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Use of Neutron Flux Calculated by Shift in a Grizzly Reactor Pressure Vessel Fracture Simulation

The reactor pressure vessel (RPV) plays the critical role of containing the reactor and coolant in a light water reactor nuclear power plant, and must be able to safely perform this function under a variety of normal and off-normal transient loading conditions. The RPV is subjected to harsh environmental conditions (elevated temperature and high neutron flux) whenever the plant is operating, which leads to embrittlement of the steel over time. RPVs contain populations of flaws introduced during the manufacturing process, and the primary safety concern is that during a transient event, a fracture could initiate at the site of one of these flaws and lead to rupture of the RPV. RPVs are very rugged structures, and the probability of this occurring is very low, but as the RPV's steel becomes embrittled over time, its resistance to fracture decreases and this becomes more likely. Assessing the likelihood of RPV fracture during a transient event involves performing a probabilistic fracture mechanics analysis, in which random sampling procedures are used to assess the probability of fracture of a population of flaws. Grizzly offers unique capabilities for modeling the RPV using 1D, 2D, or 3D representations, taking advantage of parallel computing for this type of analysis. One of the important inputs to Grizzly is the spatial distribution of the neutron fluence, which has a large impact on the material embrittlement, and should thus be characterized as accurately as possible. The VERA core simulator developed by the CASL program takes advantage of high performance computing resources to perform high-fidelity multiphysics simulations of reactor physics, including the effects of neutron transport, fuel performance, and thermal hydraulics. Recently a capability was developed to also evaluate neutron fluxes away from the reactor core through the Shift code. This allows for a detailed 3D map of the spatial variation of the fluence in components such as the RPV to be computed, which is ideal for use with Grizzly. This report documents a procedure developed to use the fluences computed in Shift in a Grizzly simulation, which allows for improved realisim in the prediction of the effects of environmental exposure on propensity for reactor pressure vessel fracture. This capability demonstrated on RPVs with multiple types of configurations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

SURFACE FINISHING AND ELECTROLESS NICKEL PLATING OF ADDITIVELY MANUFACTURED (AM) METAL COMPONENTS

This study investigates the application of electroless nickel deposition on additively manufactured stainless steel samples. Current additive manufacturing (AM) technologies produce metal components with a rough surface. Rough surfaces generally exhibit fatigue characteristics, increasing the probability of initiating a crack or fracture to the printed part. For this reason, the direct use of as-produced parts in a finished product cannot be actualized, which presents a challenge. Post-processing of the AM parts is therefore required to smoothen the surface. This study analyzes chempolish (CP) and electropolish (EP) surface finishing techniques for post-processing AM stainless steel components CP has a great advantage in creating uniform, smooth surfaces regardless of size or part geometry EP creates an extremely smooth surface, which reduces the surface roughness to the sub-micrometer level. In this study, we also investigate nickel deposition on EP, CP, and as-built AM components using electroless nickel solutions. Electroless nickel plating is a method of alloy treatment designed to increase manufactured component's hardness and surface resistance to the unrelenting environment. The electroless nickel plating process is more straightforward than its counterpart electroplating.. We use low-phosphorus (2-5% P), medium-phosphorus (6-9% P), and high-phosphorus (10-13% P). These Ni deposition experiments were optimized using the L9 Taguchi design of experiments (TDOE), which compromises the prosperous content in the solution, surface finish, plane of the geometry, and bath temperature. The pre-and post-processed surface of the AM parts was characterized by KEYENCE Digital MicroscopeVHX-7000 and Phenom XL Desktop SEM. The experimental results show that electroless nickel deposition produces uniform Ni coating on the additively manufactured components up to 20 μm per hour. Mechanical properties of as-built and Ni coated AM samples were analyzed by applying a standard 10 N scratch test. Nickel coated AM samples were up to two times scratch resistant compared to the as-built samples. This study suggests electroless nickel plating is a robust viable option for surface hardening and finishing AM components for various applications and operating conditions.

Keywords: additive manufacturing, fatigue, chempol↗

Prediction and Analysis of Utah FORGE Injection Activities using a Coupled Thermo-hydro-mechanical and Earthquake (THM+E) Modeling Workflow

A coupled thermo-hydro-mechanical (THM) numerical workflow that is capable of modeling seismic slip is critical for the successful development of enhanced geothermal systems (EGS). By integrating key physical processes, this workflow enables accurate simulation of temperature and pressure diffusions, stress changes, and induced seismicity. As a result, it serves as a vital tool for predicting induced seismicity and optimizing reservoir stimulation strategies. The Utah FORGE (Frontier Observatory for Research in Geothermal Energy) project, located near Milford, Utah, is a U.S. Department of Energy initiative aimed at advancing EGS technology. In April 2024, eight new stimulation stages (Stages 3R-10) were conducted in well 16A (injection well) subsequent to the first series of stimulation (Stages 1-3) performed in April, 2022. To monitor the induced seismicity, geophones were deployed in wells 58-32, 56-32, and 78B-32, while fiber optic cables were also installed in wells 16B, 78-32, and 78B-32 to collect microseismic data and detect frac hits Preliminary analyses of microseismic catalogs and fiber optic data suggest that the stimulated fractures in Stages 3R–6 closely align with that generated during Stage 3, indicating that the new stimulations were likely reactivating the previously stimulated fracture. To better understand the underlying process, a comprehensive modeling approach that can accurately capture thermal, hydrological, mechanical, and seismic responses is essential. In this work, we propose and utilize a coupled thermo-hydro-mechanical and earthquake (THM+E) simulation workflow to numerically investigate the stimulation activities on well 16A. The specific objective is to confirm whether the new stimulation stages (Stages 3R–6) reactivated fractures previously stimulated during Stage 3. For this purpose, we perform THM+E simulations individually for Stages 3, 3R, 4, and 5, incorporating the discrete fracture networks (DFNs) created by the plane-fitting technique based on the microseismic catalogs. The simulation workflow consists of two separate models: a THM model and an earthquake model, coupled in a one-way manner. Detailed descriptions of the workflow are provided in Section 3. Simulation results are presented in terms of injection pressure, permeability evolution, and predicted seismic catalogs, which are then compared with field data for further analyses. This report is structured as follows. In Section 2, we present detailed analyses of the field data and propose the hypothesis that the new stimulation stages (Stages 3R–6) were probably reactivating the previously stimulated fractures in Stage 3. In Section 3, we introduce the coupled THM+E workflow and the problem setup to validate our hypothesis, followed by the simulation results for each stage in Section 4. Meanwhile, discussions are included to analyze the model predictions and their comparison with field data. Lastly, we conclude the report and outline future plans in Section 5.

15 GEOTHERMAL ENERGY↗

Hawaii Play Fairway Analysis: Lanai Resistivity and Density 3D Inversion Models

To prepare for its third phase, the Hawaii Play Fairway project conducted groundwater sampling and analyses in ten locations in the Hawaiian islands, magnetotelluric (MT) and gravity surveys, as well as calculations of 3D subsurface stress due to the weight of the rock underlying the topography of the volcano. The subsurface stresses were used to evaluate the potential for fracture-induced permeability. Inversions of the MT and gravity data produce 3D models of resistivity and density, respectively, on Lanai, across Haleakala's SW rift (Maui), and surrounding Mauna Kea (Hawaii Island). The project developed and applied a new method for incorporating depth information about resistivity, density, and potential for fracture-induced permeability into the statistical method for computing resource probability in these three focus areas. The project then incorporated the new groundwater results with the new geophysical results and the calculations of potential for fracture-induced permeability to produce updated maps of resource probability and confidence. These results were used to identify target sites for exploratory drilling. Spreadsheet information: Each sheet contains data for a particular depth in kilometers. Positive depths are above sea level, and negative below. For more information, go to the Hawaii Groundwater and Geothermal Resources Center website linked in the resources.

15 GEOTHERMAL ENERGY↗

Hawai‘i Play Fairway (Final Report)

Most of Hawai'i's geothermal resources are blind—their manifestations, such as hot springs and steam vents, do not appear on the ground surface because the heated water flows far below. With the exception of $K\bar{i}lauea East Rift Zone$, in most areas of Hawai'i, high lateral permeability in the first kilometer below ground surface prevents surface thermal features from developing. As a methodology for discovering these blind resources, Play Fairway Analysis (PFA) involves finding potential locations of blind hydrothermal systems and describing potential geothermal sources in rift-zone settings. Using the PFA to find Hawai'i's geothermal resources, the University of Hawai'i (UH) conducted the Hawai‘i Play Fairway Project, Hawai'i's first statewide geothermal resource assessment since 1985. Sponsored by the U.S. Department of Energy, the Hawai'i Play Fairway Project provided an updated resource assessment, a roadmap for additional exploration activities, and the identification of areas for further exploration. Benefitting from UH's core competency in earth sciences and experienced geothermal researchers, the project comprised three phases. During the first phase, the team identified, compiled, and ranked existing geologic, groundwater, and geophysical datasets relevant to subsurface heat, fluid and permeability. Using a Bayesian statistical approach, the team developed a statistical methodology to integrate these data into a resource probability map. The team evaluated the confidence in the probability value and considered development viability of areas with geothermal resources. With these analyses, the team identified 10 locations in the Hawaiian Islands for exploration activities. For the second phase, the team collected new groundwater data in 10 locations across the state and new geophysical data on $L\bar{a}na‘i, Maui$, and central Hawai'i Island and modeled topographically induced stress to better characterize subsurface permeability. Analyzing the subsurface stresses, the team evaluated the potential for fracture-induced permeability. The team inverted the MT and gravity data to produce 3D models of resistivity and density, respectively, on $L\bar{a}na‘i$, across $Haleakal\bar{a}'s$ SW rift (Maui), and surrounding Mauna Kea (Hawai‘i Island). The team developed and applied a new method for incorporating depth information about resistivity, density, and potential for fracture-induced permeability into the statistical method for computing resource probability in these three focus areas. The team incorporated the new groundwater results with the new geophysical results and the calculations of potential for fracture-induced permeability to produce updated maps of resource probability and confidence. Through combining data from the first and second phases, the team determined locations for further exploration during the third phase. For MT and gravity surveys, the team recommended $Kaua'i's$ $L\bar{i}hu'e$ $Basin$, the east rift of $Maui's$ $Haleakal\bar{a}$ volcano, and the southwest rift of Hawai'i Island's Mauna Loa volcano. The MT and gravity surveys aimed to enable improved confidence in the resource potential in these locations. For drilling deep groundwater well(s), the team recommended Southeast Mauna Kea and $L\bar{a}na's$ $P\bar{a}l\bar{a}wai$ $Basin$. During the third phase, further exploration involved drilling a groundwater well in $L\bar{a}na's$ $P\bar{a}l\bar{a}wai$ $Basin$ and performing more geophysical surveys. We deepened an existing water well proximal to our target area on $L\bar{a}na'i$ due to funding constraints that precluded us from spudding a new well that would exceed 1km depth. Drilling was preceded by a number of substantial elements including: writing an Environmental Assessment and the subsequent legal process, performance of deviation logging, lowering a camera down the well, coordinating site preparation with $P\bar{u}lama$ $L\bar{a}na'i$, shipping the UH-owned rig interisland, procuring supplies, and leading 3 community meetings on $L\bar{a}na'i$. Drilling occurred 24/7 the entire month of June 2019 over which time $L\bar{a}na'i$ $Well$ 10 was deepened from 427 m to 1057 m, with continuous core collected. We measured a roughly linear temperature gradient averaging 42°C/km and a maximum bottom hole temperature of 66°C. This gradient is more than twice the background for Hawai'i and within a range of gradients measured in this depth range for some exploration wells within KERZ. We consider these results encouraging for $L\bar{a}na'i's$ resource potential and recommend following with a slim hole within $L\bar{a}na'i's$ caldera (our target zone) to ~ 2 km. Further, the positive implications such results have for the island of O‘ahu are substantial - the shield stage of O'ahu's volcanoes ended 1-2 My earlier. However, O'ahu uses more electricity than the rest of the islands combined, and the utility recently called for 500-700MW of firm, dispatchable renewable electricity on O'ahu by 2033. In Phase 3, we also collected limited new encouraging groundwater data, and updated our thoughts on the probabilities of fluid and permeability at resource depths (Pr F = 1; Pr P = mostly unconstrained). Ultimately, we advocate for using our final probability of heat, and confidence in this probability, to drive the next phase of exploration. We contend further development of geothermal in Hawai‘i will enable the state to achieve its 100% renewable policy objective and Hawai'i to transition off of fossil fuels through geothermal discovery and development. The project not only produced a large amount of data and expanded the existing knowledge of Hawai'i's geothermal resources, but also produced publications, theses, presentations, core photos, datasets, media reports, television interviews, community events, and a blog. Students and new professionals benefitted from the project's hands-on research experiences and educational opportunities and earned awards and recognition.

15 GEOTHERMAL ENERGY↗

A probabilistic-phase field model for the fracture of brittle materials

Abstract We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abeet al2003J. Am. Ceram. Soc.861019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

Materials Science↗

Hydrogen Extremely Low Probability of Rupture Version 1

SAND2024-08511O The Hydrogen Extremely Low Probability of Rupture (HELPR) software toolkit provides probabilistic fracture assessments of natural gas infrastructure for transporting hydrogen. Using probabilistic sampling and sensitivity analysis—along with engineering fatigue and fracture mechanics— the software develops models that can predict structural integrity measures for natural gas pipelines under stress. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Schroeder, Benjamin↗

HELPR Version 1.1.0 User Guide

Hydrogen Extremely Low Probability of Rupture (HELPR) is a modular probabilistic fracture mechanics modeling platform developed to assess structural integrity of pipelines for transmission and distribution of hydrogen. HELPR couples fatigue and fracture engineering models with probabilistic methods to generate fast predictions and enables quantification of prediction uncertainty and sensitivity. This user manual serves as a guide through the various analysis features HELPR contains.

08 HYDROGEN↗

Anomaly Detection in Materials Digital Twins with Multiscale ICME for Additive Manufacturing

Detecting anomaly in fatigue and fracture experimental materials science is an interesting yet challenging topic. The reasons are threefold. First, the anomalous microstructure feature that gives rise to structural failure is small, sometimes in the order of 10 -7 of the interrogated volume. This, in turn, results in a highly imbalanced classification problem in machine learning (ML). Second, the consequence is high, in the sense that the test specimen is destructed in such case. Third, the convolution between microstructure stochasticity and the small probability of void nucleation, growth, and coalescence makes failure and fracture a hard-to-predict and challenging problem in materials science due to its irreproducibility, even experimentally. In this paper, we developed a materials digital twin and applied anomaly detection methods to detect voids and anomaly in additive manufacturing (AM). The materials digital twin is driven by two integrated computational materials engineering (ICME) models, which are kinetic Monte Carlo (kMC) and crystal plasticity finite element method (CPFEM). In conclusion, we demonstrated that by using anomaly detection, it is possible to detect voids and other defects in materials digital twin, which paves way for future research in integrating materials digital twin with its physical counterpart.

ICME↗

Visualisation and outlier detection for probability density function ensembles

Abstract Exploratory data analysis (EDA) for functional data—data objects where observations are entire functions—is a difficult problem that has seen significant attention in recent literature. This surge in interest is motivated by the ubiquitous nature of functional data, which are prevalent in applications across fields such as meteorology, biology, medicine and engineering. Empirical probability density functions (PDFs) can be viewed as constrained functional data objects that must integrate to one and be nonnegative. They show up in contexts such as yearly income distributions, zooplankton size structure in oceanography and in connectivity patterns in the brain, among others. While PDF data are certainly common in modern research, little attention has been given to EDA specifically for PDFs. In this paper, we extend several methods for EDA on functional data for PDFs and compare them on simulated data that exhibit different types of variation, designed to mimic that seen in real‐world applications. We then use our new methods to perform EDA on the breakthrough curves observed in gas transport simulations for underground fracture networks.

97 MATHEMATICS AND COMPUTING↗

Role of Intersections in Fracture Connectivity

Networks of intersecting fractures often provide the flow paths through subsurface reservoirs. Assessing network connectivity is challenging because fracture intersections compose a vanishingly small fraction of the network void volume. In this paper, motivated by 3D X-ray imaging of the simplest element of fracture network, that is, two orthogonal fractures, we perform a percolation and finite-size scaling analysis to study the connectivity provided by fracture intersections. The conditions when an intersection enhances connectivity across a sample depend on spatial correlations in the fracture aperture distributions, on the stress state, and on the direction of flow. Here we consider three flow directions: (a) across intersections, (b) parallel to intersections and (c) around corners. For (a), intersections provide minimal enhancement of connectivity because they contribute little additional void area. For (b), intersections increase the probability of a connected path near threshold by enabling 3D connected pathways that are not possible in parallel fractures. Flow around corners, (c), is fundamentally the result of the intersection connecting two fractures in series and spatial correlations are broken around corners, suppressing the connectivity relative to (a). When the connected fractures are stressed equally, a joint percolation threshold emerges that continues to have scale invariance. However, when the fractures are stressed unequally, the system has mixed percolation without clearly defined percolation thresholds. In all cases, percolation probabilities are found to be scale dependent which has important consequences for the connectivity of larger fracture networks composed of the fundamental element studied here.

02 PETROLEUM↗

Develop and Connect TRISO Failure Analysis and Uncertainty Quantification to Fission Product Release Calculation Capability

The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. Stress-based failure probability has been developed and analyzed to assess the integrity of tri-structural isotropic (TRISO) fuel particles during fuel life cycles. While simple, stress-based approaches to failure probability leveraging the Weibull statistical distribution entails a number of drawbacks when stress concentration occurs near crack tips, including finite element mesh size dependency. In this report, we use an interaction integral approach to the computation of stress intensity factors in functionally graded materials (FGM) for axisymmetric models. The inner pyrolytic carbon (IPyC) cracking induced silicon carbide (SiC) failure is one of the dominated failure modes in TRISO failure analysis. In this study, we consider a crack in the IPyC layer perpendicular to the SiC layer. The interface between these two TRISO layers is considered to be porous, which we simulate considering a transition of mechanical properties over the porous length. These aspects are considered in the computation of stress intensity factor (SIF) from a fracture mechanics approach and compared with the known stress-based failure probability approach.

42 ENGINEERING↗

Unconventional Wells Interference: Supervised Machine Learning for Detecting Fracture Hits

The primary objective of the study was development of a machine learning (ML)-based workflow for fracture hit (“frac hit”) detection and monitoring using shale oil-field data such as drilling surveys, production history (oil and produced water), pressure, and fracking start time and duration records. The ML method takes advantage of long short-term memory (LSTM) and multilayer perceptron (MLP) neural networks to identify the frac hits due to hydraulic communication between the fracking child well(s) and the producing parent well(s) within the same pad (intra-pad interaction) and/or on different pads (inter-pad interaction). It utilizes time series of pressure and production data from within a pad and from adjacent pads. The workflow can capture time variable features of frac hits when the model architecture is deep and wide enough, with enough trainable parameters for deep learning and feature extraction, as demonstrated in this paper by using training and testing subsets of the field data from selected neighboring pads with over a couple of hundred wells. The study was focused on frac-hit interaction among paired wells and demonstrated that the ML model, once trained, can predict the frac-hit probability.

58 GEOSCIENCES↗

Elastic-plastic conductor damage evaluation at over 0.4% strain using a high-stress REBCO coil

Abstract Recent reports on screening current stress simulations of high-field REBCO magnets frequently present peak stresses over 1 GPa. However, this result is probably an unrealistic artifact of purely elastic calculations, considering the macroscopic yield and fracture stresses of approximately 900 MPa and less than 1.1 GPa for Hastelloy substrate-coated conductors. Here, we evaluate elastic-plastic conductor damage at over 0.4% strain using a high-stress REBCO coil exposed to a high field to explore this elastic-plastic regime. The coil was located off-center in a low-temperature superconductor magnet so as to induce a significant screening current in the enhanced radial field. Voltage taps, a Hall sensor, and two strain gauges were used for the instrumentation. We obtained strains exceeding 0.4% near the outward edge during the coil current charge from 350 A to 390 A, where the coil was exposed to external axial and radial magnetic fields of 13 T and 0.5 T. Post mortem results showed wavy plastic deformation, electrical damage, and REBCO defects. An elastic-plastic simulation reproduced the measured strains and predicted that ∼1 GPa stress is sufficient to induce ∼0.9% strain, thus validating our initial concerns with purely elastic models. This paper provides our experimental and simulation results.

Bang, Jeseok (ORCID:0000000247616334)↗

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↗

Quantifying Holocene Cliff Retreat Rates at Technical Area 54, a Low- and Mixed-Level Radioactive Waste Disposal Site, Los Alamos National Laboratory, Los Alamos, New Mexico [Slides]

Cliff failure is occurring and threatens to expose pits and shafts. Steep slope angles = FoS < 1 = high probability of failure and retreat. EQ magnitude > 5.5 could initiate failure where FoS > 1. Fracture characterization (location, orientation, etc.) is essential for predictive analysis of at-risk cliff failure locations. Additional surface exposure dating would be helpful and further constrain the effect of fracture characteristics. Continued monitoring is essential for change detection and identification of areas with higher cliff retreat rates.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

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↗

Statistical perspective on embrittling potency for intergranular fracture

Embrittling potency is a thermodynamic metric that assesses the influence of solute segregation to a grain boundary (GB) on intergranular fracture. Historically, authors of studies have reported embrittling potency as a single scalar value, assuming a single segregation site of importance at a GB and a particular cleavage plane. However, the topography of intergranular fracture surfaces is not generally known a priori. Accordingly, we, in this study, present a statistical ensemble approach to compute embrittling potency, where many free surface (FS) permutations are systematically considered to model fracture of a GB. The result is a statistical description of the thermodynamics of GB embrittlement. As a specific example, embrittling potency distributions are presented for Cr segregation to sites at two Ni $\langle 111 \rangle$ symmetric tilt GBs using atomistic simulations. We show that the average embrittling potency for a particular GB site, considering an ensemble of FS permutations, is not equal to the embrittling potency computed using the lowest energy pair of FSs. A mean GB embrittlement is proposed, considering both the likelihood of formation of a particular FS and the probability of solute occupancy at each GB site, to compare the relative embrittling behavior of two distinct GBs.

36 MATERIALS SCIENCE↗