A rate-type constitutive model for soil with a critical state

A continuum representation for soil which incorporates the concepts of hypoelasticity and critical state theory is proposed. General, three-dimensional constitutive equations are formulated to relate specific volume, stress, rate of deformation and rate of change of stress, resulting in a mathematical material model which exhibits phenomenological features typical of soil response. The general constitutive equations are specialized to represent the particular cases of isotropic compression, constant, volume deformation, uniaxial compression and biaxial deformation. Methods are suggested for determining the model parameters to represent a specific soil using conventional triaxial test data. Comparisons of stress-strain response with published experimental data are shown.     

Coseismic and other short-term strain changes recorded with Sacks-Evertson strainmeters in a deep mine, South Africa

Summary. During 1977 March and April, three Sacks-Evertson borehole dilatometers were installed at the ends of boreholes drilled into the sidewall of an experimental tunnel at a depth of 3.1 km in the ERPM gold mine near Johannesburg. In the following year coseismic strain changes ranging from 5 ± 10⁻¹⁰ to values exceeding 5 ± 10⁻⁶ were recorded for hundreds of mine tremors in the magnitude range -1 to 3.7 and at hypocentral distances of 50 m to about 2 km. Hypocentral coordinates and magnitudes were determined from seismograms recorded from an underground array of geophones. Amplitudes and polarities of the coseismic strain steps are generally in excellent agreement with theoretical expectations based on point-source dislocation theory; specifically, the strain steps are proportional to the seismic moment divided by the cube of hypocentral distance. At a strain level of 5 ± 10⁻⁹ or greater the tremors do not appear to be preceded by any short-term indications of instability even for tremors producing coseismic steps greater than 5 ± 10⁻⁶ and for which the strainmeters were within a source radius of the hypocentre. Continuous strain changes observed at the times when the mine excavation, at a distance of about 100 m, is extended are in good agreement with calculated changes based on the theory of elasticity. A similar calculation is consistent with post-seismic strain changes observed to follow some of the closer tremors. These post-seismic strains show a logarithmic dependence on time following the tremor and appear to be due to the interaction of a tremor with the adjacent mine excavation rather than to deformation within the actual seismic source region.     

A three-dimensional numerical model of particulate transport for coastal waters

A Lagrangian marker particle in Eulerian finite difference cell solution to the three-dimensional incompressible mass transport equation was developed for predicting particulate transport in coastal and estuarine waters. Special features of the solution procedure include a finite difference grid network which translates horizontally and vertically with the mean particle motion and expands with the dispersive growth of the marker particle cloud. The cartesian vertical coordinate of the three-dimensional mass transport equation has been transformed, using instantaneous water column depth to allow adaptation to flow situations with a temporally and spatially varying bottom topography and free surface. Results from this model for turbulent diffusion and advection of a uniform plug flow of sediment in an unbounded uniform flow field with various sediment settling velocities were in excellent agreement with the corresponding analytic solutions. Using current information from a two-dimensional vertically averaged hydrodynamic's model, the model was utilized to predict the long term diffusion and advection of dilute neutrally and negatively buoyant suspended sediment clouds resulting from a hypothetical instantaneous release of dredge spoil waste at Brown's Ledge in Rhode Island Sound.