I. Applications of Double-Exposure Holography to the Measurement of In Situ Stress and the Elastic Moduli of Rock from Boreholes. II. Shock Temperature Measurements in Fused Quartz and Crystalline NaCl to 35 GPa

Citation

Schmitt, Douglas Ray (1987) I. Applications of Double-Exposure Holography to the Measurement of In Situ Stress and the Elastic Moduli of Rock from Boreholes. II. Shock Temperature Measurements in Fused Quartz and Crystalline NaCl to 35 GPa. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/vr7c-6j57. https://resolver.caltech.edu/CaltechTHESIS:10242023-225432851

Abstract

Part I.

The application of a new borehole technique using holographic inter­ ferometry to measure the in situ state of stress and the modulus of elasti­city of rock is discussed. The apparatus exposes two holograms which are taken both before and after micron scale displacements are induced by (1) drilling a small stress-relieving hole in the wall of a borehole, and (2) applying a normal point force to the borehole wall. Maximum induced displacements are approximately 10 microns; the holograms are sensitive to movements on the order of 0.1 micron. Raw data take the form of a series interference holograms which have dark fringes superimposed on the three dimensional holographic borehole wall image. Synthetic fringe patterns are used to forward model the observed in the present method of data analysis. Calibrations of the normal force method of measuring the elastic moduli is carried out on metals with well defined elastic properties. Typi­cally each test yields elastic (Young's) moduli for brass and aluminum of 100 ± 10 GPa and 70 ± 5 GPa, respectively, which are in close agreement with standard tests. Laboratory holographic measurements of the Young's modulus on a sample of keragenaceous dolomitic marlstone (taken from the same mine as which the in situ experiments were conducted) yielded 16.8 ± 2.8 GPa in agreement with the predicted modulus of 17.2 ± 2.0 GPa based upon published density-modulus relationships. Sonic velocity determinations of the dynamic Young's modulus on cores taken from the rock sample give values consistent with the holographic measurements of 13.5 to 19.1 GPa for assumed values of Poisson's ratio of 0.35 to 0.25. The results of field tests in a horizontal borehole in a mine pillar in the Mahogany formation of Garfield County, Colorado, are presented for both experiments. The elastic modulus was found to vary with position in the borehole from 26.9 to 36.0 GPa. The farfield stresses for a borehole station 4 m from the mine pillar free surface were found from analysis of several stress-relief holograms; the determined vertical stress within the mine pillar was -10.2 MPa (compressive) close to the predicted magnitude of -11.2 MPa.

Part II.

Greybody temperatures and emittances of fused quartz under shock compression between 10 and 30 GPa are determined. Observed radiative temperatures are higher than computed continuum temperatures for shock compressed fused quartz, however; below ~26 GPa observed emittances are < 0.02. This suggests that fused quartz deforms heterogeneously in this shock pressure range, as has been observed in other minerals. Between 10 and 16 GPa, radiative temperatures decrease from 4400 K to 3200 K, above 16 GPa to 30 GPa greybody temperatures of ~3000 K with low emit­tances are observed. The emittances increase with pressure from 0.02 to 0.9. The pressure range from 10 to 16 GPa coincides with the permanent densification region while the 16 to 30 GPa range coincides with the mixed phase region along the fused quartz Hugoniot. The differing radiative behaviors relate to these modes of deformation. Based upon shock recovery experiments and a proposed model of heterogeneous deformation under shock compression, the temperatures associated with low emittances in the mixed phase region probably represents the melting temperature of the high pressure phase. Above 20 GPa to 30 GPa the melting temperature of stishovite would therefore be approximately 3000 K and almost independent of pressure. The effect of pressure on melting relations for the phase system SiO₂-Mg₂SiO₄ are considered together with the proposed melting curve of stishovite and suggest that maximum solidus temperatures within the mantle of ~2370 K at 12.5 GPa and ~2520 K at 20.0 GPa. Using the proposed stishovite melting temperatures (T_m) and reasonable upper mantle temperatures (T), the effective viscosity (which is a function of the homologous temperature (T_m/T)) appears to remain nearly constant from 600 to 200 km depth in the Earth.

Radiative color temperatures were measured in single crystal sodium chloride under shock compression parallel to [100] over a pressure range from 20 to 35 GPa. Color temperatures from 2500 to 4500 K and emittances from 0.003 to 0.3 were determined by fitting observed spectra (450 to 850 nm) to the Planck greybody radiation law. These data support a heterogeneous shock deformation model of shocked halite in this pressure range. A 2500 K temperature rise is observed over the Bl-B2 mixed phase region from 25 to 30 GPa. Assuming that shock deformation occurs via yielding in localized planar zones which become melt and the melting temperature at high pressure controls the temperature, we infer that the temperature of the B2 fusion curve from 30 to 35 GPa rises from 3200 to 3300 K. The Bl-B2-liquid triple point is predicted at a temperature of 2250 K and 23.5 GPa.

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