Mechanistic Corrections for Determining the Resilient Modulus of Base Course Materials Based on Elastic Wave Measurements

The mechanical performance of pavement systems depends on the stiffness of subsurface soil and aggregate materials. The moduli of base course, subbase, and subgrade soils included in pavement systems need to be characterized for their use in the new empirical-mechanistic design procedure (NCHRP 1-37A). Typically, the resilient modulus test is used in the design of base and subbase layers under repetitive loads. Unfortunately, resilient modulus tests are expensive and cannot be applied to materials that contain particles larger than 25 mm (for 125-mm diameter specimens) without scalping the large grains. This paper examines a new methodology for estimating resilient modulus based on the propagation of elastic waves. The method is based on using a mechanistic approach that relates the P-wave velocity-based modulus to the resilient modulus through corrections for stress, void ratio, strain, and Poisson’s ratio effects. Results of this study indicate that resilient moduli are approximately 30% of Young’s moduli based on seismic measurements. The technique is then applied to specimens with large-grain particles. Results show that the methodology can be applied to large-grained materials and their resilient modulus can be estimated with reasonable accuracy based on seismic techniques. An approach is proposed to apply the technique to field determinations of modulus.     

Particle Image Velocity Measurements of Undular and Hydraulic Jumps

Measurements of the mean and turbulent flow fields in undular and hydraulic jumps have been acquired with single-camera particle image velocimetry (PIV). Three Froude numbers, ranging from 1.4 to 3.0, were studied, and in each case data were collected at numerous streamwise locations. The data from these streamwise locations were subsequently compiled into spatially dense ( ～ 80,000 grid points) “mosaic” images encompassing both the supercritical and subcritical portions of the flow. The measured mean and turbulent velocity fields provide more detailed views inside undular and hydraulic jumps than were previously available from studies using pointwise measurement techniques. The two-dimensional spatial density of the measurements provides for the determination of gradient-based quantities such as vorticity. The potential for determining boundary shear stress from the velocity data is evaluated with several methodologies. The results are found to be consistent with recent measurements made using Preston tubes. Discussion of the technical aspects of and difficulties involved with applying PIV to hydraulic jumps is provided. These challenges included the identification and tracking of the free surface through image analysis and the scattering of laser light by entrained air bubbles in the roller region.     

Interpretation of Impact Penetration Measurements in Soft Clays

The need for obtaining estimates of undrained shear strength of shallow seafloor sediments often arises in offshore engineering practice. Impact penetrometers offer a promising means of obtaining strength estimates in such sediments. However, variable conditions of embedment and velocity require careful consideration in the interpretation of impact penetration tests. This paper presents an analysis of the expendable bottom penetrometer (XBP), a device that measures acceleration during impact penetration. The analyses indicate that acceleration measurements can be reasonably related to undrained shear strength of soft clays. Further, acceleration measurements can be integrated to obtain velocity and embedment depth data at any point during the penetration analysis, thereby providing a basis for accounting for rate and embedment effects. Applying the proposed analysis to data from a series of test sites in the Gulf of Mexico indicate satisfactory agreement between XBP and reference strength profiles in soft clays.     

Acoustic Measurements of the Anisotropy of Dynamic Elastic and Poromechanics Moduli under Three Stress/Strain Pathways

A series of triaxial compression experiments have been conducted to investigate the effects of induced stress on the anisotropy developed in dynamic elastic and poroelastic parameters in rocks. The measurements were accomplished by utilizing an array of piezoelectric compressional and shear wave sensors mounted around a cylindrical sample of porous Berea sandstone. Three different types of applied states of stress were investigated using hydrostatic, triaxial, and uniaxial strain experiments. During the hydrostatic experiment, where an isotropic state of stress was applied to an isotropic porous rock, the vertical and horizontal acoustic velocities and dynamic elastic moduli increased as pressure was applied and no evidence of stress induced anisotropy was visible. The poroelastic moduli (Biot’s effective stress parameter, α) decreased during the test but also with no evidence of anisotropy. The triaxial compression test involved an axisymmetric application of stress with an axial stress greater than the two constant equal lateral stresses. During this test a marked anisotropy developed in the acoustic velocities, and in the dynamic elastic and poroelastic moduli. As axial stress increased the magnitude of the anisotropy increased as well. The uniaxial strain test involved axisymmetric application of stresses with increasing axial and lateral stresses but while maintaining a zero lateral strain condition. The uniaxial strain test exhibited a quite different behavior from either the triaxial or hydrostatic tests. As both the axial and lateral stresses were increased, an anisotropy developed early in the loading phase but then was effectively “locked in” with little or no change in the magnitude of the values of the acoustic velocities, or the dynamic elastic and poroelastic parameters as stresses were increased. These experimental results show that the application of triaxial states of stress induced significant anisotropy in the elastic and poroelastic parameters in porous rock, while under the uniaxial strain condition the poromechanics, Biot’s effective stress parameter, exhibited the largest variation among the three test conditions.     

Effective Soil Density for Propagation of Small Strain Shear Waves in Saturated Soil

This technical note defines an “effective soil density” that controls the velocity of small strain shear waves in saturated soil. Biot theory indicates that the ratio of effective density to saturated density will generally range from 0.75 to 1.0 and is a function of specific gravity of solids, porosity, hydraulic conductivity, and shear wave frequency. For many geotechnical applications, effective density will be equal to saturated density for low hydraulic conductivity soils (clays and silts) and may be less than saturated density for high hydraulic conductivity soils (clean sands and gravels). The findings are relevant to applications involving the propagation of small strain shear waves through saturated soil, and in particular for laboratory and field tests in which shear modulus is back-calculated from measured shear-wave velocity.     

Stress Integration Approach in Resonant Column and Torsional Shear Testing for Soils

Determination of strain in resonant column and torsional shear (RC/TS) tests is complicated due to nonuniform stress–strain variation occurring linearly with the radius in a soil specimen in torsion. The equivalent radius approach is adequate when calculating strain at low to intermediate levels, however, the approach is less accurate when performing the tests at higher strains. The stress integration approach involving integration of an assumed soil stress–strain model was developed to account for this problem more precisely. This approach was used to generate the plots of equivalent radius ratio versus strain developed based upon shear modulus and damping. Results showed that the equivalent radius ratio curves converge to a value of approximately 0.8 at low strains and decrease as strain increases. The equivalent radius ratio curves based upon damping decrease to significantly lower values at high strain than curves based upon shear modulus. This study suggests that using the same values of equivalent radius ratio to calculate strains for both shear modulus and damping is not appropriate. The stress integration approach provides an accurate analysis technique for evaluating both modulus and damping behavior of soil, over any range of strains in RC/TS testing.     

Fast Stacking and Phase Corrections of Shear Wave Signals in a Noisy Environment

Hardware, software, and analysis of transient response of sources and receivers are presented for a piezoelectric bender element system designed to measure shear wave velocities in noisy environments. Signal-to-noise ratio is improved by signal stacking, wherein data vectors from many pulses are summed. A new fast-stacking algorithm enables signal quality to be improved much more rapidly than conventional stacking. Conventional stacking is accomplished by repeatedly sending an excitation pulse to a source, waiting for the signal and secondary reflections to pass the receiver and then introducing a subsequent excitation pulse. Using conventional stacking, it is important to wait for the signal and secondary reflections to die out before exciting subsequent pulses. In the new fast-stacking algorithm, a varied interval between consecutive pulses is used so that high quality signals can be obtained even if consecutive pulses are excited in rapid succession. Transient behavior of soil–bender interaction was characterized using closed-form analytical solutions of single-degree-of-freedom oscillators, numerical solutions using a beam-on-springs method, and measurements from an array of bender elements in a sand model. The time delay caused by soil–bender interaction was calculated to be half of the natural period of the bender element, and this theoretical time delay was supported by experimental data. This system makes it feasible to rapidly collect accurate shear wave velocity information so that transient changes in shear wave velocity can be monitored even if background noise is large.     

Elastic Anisotropic Viscoplastic Modeling of the Strain-Rate-Dependent Stress–Strain Behavior of K0-Consolidated Natural Marine Clays in Triaxial Shear Tests

This paper presents a new three-dimensional (3D) anisotropic elastic viscoplastic (EVP) model for the time-dependent stress–strain behavior of K0-consolidated marine clays. A nonlinear creep function with a limit for the creep volumetric strain under an isotropic or odometer K0-consolidated stressing condition and a nonsymmetrical elliptical loading locus are incorporated in the 3D anisotropic EVP model. An α-line defines the inclination of the nonsymmetrical elliptical loading locus in the p′-q plane and is commonly used for natural soils. All model parameters are determined from the results of one set of consolidated undrained compression tests and an isotropic consolidation/creep test. With the parameters determined, the 3D anisotropic EVP model is used to simulate the behavior of K0-consolidation tests and the strain-rate-dependent stress–strain behaviors of the K0-consolidated triaxial compression and extension tests on natural Hong Kong marine deposit clay specimens. These triaxial K0-consolidated specimens were sheared at step-changed axial strain rates from +2?to?+0.2, +20, ?2 (unloading) and +2%/h (reloading) for compression tests; or from ?2?to??0.2, ?20, +2 (unloading), and ?2%/h (reloading) for extension tests, all in an undrained condition. The simulation results of all these tests are compared with the test results. The validation and limitations of the model are then evaluated and discussed.     

Errors in the Bed Shear Stress as Estimated from Vertical Velocity Profile

In this study, errors in determining bed shear stress caused by errors in theoretical bed surface data or roughness size selection using one-point velocity, two-point velocity, or a group of velocity measurements within the log-velocity region are systematically and quantitatively analyzed. The smaller the roughness element, the smaller the error in the bed shear stress estimate. For a fixed roughness size and absolute error in selecting the theoretical bed data, the closer to the bed the velocity measurement is taken, the larger the error in the friction velocity estimate. The velocity profile near the bed is very sensitive to the selection of the theoretical bed surface data. The velocity profile near the bed will deviate significantly from the true log profile if the theoretical bed surface data is over- or underestimated by 5?mm or more. This study shows conclusively that using the upper measurement data points, instead of the near-bed measurement, in the regression analysis yields better roughness size and bed shear stress estimates.     

Redistribution of Velocity and Bed-Shear Stress in Straight and Curved Open Channels by Means of a Bubble Screen: Laboratory Experiments

Open-channel beds show variations in the transverse direction due to the interaction between downstream flow, cross-stream flow, and bed topography, which may reduce the navigable width or endanger the foundations of structures. The reported preliminary laboratory study shows that a bubble screen can generate cross-stream circulation that redistributes velocities and hence, would modify the topography. In straight flow, the bubble-generated cross-stream circulation cell covers a spanwise extent of about four times the water depth and has maximum transverse velocities of about 0.2?ms?1. In sharply curved flow, it is slightly weaker and narrower with a spanwise extent of about three times the flow depth. It shifts the counter-rotating curvature-induced cross-stream circulation cell in the inwards direction. Maximum bubble-generated cross-stream circulation velocities are of a similar order of magnitude to typical curvature-induced cross-stream circulation velocities in natural open-channel bends. The bubble screen technique is adjustable, reversible, and ecologically favorable. Detailed data on the 3D flow field in open-channel bends is provided, which can be useful for validation of numerical models.