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DOE OSTI2021

LLNL Response to the DOE ASCR RFI, "Stewardship of Software for Scientific and High-Performance Computing"

For decades, Lawrence Livermore National Laboratory (LLNL) has been engaged in significant research, development, and support for software to enable scientific computing and, particularly, the use of high performance computing (HPC) in the NNSA mission space. In particular, the move in the mid-1990’s to simulation as a leading component of stockpile stewardship through the ASCI and the successor ASC programs, as well as the need for reliable data acquisition and control software for the National Ignition Facility, have been important drivers in building expertise in production-quality software development at LLNL. LLNL has also been a leader in the DOE SciDAC FASTMath Institute and the DOE Exascale Computing Project (ECP), both of which have striven to make scientific computing software – in particular, the enabling technologies underpinning simulation capabilities – more widely adopted and sustainable. As such, we believe that our experience can inform the broader goal of software stewardship for scientific and high-performance computing. LLNL strongly supports the formation of a new DOE ASCR program element in software stewardship and sustainment. Historically, DOE ASCR has funded applied mathematics and computer science research that has led to the development of important new capabilities and algorithms that are expressed as artifacts in research software. Such frameworks, libraries, and tools have seldom been directly funded to address the important issues of code maintenance, documentation, robustness, and community building. Software engineering and support have typically been done on the side in support of the ASCR-driven research products. DOE funding priorities have been slow to recognize that good software engineering, the kind that ensures research investments have more adoption and longevity, requires significant resources. Based upon our experiences, we have prepared this response to highlight the concerns and issues we believe to be important as DOE ASCR considers its role in scientific software stewardship. We believe that role is important and will require a significant investment of new funding to legitimately support the technologies past and future DOE ASCR investments have and will produce to facilitate their uptake and adoption in the broader scientific computing community. Following a summary of our involvement in scientific software development, the remainder our response is organized around the nine topics specifically identified in the RFI.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Open source implementation of glued sphere discrete element method and nonspherical biomass fast pyrolysis simulation

Here, in this research, a glued-sphere Discrete Element Method (DEM) method was implemented in the open-source, Computational Fluid Dynamics (CFD) software MFiX. The implementation was verified using a cylinder-wall collision and then validated by simulating the packing and fluidization of non-spherical particles. The validated code was applied to simulate fast pyrolysis of non-spherical biomass particles in a bubbling fluidized bed. The glued sphere occupancy ratio was proposed to quantify the quality of shape resolution using glued sphere. Shape resolution showed significant influence on the packing height in the simulation of particle packing and an occupancy ratio of 80 % was recommended. Its influence is minor in fully fluidized bed but can be 8 times higher in fixed fluidized bed. Three tested heat transfer models predicted similar yields of elongated biomass fast pyrolysis. The solver developed in this research can be used to simulate other multiphase reacting flows involving non-spherical particles.

42 ENGINEERING↗

DOE OSTI2023

Computational studies of impurity migration during induction stirring of molten uranium

Understanding and controlling impurity behavior in actinide metal casting processes are foundational for efficient part production yet remain major challenges for researchers and industry. To help provide insight regarding impurity distribution during actinide metal casting, we have developed computational fluid dynamics (CFD) models for a laboratory-scale system using commercial and open-source code. Multiple simulation frameworks allow for improved confidence in the resulting outputs, while taking advantage of the maturity and convenience offered by commercial platforms and simultaneously maintaining the transparency and flexibility often provided by open-source software. Here, we describe multiple experiment-informed models designed to simulate a specific laboratory system in which uranium melt, containing a known starting concentration of carbon impurity, is electromagnetically stirred in an induction furnace. Here, the goal of the simulations is to predict the motion of uranium carbide microparticles in the velocity field of the melt. Prior to simulating the uranium-carbon system, numerical models were validated using a previously published nonradioactive experimental system. Effects of the size and shape of impurity particles in the models were investigated and agree with experimental findings. Simulation of smaller particles (< 50 µm) shows more homogenous distribution throughout the stirred melt. With increased particle size (100 µm), the body forces, which include the buoyancy force, dominate over the drag force, causing larger particles to move toward the crucible walls and upward in the system.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Physical vapor deposition simulator by graphical processor unit ray casting

This paper presents fast, accurate software for modeling physical vapor deposition systems over irregular surfaces. The model is implemented using graphics processing unit (GPU) ray casting. Applied models are viewed as a cross section of the area of interest. Given evaporation rate, time, and angular profiles in a vacuum system, an iterative time-step approach for calculating deposition profiles is calculated in the GPU architecture following a ballistic modeling approach. Thin-film technologies for the electronics industry will require evaporations on complex surfaces. Depending on the nature of the surface, a uniform thin film across the topology is wanted for various device parameters. The ray casting method is tested against various profiles. The code is freely distributed on GitHub (see https://github.com/adam-r-thomas/PVDS).

Engineering↗

DOE OSTI2021

Modeling FLEX Human Actions Using the EMRALD Dynamic Risk Assessment Tool

Most current efforts have modified and applied existing human reliability analysis (HRA) methods to treat human actions related to beyond-design-basis external events in which diverse and flexible coping strategies (FLEX) equipment would be deployed. However, many questions remain regarding the suitability of legacy HRA methods to address FLEX human actions, sparking the need for a new method of reasonably evaluating them. In this context, Idaho National Laboratory (INL) researched a relatively new approach to treating FLEX human actions via Event Modeling Risk Assessment Using Linked Diagrams (EMRALD) software. EMRALD was developed to support the increasing need for dynamic probabilistic risk assessment (PRA) models that can respond to evolving plant conditions during simulations. A couple benefits were identified when analyzing FLEX human actions through this software. In general, it is especially useful for evaluating a strategy’s feasibility, including FLEX human actions that require a relatively long time to perform. In this paper, we suggest how FLEX human actions can be modeled using the EMRALD software. Two different HRA modeling approaches using EMRALD are introduced: (1) procedure-based modeling and (2) PRA/HRA-based modeling. The former approach was introduced in the authors’ previous paper, whereas this paper mainly discusses how the latter approach works for an extended loss of AC power (ELAP) scenario with relevant procedures and PRA models. A hybrid method combining the two modeling approaches is introduced at the paper’s conclusion.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2022

Bay Area Regional Energy: Network Integrated Commercial Retrofits (BRICR) Project. Final Report

The BRICR project applied large-scale building energy modeling concepts with the aim of reducing the cost of energy efficiency targeting, design, and project development, and measurement of energy savings for energy efficiency programs implemented by local governments that serve small and medium commercial buildings (SMB). The project leveraged the services and resources of existing local government energy programs serving disadvantaged and hard-to-reach SMB customers. In contrast to programs run by utilities, local government programs generally do not have direct access to energy billing records for an entire class of customers in a geographic area, which prior research demonstrated useful for large-scale building energy model baseline development and calibration. , However, local governments are rich in public records that offer important clues about physical attributes and uses that, along with behavior, determine energy use. Relying only on public records, BRICR demonstrated development of credible baseline energy models for 3,792 office, retail, and hotel buildings. Publicly disclosed annual energy use data from a local energy benchmarking program and anonymized data from the Building Performance Database, the nation’s largest dataset about energy-related characteristics of buildings, were utilized to validate and calibrate energy models via an innovative method comparing distributions of energy intensity by fuel type for portfolios of buildings of similar size, vintage, and use. Portfolio calibration does not provide certainty that an energy model fits an individual building; the method is useful when billing data is not accessible – a common situation for researchers, energy service providers and ESCOs, local governments, and any party other than a utility. A software component was developed, the BRICR gem, which automates simulation when relevant data is added or edited by the user to a file saved in the standardized BuildingSync XML schema for energy audit data. The component was demonstrated as a simplified means to generate a mass of energy models corresponding to public records containing basic attributes such as building scale, location, use, year built, and aspect ratio in combination with building energy code prototype data corresponding to use and vintage. The component was also demonstrated as a simplified means to automate energy simulation when attributes are revised; the intention was to enable iterative improvement of the baseline model and energy savings estimates for common energy conservation measures as users revise relevant attributes based on their observations. In the context of institutional change and uncertainty for the participating local government energy programs, 13 whole building retrofits were completed. Impacts were measured by applying the CalTRACK2.0 methods to standardize measurement of normalized metered energy consumption. The GRIDMeter methods of stratified sampling and individual load shape analysis were applied to adjust for impacts of the effect of COVID-19 on retrofitted buildings in the context of all local buildings of similar size and use. Excluding impacts of the pandemic, retrofitted buildings demonstrated between 1.6% and 25.1% reduction in energy use. The project contributed use cases and feedback that helped inform evolution of the software tools and data formats that were combined for the first time in the BRICR project.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

New developments and verification of fusion blanket simulation capabilities in the MOOSE framework

Multiphysics modeling capabilities have a crucial role to play in the accelerated deployment of fusion energy. To that end, we developed new multiphysics fusion blanket simulation capabilities in the Multiphysics Object-Oriented Simulation Environment (MOOSE). Firstly, we expanded on the existing capabilities of the previously published work, by coupling 3D tritium transport modeling capabilities using the Tritium Migration Analysis Program, version 8 (TMAP8) to an existing tool including thermal hydraulics, fully three-dimensional (3D) heat transfer, and loosely coupled neutronics analysis. Secondly, we performed a thorough verification of the new capabilities and increased testing code coverage to meet MOOSE’s software quality standards. The MOOSE framework follows a strict software quality assurance plan to be Nuclear Quality Assurance, Level 1 compliant. The new multiphysics fusion blanket simulation capabilities are now held to the same standard. Thirdly, to demonstrate MOOSE’s new fusion blanket modeling capabilities, we performed a fully integrated, multiphysics simulation of a 3D solid ceramic breeder blanket design. This proof-of-concept simulation provides the temperature and tritium distribution across the blanket. In conclusion, the combined efforts towards software quality and the development of multiphysics coupling capabilities provide an effective and reliable framework for modeling solid ceramic fusion blankets using MOOSE.

modeling and simulation↗

DOE OSTI2024

Monte Carlo Simulation with CAD Interface for Calculation of 3D Maps of Residual Dose (CRADA)

Objective: To develop an easy-to-use software application to predict and mitigate radiation effects in research environment, space instruments, nuclear plants and medical facilities and help nonproliferation and national security efforts. Tech-X will develop standalone software libraries and command-line tools for ( 1) translating CAD into tessellated surfaces and tetrahedral meshes in GDML (for Geant4 and MARS 15), ROOT (for MARS 15) and HDF5 (for compact representation and for the visualization) formats, (2) healing CAD geometries to make them suitable for Monte Carlo simulations; (3) creating uniform and variable Cartesian and cylindrical meshes for detailed scoring; and ( 4) efficient Monte Carlo navigation in CAD geometries. JLAB will finish automation of simulations of residual dose in CAD geometries and integrate Tech-X software into Geant4 and MARS15. Finally, Tech-X will develop a Graphical User Interface to set up and heal CAD geometries, create input files, run and visualize simulations for residual dose. This application will run on local desktops, local and remote clusters and supercomputers and will be made available through public clouds, such as Amazon Web Services.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Characterizing the Roman Grism Redshift Efficiency of Type Ia Supernova Host Galaxies for the High-latitude Time-domain Survey

The High-latitude Time-domain Survey (HLTDS) for the Nancy Grace Roman Space Telescope (Roman) will discover thousands of high-redshift Type Ia supernovae (SNe Ia) to set generation-defining cosmological constraints on dark energy. To construct the Roman SN Hubble diagram, a strategy to obtain redshifts must be determined. While the nominal HLTDS will use only the Roman prism, in this work, we consider the utility of the Roman grism observations from overlap with the High-latitude Wide-area Survey for SN Ia cosmology. We determine a galaxy grism redshift recovery rate by simulating dispersed grism images and measuring redshifts with the Grizli software, obtaining an H-band 50% redshift recovery at magnitude 20.61 and 90% recovery at magnitude 19.27. To estimate the total number of spectroscopic redshifts expected for Roman SN cosmology, we also consider a Roman prism SN redshift efficiency and a ground-based telescope redshift efficiency for host galaxies. We apply these redshift efficiencies to SN Ia catalog-level simulations and predict that ∼6800 SNe will have an SN or host spectroscopic redshift. Second, we evaluate the size of potential systematics related to modeling the grism redshift efficiency by considering the impact of additional dependences on stellar mass and host-galaxy color. We estimate the largest potential size of this systematic to be 0.0066 ± 0.002 and −0.0266 ± 0.0079, roughly 42.9% and 49.6% of the statistical uncertainty, for w 0 and w a , respectively. Lastly, we consider the effects of assuming different redshift sources on the optimization of the HLTDS survey strategy by measuring relative changes to the dark energy figure of merit.

Chen, Rebecca C. [Duke Univ., Durham, NC (United S↗

DOE OSTI2022

Issues in Bi-Directional Interoperability between BIM and BEM

The state-of-the-art interoperability between Building Information Modeling (BIM) and Building Energy Modeling (BEM) is mainly one-way. BEM software like EnergyPlus takes design input from BIM and simulates the energy consumption of the building. BIM, however, is unable to leverage energy simulation results from BEM smoothly. This lack of bi-directional interoperability between BIM and BEM prevents buildings from seeking more energy-efficient design options and limits BIM applications in optimal generative design. In this research, the authors have conducted the following activities related to two-way interoperability between BIM and BEM: (1) surveyed its current status through literature review, (2) investigated barriers to the bi-directional interoperability, and (3) suggested possible approaches to enable bi-directional interoperability and research outlook in the field. As a result, the authors have identified three main barriers to BIM BEM interoperability, namely, inefficient collaboration, limited scope in information transformation, and lack of BEM to BIM transformation. Future directions are suggested to address these barriers.

building design↗

DOE OSTI2020

Planck intermediate results

We present the NPIPE processing pipeline, which produces calibrated frequency maps in temperature and polarization from data from the Planck Low Frequency Instrument (LFI) and High Frequency Instrument (HFI) using high-performance computers. NPIPE represents a natural evolution of previous Planck analysis efforts, and combines some of the most powerful features of the separate LFI and HFI analysis pipelines. For example, following the LFI 2018 processing procedure, NPIPE uses foreground polarization priors during the calibration stage in order to break scanning-induced degeneracies. Similarly, NPIPE employs the HFI 2018 time-domain processing methodology to correct for bandpass mismatch at all frequencies. In addition, NPIPE introduces several improvements, including, but not limited to: inclusion of the 8% of data collected during repointing manoeuvres; smoothing of the LFI reference load data streams; in-flight estimation of detector polarization parameters; and construction of maximally independent detector-set split maps. For component-separation purposes, important improvements include: maps that retain the CMB Solar dipole, allowing for high-precision relative calibration in higher-level analyses; well-defined single-detector maps, allowing for robust CO extraction; and HFI temperature maps between 217 and 857 GHz that are binned into 0'.9 pixels (Nside = 4096), ensuring that the full angular information in the data is represented in the maps even at the highest Planck resolutions. The net effect of these improvements is lower levels of noise and systematics in both frequency and component maps at essentially all angular scales, as well as notably improved internal consistency between the various frequency channels. Based on the NPIPE maps, we present the first estimate of the Solar dipole determined through component separation across all nine Planck frequencies. The amplitude is (3366.6 ± 2.7) μK, consistent with, albeit slightly higher than, earlier estimates. From the large-scale polarization data, we derive an updated estimate of the optical depth of reionization of τ = 0.051 ± 0.006, which appears robust with respect to data and sky cuts. There are 600 complete signal, noise and systematics simulations of the full-frequency and detector-set maps. As a Planck first, these simulations include full time-domain processing of the beam-convolved CMB anisotropies. The release of NPIPE maps and simulations is accompanied with a complete suite of raw and processed time-ordered data and the software, scripts, auxiliary data, and parameter files needed to improve further on the analysis and to run matching simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

WISP: Watching grid Infrastructure Stealthily through Proxies (Final Technical Report)

The complex interdependencies of cyber systems (sensors and communications), physical grids and associated electricity market operations make protecting electric power grids a significant challenge. The energy sector is constantly under new, targeted, advanced and dangerous cyber-attacks that have the potential to result in the loss of human life. These threats are further exacerbated by our need to modernize the grid. One focus of cyber security research in smart grids is the securing of the SCADA system through advanced intrusion detection systems (IDS) and bad data detection algorithms in state estimation. These methods either require full knowledge of the system topology and parameters or fail to understand the physical behaviors under attack. WISP (Watching grid Infrastructure Stealthily through Proxies) is designed to provide additional protection to the power grid using only publicly available data. In particular, WISP exploits the spatio-temporal nature of the real time locational marginal prices (LMPs), in conjunction with other information such as bids, weather, outages and load data to analyze anomalous power pricing behaviors and then correlate those observations to localize regions of interest and identify potential cyber events. WISP is non-intrusive as the tool is deployed as a service in the Cloud or on premise and provides reliable information to system operators for enhanced situational awareness, without impeding energy delivery functions. The WISP technology comprises three modules: the data-driven anomaly detection core, the vulnerability and risk analysis and the root cause analysis. The data-driven anomaly detection core performs the tasks of feature selection, anomaly detection and attack region localization. The vulnerability and risk analysis module provides system level information of the vulnerable variables and times, assisting the operators in selecting monitoring and protection nodes. The root cause analysis module takes the detection results and identifies potential operational conditions that contribute to the detected anomalies. In Phase I, we have demonstrated the feasibility and effectiveness of WISP. We developed a realistic electricity market simulator capable of generating normal and attack market data under various operational conditions. We developed a series of cyber-attack detection and analysis algorithms and evaluated them under multiple data sources. Finally, we integrated all modules into an end-to-end software, providing functions for data management, data analytics and visualization. Specifically, we have achieved: (i) real-time data acceptance from external utility interfaces with >99% acceptance rate; (ii) high performance anomaly detection algorithms with >98% detection accuracy and <0.1% false alarm rate; and (iii) ultra-low computing delay <50 milliseconds. Additionally, our team developed algorithms to identify the vulnerable variables in electricity market operations and root cause analysis functions to identify major contributors to the price spikes. These ancillary modules are necessary when deploying WISP in real world industry environment. In Phase II, we have demonstrated the effectiveness of WISP software on realistic largescale power systems. We performed red team testing for the Phase I WISP software and identified software vulnerabilities and implemented corresponding mitigation solutions. We adapted the electricity market simulator for the Texas synthetic 2000-bus system and generated datasets for the false data injection attacks. We created database and visualization interfaces for the Texas system and the ISO New England system. We performed software optimization in terms of operation efficiency, computing speed and detection accuracy. Finally, we tested the software on the Texas system and the ISO New England system and evaluated the detection performance. Overall, we achieved above 89% detection rate, below 3% false alarm rate and below 37 seconds of end-to-end detection delay.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

A Cast of Thousands: How the IDEAS Productivity Project Has Advanced Software Productivity and Sustainability

Computational and data-enabled science and engineering are revolutionizing advances throughout science and society, at all scales of computing. For example, teams in the U.S. Department of Energy’s Exascale Computing Project have been tackling new frontiers in modeling, simulation, and analysis by exploiting unprecedented exascale computing capabilities—building an advanced software ecosystem that supports next-generation applications and addresses disruptive changes in computer architectures. However, concerns are growing about the productivity of the developers of scientific software. Members of the Interoperable Design of Extreme-scale Application Software project serve as catalysts to address these challenges through fostering software communities, incubating and curating methodologies and resources, and disseminating knowledge to advance developer productivity and software sustainability. This article discusses how these synergistic activities are advancing scientific discovery—mitigating technical risks by building a firmer foundation for reproducible, sustainable science at all scales of computing, from laptops to clusters to exascale and beyond.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Trilinos: Enabling Scientific Computing across Diverse Hardware Architectures at Scale

Trilinos is a community-developed, open-source software framework that facilitates building large-scale, complex, multiscale, multiphysics simulation code bases for scientific and engineering problems. Since the Trilinos framework has undergone substantial changes to support new applications and new hardware architectures, this document is an update to “An Overview of the Trilinos project” by Heroux et al. (ACM Transactions on Mathematical Software, 31(3):397–423, 2005). It describes the design of Trilinos, introduces its new organization in product areas, and highlights established and new features available in Trilinos. Particular focus is put on the modernized software stack based on the Kokkos ecosystem to deliver performance portability across heterogeneous hardware architectures. This article also outlines the organization of the Trilinos community and the contribution model to help onboard interested users and contributors.

Heterogeneous Hardware Architectures↗

DOE OSTI2025

Modeling of Vertical Motor-driven Pump for Simulation of a Fault Signature \\ for Condition Monitoring

As part of the ongoing effort to transition from preventive maintenance strategies to condition-based maintenance strategies in nuclear power plants, there is significant reliance on using machine learning techniques. To develop a robust machine learning model that can diagnose all the fault modes of a vertical motor-driven pump, data capturing the unique signature of each fault mode is required. In practice, it is difficult to collect or capture data that captures all the fault modes from a single plant site. So to address this situation, a computational model of a vertical motor-driven pump is developed using the multipurpose finite element software COMSOL Multiphysics. The developed model is used to generate simulated data under normal operation and is compared with the vibration data collected using vibration sensors. Once the simulation model is verified under normal operating condition, simulated data for the fault mode for which minimal or no evidence is available in historical plant process data is developed. This simulated data is used to develop fault signatures to achieve robust predictive models. This paper presents modeling details and verification of the model that can used to generate data for fault modes that are not available at a plant site for condition monitoring purpose.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

DOE OSTI2023

Modeling of Vertical Motor-driven Pump for Simulation of a Fault Signature \\ for Condition Monitoring

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

DOE OSTI2025

Simulating Alpha Particles Incident on MKID Chips for Quantum Sensitivity Analysis

Superconducting quantum devices, such as microwave kinetic inductance detectors (MKIDs), are highly sensitive instruments used in quantum computing and advanced sensing technologies. However, their extreme sensitivity also makes them vulnerable to background noise from natural sources like radiation. One significant contributor to this noise is alpha particles emitted by 210Po, a radon decay daughter that accumulates on surfaces near the detector. This project investigates how alpha particles emitted from 210Po interact with MKID chips. These particles can deposit energy on the detector surface, disrupting its operation and generating false signals. Understanding the energy and behavior of these particles is crucial for improving the design and reliability of quantum devices. To explore this, we first modeled the decay chain starting from 210Pb to 210Po using differential equations. This allowed us to predict how the activity of alpha-emitting isotopes changes over time, reaching a steady state after about two years. Next, we simulated alpha particle interactions with the MKID chip using the Geant4 software toolkit. We built a detailed computer model of the detector housing, including the copper lid where alpha particles originate, the silicon chip, and a thin aluminum sensor layer. Alpha particles were emitted isotropically from just beneath the copper lid’s surface, mimicking natural decay conditions. The simulation tracked how these particles deposit energy on the chip, generating electron-hole pairs and phonons. The results provide insight into the behavior of the resultant electron-hole pairs and phonons, giving us a clear understanding of the energy deposition distribution on the chip. This work supports efforts to mitigate background noise in superconducting sensors, advancing their use in quantum computing and sensitive physics experiments.

Hall, Matthew [Fermilab; UCLA]↗

DOE OSTI2025

Building confidence in models for complex barrier systems for radionuclides

The modeling and simulation of the Cement-clay Interaction-Diffusion field (CI-D) experiment at the Mont Terri site in Switzerland presented here demonstrates that it is possible to capture the multiscale physical and chemical features of natural and engineered barrier systems for radionuclides. The simulations are successfully carried out with the newly developed CrunchODiTi high-performance computing software that accounts for multiple continua, including a continuum representing the electrical double layer (EDL) developed along negatively charged clay particles in clay rock. The simulation also accounts for both the complex three-dimensional (3D) geometry, expected as the norm in a geological waste repository, and the anisotropy of the geological formation. In addition, the high resolution of the model makes it possible to include "skin effects" developed at the interface between highly reactive materials, in this case between the high pH cement and the circumneutral but electrostatic Opalinus Clay. The successful history matching with the field experiment demonstrates that the distinct geochemical and physical properties of the cement and the Opalinus Clay in the CI-D experiment can be accounted for. Such analyses are essential for developing a defensible safety case for the underground storage of radioactive waste.

Sarsenbayev, Dauren↗