimens in Figures 9a and 9b, respectively. Again, an excellent agreement between the two sets of values can be recognised. Normalised shear modulus, /G Secant shear modulus, (MPa) Santa Barbara clay #1 Santa Barbara clay #2 σ' vc = 4 kpa Santa Barbara clay #1 Santa Barbara clay #2 σ' vc = 4 kpa Cyclic shear strain amplitude, Cyclic shear strain amplitude, Damping ratio, D Cyclic shear strain amplitude, Figure 9. Results of tests #1 and #2 on reconstituted Santa Barbara clay: variation of normalised shear modulus, /G, with cyclic shear strain amplitude ; variation of damping ratio, D, with cyclic shear strain amplitude CONCLUSIONS A recently developed double specimen direct simple shear (DSDSS) device was employed to basically investigate the small-strain nonlinear and hysteretic behaviour of reconstituted Toyoura sand and Santa Barbara clay. For Toyoura sand the cyclic stress-strain curves were determined with reasonable 7

8 accuracy in the range of cyclic strain amplitude between about.4% and.4% while for Santa Barbara clay a much wider range of strains was studied, spanning from cyclic strain amplitude as small as.4% up to almost 1%. The test results were elaborated in terms of secant shear modulus, normalised shear modulus and damping ratio. For both Toyoura sand and Santa Barbara clay the repeatability of the DSDSS testing technique was investigated and established, as very consistent results were obtained for both shear moduli and damping values. Further, for Toyoura sand a comparison between the shear moduli and damping values obtained in this study and those obtained in the original DSDSS device was also presented and showed a very satisfactory agreement. From the above results, it can be concluded that the DSDSS device can successfully used to determine the modulus reduction curves as well as the damping curves to be employed for design, covering very small and very large strains. ACKNOWLEDGMENTS The research was carried out with the financial support of Ministero Università e Ricerca Scientifica e Tecnologica (M.U.R.S.T., 6%). REFERENCES: Airey, D.W. & Wood, D.M An evaluation of direct simple shear tests on clay. Géotechnique. 37 (1) Bjerrum, L. & Landva, A Direct Simple-Shear Test on a Norwegian Quick Clay. Géotechnique, 16 (1) Doroudian, M. & Vucetic, M A direct Simple Shear Device for Measuring Small-Strain Behavior. Geotechnical Testing Journal. 18 (1) Dyvik, R., Berre, T., Lacasse S., & Raadim, S Comparison of truly undrained and constant volume direct simple shear tests. Géotechnique. 37 (1) Iwasaki, T. & Tatsuoka, F Effects of grain size and grading on dynamic shear modulus of sands. Soils and Foundations. 17 (3) Iwasaki, T., Tatsuoka, F. & Takagi, Y Shear moduli of sands under cyclic torsional shear loading. Soils and Foundations. 18 (1) Kokusho, T Cyclic Triaxial Test of Dynamic Soil Properties for Wide Strain Range. Soils and Foundations Lanzo, G. & Vucetic, M Small-strain behavior parameters for site response analyses. Earthquake Resistant Engineering Structures II, Catania, June Lanzo, G., Vucetic, M. & Doroudian, M Reduction of shear modulus at small strains in simple shear. Journal of Geotech. and Geoenv. Eng. 123 (11) Lanzo, G., Vucetic, M. & Doroudian, M Small-strain cyclic behavior of Augusta clay in simple shear. Proc. of the 2nd Int. Symposium on Pre-failure Deformations Characteristics of Geomaterials. IS-Torino99, Torino, Italy, 28-3 settembre Milillo, A., D Elia, B. & Esu, F Modelling the consolidation processes of clayey block waste materials. Rivista Italiana di Geotecnica Vucetic, M, Lanzo G. & Doroudian, M Damping at small strains in cyclic simple shear test. Journal of Geotech. and Geoenv. Eng. 124 (7)