Dielectric recovery of short A-C arcs between low-boiling-point electrodes

The re-ignition characteristics (variation of re-ignition voltage with time after current zero) of short alternating current arcs between plane brass electrodes in air were studied by observing the average re-ignition voltages on the screen of a cathode-ray oscilloscope and controlling the rates of rise of voltage by varying the shunting capacitance and hence the natural period of oscillation of the reactors used to limit the current. The shape of these characteristics and the effects on them of varying the electrode separation, air pressure, and current strength were determined.

The results show that short arc spaces recover dielectric strength in two distinct stages. The first stage agrees in shape and magnitude with a previously developed theory that all voltage is concentrated across a partially deionized space charge layer which increases its breakdown voltage with diminishing density of ionization in the field-tree space. The second stage appears to follow complete deionization by the electric field due to displacement of the field-free region by the space charge layer, its magnitude and shape appearing to be due simply to increase in gas density due to cooling. Temperatures calculated from this second stage and ion densities determined from the first stage by means of the space charge equation and an extrapolation of the temperature curve are consistent with recent measurements of arc value by other methods. Analysis or the decrease with time of the apparent ion density shows that diffusion alone is adequate to explain the results and that volume recombination is not. The effects on the characteristics of variations in the parameters investigated are found to be in accord with previous results and with the theory if deionization mainly by diffusion be assumed.

Applications of plasticity theory to selected problems in soil mechanics

Two topics in plane strain perfect plasticity are studied using the method of characteristics. The first is the steady-state indentation of an infinite medium by either a rigid wedge having a triangular cross section or a smooth plate inclined to the direction of motion. Solutions are exact and results include deformation patterns and forces of resistance; the latter are also applicable for the case of incipient failure. Experiments on sharp wedges in clay, where forces and deformations are recorded, showed a good agreement with the mechanism of cutting assumed by the theory; on the other hand the indentation process for blunt wedges transforms into that of compression with a rigid part of clay moving with the wedge. Finite element solutions, for a bilinear material model, were obtained to establish a correspondence between the response of the plane strain wedge and its axi-symmetric counterpart, the cone. Results of the study afford a better understanding of the process of indentation of soils by penetrometers and piles as well as the mechanism of failure of deep foundations (piles and anchor plates).

The second topic concerns the plane strain steady-state free rolling of a rigid roller on clays. The problem is solved approximately for small loads by getting the exact solution of two problems that encompass the one of interest; the first is a steady-state with a geometry that approximates the one of the roller and the second is an instantaneous solution of the rolling process but is not a steady-state. Deformations and rolling resistance are derived. When compared with existing empirical formulae the latter was found to agree closely.

Understanding Micro- and Macro-Mechanics of Soil Liquefaction: A Necessary Step for Field-Scale Assessment

Liquefaction is a devastating instability associated with saturated, loose, and cohesionless soils. It poses a significant risk to distributed infrastructure systems that are vital for the security, economy, safety, health, and welfare of societies. In order to make our cities resilient to the effects of liquefaction, it is important to be able to identify areas that are most susceptible. Some of the prevalent methodologies employed to identify susceptible areas include conventional slope stability analysis and the use of so-called liquefaction charts. However, these methodologies have some limitations, which motivate our research objectives. In this dissertation, we investigate the mechanics of origin of liquefaction in a laboratory test using grain-scale simulations, which helps (i) understand why certain soils liquefy under certain conditions, and (ii) identify a necessary precursor for onset of flow liquefaction. Furthermore, we investigate the mechanics of liquefaction charts using a continuum plasticity model; this can help in modeling the surface hazards of liquefaction following an earthquake. Finally, we also investigate the microscopic definition of soil shear wave velocity, a soil property that is used as an index to quantify liquefaction resistance of soil. We show that anisotropy in fabric, or grain arrangement can be correlated with anisotropy in shear wave velocity. This has the potential to quantify the effects of sample disturbance when a soil specimen is extracted from the field. In conclusion, by developing a more fundamental understanding of soil liquefaction, this dissertation takes necessary steps for a more physical assessment of liquefaction susceptibility at the field-scale.