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Results for “Probability Of Fracture”

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All sources NASA NTRS DOE OSTI

DOE OSTI2026

3D probabilistic fracture mechanics / computational fluid dynamics simulation of a reactor pressure vessel under transient conditions

Reactor pressure vessels (RPVs) are safety-critical light-water-reactor components that, under irradiation, experience long-term material degradation in the form of embrittlement. This can increase their susceptibility to fracture under thermal-shock conditions, which could occur during off-normal transients such as loss-of-coolant accidents (LOCAs). During a LOCA, the most severe conditions for the RPV occur when emergency core cooling water is injected through the cold legs into the water-and-steam-filled RPV. The rapid cooling of the downcomer and internal RPV surface causes decreased temperature and elevated thermally driven tensile stresses in the RPV wall. This, combined with long-term material embrittlement, may cause fracture initiation at pre-existing flaws, challenging the integrity of the RPV. Assessing RPV integrity during transients with a large spatial variation in the coolant temperature requires a modeling approach that considers the effects of spatially varying coolant temperature on the fracture probability of a population of flaws distributed throughout the RPV, accounting for spatially varying embrittlement. Here, the present study addresses this need by demonstrating first-of-its-kind coupling of a high-fidelity 3D computational fluid dynamics code with 3D probabilistic fracture mechanics This was accomplished using representative models of a pressurized-water reactor subjected to small- and medium-break LOCA conditions, both of which can result in large spatial temperature variations. While the observed impact of accounting for 3D effects was minimal under the small-break LOCA this study indicates a significant increase in the probability of fracture initiation under the medium-break LOCA when 3D effects are considered, relative to a spatially uniform cooling scenario.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Experimental Validation of a Module Cell Cracking Model

The What's Cracking app can predict how changes in crystalline silicon photovoltaic (PV) module materials, design, and mounting affect its susceptibility for cell fracture under uniform loading. This work has experimentally validated the app. A set of commercial crystalline silicon PV modules was obtained for this study. The modules were uniformly loaded at three different mounting points, and their subsequent cell fractures were recorded. A large sample size allowed for the development of an experimental statistical model for cell fracture. Here, the comparison of the experiment to predictions from the app is in excellent agreement. Both experimental and modeling results also elucidate how moving the module mounting points toward the center of the module increases the probability of cell fracture.

14 SOLAR ENERGY↗

DOE OSTI2025

Uniform Mechanical Loading Can Test for Nonuniform Loading Durability

In this work, we present a method to evaluate the equivalency between any module mechanical loading conditions. The method is developed to address the specific failure mode of glass fracture and is based on Weibull analysis and weakest link theory. It considers the varying stress profile across the module to calculate the probability of glass fracture, which is used as the metric of equivalency. An idealized nonuniform loading scheme is employed to demonstrate the method and introduce the concept of the equivalent uniform load factor: a factor applied to the maximum pressure of the nonuniform load to obtain the equivalent uniform load value. It is demonstrated that this factor is less than unity for all nonuniform load cases considered, including snow and various characters of wind loading. These significant results suggest that uniform loading may be reliably, and practically, employed to evaluate photovoltaic module glass for nonuniform loading durability.

14 SOLAR ENERGY↗

DOE OSTI2025

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↗

DOE OSTI2025

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↗

DOE OSTI2025

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↗

DOE OSTI2024

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↗

DOE OSTI2026

Uncertainty quantification for competing failure mechanisms in unidirectionally reinforced carbon–carbon composites

Microstructure-informed finite element models play a key role in the carbon–carbon composite design process. Variability in manufacturing process parameters and experimental limitations introduce model parameter uncertainty. This study quantifies the effect of model parameter uncertainty on transverse tensile fracture behavior and proposes a methodology to predict the failure mode based on competing microscale damage mechanisms. Finite element simulations incorporate fiber–matrix interface debonding with cohesive zones and matrix damage with a smeared crack band approach in a unidirectional carbon–carbon composite. Results from a variance-based global sensitivity analysis identifies interfacial and matrix damage parameters as the primary source of variability in fracture behavior. Sobol’ indices indicate that matrix and cohesive zone strengths contribute 94% of the variance in the effective ultimate stress. A local analysis elucidates the relationship between these constituent strength parameters and failure mode by estimating the probability of cohesive, matrix, and mixed-mode dominated failure. Based on the results for 4000 simulations, 93% exhibit mixed-mode or interfacial dominated failure, which underscores the crucial role of fiber–matrix interface debonding in the transverse tensile failure of carbon–carbon composites. These uncertainty quantification results facilitate more efficient model calibration and provide a framework for microstructure-informed failure predictions in the face of manufacturing-induced uncertainty.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Osmotic control of the spacing of parallel shear cracks in shale growing subcritically in geologic past

The geological genesis of natural cracks in sedimentary rocks such as shale is a problem that needs to be understood to improve the technology of hydraulic fracturing as well as deep sequestration of harmful fluids. Why are the vertical natural cracks roughly parallel and equidistant, and why is the spacing roughly 10 cm rather than 1 cm or 100 cm? Fracture mechanics of critical cracks cannot answer this question. Neither can the material heterogeneity. The growth of critical parallel cracks is impossible because the relative crack face displacements would immediately localize into one crack, leading to an earthquake. The cracks must have formed, on the tectonic time scale, by a slow growth of subcritical shear cracks governed by the Charles-Evans law. The idea advanced here is that what controls the crack spacing is the balance between the reduction, due to shear dilatancy, of the concentration of ions such as Na + and Cl - in each fracture process zone (PFZ), which decelerates the cracks, and the restoration of ion concentration by diffusion of ions from the space between the cracks into the FPZ. This diffusion of water is driven mainly by the osmotic pressure gradient, which offsets the deceleration and depends strongly on the crack spacing. A simple analytical solution of the steady state is rendered possible by approximating the ion concentration profiles between adjacent cracks by parabolic arcs. Applying this theory to Woodford shale yields the approximate crack spacing of 10 cm, which is realistic. Furthermore, the stability of unlimited parallel mode II frictional crack growth is proven by examining the second variation of the free energy. Water concentration drop in the FPZ due to shear dilatancy and its restoration by water diffusion from the inter-crack space have similar effect, although probably much weaker.

42 ENGINEERING↗

DOE OSTI2024

Tough Break: Many Factors Make Glass Breakage More Likely

We have seen cases of glass in PV modules breaking differently, and more often, than it did five years ago. There have been many changes to PV module design and materials in that time. But there is probably no single change that is responsible for the problem. Here we summarize the current thinking on PV glass breakage in utility-scale power plants. We share insights from multiple still-running projects at NREL.

14 SOLAR ENERGY↗

DOE OSTI2025

Modeling and Simulation of Fuel Dispersal During the Loss-of-Coolant Accident

This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Transportability of exogenous microbial community correlates with interwell connectivity in deep aquifers

Subsurface resource engineering operations often utilize continuous injection of externally-sourced water into geological reservoirs for formation pressure maintenance, resource recovery or energy/waste storage. Such injected water generally contains naturally occurring microbes. Little is known, however, about how the injectate microbes transport through geological media as a community, how such transportability is affected by injector-producer connectivity, and whether such knowledge can be utilized for flowpath characterization. In this study, we analyzed daily-to-weekly timeseries microbial community data from the injected- and produced-fluids of a ten-month flow test at a deep, well-characterized engineered aquifer. We found that the injectate microbial community was distinct from the indigenous community at the amplicon sequence variant (ASV) level, and that the transportability of injectate community towards a given producer, quantified by an “nASV-Overlap” metric we propose, had strong and significant positive correlation with known injector-producer connectivities at our site. This suggests that the better the connectivity, the higher the probability for more injectate species to flow through the interwell region and arrive at a producer. Because interwell connectivity is an important yet usually unknown parameter in subsurface resource engineering, such correlation in turn points to nASV-Overlap as a useful indicator of interwell connectivity for aquifer characterization and long-term monitoring. Based on our findings, an nASV-Overlap-based microbial tracing approach was developed for characterizing and monitoring the relative connectivities across multiple producers with a given injector. A side-by-side comparison between the new nASV-Overlap approach and traditional artificial tracer methods is presented, and their respective strengths and limitations are discussed.

Deep biosphere↗