ON THE LARGE AND SMALL STRAIN CYCLIC BEHAVIOR OF SANDS

Abstract

Monotonic, cyclic and shear wave response of five different quartz and silica sands was investigated from a varied and extensive data base consisting of drained monotonic direct simple shear tests, undrained cyclic direct simple shear tests, undrained cyclic triaxial tests and shear wave velocity tests. Test data sets were obtained from the experimental studies conducted by previous researchers. Approximately 500 tests in all were analyzed to examine cyclic sand behavior at large strains (0.1% to 4%) and small strains (less than 0.1%) under a range of constituent and initial conditions. The findings are presented in three chapters. The overall objective of this research is to obtain a better understanding of the strength and degradation characteristics of sands over a wide range of strains for various constituent and initial parameters. Extensive studies in the past showed that sand behavior becomes significantly nonlinear at large strains. The application of linear equivalent methods for shear strains larger than 0.1% can lead to erroneous results in the calculation of degradation parameters of sands. Numerical analyses and constitutive models are helpful to consider the nonlinear behavior of soil at these large strains. However, numerical models are required to be calibrated based on experimental data. The question is how to perform a reliable calibration with experimental results for high strains where the standard linear equivalent methods applied to laboratory experimental data becomes erroneous. This question was the main motivation of this study. The overall contribution here can be summarized as the development of a new calculation method to evaluate soil damping ratio more realistically at large strains (i.e., 0.1% to 4% shear strain, or the onset of liquefaction), and investigating the effect of various parameters on the soil behavior at these large strains with this new method. In order to make a better assessment on the plausibility of the new method, sand behavior was investigated both in the small and large strain range by means of laboratory experimental data on the monotonic and cyclic strength of a series of sands, as well as on the shear wave velocity response of some of these sands. In Chapter 1, the behavior of sands was examined under drained monotonic and undrained cyclic loading at moderately small to large strains. A previous data set developed at the University of Hawaii was used for this. This allowed consideration of the combined effects of gradation and fines content on sand behavior. The data analysis was extended to the range of very small strains by means of pre-shear and post-liquefaction shear wave velocity measurements. The combined effect of gradation and fines content represents a unique investigation, as previous studies have focused either solely on the fines content, or solely on gradation characteristics. Earlier studies on the effects of fines content typically involved combination of a clean sand base with various amounts of non-plastic silt and clay fractions, which can lead to unnatural gradations, especially at the transition from fine sand to silt and clay. A more careful approach, as followed in this study, is based on experimental data from assembled gradations that cover a range of smooth grain size distributions spanning from coarse sand to silt and clay sizes. Both poorly graded and well-graded distributions were considered. The key parameters in this study were the amount of fines (fines content FC), texture (mean grain size D50) and gradation (uniformity coefficient Cu). Monotonic and cyclic response was investigated with regard to these parameters. The main findings of Chapter 1 show that the overall monotonic, cyclic and shear wave behavior of sands is primarily a function of the amount of non-plastic fines and gradation plays a secondary but still important role. Whereas static shear strength of clean sands decreases slightly with a decreasing mean grain size, cyclic shear strength and shear wave velocity appear to be relatively independent of D50. An increase in Cu leads to a decrease both in the static and cyclic strength of sands. Shear wave transmission becomes slower with an increase in Cu, which indicates less stiffness of the sand, as can be assessed by the initial shear modulus from shear wave velocity measurements. Addition of small amount of fines causes an initial strength increase in both static and cyclic tests, which is followed by a continuous decrease after a threshold value of fines (in static tests less than 5%, in cyclic tests around 15%). The drop in the cyclic strength by addition of fines was more pronounced when Cu increased, indicating the important role of the gradation parameter Cu on silty sands, although the major effect is still the amount of fines. Trends in post-liquefaction shear wave measurements over different gradations and fines contents also indicate that fines content has a more significant effect on the overall sand behavior than the gradation does. Chapter 2 describes a new method developed in this study to calculate damping ratio of sands from undrained, load-controlled cyclic tests. Different calculation approaches available in the literature were first examined in terms of their plausibility in the high strain range. The data analysis on five widely ranging sands covering a significant set of initial conditions shows that the available linear equivalent methods of damping calculation lead to erroneous results, starting from shear strains around 0.1%, due to the observed highly nonlinear behavior of sands at large strains. The new numerical method calculates a more realistic damping value, and this follows from consideration of the pore water pressure accumulation during undrained testing. The new computational method follows the natural form of every hysteresis loop instead of relying on approximations inherent in linear equivalent methods. The main findings of the Chapter can be summarized as follows: 1) A new method is developed, validated and implemented numerically to estimate damping more accurately in laboratory cyclic direct simple shear and triaxial tests, which is also deemed to yield more plausible results at high and very high strains (larger than 1% shear), for which there is very little published experimental data in the literature. 2) Previous small-strain studies are based largely on strain-controlled cyclic tests, whereas the new method is developed for undrained load-controlled cyclic triaxial or direct simple shear tests, which are the most common types of laboratory cyclic tests. 3) A new guideline for damping ratio of clean sands covering a very wide range of shear strains (0.1 to 4%) is proposed as an alternative to the classic bounds by Seed and Idriss (1971). Almost all previous laboratory studies document the damping ratio behavior of sands only up to a shear strain level of about 1%. This new chart extends the bounds to 4% strain and is more helpful for the estimation of pre-liquefaction damping behavior of sands, given that failure state during an earthquake is very likely to occur at shear strains well in excess of 1%. These relatively large strains can become quite important in many practical projects, such as in the design of offshore platforms, soil embankments, excavations, slopes, levees, earth dams, dikes, etc. Chapter 2 finds a clear relationship between cyclic shear data and pore water pressure accumulation in undrained tests. While previous studies have suggested that there is a correlation between dissipated energy during cyclic shear and accumulated excess pore water pressure in undrained tests, a re-interpretation of previous test results on five different sands with various initial material properties and test conditions indicates that there is a distinct correlation between stored strain energy and accumulated pore water pressure, which was used to validate the new calculation method to compute damping from undrained cyclic triaxial and direct simple shear tests. The newly developed method leads to a new interpretation of damping behavior at large strains, which is distinctly different from trends noted by earlier studies that are based on variations of the linear equivalent method. In Chapter 3, the new method to compute damping is applied to a range of data sets from various sources in order to understand the effects of constitutive and initial state parameters on the damping behavior of sands at high strains. The controlling parameters of interest include shear strain, number of cycles, cyclic stress ratio, void ratio, cyclic strength, gradation, confining stress, non-plastic fines content and over-consolidation ratio. Other parameters affecting the damping behavior are also considered, such as initial shear stress, drainage, degree of saturation, frequency of loading, and plastic fines content. The newly calculated damping ratios at high strains are consistent with those based on linear equivalent methods at small strains. A significant correlation between cyclic strength and damping ratio further verifies the plausibility of the proposed calculation method. At constant cyclic stress ratio, confining stress and void ratio, a decrease in cyclic strength (e.g., due to increasing non-plastic fines content) leads to a faster material degradation (smaller number of cycles to liquefaction) and larger energy dissipation, resulting in a larger damping ratio. On the other hand, a soil specimen with higher cyclic strength requires more loading cycles to liquefy due to a slower material degradation and smaller energy dissipation (smaller damping ratio) at similar high strains. The proposed damping ratio bounds for a wide range of clean sands in Chapter 2 are also in a good agreement with test results for sands with non-plastic fines content up to 25%. The results from Chapter 2 and 3 also suggest that energy-based liquefaction assessment is inherently superior to stress- or strain-based liquefaction methods. Due to the strong correlation between cyclic strength and damping ratio, general cyclic strength evaluations (e.g. increase or decrease in cyclic strength) can substitute for assessments based on damping ratio, and this may be more convenient in many cases. Chapter 4 provides the major conclusions of this study. In addition, recommendations are made for further improvements to the new damping calculation method so that it can be extended to other testing conditions. Additional recommendations are made for the development of a nonlinear equivalent calculation method for evaluating shear modulus from cyclic experimental data. Other recommendations are presented on the damping behavior of soils during the liquefaction and post-liquefaction phase. The Appendix includes Matlab scripts, which were developed to analyze existing laboratory data sets. Scripts were developed to calculate damping based on four different linear approaches, and also for the newly devised method. Additional scripts were developed for evaluating linear equivalent shear modulus based on different approaches. Other scripts are presented to analyze the net energy gain portions of pore water pressure data with regard to dissipated and stored energy.