Evaluation of Volumetric Threshold Strain Considering Noisy Feedback Signals from Simple Shear Device

Statistical methods are presented to help evaluate cyclic test results in the small amplitude range. We utilize several statistical methods to extract from noisy feedback signals meaningful response parameters at very small strain levels. Previous work has shown that the uncertainty in the estimation of vertical strains is much greater than that for shear strains. Hence, we focus in this article on the procedures for estimation of vertical strain. Kernel regression with the NadarayaWatson estimator and a Gaussian kernel was utilized in evaluating vertical strain response. The calculated response is dependent on the bandwidth, which is userselected and takes the form of a kernel regression parameter. We select the bandwidth by minimizing the difference between the bias and 95% confidence interval range. We utilize these statistical methods to infer shear strain amplitudes and vertical strains for cyclic simple shear tests conducted at low levels of applied shear strains on dry soil specimens. We identify the threshold shear strain for a soil material as the largest level of shear strain where the 95% confidence interval range on vertical strain spans the null value. Introduction Dynamic soil testing at small strains is required to measure several critical parameters such as maximum shear modulus Gmax (e.g., Zeng and Ni, 1999; Youn et al., 2008) and threshold shear strain !tv (e.g., Vucetic, 1994). Many soil test machines, such as cyclic simple shear, cyclic triaxial, or cyclic torsional shear, are designed to measure large strain properties such as shear strength and liquefaction characteristics, and may have a limited ability to reliably measure small strain properties as displacement and force signals approach system noise levels. Recent improvements in control system technologies hold the potential to extend the range of displacements and frequencies that are reliably controlled and measured (e.g., Duku et al., 2007). Yee et al. (2010, in review) describe procedures for evaluating cyclic shear strain amplitudes and vertical strains from feedback signals that might visually appear to be noise-dominated. This conference paper summarizes some of the key findings from that work, especially focusing on the vertical displacement estimates, which have the greater uncertainty. The results are then applied to a data Graduate Research Assistant, Dept. of Civil and Environmental Engineering, University of California, Los Angeles, CA 90095 Professor, Dept. of Civil and Environmental Engineering, University of California, Los Angeles, CA 90095 Professor, Dept. of Statistics, University of California, Los Angeles, CA 90095 set to illustrate how the volumetric threshold shear strain can be evaluated in consideration of the measurement noise. Simple Shear Device We utilize the Digitally-Controlled Simple Shear (DC-SS) device described by Duku et al. (2007). The DC-SS device features servohydraulic actuation and true digital control, and is capable of applying broadband (earthquake-like) horizontal displacement demands on soil specimens in two directions and with minimal cross coupling between the motions. Duku et al. (2007) found that the principal source of the errors in the feedback signals from the DC-SS device is noise introduced by the analog-to-digital (A/D) conversion of the feedback signal. As such, this noise is independent of the specimen response (i.e., the specimen does not experience the noise portion of the signal). Vertical Measurements Quantification of Noise In the tests with the DC-SS device discussed here, three LVDTs are used to measure vertical displacement and potential rotation of the specimen top cap, which is free to displace (constant volume is not enforced). Figure 1(a) shows vertical displacements from a constant height test with displacement histograms from sample feedback signals of LVDTs v2, v3, and v4 are shown in Figure 1(b), (c), and (d) respectively. The noise for LVDTs v2 and v3 is normally distributed with zero mean and standard deviations of 0.0007 mm and 0.0006 mm respectively, whereas the noise for LVDT-v4 takes on one of two values with a standard deviation of 0.0014 mm. LVDT v4 has lower resolution than the others due to the type of analog-to-digital converter channel used. LVDT-v4 uses a 12-bit channel whereas LVDTs-v2 and v3 use 16-bit channels, thereby producing higher resolution signals for the fixed range of displacement. The standard deviations for the vertical LVDTs are higher than the horizontal LVDT because the horizontal LVDTs are connected to a scaling amplifier which increases the signal resolution. This higher resolution allows the data acquisition system to record more data near the mean whereas the resolution levels for the vertical LVDTs will show relatively more scatter. Mean Vertical Displacements from Noisy Signals We estimate the mean specimen vertical displacement by smoothing out the noise effects with nonparametric regression. Nonparametric regression can track complex displacement patterns occurring over a wide range of values without the constraint of an assumed functional form. -0.003 0 0.003 Displacement (mm) 0 0.1 0.2 0.3 0.4 R el at iv e Fr eq ue nc y LVDT-v2 Statistics N = 2,501 points mean = 0 mm " = 0.0007 mm -0.003 0 0.003 Displacement (mm) 0 0.2 0.4 0.6 0.8 1 R el at iv e Fr eq ue nc y LVDT-v4 Statistics N = 2,501 points mean = 0 mm " = 0.0014 mm -0.003 0 0.003 Displacement (mm) 0 0.1 0.2 0.3 0.4 R el at iv e Fr eq ue nc y LVDT-v3 Statistics N = 2,501 points mean = 0 mm " = 0.0006 mm -0.005 0.000 0.005 D is pl ac em en t ( m m ) 0 5 10 Time (sec) lvdt v2 lvdt v3 lvdt v4 (a) (b)