Ali Karrech

Time-dependent, irreversible entropy production and geodynamics

We present an application of entropy production as an abstraction tool for complex processes in geodynamics. Geodynamic theories are generally based on the principle of maximum dissipation being equivalent to the maximum entropy production. This represents a restriction of the second law of thermodynamics to its upper bound. In this paper, starting from the equation of motion, the first law of thermodynamics and decomposition of the entropy into reversible and irreversible terms,1 we come up with an entropy balance equation in an integral form. We propose that the extrema of this equation give upper and lower bounds that can be used to constrain geodynamics solutions. This procedure represents an extension of the classical limit analysis theory of continuum mechanics, which considers only stress and strain rates. The new approach, however, extends the analysis to temperature-dependent problems where thermal feedbacks can play a significant role. We apply the proposed procedure to a simple convective/conductive heat transfer problem such as in a planetary system. The results show that it is not necessary to have a detailed knowledge of the material parameters inside the planet to derive upper and lower bounds for self-driven heat transfer processes. The analysis can be refined by considering precise dissipation processes such as plasticity and viscous creep.

From transient to steady state deformation and grain size: A thermodynamic approach using elasto‐visco‐plastic numerical modeling

Numerical simulation experiments give insight into the evolving energy partitioning during high-strain torsion experiments of calcite. Our numerical experiments are designed to derive a generic macroscopic grain size sensitive flow law capable of describing the full evolution from the transient regime to steady state. The transient regime is crucial for understanding the importance of micro structural processes that may lead to strain localization phenomena in deforming materials. This is particularly important in geological and geodynamic applications where the phenomenon of strain localization happens outside the time frame that can be observed under controlled laboratory conditions. Ourmethod is based on an extension of the paleowattmeter approach to the transient regime. We add an empirical hardening law using the Ramberg-Osgood approximation and assess the experiments by an evolution test function of stored over dissipated energy (lambda factor). Parameter studies of, strain hardening, dislocation creep parameter, strain rates, temperature, and lambda factor as well asmesh sensitivity are presented to explore the sensitivity of the newly derived transient/steady state flow law. Our analysis can be seen as one of the first steps in a hybrid computational-laboratory-field modeling workflow. The analysis could be improved through independent verifications by thermographic analysis in physical laboratory experiments to independently assess lambda factor evolution under laboratory conditions.

Thermal‐elastic stresses and the criticality of the continental crust

Heating or cooling can lead to high stresses in rocks due to the different thermal-elastic properties of minerals. In the upper 4 km of the crust, such internal stresses might cause fracturing. Yet it is unclear if thermal elasticity contributes significantly to critical stresses and failure deeper in Earths continental crust, where ductile creep causes stress relaxation. We combined a heating experiment conducted in a Synchrotron microtomograph (Advanced Photon Source, USA) with numerical simulations to calculate the grain-scale stress field in granite generated by slow burial. We find that deviatoric stresses >100 MPa can be stored during burial, with relaxation times from 100s to 1000s ka, even in the ductile crust. Hence, grain-scale thermal-elastic stresses may serve as nuclei for instabilities, thus rendering the continental crust close to criticality.

Multiscale, multiphysics geomechanics for geodynamics applied to buckling instabilities in the middle of the Australian craton

We propose a new multi-physics, multi-scale Integrated Computational Materials Engineering framework for ‘predictive’ geodynamic simulations. A first multiscale application is presented that allows linking our existing advanced material characterization methods from nanoscale through laboratory-, field and geodynamic scales into a new rock simulation framework. The outcome of our example simulation is that the diachronous Australian intraplate orogenic events are found to be caused by one and the same process. This is the non-linear progression of a fundamental buckling instability of the Australian intraplate lithosphere subject to long-term compressive forces. We identify four major stages of the instability: (1) a long wavelength elasto-visco-plastic flexure of the lithosphere without localized failure (first 50 Myrs of loading); (2) an incipient thrust on the central hinge of the model (50–90 Myrs); (3) followed by a secondary and tertiary thrust (90–100 Myrs) 200 km away to either side of the central thrust; (4) a progression of subsidiary thrusts advancing towards the central thrust ( Myrs). The model is corroborated by multiscale observations which are: nano–micro CT analysis of deformed samples in the central thrust giving evidence of cavitation and creep fractures in the thrust; mm–cm size veins of melts (pseudotachylite) that are evidence of intermittent shear heating events in the thrust; and 1–10 km width of the thrust – known as the mylonitic Redbank shear zone – corresponding to the width of the steady state solution, where shear heating on the thrust exactly balances heat diffusion.

Dynamic response of cracked Timoshenko beams on elastic foundations under moving harmonic loads

A thorough understanding of the dynamic behavior of one-dimensional structural members such as beams plays a crucial role in specialized disciplines including ocean, bridge and railway engineering. The vibratory response of an in-service beam-like component may deviate from that expected from the intact structure when defects are present. In this work, we present a semi-analytical approach to predict the forced response of a multi-cracked Timoshenko beam traversed by a moving harmonic load with constant speed. The beam is fully or partially supported by the viscoelastic foundation, where the normal stiffness and shear modulus of the subgrade are considered. The effects of transverse open cracks are modeled by massless rotational springs with a linear moment-rotation constitutive law to account for the local flexibility induced by the damage. Based on the transfer matrix method, the defective structure is treated as an assembly of sub-beams to derive the eigenvalue solution of the system. The time response is then obtained by utilizing identical generalized coordinates for lateral and rotational displacement components when applying the modal expansion technique. The use of general elastic end constraints allows us to recover all possible boundary conditions. Numerical examples are also provided to demonstrate the robustness and accuracy of the proposed method, and also to investigate the influence of important parameters on the dynamic behavior of the damaged structure.

A parallel computing tool for large-scale simulation of massive fluid injection in thermo-poro-mechanical systems

Massive fluid injections into the earth’s upper crust are commonly used to stimulate permeability in geothermal reservoirs, enhance recovery in oil reservoirs, store carbon dioxide and so forth. Currently used models for reservoir simulation are limited to small perturbations and/or hydraulic aspects that are insufficient to describe the complex thermal-hydraulic-mechanical behaviour of natural geomaterials. Comprehensive approaches, which take into account the non-linear mechanical deformations of rock masses, fluid flow in percolating pore spaces, and changes of temperature due to heat transfer, are necessary to predict the behaviour of deep geo-materials subjected to high pressure and temperature changes. In this paper, we introduce a thermodynamically consistent poromechanics formulation which includes coupled thermal, hydraulic and mechanical processes. Moreover, we propose a numerical integration strategy based on massively parallel computing. The proposed formulations and numerical integration are validated using analytical solutions of simple multi-physics problems. As a representative application, we investigate the massive injection of fluids within deep formation to mimic the conditions of reservoir stimulation. The model showed, for instance, the effects of initial pre-existing stress fields on the orientations of stimulation-induced failures.

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.

Green Concrete with High-Volume Fly Ash and Slag with Recycled Aggregate and Recycled Water to Build Future Sustainable Cities

AbstractBuilding sustainable green cities for the future can be difficult or highly challenging as such cities need to reduce their environmental footprint through eco-friendly materials, resource and energy conservation, as well as renewable energy generation. A recent paper by the first author has proposed sustainable concrete with 80% ground granulated blast furnace slag (GGBFS) to build Masdar City in the UAE with a 153  kg/m3 carbon footprint. This paper proposes three new types of sustainable concretes in an attempt to further reduce the carbon footprint. In Type I, a total of 4 concrete mixes were made with a high volume GGBFS with 60, 70, 80, and 90% replacement of ordinary portland cement (OPC), 100% recycled water (RW), and 100% recycled aggregate (RA). The same replacement ratios were used in Type II but with only 100% RA. In Type III, a total of four concrete mixes made with a high volume fly ash (FA) cement with 40, 50, 60, and 70% replacement of OPC. The paper provides information on the mix...

Improvements to local projective noise reduction through higher order and multiscale refinements

The broad spectrum characteristic of signals from nonlinear systems obstructs noise reduction techniques developed for linear systems. Local projection was developed to reduce noise while preserving nonlinear deterministic structures, and a second order refinement to local projection which was proposed ten years ago does so particularly effectively. It involves adjusting the origin of the projection subspace to better accommodate the geometry of the attractor. This paper describes an analytic motivation for the enhancement from which follows further higher order and multiple scale refinements. However, the established enhancement is frequently as or more effective than the new filters arising from solely geometric considerations. Investigation of the way that measurement errors reinforce or cancel throughout the refined local projection procedure explains the special efficacy of the existing enhancement, and leads to a new second order refinement offering widespread gains. Different local projective filters are found to be best suited to different noise levels. At low noise levels, the optimal order increases as noise increases. At intermediate levels second order tends to be optimal, while at high noise levels prototypical local projection is most effective. The new higher order filters perform better relative to established filters for longer signals or signals corresponding to higher dimensional attractors.

Entropic Bounds for Multi-Scale and Multi-Physics Coupling in Earth Sciences

The ability to understand and predict how thermal, hydrological,mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal– Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is incorporated in the thermodynamic approach; (3) suggest a unifying thermodynamic framework for multi-scaling; and (4) formulate a new rationale for assessing upper and lower bounds of dissipation for THMC processes. The technique is based on deducing time and length scales suitable for separating processes using a macroscopic finite time thermodynamic approach. We show that if the time and length scales are suitably chosen, the calculation of entropic bounds can be used to describe three different types of material and process uncertainties: geometric uncertainties,stemming from the microstructure; process uncertainty, stemming from the correct derivation of the constitutive behavior; and uncertainties in time evolution, stemming from the path dependence of the time integration of the irreversible entropy production. Although the approach is specifically formulated here for THMC coupling we suggest that it has a much broader applicability. In a general sense it consists of finding the entropic bounds of the dissipation defined by the product of thermodynamic force times thermodynamic flux which in material sciences corresponds to generalized stress and generalized strain rates, respectively.