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DOE OSTI2024

Poromechanical cohesive interface element with combined Mode I-II cohesive zone elastoplasticity for simulating fracture in fluid-saturated porous media

A combined Mode I-II cohesive zone (CZ) elasto-plastic constitutive model, and a two-dimensional (2D) cohesive interface element (CIE) are formulated and implemented at small strain within an ABAQUS User Element (UEL) for simulating 2D crack nucleation and propagation in fluid-saturated porous media. Here, the CZ model mitigates problems of convergence for the global Newton-Raphson solver within ABAQUS, which when combined with a viscous stabilization procedure allows for simulation of post-peak response under load control for coupled poromechanical finite element analysis, such as concrete gravity dam stability analysis. Verification examples are presented, along with a more complex ambient limestone-concrete wedge fracture experiment, water-pressurized concrete wedge experiment, and concrete gravity dam stability analyses. A calibration procedure for estimating the CZ parameters is demonstrated with the limestone-concrete wedge fracture process. For the water-pressurized concrete wedge fracture experiment it is shown that the inherent time-dependence of the poromechanical CIE analysis provides a good match with experimental force versus displacement results at various crack mouth opening rates, yet misses the pore water pressure evolution ahead of the crack tip propagation. This is likely a result of the concrete being partially-saturated in the experiment, whereas the finite element analysis assumes fully water saturated concrete. For the concrete gravity dam analysis, it is shown that base crack opening and associated water uplift pressure leads to a reduced Factor of Safety, which is confirmed by separate analytical calculations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials

Ductile materials, such as metal alloys, can undergo substantial deformation before failure. Additionally, these materials are usually of polycrystalline composition and exhibit strongly anisotropic behavior at small length scales. Previously developed fast Fourier transform (FFT)-based models can model ductile fracture of isotropic materials or the elastic–plastic behavior of anisotropic polycrystalline materials; however, there remains a need to couple both capabilities. This work extends a large-strain FFT-based crystal plasticity model to simulate ductile fracture of polycrystalline materials. In this work, a triaxiality-based continuum damage mechanics (CDM) formulation is incorporated into a large-strain elasto-viscoplastic FFT (LS-EVPFFT) framework. The CDM formulation is augmented with an integral-based nonlocal regularization approach that correctly handles gas-phase material necessary to model unconstrained surfaces. To validate the damage-enabled LS-EVPFFT framework, mesoscale copper tensile coupons were machined using microwire electrical discharge machining and experimentally characterized using electron backscatter diffraction. In-situ optical digital image correlation was performed during uniaxial testing to provide a side-by-side comparison of the experimental and computational strain fields and stress–strain responses. The damage-enabled LS-EVPFFT framework can simulate the complete macroscopic stress–strain response of ductile polycrystals to failure. The model reproduces necking behavior that qualitatively agrees with experimental observations. By leveraging the relatively low computational cost of the damage-enabled LS-EVPFFT framework, the framework presented here allows the ductile fracture response of 3D polycrystalline materials to be tractably predicted.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Weight function procedure for reduced order fracture analysis of arbitrary flaws in cylindrical pressure vessels

Fracture mechanics calculations using the finite element method can be computationally expensive, which makes them challenging to use in engineering evaluations of flaws in pressure vessels. The weight function (WF) technique is a reduced order fracture modeling method that is widely used to greatly reduce these computational costs. Its computational efficiency is essential for use in probabilistic fracture mechanics evaluations of embrittled nuclear reactor pressure vessels (RPVs), due to the large number of sampled flaws that must be evaluated. Although the WF technique is general, it is typically used only for axis-aligned flaws. Recent discoveries of off-axis flaws in operating nuclear reactors have necessitated detailed simulations of such flaws and the interactions between neighboring flaws. This paper presents a generalized WF approach applicable for analyzing arbitrary flaw geometries in thick-walled cylindrical vessels, including surface-breaking and subsurface flaws, which can either axis-aligned or off-axis, and can account for interactions with other flaws. Herein, this approach is demonstrated on representative simulations of multiple flaw geometries in a RPV subjected to transient loading conditions. In all cases, the WF technique gives good comparison with benchmark results from direct simulation with greatly reduced computational effort.

42 ENGINEERING↗

DOE OSTI2026

Coupling geophysical, geological, geochemical and mineralogical assessments to examine preferential contaminant transport pathways in interbedded fractured bedrock

This study shows that a multi-faceted approach, combining borehole geophysical logging and surface seismic P-wave first-arrival tomography with confirmatory coring, well installation, and chemical and mineralogical analysis, is effective for identifying difficult-to-locate preferential contaminant transport pathways in deeper fractured bedrock. Seismic tomography detected porous 10–20 m wide elongated fractured conduits that allow acidic groundwater contaminated with uranium (U) and nitrate (NO 3 - ) to migrate within interbedded shale-limestone bedrock over 1000 m from a former disposal facility (S-3 Ponds site) located at the DOE Y-12 National Security Complex in Tennessee (USA). Conventional drilling techniques would easily miss these conduits because they are oriented parallel with fractured bedding planes. Synchrotron analysis of aquifer solids revealed that > 95 % of the U is hexavalent (U VI ). This uranyl (UO 2 2+ ) species is coordinated with carbonate, iron oxide, silicate and phosphate minerals within cemented white to yellow precipitates, which contain U concentrations as high as ∼21.6 % by weight fraction. Identifying the presence of these mineral phases, enables a further understanding of the potential effectiveness of remediation actions. The combination of methodologies presented here can also be applied to other explorations, such as the detection of water supply.

Fate and transport↗

DOE OSTI2022

Mesh objective stochastic simulations of quasibrittle fracture

Continuum finite element (FE) modeling of damage and failure of quasibrittle structures suffers from the spurious mesh sensitivity due to strain localization. Here this issue has been addressed for deterministic analysis through the development of localization limiters. Here this study proposes a mechanism-based model to mitigate the mesh sensitivity in stochastic FE simulations of quasibrittle fracture. The interest is placed on the analysis of large-size structures, where the mesh size is conveniently chosen to be larger than the width of the fracture process zone as well as the correlation length of the random fields of constitutive properties. The present model is formulated within the framework of continuum damage mechanics. Two localization parameters are introduced to describe the evolution of the damage pattern of each finite element. These parameters are used to guide the energy regularization of the constitutive law, as well as to formulate the mesh-dependent probability distributions of constitutive properties. Depending on the prevailing damage pattern, different energy regularization schemes and mesh dependence of the probability distribution functions are used in the constitutive law. The model is applied to simulate the stochastic failure behavior of quasibrittle structures of different geometries featuring different failure processes including damage initiation, localization, and propagation. It is shown that using fixed probability distribution functions of constitutive properties could lead to strong mesh dependence of the prediction of the mean and variance of the structural load capacity. The probability distribution functions of constitutive properties must be linked to the damage pattern, which may evolve during the failure process. Such a mechanism-based modeling of the probability distributions of constitutive properties is essential for mitigating the spurious mesh sensitivity in stochastic FE analysis of quasibrittle fracture.

42 ENGINEERING↗

DOE OSTI2023

The comparative strength and fracture toughness properties of commercial 95W-3.5Ni1.5Fe and 95W-3.5Ni1.5Cu tungsten heavy alloys

Due to the sharp surface cracks resulting from high and cyclic thermal loads, fracture toughness is a crucial property for fusion divertor materials. Tungsten heavy alloys (WHA) have emerged as a leading candidate for plasma facing component applications. Both the WNiFe and WNiCu WHAs have been considered. However, there is no fracture toughness data in the literature on the WNiCu WHA. Therefore, maximum load elastic–plastic fracture toughness (K Jm ) of a commercial 95W-3.5Ni1.5Cu (NiCu) WHA plate is reported here for the first time. The NiCu WHA K Jm is compared to a corresponding K Jm for commercial 95W-3.5Ni1.5Fe (NiFe) WHA, along with comparisons of their respective microstructures, microhardness, and tensile properties. Although their room temperature yield strengths are similar (≈ 600 MPa), the NiFe WHA has higher ultimate stress (818 MPa vs. 642 MPa) and total elongation (8% vs. 1.2%) compared to the NiCu WHA. Most notably, the room temperature elastic–plastic K Jm for the NiFe WHA of ≈ 80 ± 8 MPa$\sqrt{m}$, is nearly twice that of the NiCu WHA at ≈ 47 ± 4 MPa$\sqrt{m}$. Further, while the NiFe WHA experienced stable ductile tearing, the crack propagated unstably (approximately elastically) after reaching the maximum load in the NiCu WHA. The higher K Jm of the NiFe WHA is attributed to its higher flow stress and ductility, along with the energy dissipation and microcrack dilatational stress shielding, provided by a wide distribution of arrested process-zone microcracks, which are largely absent in the NiCu WHA. Since, the 95W-NiFe WHA has distinctly better mechanical properties than 95W-NiCu WHA, it is a more suitable candidate for the fusion reactor application.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

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↗

DOE OSTI2020

Mobility of Radionuclides in Fractured Carbonate Rocks: Lessons from a Field-Scale Transport Experiment

Current research on radionuclide disposal is mostly conducted in granite, clay, saltstone, or volcanic tuff formations. These rock types are not always available to host a geological repository in every nuclear waste-generating country, but carbonate rocks may serve as a potential alternative. To assess their feasibility, a forced gradient cross-borehole tracer experiment was conducted in a saturated fractured chalk formation. The mobility of stable Sr and Cs (as analogs for their radioactive counterparts), Ce (an actinide analog), Re (a Tc analog), bentonite particles, and fluorescent dye tracers through the flow path was analyzed. The migration of each of these radionuclide analogs (RAs) was shown to be dependent upon their chemical speciation in solution, their interactions with bentonite, and their sorption potential to the chalk rock matrix. The brackish groundwater resulted in flocculation and immobilization of most particulate RAs. Nevertheless, the high permeability of the fracture system allowed for fast overall transport times of all aqueous RAs investigated. This study suggests that the geochemical properties of carbonate rocks may provide suitable conditions for certain types of radionuclide storage (in particular, brackish, high-porosity, and low-permeability chalks). Nevertheless, careful consideration should be given to high-permeability fracture networks that may result in high radionuclide mobility.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2023

Molecular Dynamics Simulations of Calcite Fracture in Water

Calcite (CaCO 3 ) is one of the most common minerals in geologic and engineered systems. It is often in contact with aqueous solutions, causing chemically assisted fracture that is critical to understanding the stability of subsurface systems and manmade structures. Calcite fracture was evaluated with reactive molecular dynamics simulations, including the impacts of crack tip geometry (notch), the presence of water, and surface hydroxyl groups. Chemo-mechanical weakening was assessed by comparing the loads where fracture began to propagate. Our analyses show that in the presence of a notch, the load at which crack growth begins is lower, compared to the effect of water or surface hydroxyls. Additionally, the breaking of two adjacent Ca–O bonds is the kinetic limitation for crack initiation, since transiently broken bonds can reform, not resulting in crack growth. In aqueous environments, fresh (not hydroxylated) calcite surfaces exhibited water strengthening. Manual addition of H + and/or OH – species on the (104) calcite surface resulted in chemo-mechanical weakening of calcite by 9%. Achieving full hydroxylation of the calcite surface was thermodynamically and kinetically limited, with only 0.17–0.01 OH/nm 2 surface hydroxylation observed on the (104) surface at the end of the simulations. In conclusion, the limited reactivity of pure water with the calcite surface restricts the chemo-mechanical effects and suggests that reactions between physiosorbed water and localized structural defects may be dominating the chemo-mechanical process in the studies where water weakening has been reported.

Calcite↗

DOE OSTI2020

The Complexity of Nonlinear Flow and non-Fickian Transport in Fractures Driven by Three-Dimensional Recirculation Zones

Subsurface fluid flow and solute transport are typically described by first-order or linear rate laws. However, deviations from the first-order rate laws (or anomalous behavior) are typical and lead to nonlinear flow and non-Fickian transport phenomena. The shared underlying mechanisms for these “anomalous” flow and transport phenomena, which are actually typical of fractures, are seldom analyzed. We investigated the co-occurrence of nonlinear flow and non-Fickian transport through numerical simulation experiments of pore-scale flow and solute transport processes through three-dimensional natural fractures. In these fractures, 3-D recirculation zones (RZs) developed and grew with increasing flow rates. Flow nonlinearity resulted from the RZ development and growth, which shrank the main flow channel. Moreover, the same RZs also captured solutes from the main flow channel and released them back later. This retardation resulted in non-Fickian transport. Thus, nonlinear flow and non-Fickian transport are intertwined via their shared dependence on RZs.

58 GEOSCIENCES↗

DOE OSTI2022

A Comparison of Linear Solvers for Resolving Flow in Three-Dimensional Discrete Fracture Networks

We compare various methods for resolving steady flow within three-dimensional discrete fracture networks, including direct methods, Krylov subspace methods with and without preconditioning, and multi-grid methods. We compared the performance of the methods based on compute times and scaling of the solution as a function of the number of grid nodes and log-variance of the hydraulic aperture. The methods are applied to three test cases: (a) variable density of networks with a truncated power-law distribution of fracture lengths, (b) a fixed network composed of monodisperse fracture sizes but varied permeability/aperture heterogeneity, (c) and a network based on field site in Nevada, US. We chose these cases to allow us to study the impact of the mesh size and flow properties, as well as to demonstrate our conclusions on a large-scale, realistic problem (more than 40 million mesh nodes). A direct solution using Cholesky factorization outperformed other methods for every example but was closely followed in performance by some algebraic multigrid (AMG) preconditioned Krylov subspace methods. Among the Krylov methods, conjugate gradients (CG) with an AMG preconditioner performs the best. Generally, Cholesky factorization is recommended, but CG with an AMG preconditioner may be suitable for very large problems beyond 40 million nodes where the entire linear system cannot reside in memory.

58 GEOSCIENCES↗

DOE OSTI2024

Carbon Mineralization in Fractured Mafic and Ultramafic Rocks: A Review

Mineral carbon storage in mafic and ultramafic rock masses has the potential to be an effective and permanent mechanism to reduce anthropogenic CO 2 . Several successful pilot-scale projects have been carried out in basaltic rock (e.g., CarbFix, Wallula), demonstrating the potential for rapid CO 2 sequestration. However, these tests have been limited to the injection of small quantities of CO 2 . Thus, the longevity and feasibility of long-term, large-scale mineralization operations to store the levels of CO 2 needed to address the present climate crisis is unknown. Moreover, CO 2 mineralization in ultramafic rocks, which tend to be more reactive but less permeable, has not yet been quantified. In these systems, fractures are expected to play a crucial role in the flow and reaction of CO 2 within the rock mass and will influence the CO 2 storage potential of the system. Therefore, consideration of fractures is imperative to the prediction of CO 2 mineralization at a specific storage site. In this review, we highlight key takeaways, successes, and shortcomings of CO 2 mineralization pilot tests that have been completed and are currently underway. Laboratory experiments, directed toward understanding the complex geochemical and geomechanical reactions that occur during CO 2 mineralization in fractures, are also discussed. Experimental studies and their applicability to field sites are limited in time and scale. Many modeling techniques can be applied to bridge these limitations. We highlight current modeling advances and their potential applications for predicting CO 2 mineralization in mafic and ultramafic rocks.

25 ENERGY STORAGE↗

DOE OSTI2026

Effects of Dissolution Regimes on Flow Channelization and Solute Transport in 3D Fracture Networks: Insights From Graph‐Based Reactive Transport Modeling

We investigate how mineral dissolution reshapes flow pathways and solute transport in three‐dimensional discrete fracture networks using a computationally efficient graph‐based reactive transport model. The DFNs are inspired by field‐site observations of fractured carbonate and represent realistic connectivity and structural heterogeneity. Flow is simulated with the Reynolds equation, and dissolution follows first‐order kinetics with diffusive limitations captured through an effective mass‐transfer coefficient. By systematically varying two key dimensionless parameters, the effective Damköhler number (Da), governing reaction versus advection rates, and a transport parameter (Da), analogous to the Thiele modulus, distinct flow channelization regimes emerge: mildly channelized at low G, highly channelized at intermediate Da, and extreme wormhole formation at high Da and low G. Eulerian and Lagrangian analyses, including breakthrough curves, particle tortuosity, dispersivity, and flow channeling indicators quantitatively characterize the progression of dissolution‐driven network restructuring. Across all regimes, initial fracture heterogeneity persists. The results underscore how the interplay between this initial structure, advection, reaction, and diffusion critically shapes subsurface flow pathways, with implications for applications ranging from groundwater remediation to enhanced geothermal systems.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Quantum algorithms for geologic fracture networks

Abstract Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales, an approach known as coarse-graining. For many practical applications, such as flow in porous, homogenous materials, coarse-graining offers a sufficiently-accurate approximation of the solution. Unfortunately, fractured systems cannot be accurately coarse-grained, as critical network topology exists at the smallest scales, including topology that can push the network across a percolation threshold. Therefore, new techniques are necessary to accurately model important fracture systems. Quantum algorithms for solving linear systems offer a theoretically-exponential improvement over their classical counterparts, and in this work we introduce two quantum algorithms for fractured flow. The first algorithm, designed for future quantum computers which operate without error, has enormous potential, but we demonstrate that current hardware is too noisy for adequate performance. The second algorithm, designed to be noise resilient, already performs well for problems of small to medium size (order 10–1000 nodes), which we demonstrate experimentally and explain theoretically. We expect further improvements by leveraging quantum error mitigation and preconditioning.

58 GEOSCIENCES↗

DOE OSTI2021

Toxicity of hydraulic fracturing wastewater from black shale natural-gas wells influenced by well maturity and chemical additives

Hydraulic fracturing of deep shale formations generates large volumes of wastewater that must be managed through treatment, reuse, or disposal. Produced wastewater liberates formation-derived radionuclides and contains previously uncharacterized organohalides thought to be generated within the shale well, both posing unknown toxicity to human and ecological health. Here, we assess the toxicity of 42 input media and produced fluid samples collected from four wells in the Utica formation and Marcellus Shale using two distinct endpoint screening assays. Broad spectrum acute toxicity was assessed using a bioluminescence inhibition assay employing the halotolerant bacterium Aliivibrio fischeri, while predictive mammalian cytotoxicity was evaluated using a N-acetylcysteine (NAC) thiol reactivity assay. The acute toxicity and thiol reactivity of early-stage flowback was higher than later produced fluids, with levels diminishing through time as the natural gas wells matured. Acute toxicity of early stage flowback and drilling muds were on par with the positive control, 3,5-dichlorophenol (6.8 mg L -1 ). Differences in both acute toxicity and thiol reactivity between paired natural gas well samples were associated with specific chemical additives. Samples from wells containing a larger diversity and concentration of organic additives resulted in higher acute toxicity, while samples from a well applying a higher composition of ammonium persulfate, a strong oxidizer, showed greater thiol reactivity, predictive of higher mammalian toxicity. Both acute toxicity and thiol reactivity are consistently detected in produced waters, in some cases present up to nine months after hydraulic fracturing. These results support that specific chemical additives, the reactions generated by the additives, or the constituents liberated from the formation by the additives contribute to the toxicity of hydraulic fracturing produced waters and reinforces the need for careful consideration of early produced fluid management.

03 NATURAL GAS↗

DOE OSTI2021

Knowledge extraction and transfer in data-driven fracture mechanics

Significance Data-driven approaches have launched a new paradigm in scientific research that is bound to have an impact on all disciplines of science and engineering. However, at this juncture, the exploration of data-driven techniques in the century-old field of fracture mechanics is highly limited, and there are key challenges including accurate and intelligent knowledge extraction and transfer in a data-limited regime. Here, we propose a framework for data-driven knowledge extraction in fracture mechanics with rigorous accuracy assessment which employs active learning for optimizing data usage and for data-driven knowledge transfer that allows efficient treatment of three-dimensional fracture problems based on two-dimensional solutions.

Liu, Xing↗

DOE OSTI2025

Silicon wafer fracture stress for tracking sensors in particle physics experiments

For the construction of the ATLAS Inner Tracker strip detector, silicon strip sensor modules are glued directly onto carbon fibre support structures using a soft silicone gel. During tests at temperatures below -35°C, several of the sensors were found to crack due to a mismatch in coefficients of thermal expansion between polyimide circuit boards with copper metal layers (glued onto the sensor) and the silicon sensor itself. While module assembly procedures were developed to minimise variations between modules, cold tests showed a wide range of temperatures at which supposedly comparable modules failed. The observed variance (fracture temperatures between -35°C and -70°C) for supposedly comparable modules suggests an undetected variation between modules suspected to be intrinsic to the silicon wafer itself. Therefore, a test programme was developed to investigate the fracture stress of representative sensor wafer cutoffs. This paper presents results for the fracture stress of silicon sensors used in detector modules.

Detector design and construction technologies and ↗

DOE OSTI2020

Estimating perturbed stress from 3-D borehole displacements induced by fluid injection in fractured or faulted shales

SUMMARY Hydrofracturing stress measurements in fractured and anisotropic shales are notoriously difficult, because opening of existing geological features tends to prevent the creation of a pure hydraulic fracture perpendicular to the least compressive principal stress. Here we show how adding 3-D borehole-displacement measurements while conducting the hydraulic injection test helps to better constrain the principal stress orientations and magnitudes. We developed a 3-D fully coupled hydromechanical numerical model to analyse the displacement, fluid pressure and injection flow-rate data measured during an injection pressure-step-rate test conducted to activate a faulted borehole interval in the Mont Terri Opalinus Clay (Switzerland). We find that injected fluids can only penetrate the fault when it is at or above the Coulomb failure pressure. Borehole displacement orientations are sensitive to a ∼15° variation in the stress–tensor orientation and a 1 MPa stress magnitude variation. Although some dispersion occurs while rupture is propagating along the fault plane ∼4 m away from the borehole, the maximum density of displacement orientations consistently informs about the stress orientation. Thus, an extended injection step-rate approach coupled with an accurate in situ measurement of the borehole wall displacements can be used to better constrain the local stress field perturbations in fractured shales and in heterogeneous rock in general.

Guglielmi, Yves↗