Intelligent prediction of the stress-strain response of intact and jointed rocks

An application of Artificial Neural Networks for predicting the stress-strain response of jointed rocks under different confining pressures is presented in this paper. Rocks of different compressive strength with different joint properties (frequency, orientation and strength of joints) are considered in this study. The database for training the neural network is formed from the results of triaxial compression tests on different intact and jointed rocks with different joint properties tested at different confining pressures reported by various researchers in the literature. The network was trained using a three-layered network with the feed-forward back propagation algorithm.About 85% of the data was used for training and the remaining 15% was used for testing the network. Results from the analyses demonstrated that the neural network approach is effective in capturing the stress-strain behaviour of intact rocks and the complex stress-strain behaviour of jointed rocks. A single neural network is demonstrated to be capable of predicting the stress-strain response of different jointed rocks, whose intact strength varies from 11.32 MPa to 123 MPa, spacing of joints varies from 10 cm to 100 cm. and confining pressures range from 0 to 13.8 MPa. (C) 2010 Elsevier Ltd. All rights reserved.

Geochemistry and petrology of the ferropicrite dikes and associated rocks of Vestfjella, western Dronning Maud Land, Antarctica

This study provides insights into the composition and origin of ferropicrite dikes (FeOtot = 13 17 wt. %; MgO = 13 19 wt. %) and associated meimechite, picrite, picrobasalt, and basalt dikes found at Vestfjella, western Dronning Maud Land, Antarctica. The dikes crosscut Jurassic Karoo continental flood basalts (CFB) that were emplaced during the early stages of the breakup of the Gondwana supercontinent ~180 Ma ago. Selected samples (31 overall from at least eleven dikes) were analyzed for their mineral chemical, major element, trace element, and Sr, Nd, Pb, and Os isotopic compositions. The studied samples can be divided into two geochemically distinct types: (1) The depleted type (24 samples from at least nine dikes) is relatively depleted in the most incompatible elements and exhibits isotopic characteristics (e.g., initial εNd of +4.8 to +8.3 and initial 187Os/188Os of 0.1256 0.1277 at 180 Ma) similar to those of mid-ocean ridge basalts (MORB); (2) The enriched type (7 samples from at least two dikes) exhibits relatively enriched incompatible element and isotopic characteristics (e.g., initial εNd of +1.8 to +3.6 and initial 187Os/188Os of 0.1401 0.1425 at 180 Ma) similar to those of oceanic island basalts. Both magma types have escaped significant contamination by the continental crust. The depleted type is related to the main phase of Karoo magmatism and originated as highly magnesian (MgO up to 25 wt. %) partial melts at high temperatures (mantle potential temperature >1600 °C) and pressures (~5 6 GPa) from a sublithospheric, water-bearing, depleted peridotite mantle source. The enriched type sampled pyroxene-bearing heterogeneities that can be traced down to either recycled oceanic crust or melt-metasomatized portions of the sublithospheric or lithospheric mantle. The source of the depleted type represents a sublithospheric end-member source for many Karoo lavas and has subsequently been sampled by the MORBs of the Indian Ocean. These observations, together with the purported high temperatures, indicate that the Karoo CFBs were formed in an extensive melting episode caused mainly by internal heating of the upper mantle beneath the Gondwana supercontinent. My research supports the view that ferropicritic melts can be generated in several ways: the relative Fe-enrichment of mantle partial melts is most readily achieved by (1) relatively low degree of partial melting, (2) high pressure of partial melting, and (3) melting of enriched source components (e.g., pyroxenite and metasomatized peridotite). Ferropicritic whole-rock compositions could also result from accumulation, secondary alteration, and fractional crystallization, however, and caution is required when addressing the parental magma composition.

Stress-Strain Prediction of Jointed Rocks using Artificial Neural Networks

The applicability of Artificial Neural Networks for predicting the stress-strain response of jointed rocks at varied confining pressures, strength properties and joint properties (frequency, orientation and strength of joints) has been studied in the present paper. The database is formed from the triaxial compression tests on different jointed rocks with different confining pressures and different joint properties reported by various researchers. This input data covers a wide range of rock strengths, varying from very soft to very hard. The network was trained using a 3 layered network with feed forward back propagation algorithm. About 85% of the data was used for training and remaining15% for testing the predicting capabilities of the network. Results from the analyses were very encouraging and demonstrated that the neural network approach is efficient in capturing the complex stress-strain behaviour of jointed rocks. A single neural network is demonstrated to be capable of predicting the stress-strain response of different rocks, whose intact strength vary from 11.32 MPa to 123 MPa and spacing of joints vary from 10 cm to 100 cm for confining pressures ranging from 0 to 13.8 MPa.

Elasto-plastic analysis of jointed rocks using discrete continuum and equivalent continuum approaches

Results from elasto-plastic numerical simulations of jointed rocks using both the equivalent continuum and discrete continuum approaches are presented, and are compared with experimental measurements. Initially triaxial compression tests on different types of rocks with wide variation in the uniaxial compressive strength are simulated using both the approaches and the results are compared. The applicability and relative merits and limitations of both the approaches for the simulation of jointed rocks are discussed. It is observed that both the approaches are reasonably good in predicting the real response. However, the equivalent continuum approach has predicted somewhat higher stiffness values at low strains. Considering the modelling effort involved in case of discrete continuum approach, for problems with complex geometry, it is suggested that a proper equivalent continuum model can be used, without compromising much on the accuracy of the results. Then the numerical analysis of a tunnel in Japan is taken up using the continuum approach. The deformations predicted are compared well against the field measurements and the predictions from discontinuum analysis. (C) 2012 Elsevier Ltd. All rights reserved.

Orientation-based Continuum Damage Models for Rocks

A general formulation of the Helmholtz free energy used in thermodynamics of damage process of rocks is derived within a multi-scale framework. Such a physically-based thermodynamic state potential has a hybrid, discrete/continuum, nature in the sense tha

Identifying and interpreting stratification in sedimentary rocks on Mars : insight from Rover and orbital observations and terrestrial field analogs

Sedimentary rocks on Mars provide insight into past aqueous and atmospheric processes, climate regimes, and potential habitability. The stratigraphic architecture of sedimentary rocks on Mars is similar to that of Earth, indicating that the processes that govern deposition and erosion on Mars can be reasonably inferred through reference to analogous terrestrial systems. This dissertation aims to understand Martian surface processes through the use of (1) ground-based observations from the Mars Exploration Rovers, (2) orbital data from the High Resolution Imaging Science Experiment onboard the Mars Reconnaissance Orbiter, and (3) the use of terrestrial field analogs to understand bedforms and sediment transport on Mars. Chapters 1 and 2 trace the history of aqueous activity at Meridiani Planum, through the reconstruction of eolian bedforms at Victoria crater, and the identification of a potential mudstone facies at Santa Maria crater. Chapter 3 uses Terrestrial Laser Scanning to study cross-bedding in pyroclastic surge deposits on Earth in order to understand sediment transport in these events and to establish criteria for their identification on Mars. The final chapter analyzes stratal geometries in the Martian North Polar Layered Deposits using tools for sequence stratigraphic analysis, to better constrain past surface processes and past climate conditions on Mars.

Probing the thermodynamic properties of mantle rocks in solid and liquid states

Our understanding of the structure and evolution of the deep Earth is strongly linked to knowledge of the thermodynamic properties of rocky materials at extreme temperatures and pressures. In this thesis, I present work that helps constrain the equation of state properties of iron-bearing Mg-silicate perovskite as well as oxide-silicate melts. I use a mixture of experimental, statistical, and theoretical techniques to obtain knowledge about these phases. These include laser-heated diamond anvil cell experiments, Bayesian statistical analysis of powder diffraction data, and the development of a new simplified model for understanding oxide and silicate melts at mantle conditions. By shedding light on the thermodynamic properties of such ubiquitous Earth-forming materials, I hope to aid our community’s progress toward understanding the large-scale processes operating in the Earth’s mantle, both in the modern day and early in Earth’s history.

I. Impact spallation experiments: fracture patterns and spall velocities. II. Craters in carbonate rocks: an electron paramagnetic resonance analysis of shock damage

This work is divided into two independent papers.

PAPER 1.

Spall velocities were measured for nine experimental impacts into San Marcos gabbro targets. Impact velocities ranged from 1 to 6.5 km/sec. Projectiles were iron, aluminum, lead, and basalt of varying sizes. The projectile masses ranged from a 4 g lead bullet to a 0.04 g aluminum sphere. The velocities of fragments were measured from high-speed films taken of the events. The maximum spall velocity observed was 30 m/sec, or 0.56 percent of the 5.4 km/sec impact velocity. The measured velocities were compared to the spall velocities predicted by the spallation model of Melosh (1984). The compatibility between the spallation model for large planetary impacts and the results of these small scale experiments are considered in detail.

The targets were also bisected to observe the pattern of internal fractures. A series of fractures were observed, whose location coincided with the boundary between rock subjected to the peak shock compression and a theoretical "near surface zone" predicted by the spallation model. Thus, between this boundary and the free surface, the target material should receive reduced levels of compressive stress as compared to the more highly shocked region below.

PAPER 2.

Carbonate samples from the nuclear explosion crater, OAK, and a terrestrial impact crater, Meteor Crater, were analyzed for shock damage using electron para- magnetic resonance, EPR. The first series of samples for OAK Crater were obtained from six boreholes within the crater, and the second series were ejecta samples recovered from the crater floor. The degree of shock damage in the carbonate material was assessed by comparing the sample spectra to spectra of Solenhofen limestone, which had been shocked to known pressures.

The results of the OAK borehole analysis have identified a thin zone of highly shocked carbonate material underneath the crater floor. This zone has a maximum depth of approximately 200 ft below sea floor at the ground zero borehole and decreases in depth towards the crater rim. A layer of highly shocked material is also found on the surface in the vicinity of the reference bolehole, located outside the crater. This material could represent a fallout layer. The ejecta samples have experienced a range of shock pressures.

It was also demonstrated that the EPR technique is feasible for the study of terrestrial impact craters formed in carbonate bedrock. The results for the Meteor Crater analysis suggest a slight degree of shock damage present in the β member of the Kaibab Formation exposed in the crater walls.

Oxygen isotope ratios in coexisting minerals of regionally metamorphosed rocks

The O¹⁸/O¹⁶ ratios of coexisting minerals from a number of regionally metamorphosed rocks have been measured, using a bromine pentafluoride extraction-technique. Listed in order of their increasing tendency to concentrate O¹⁸, the minerals analyzed are magnetite, ilmenite, chlorite, biotite, garnet, hornblende, kyanite, muscovite, feldspar, and quartz. The only anomalous sequence detected occurs in a xenolith of schist, in which quartz, muscovite, biotite, and ilmenite, but not garnet, have undergone isotopic exchange with surrounding trondjemite.

With few exceptions, quartz-magnetite and quartz-ilmenite fractionations decrease with increasing metamorphic grade determined by mineral paragenesis and spatial distribution. This consistency does not apply to quartz-magnetite and quartz-ilmenite fractionations obtained from rocks in which petrographic evidence of retrogradation is present.

Whereas measured isotopic fractionations among quartz, garnet, ilmenite, and magnetite are approximately related to metamorphic grade, fractionations between these minerals and biotite or muscovite show poor correlation with grade. Variations in muscovite-biotite fractionations are relatively small. These observations are interpreted to mean that muscovite and biotite are affected by retrograde re-equilibration to a greater extent than the anhydrous minerals analyzed.

Measured quartz-ilmenite fractionations range from 12 permil in the biotite zone of central Vermont to 6.5 permil in the sillimanite-orthoclase zone of southeastern Connecticut. Analyses of natural assemblages from the kyanite and sillimanite zones suggest that equilibrium quartz-ilmenite fractionations are approximately 8 percent smaller than corresponding quartz-magnetite fractionations. Employing the quartz-magnetite geothermometer calibrated by O'Neil and Clayton (1964), a temperature of 560°C was obtained for kyanite-bearing schists from Addison County, Vermont. Extending the calibration to quartz-ilmenite fractionations, a temperature of 600°C was obtained for kyanite-schists from Shoshone County, Idaho. At these temperatures kyanite is stable only at pressures exceeding 11 kbars (Bell, 1963), corresponding to lithostatic loads of over 40 km.

The geochronology of the plutonic and metamorphic rocks of New Zealand

Extensive Rubidium-Strontium age determinations on both mineral and total rock samples of the crystalline rocks of New Zealand, which almost solely crop out in the South Island, indicate widespread plutonic and metamorphic activity occurred during two periods, one about 100-118 million years ago and the other about 340-370 million years ago. The former results date the Rangitata Orogeny as Cretaceous. They associate extensive plutonic activity with this orogeny which uplifted and metamorphosed the rocks of the New Zealand Geosyncline, although no field association between the metamorphosed geosynclinal rocks and plutonic rocks has been found. The Cretaceous plutonic rocks occur to the west in the Foreland Province in Fiordland, Nelson, and Westland, geographically separated from the Geosynclinal Province. Because of this synchronous timing of plutonic and high pressure metamorphic activity in spatially separated belts, the Rangitata Orogeny in New Zealand is very similar to late Mesozoic orogenic activity in many other areas of the circum-Pacific margin (Miyashiro, 1961).

The 340-370 million year rocks, both plutonic and metamorphic, have been found only in that part of the Foreland Province north of the Alpine Fault. There, they are concentrated along the west coast over a distance of 500 km, and appear scattered inland from the coast. Probably this activity marks the outstanding Phanerozoic stratigraphic gap in New Zealand which occurred after the Lower Devonian.

A few crystalline rocks in the Foreland Province north of the Alpine Fault with measured ages intermediate between 340 and 120 million years have been found. Of these, those with more than one mineral examined give discordant results. All of these rocks are tentatively regarded as 340-370 million year old rocks that have been variously disturbed during the Rangitata Orogeny, 100-120 million years ago.

In addition to these two periods, plutonic activity, dominantly basic and ultrabasic, but including the development of some rocks of intermediate and acidic composition, occurred along the margin of the Geosynclinal Province at its border with the Foreland Province during Permian times about 245 million years ago, and this activity possibly extended into the Mesozoic.

Evidence from rubidium-strontium analyses of minerals and a total rock, and from uranium, thorium, and lead analyses of uniform euhedral zircons from a meta-igneous portion of the Charleston Gneiss, previously mapped as Precambrian, indicate that this rock is a 350-370 million year old plutonic rock metamorphosed 100 million yea rs ago during the Rangitata Orogeny. No crystalline rocks with primary Precambrian ages have been found in New Zealand. However, Pb²⁰⁷/Pb₂₀₆ ages of 1360 million years and 1370 million years have been determined for rounded detrital zircons separated from each of two hornfels samples of one of New Zealand's olde st sedimentary units, the Greenland Series. These two samples were metamorphosed 345- 370 million years ago. They occur along the west coast, north of the Alpine Fault, at Waitaha River and Moeraki River, separated by 135 km. The Precambrian measured ages are most likely minimum ages for the oldest source area which provided the detrital zircons because the uranium, thorium and lead data are highly discordant. These results are of fundamental importance for the tectonic picture of the Southwest Pacific margin and demonstrate the existence of relatively old continental crust of some lateral extent in the neighborhood of New Zealand.