Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock

We present a rigorous validation of the analytical Amadei solution for the stress concentration around an arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients b11 and b55 are not equal. It is shown from theoretical considerations and published experimental data that the b11 and b55 are not equal for realistic rocks. Second, we develop a 3D finite element elastic model within a hybrid analytical–numerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic, transverse isotropic and orthorhombic symmetries. It is concluded that the analytical Amadei solution is valid with no restriction on the borehole orientation or the symmetry of the elastic anisotropy.

Anisotropic damage mechanics as a novel approach to improve pre-and post-failure borehole stability analysis

Anisotropic damage distribution and evolution have a profound effect on borehole stress concentrations. Damage evolution is an irreversible process that is not adequately described within classical equilibrium thermodynamics. Therefore, we propose a constitutive model, based on non-equilibrium thermodynamics, that accounts for anisotropic damage distribution, anisotropic damage threshold and anisotropic damage evolution. We implemented this constitutive model numerically, using the finite element method, to calculate stress–strain curves and borehole stresses. The resulting stress–strain curves are distinctively different from linear elastic-brittle and linear elastic-ideal plastic constitutive models and realistically model experimental responses of brittle rocks. We show that the onset of damage evolution leads to an inhomogeneous redistribution of material properties and stresses along the borehole wall. The classical linear elastic-brittle approach to borehole stability analysis systematically overestimates the stress concentrations on the borehole wall, because dissipative strain-softening is underestimated. The proposed damage mechanics approach explicitly models dissipative behaviour and leads to non-conservative mud window estimations. Furthermore, anisotropic rocks with preferential planes of failure, like shales, can be addressed with our model.

First steps towards modeling a multi-scale Earth system

Recent advances in computational geodynamics are applied to explore the link between Earth’s heat, its chemistry and its mechanical behavior. Computational thermal-mechanical solutions are now allowing us to understand Earth patterns by solving the basic physics of heat transfer. This approach is currently used to solve basic convection patterns of terrestrial planets. Applying the same methodology to smaller scales delivers promising similarities between observed and predicted structures which are often the site of mineral deposits. The new approach involves a fully coupled solution to the energy, momentum and continuity equations of the system at all scales, allowing the prediction of fractures, shear zones and other typical geological patterns out of a randomly perturbed initial state. The results of this approach are linking a global geodynamic mechanical framework over regional-scale mineral deposits down to the underlying micro-scale processes. Ongoing work includes the challenge of incorporating chemistry into the formulation.

A new ambiguity acceptance test threshold determination method with controllable failure rate

The ambiguity acceptance test is an important quality control procedure in high precision GNSS data processing. Although the ambiguity acceptance test methods have been extensively investigated, its threshold determine method is still not well understood. Currently, the threshold is determined with the empirical approach or the fixed failure rate (FF-) approach. The empirical approach is simple but lacking in theoretical basis, while the FF-approach is theoretical rigorous but computationally demanding. Hence, the key of the threshold determination problem is how to efficiently determine the threshold in a reasonable way. In this study, a new threshold determination method named threshold function method is proposed to reduce the complexity of the FF-approach. The threshold function method simplifies the FF-approach by a modeling procedure and an approximation procedure. The modeling procedure uses a rational function model to describe the relationship between the FF-difference test threshold and the integer least-squares (ILS) success rate. The approximation procedure replaces the ILS success rate with the easy-to-calculate integer bootstrapping (IB) success rate. Corresponding modeling error and approximation error are analysed with simulation data to avoid nuisance biases and unrealistic stochastic model impact. The results indicate the proposed method can greatly simplify the FF-approach without introducing significant modeling error. The threshold function method makes the fixed failure rate threshold determination method feasible for real-time applications.

Deep geothermal: The ‘Moon Landing’ mission in the unconventional energy and minerals space

Deep geothermal from the hot crystalline basement has remained an unsolved frontier for the geothermal industry for the past 30 years. This poses the challenge for developing a new unconventional geomechanics approach to stimulate such reservoirs. While a number of new unconventional brittle techniques are still available to improve stimulation on short time scales, the astonishing richness of failure modes of longer time scales in hot rocks has so far been overlooked. These failure modes represent a series of microscopic processes: brittle microfracturing prevails at low temperatures and fairly high deviatoric stresses, while upon increasing temperature and decreasing applied stress or longer time scales, the failure modes switch to transgranular and intergranular creep fractures. Accordingly, fluids play an active role and create their own pathways through facilitating shear localization by a process of time-dependent dissolution and precipitation creep, rather than being a passive constituent by simply following brittle fractures that are generated inside a shear zone caused by other localization mechanisms. We lay out a new theoretical approach for the design of new strategies to utilize, enhance and maintain the natural permeability in the deeper and hotter domain of geothermal reservoirs. The advantage of the approach is that, rather than engineering an entirely new EGS reservoir, we acknowledge a suite of creep-assisted geological processes that are driven by the current tectonic stress field. Such processes are particularly supported by higher temperatures potentially allowing in the future to target commercially viable combinations of temperatures and flow rates.

Characterization of frequency‐dependent magnetic susceptibility in UXO electromagnetic geophysics

Soils at many locations that have their origin in volcanic parent material and have undergone extensive weathering often exhibit strong frequency-dependent magnetic susceptibilities. The presence of such susceptibility has a profound effect on electromagnetic induction data acquired in such environments. Their transient electromagnetic response is characterized by a t-1 decay that is strong enough to mask UXO responses. In a field study and associated laboratory work on characterizing the frequency-dependent magnetic susceptibility and its influence on transient electromagnetic data, we collected soil samples on the surface and in soil pits from the Island of Kaho'olawe, Hawaii, and measured their frequency dependent magnetic susceptibilities. We present the details of the field investigation, confirm previous theoretical work with field and laboratory measurements, characterize the susceptibility with a Cole-Cole model, and investigate the response specific to the measured susceptibility.

Tracking the magmatic evolution of island arc volcanism : insights from a high-precision Pb isotope record of Montserrat, Lesser Antilles

The volcanic succession on Montserrat provides an opportunity to examine the magmatic evolution of island arc volcanism over a ∼2.5 Ma period, extending from the andesites of the Silver Hills center, to the currently active Soufrière Hills volcano (February 2010). Here we present high-precision double-spike Pb isotope data, combined with trace element and Sr-Nd isotope data throughout this period of Montserrat's volcanic evolution. We demonstrate that each volcanic center; South Soufrière Hills, Soufrière Hills, Centre Hills and Silver Hills, can be clearly discriminated using trace element and isotopic parameters. Variations in these parameters suggest there have been systematic and episodic changes in the subduction input. The SSH center, in particular, has a greater slab fluid signature, as indicated by low Ce/Pb, but less sediment addition than the other volcanic centers, which have higher Th/Ce. Pb isotope data from Montserrat fall along two trends, the Silver Hills, Centre Hills and Soufrière Hills lie on a general trend of the Lesser Antilles volcanics, whereas SSH volcanics define a separate trend. The Soufrière Hills and SSH volcanic centers were erupted at approximately the same time, but retain distinctive isotopic signatures, suggesting that the SSH magmas have a different source to the other volcanic centers. We hypothesize that this rapid magmatic source change is controlled by the regional transtensional regime, which allowed the SSH magma to be extracted from a shallower source. The Pb isotopes indicate an interplay between subduction derived components and a MORB-like mantle wedge influenced by a Galapagos plume-like source.

Pore formation during dehydration of polycrystalline gypsum observed and quantified in a time-series synchrotron radiation based X-ray micro-tomography experiment

We conducted an in-situ X-ray micro-computed tomography heating experiment at the Advanced Photon Source (USA) to dehydrate an unconfined 2.3 mm diameter cylinder of Volterra Gypsum. We used a purpose-built X-ray transparent furnace to heat the sample to 388 K for a total of 310 min to acquire a three-dimensional time-series tomography dataset comprising nine time steps. The voxel size of 2.2 μm3 proved sufficient to pinpoint reaction initiation and the organization of drainage architecture in space and time. We observed that dehydration commences across a narrow front, which propagates from the margins to the centre of the sample in more than four hours. The advance of this front can be fitted with a square-root function, implying that the initiation of the reaction in the sample can be described as a diffusion process. Novel parallelized computer codes allow quantifying the geometry of the porosity and the drainage architecture from the very large tomographic datasets (20483 voxels) in unprecedented detail. We determined position, volume, shape and orientation of each resolvable pore and tracked these properties over the duration of the experiment. We found that the pore-size distribution follows a power law. Pores tend to be anisotropic but rarely crack-shaped and have a preferred orientation, likely controlled by a pre-existing fabric in the sample. With on-going dehydration, pores coalesce into a single interconnected pore cluster that is connected to the surface of the sample cylinder and provides an effective drainage pathway. Our observations can be summarized in a model in which gypsum is stabilized by thermal expansion stresses and locally increased pore fluid pressures until the dehydration front approaches to within about 100 μm. Then, the internal stresses are released and dehydration happens efficiently, resulting in new pore space. Pressure release, the production of pores and the advance of the front are coupled in a feedback loop.

Micas in experimentally shocked gneiss

Biotites and muscovites from a gneiss have been experimentally shocked between 18 and 70 GPa using powder-propellant guns at NASA Johnson Space Center and at the California Institute of Technology. This study shows that shock in biotite and muscovite can produce homogeneous and devolatilized glasses within microseconds. Shock-deformed micas display fracturing, kinking, and complex extinction patterns over the entire pressure range investigated. However, these deformation features are not a sensitive pressure indicator. Localized melting of micas begins at 33 GPa and goes to completion at 70 GPa. Melted biotite and muscovite are optically opaque, but show extensive microvesiculation and flow when observed with the SEM. Electron diffraction confirms that biotite and muscovite have transformed to a glass. The distribution of vesicles in shock-vitrified mica shows escape of volatiles within the short duration of the shock experiment. Experimentally shocked biotite and muscovite undergo congruent melting. Compositions of the glasses are similar to the unshocked micas except for volatiles (H2O loss and K loss). These unusual glasses derived from mica may be quenched by rapid cooling conditions during the shock experiment. Based on these results, the extremely low H2O content of tektites may be reconciled with a terrestrial origin by impact. Release of volatiles in shock-melted micas affects the melting behavior of coexisting dry silicates during the short duration of the shock experiment. Transportation and escape of volatiles released from shock-melted micas may provide plausible mechanisms for the origin of protoatmospheres on terrestrial planets, hydrothermal activity on phyllosilicate-rich meteorite parent bodies, and fluid entrapment in meteorites.