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At least 37 records · Page 2

Effects of secondary void-initiating particles on the steady-state crack growth resistance of high-strength steel

In this investigation, we focus on the dependence of stable crack growth resistance, as measured by the short-rod fracture toughness test, on secondary void-initiating particles such as AlN and Ti-based grain-refining precipitates in a variety of high-strength steels with tempered martensitic microstructures. The model developed by Ritchie and Thompson is modified to illustrate the significant amounts of toughening that can result from the refinement of secondary particles. Analysis of the data suggests that material strength is a predominant factor in increasing the short-rod fracture toughness relative to linear-elastic measures of initiation fracture toughness, but the extent of toughening is limited by the size and number density of secondary particles in the microstructure. The variation in estimates of secondary microvoid initiation and growth strains with precipitate size reinforce the notion that primary fracture at non-metallic inclusions and secondary fracture at smaller particles occur as sequential processes with a degree of concurrence that is dependent on the state of precipitation in both particle dispersions. Toughening in this connection is maximized by increases in microvoid growth strain that result from decreases in the size and areal number density of secondary void-initiating particles. Finally, the occurrence of transient instabilities during crack extension in short-rod specimens is explained with a phenomenological model that relates crack growth stability to natural variations in the dispersion of secondary void-initiating particles in the microstructure.

42 ENGINEERING↗

Grain detachment and transport clogging during mineral dissolution in carbonate rocks with permeable grain boundaries

In this paper, we explore the effect of permeable grain boundaries on carbonate rock dissolution in order to improve our understanding of grain detachment and migration during reactive flow. To do so we investigated the effects of grain size and enhanced reactivity along grain boundaries on global dissolution kinetics. Variations of permeability and porosity were calculated, and exponential relationships were observed in fractured rocks. Our model employed a reactive transport framework based on the Darcy-Brinkman equation to simulate calcite dissolution in carbonate rocks composed of microporous grains and, included fluid transport along grain boundaries. The model includes fluid flow, solute transport by advection–diffusion, heterogeneous reaction between fluid and minerals and grain detachment with subsequent grain transport in macropores. The migration of solid particles due to dissolution was based on cluster analysis and local movement, and the results show that grain detachment can lead to significant decreases in permeability due to the clogging of transport pathways. Microporous media with smaller grain sizes (fine grains in this study) showed a higher average reaction rate than those with coarser grains. In addition, as the overall rates of geochemical processes are commonly affected by the presence of texture heterogeneities such as fractures, a single fracture (macropore) introduced into a microporous matrix composed of permeable grains and grain boundaries was modelled as a large channel connecting the inlet and outlet of the simulation domain. It was found that macropore clogging by grain detachment temporary decreased permeability, lowering the long-term global reaction rates. Lastly, we observed that increases in flow rate can reduce detachment and fracture clogging by reducing local dissolution along grain boundaries.

58 GEOSCIENCES↗

A phase-field model of quasi-brittle fracture for pressurized cracks: Application to UO 2 high-burnup microstructure fragmentation

Here, in this paper, we present a phase-field model of quasi-brittle fracture with pressurized cracks, with dedicated applications for polycrystalline materials. The model is formulated as a minimization problem within the variational framework. The external work done by pressure on the crack surfaces is included in the objective function. Several careful modeling choices lead to a regularization-length-independent critical strength. The model is constructed to give a softening response with an underlying linear traction-separation law. The pressure-dependent softening response and the regularization of the prescribed pressure are demonstrated with a (quasi) one-dimensional numerical analysis. In a two-dimensional numerical analysis under plane strain assumptions, the critical stress corresponding to crack propagation (as predicted by our quasi-brittle fracture model) is compared with linear elastic fracture mechanics (LEFM) analytical solutions. Our model is further utilized to simulate fission-gas-induced fragmentation of the UO 2 high-burnup structure (HBS). Simulation results show that pressurized bubbles can cause crack nucleation and propagation, and that the bubble size and the surrounding external pressure affect the critical pressure corresponding to crack nucleation. Simulations of a partial HBS at different recrystallization stages show that different grain structures (due to recrystallization) also influence crack paths and fragmentation morphology.

36 MATERIALS SCIENCE↗

Hydraulic characterization of a fault zone from fracture distribution

A quantitative assessment of how faults control the migration of geofluids is critical in many areas of geosciences. Here we integrated geological fieldwork, quantitative analysis of the fractures distribution and numerical modeling to build a geometrical representation of a fault zone and to characterize its hydraulic properties. Our target is a fault located in the Majella Mountain (Italy). We collected 21 scan lines across the fault profile in order to characterize its architecture. The numerical modeling of the fracture network of the damage zones and their hydraulic parameters was performed using both commercial (Move ® ) and open source software (dfnWorks and PFLOTRAN). Move ® was used to build a representative model of the fault zone using fracture spacing as a proxy, and to model the hydraulic parameters of the different fault domains. dfnWorks and PFLOTRAN were employed to infer the hydraulic parameters of the damage zones of the fault and then upscale these properties to an equivalent continuum domain, suitable for fluid flow simulations through the whole fault zone. Our findings show how even in a relatively small area it is possible to describe changes in terms of hydraulic properties of a fault zone and to build models capable to represent these variations.

58 GEOSCIENCES↗

DECOVALEX-2023: Task A Final Report

Task A, also known as HGFrac, examines the fracturing processes that may occur in the Callovo-Oxfordian claystone (COx) in the context of the high-level (HLW) and intermediate-level long-lived (ILW-LL) radioactive waste repository in France. Understanding these processes and improving numerical models to reproduce them will aid in the design, optimization, and safety of the repository. Heat and gas fracturing are studied in two independent subtasks following a stepwise approach: laboratory tests/benchmark exercises, in-situ experiment, and finally, an application case. The in-situ heater experiment aimed to thermally induce a hydraulic fracture; temperature and pore pressure were monitored to detect any evidence of fracturing. The in-situ gas injection experiment aimed to study the effect of the stress orientation and gas injection kinetics on the gas fracturing process. The occurrence of fracturing was monitored by gas pressure measured in the injection interval. In both experiments, the excavation-induced fracture network around the heater/injection boreholes played an important role in the reduction of the compressive stress state, leading to both a tensile and shear failure response of the COx. During the first two years of the project, the research teams working on each task developed and/or proposed numerical approaches for reproducing the occurrence of fracturing in the in-situ experiments. The failure criteria were defined by reproducing the measurements from laboratory extension tests for the heat fracturing subtask. In the gas fracturing subtask, their approaches were used for simulating several benchmark exercises, and an inter-comparison between models was carried out. In both tasks, the developed approaches were compared with a simplified approach considering poro-elasticity for the mechanical behaviour of the COx. Most of the developed approaches are based on a continuous medium that takes into account variations in hydraulic properties due to mechanical degradation, such as plastic deformation or damage. Other approaches implicitly modelled weak planes or embedded discontinuities to reproduce fracture propagation. The potential for fracture initiation was also studied through of a discrete approach. In the second half of the project, the research teams mainly focused on interpretative modelling of two in-situ experiments and a blind prediction exercise to test their respective approaches. The models developed by the research teams were also applied at the repository scale to evaluate fracture initiation in a case study under vi unfavourable conditions, particularly in terms of spacing between High-Level Waste cells. The results showed that the poro-elasticity approach could be an efficient tool for understanding the main processes occurring in the COx. One example is the explicit representation of the excavation-induced fracture network around the boreholes, which yielded acceptable results compared to the measurement data. However, advanced approaches were needed to evaluate the potential increase of the excavation-induced fracture network extend and better understand fracture initiation. The stress analyses carried out by the teams revealed that hydraulic boundary conditions had a strong impact on fracture initiation in the heater experiment. Furthermore, in most cases, the results required higher pore pressure increments to reach fracturing than those measured in the experiment. This implies that the measurements may have been biased by the packer’s capacity to fully isolate the piezometric chambers, leading to lower pressures. On the contrary, there was no agreement on the fracturing mode, as some reported either shear or tensile fracturing, while others reported a combination of the two modes. In the case of gas fracturing, the research teams were limited to the comparison of a single point, which complicated their task. Nonetheless, the numerical results were able to reproduce the measurements and capture processes such as longitudinal gas flow through the excavation-induced fracture network, as suggested by some evidence in the observation piezometric chambers. The numerical models also agreed with the measurements in the sense of higher probability of developing along the injection borehole than radially towards the sound rock. The approaches developed by the research teams showed that they are capable of analysing and reproducing fracture initiation in the COx. However, areas of future work should focus on the fracture propagation and fracture aperture, which were out of the scope of this task. To this end, additional data must be gathered for the parameter characterisation and validation of the numerical models. Nonetheless, various approaches showed promising results as they were able to reproduce fracture development under certain conditions.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗

Radionuclide transport in fractured chalk under abrupt changes in salinity

Internationally, it has been agreed that geologic repositories for spent fuel and radioactive waste are considered the internationally agreed upon solution for intermediate and long-term disposal. In countries where traditional nuclear waste repository host rocks (e.g., clay, salt, granite) are not available, other low permeability lithologies must be studied. Here, chalk is considered to determine its viability for disposal. Despite chalk's low bulk permeability, it may contain fracture networks that can facilitate radionuclide transport. In arid areas, groundwater salinity may change seasonally due to the mixing between brackish groundwater and fresh meteoric water. Such salinity changes may impact the radionuclides' mobility. In this study, radioactive U(VI) and radionuclide simulant tracers (Sr, Ce and Re) were injected into a naturally fractured chalk core. The mobility of tracers was investigated under abrupt salinity variations. Two solutions were used: a low ionic strength (IS) artificial rainwater (ARW; IS ~0.002) and a high IS artificial groundwater (AGW; IS ~0.2). During the experiments, the tracers were added to ARW, then the carrier was changed to AGW, and vice versa. Ce was mobile only in colloidal form, while Re was transported as a conservative tracer. Both Re and Ce demonstrated no change in mobility due to salinity changes. In contrast, U and Sr showed increased mobility when AGW was introduced and decreased mobility when ARW was introduced into the core. These experimental results, supported by reactive transport modeling, suggest that saline groundwater solutions promote U and Sr release via ion-exchange and enhance their migration in fractured chalk. Here the study emphasizes the impact of salinity variations near spent fuel repositories and their possible impact on radionuclide mobility.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

The Sealing Mechanisms of a Fracture in Opalinus Clay as Revealed by in situ Synchrotron X-Ray Micro-Tomography

The detailed mechanisms of the sealing of a single fracture, from hydration to almost complete closure by increase of confining pressure, as monitored from in situ synchrotron X-ray microtomography during the flow of carbonated water, is here shown for the first time. Different mechanisms play the key role at different stages in the evolution of the fracture. Hydration mechanically weakens the surfaces of the fracture and induces a first closure due to microcracking at the asperity contacts, increasing their size and creating choke points. Increase in confining stress promptly hydraulically seals the fracture by closing the main choke point, with a relative small deformation of the sample. Finally, the more pervasive mechanical deformation observed at higher stresses almost completely seals the whole fracture. The evolution of the sample has been described and quantified using 4D image processing, focusing on the evolution of aperture and digital volume correlation. Hydraulic properties of the sample at different stages have been modeled via Stokes flow simulation, and the results compared to the morphometric analysis, finding positive correlations with the average fracture aperture variation along the flowpath in function of confining pressure. Opalinus Clay is found to be a rock markedly prone to sealing in case of flow with carbonated water; this behavior is the result of the large fraction of clays and of its microstructure, lacking both cementing phases and large stiff particles. CO2 in this sample has no evident role in the evolution of the fracture; chemically induced weathering on the surface has not been detected, in contrast with the behavior observed in samples with carbonates as cementing phase.

58 GEOSCIENCES↗

Attaining regularization length insensitivity in phase-field models of ductile failure

In this work, a cohesive phase-field model of ductile fracture in a finite-deformation setting is presented. The model is based on a free-energy function in which both elastic and plastic work contributions are coupled to damage. Using a strictly variational framework, the field evolution equations, damage kinetics, and flow rule are jointly derived from a scalar least-action principle. Particular emphasis is placed on the use of a rational function for the stress degradation that maintains a fixed effective strength with decreasing regularization length. The model is employed to examine crack growth in pure mode-I problems through the generation of crack growth resistance (J-R) curves. In contrast to alternative models, the current formulation gives rise to J-R curves that are insensitive to the regularization length. Numerical evidence suggests convergence of local fields with respect to diminishing regularization length as well.

42 ENGINEERING↗

Seismicity and Stress Associated With a Fluid-Driven Fracture: Estimating the Evolving Geometry

A coupled approach, combining the theory of rate- and state-dependent friction and methods from poroelasticity, forms the basis for a quantitative relationship between displacements and fluid leak-off from a growing fracture and changes in the rate of seismic events in the region surrounding the fracture. Poroelastic Green's functions link fracture aperture changes and fluid flow from the fracture to changes in the stress field and pore pressure in the adjacent formation. The theory of rate- and state-dependent friction provides a connection between Coulomb stress changes and variations in the rate of seismic events. Numerical modeling indicates that the Coulomb stress changes can vary significantly between formations with differing properties. The relationship between the seismicity rate changes and the changes in the formation stresses and fluid pressure is nonlinear, but a transformation produces a quantity that is linearly related to the aperture changes and fluid leak-off from the fracture. The methodology provides a means for mapping changes in seismicity into fracture aperture changes and to image an evolving fracture. An application to observed microseismicity associated with a hydrofracture reveals asymmetric fracture propagation within two main zones, with extended propagation in the upper zone. Furthermore, the time-varying volume of the fracture agrees with the injected volume, given by the integration of rate changes at the injection well, providing validation of the estimated aperture changes.

58 GEOSCIENCES↗

Microseismic at HFTS2: A Story of Three Stimulated Wells

A microseismic data set was acquired at Hydraulic Fracturing Test Site 2 (HFTS2) in the Delaware Basin (Texas, USA) by the HFTS2 consortium as a part of data-collection program designed to help maximize the efficiency of hydraulic fracturing, understand the impacts of nearby depleted zones, and increase the production of hydrocarbons. Advanced methods of microseismic monitoring applied at HFTS2 include 1) native synchronization of five monitor arrays, 2) real-time location of microseismic events, 3) joint event hypocenter/ velocity-model inversion that locates microseismic events simultaneously with constructing azimuthally anisotropic velocity models, 4) high-resolution reservoir imaging, utilizing microseismic events as downhole sources. HFTS2 microseismic data set illustrated the influence of geologic complexity, variations in treatment designs, and the presence of parent wells on the efficiency of hydraulic fracturing. Three Wolfcamp wells, Boxwood 1H, 2H, and 4H, were stimulated sequentially, exhibiting very different patterns of microseismicity. When the Boxwood 1H well is stimulated, its toe stages quickly reacted to the presence of depleted Bitterroot section to the east of the Boxwood pad, extending microseismic events over 3,000 ft to the east. This behavior changes dramatically after the treatment passes the Bitterroot section at the toe, and the heel stages in 1H showed tight microseismic grouping around the stimulated well, indicative of treatment of virgin reservoir rock. The Boxwood 2H demonstrates this same pattern of behavior between the toe and heel stages of the well, suggesting that the depleted Bitterroot section remains easier to refracture than adjacent non-depleted rock. Microseismic activity associated with Boxwood 4H treatment is distinctly different from those in Boxwood wells 1H and 2H. The events generated during stimulation of 4H are hardly influenced by the depleted Bitterroot section and fill the space between the previously stimulated 1H and 2H wells. Altogether, microseismic patterns suggest that treatment fluids tend to find the weakest passages through geologic formations, and the relative well positions and treatment sequence have a significant impact on fracture geometry, as indicated by microseismic event locations.

58 GEOSCIENCES↗

Simulation of hardened cement degradation and estimation of uncertainty in predicted failure times with peridynamics

Modeling the degradation of cement-based infrastructure due to aqueous environmental conditions continues to be a challenge. In order to develop a capability to predict concrete infrastructure failure due to chemical degradation, here we created a chemomechanical model of the effects of long-term water exposure on cement paste. The model couples the mechanical static equilibrium balance with reactive–diffusive transport and incorporates fracture and failure via peridynamics (a meshless simulation method). The model includes fundamental aspects of degradation of ordinary Portland cement (OPC) paste, including the observed softening, reduced toughness, and shrinkage of the cement paste, and increased reactivity and transport with water induced degradation. This version of the model focuses on the first stage of cement paste decalcification, the dissolution of portlandite. Given unknowns in the cement paste degradation process and the cost of uncertainty quantification (UQ), we adopt a minimally complex model in two dimensions (2D) in order to perform sensitivity analysis and UQ. We calibrate the model to existing experimental data using simulations of common tests such as flexure, compression and diffusion. Then we calculate the global sensitivity and uncertainty of predicted failure times based on variation of eleven unique and fundamental material properties. We observed particularly strong sensitivities to the diffusion coefficient, the reaction rate, and the shrinkage with degradation. Also, the predicted time of first fracture is highly correlated with the time to total failure in compression, which implies fracture can indicate impending degradation induced failure; however, the distributions of the two events overlap so the lead time may be minimal. Extension of the model to include the multiple reactions that describe complete degradation, viscous relaxation, post-peak load mechanisms, and to three dimensions to explore the interactions of complex fracture patterns evoked by more realistic geometry is straightforward and ongoing.

36 MATERIALS SCIENCE↗

Morphological Heterogeneity Impact of Film Solid-State Cathode on Utilization and Fracture Dynamics

Structural heterogeneity in solid-state batteries can impact material utilization and fracture mechanisms. Crystallographically oriented lithium cobalt oxide film cathodes serve as a model electrode system for exploring how void distribution contributes to stress relief and build up during cycling. Real- and reciprocal-space operando and ex situ synchrotron based experiments are utilized to understand structural changes across multiple length scales contribute to stress generation and fracture. Nanotomography uncovers a depth-dependent porosity variation in the pristine electrode and highlights preferential fracture in regions of lower porosity during delithiation. Energy-dispersive X-ray diffraction and 3D X-ray absorption near-edge spectroscopy (XANES) reveal the underutilization of cathode material in these regions. 3D XANES also confirms preferential delithiation near the sub-grain boundaries. Chemo-mechanical modeling coupled with site-specific mechanical characterization demonstrate how stress accumulation in dense regions of the electrode leads to fracture and underutilization of active material. In conclusion, our findings reveal the importance of materials design to alleviate stress in small-volume changing cathodes.

36 MATERIALS SCIENCE↗

Relating Hydro–Mechanical and Elastodynamic Properties of Dynamically Stressed Tensile–Fractured Rock in Relation to Applied Normal Stress, Fracture Aperture, and Contact Area

We exploit nonlinear elastodynamic properties of fractured rock to probe the micro-scale mechanics of fractures and understand the relation between fluid transport and fracture aperture under dynamic stressing. Experiments were conducted on rough, tensile-fractured Westerly granite subject to triaxial stresses. We measure fracture permeability for steady-state fluid flow with deionized water. Pore pressure oscillations are applied at amplitudes ranging from 0.2 to 1 MPa at 1 Hz frequency. During dynamic stressing we transmit ultrasonic signals through the fracture using an array of piezoelectric transducers (PZTs) to monitor evolution of interface properties. We examine the influence of fracture aperture and contact area by conducting measurements at effective normal stresses of 10–20 MPa. Additionally, the evolution of contact area with stress is characterized using pressure sensitive film. These experiments are conducted separately with the same fracture and map contact area at stresses from 9 to 21 MPa. The measurements are a proxy for “true” contact area for the fracture surface and we relate them to elastic properties using the calculated PZT sensor footprints via numerical modeling of Fresnel zones. We compare the elastodynamic response of the fracture using the stress-induced changes in ultrasonic wave velocities for transmitter-receiver pairs to image spatial variations in contact properties. We show that nonlinear elasticity and permeability enhancement decrease with increasing normal stress. Additionally, post-oscillation wave velocity and permeability exhibit quick recoveries toward pre-oscillation values. Estimates of fracture contact area (global and local) demonstrate that the elastodynamic and permeability responses are dominated by fracture topology.

58 GEOSCIENCES↗

On the convexity of phase-field fracture formulations: Analytical study and comparison of various degradation functions

Efficient and accurate fracture modeling is of great importance in applications where catastrophic outcomes under extreme scenarios are possible. The phase-field (PF) approach to fracture received significant attention over the past decade, due to its capability to capture complicated fracture patterns (e.g., crack merging and branching). Specifically, crack initiation and propagation are modeled via minimization of the total energy functional, which is regularized with the aid of a phase field. Despite the promising results and modeling capabilities of the PF method in many applications, the solution of fracture problems remains computationally challenging mainly due to the non-convexity of the total energy functional with respect to the combined unknown (phase field and displacement) fields. Understanding the effects of their coupling on convexity is crucial in order to address frequently encountered hurdles in fracture modeling (e.g., inefficient solvers and non-physical crack nucleation). In this paper, we develop convexity criteria for a wide class of PF fracture formulations. For this class of formulations, the second variation of the total energy functional is expressed in terms of Hessian matrices (evaluated at individual material points). Depending on the choice of geometric crack functions and degradation functions, we classify the formulations into three categories and analytically study each one separately. To study the sign of the second variation, we derive inequalities which are satisfied at material points when the Hessian matrix is locally positive semi-definite. These inequalities provide objective criteria for comparing degradation functions. Finally, the applicability of the proposed convexity criteria is demonstrated in the context of a one-dimensional problem, solved using a conventional monolithic solver.

97 MATHEMATICS AND COMPUTING↗

Mineralogical, magnetic and geochemical data constrain the pathways and extent of weathering of mineralized sedimentary rocks

The oxidative weathering of sulfidic rock can profoundly impact watersheds through the resulting export of acidity and metals. Weathering leaves a record of mineral transformation, particularly involving minor redox-sensitive phases, that can inform the development of conceptual and quantitative models. In sulfidic sedimentary rocks, however, variations in depositional history, diagenesis and mineralization can change or overprint the distributions of these trace minerals, complicating the interpretation of weathering signatures. Here we show that a combination of bulk mineralogical and geochemical techniques, micrometer-resolution X-ray fluorescence microprobe analysis and rock magnetic measurements, applied to drill core samples and single weathered fractures, can provide data that enable the development of a geochemically consistent weathering model. This work focused on one watershed in the Upper Colorado River Basin sitting within the Mesaverde Formation, a sedimentary sandstone bedrock with disseminated sulfide minerals, including pyrite and sphalerite, that were introduced during diagenesis and subsequent magmatic-hydrothermal mineralization. Combined analytical methods revealed the pathways of iron (Fe), carbonate and silicate mineral weathering and showed how pH controls element retention or release from the actively weathering fractured sandstone. Drill core logging, whole rock X-ray diffraction, and geochemical measurements document the progression from unweathered rock at depth to weathered rock at the surface. X-ray microprobe analyses of a 1-cm size weathering profile along a fracture surface are consistent with the mobilization of Fe(II) and Fe(III) into acidic pore water from the dissolution of primary pyrite, Fe-sphalerite, chlorite, and minor siderite and pyrrhotite. These reactions are followed by the precipitation of secondary minerals such as of goethite and jarosite, a Fe-(oxyhydr)oxide and hydrous Fe(III) sulfate, respectively. Microscale analyses also helped explain the weathering reactions responsible for the mineralogical transformations observed in the top and most weathered section of the drill core. For example, dissolution of feldspar and chlorite neutralizes the acidity generated by Fe and sulfide mineral oxidation, oversaturating the solution in both Fe-oxides. The combination of X-ray spectromicroscopy and magnetic measurements show that the Fe(III) product is goethite, mainly present either as a coating on fracture surfaces in the actively weathering region of the core or more homogeneously contained within the unconsolidated regolith at the top of the core. Low-temperature magnetic data reveal the presence of ferromagnetic Fe-sulfide pyrrhotite that, although it occurs at trace concentrations, could provide a qualitative proxy for unweathered sulfide minerals because the loss of pyrrhotite is associated with the onset of oxidative weathering. Pyrrhotite loss and goethite formation are detectable through room-temperature magnetic coercivity changes, suggesting that rock magnetic measurements can determine weathering intensity in rock samples at many scales. In conclusion, this work contributes evidence that the weathering of sulfidic sedimentary rocks follows a geochemical pattern in which the abundance of sulfide minerals controls the generation of acidity and dissolved elements, and the pH-dependent mobility of these elements controls their export to the ground- and surface-water.

58 GEOSCIENCES↗

Inference of phase field fracture models

The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). Furthermore, in this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Diffraction systems↗