ABSTRACT: We aim to model PDC cutter-rock interactions in 3-D through numerical study to find an optimal arrangement of parameters for efficient geothermal drilling. Using the combined finite discrete element method (FDEM), we model realistic pressure conditions and rock fracture and fragmentation. FDEM can model both continuum and discontinuous mechanical behavior, which allows for modeling of fracture in targeted rock at downhole conditions. We simulate PDC cutter-rock interaction in 3-D for a range of back rake angles, cutting speeds, and depth of cuts using granite as our target rock material. These parameters are varied to investigate the impact on the cutting force and fracture dynamics in an effort to benchmark performance. We reproduce results from numerical rock cutting tests and qualitative results from laboratory experiments. We report on the progress of the numerical analysis for this complex multi-physics problem. 1 INTRODUCTION Geothermal energy is an important form of clean energy in the United States and other parts of the world. Geothermal energy drilling involves deeper, hotter, and harder rock sources than conventional/unconventional oil and gas targets (Dwivedi et al., 2008; Kumari et al., 2017). Understanding the mechanics of geothermal energy drilling is essential to reducing the overall cost, of which drilling can be over half of the total cost (Pierce and Livesay, 1994). A commonly used drill bit due to its strength and resistance to abrasive wear is the polycrystalline diamond compact (PDC) cutter bit (Dougherty et al., 2014; Yang et al., 2018). The combination of deep, hard rock means the forces in geothermal drilling are typically larger and drilling performance needs to be increased. The rate of penetration (ROP) determines the efficiency of drilling, as in how much rock material can be removed. A high ROP would remove more rock material, however, higher ROP means higher forces on the drill bit. Determining the forces on the drill bit under a geothermal drilling interaction allows us insight into drilling performance.

ABSTRACT: Simulating the structural response of concrete and reinforced concrete structures to blast loading conditions is a challenging task, as it requires modeling the fracture and fragmentation processes in this composite material with reasonable computational efficiency for large scale simulations. To address this problem, novel shell formulations have been incorporated within Los Alamos National Laboratory's implementation of the combined finite-discrete element method, called HOSS (Hybrid Optimization Software Suite). In this numerical study, these new finite element formulations are utilized for modeling thin concrete and metal linings for applications in building construction. Both unreinforced and reinforced concrete can be modeled with this method which opens the door for addressing many practical applications. 1. INTRODUCTION Since its inception, the combined finite discrete element method (FDEM) has become a tool of choice to address a variety of problems involving fracture and fragmentation processes in solids. FDEM combines the strengths of the finite element method (FEM) and the discrete element method (DEM). The key advantage of FDEM is the utilization of finite strain-based deformability combined with suitable constitutive material laws which are then merged with discrete element based transient dynamics, contact detection, contact interaction solutions, and objective discrete crack initiation and crack propagation solutions (Munjiza, 2004). The comparison of DEM and FEM with a schematic visualization of FDEM is shown in Fig. 1. In FDEM, the solid bodies are modeled as a collection of deformable particles that are bonded with each other (Rougier et al., 2014), Fig. 1. These solid bodies (called discrete elements) are discretized into finite elements where their finite displacements and rotations are assumed a priori (Munjiza, 2004; Munjiza et al., 2011, 2015). The bonding is numerically represented with cohesion points along the boundaries of the deformable particles (Rougier et al., 2014). The cohesion of these bonds is a combination of normal cohesion and tangential cohesion. When an FDEM model experiences fracture, failure, or fragmentation and the material is exposed to high enough levels of stress, these bonds become increasingly strained until they reach their ultimate strengths and eventually break resulting in the adjacent finite elements to also become unbonded (Rougier et al., 2014). The single discrete element domains are transformed into interacting domains upon which discretized contact solutions can be used for both contact detection and contact interaction (Knight et al., 2020).

The implementation of proper strategies of conservation of heritage structures requires the collection of heterogeneous sources of information (historical evolution, past restoration works, experimental data, monitoring systems results, etc.). The handling of this data needs an effective informative modelling, able to collect different type of data by using 3D parametric model. Heritage Building Information Modelling (HBIM) can be considered a promising tool for the conservation of monuments which have to be protected along the centuries, thanks to its capability of archiving and handling the building information. This paper discusses this topic by describing the research project “CHARMING PISTOIA” (Cultural HeritAge infoRmation ModellING for PISTOIA: from monitoring data to digital twin). The goal of the project is to deliver tools and methodologies to improve conservation of historical constructions by ensuring the optimal use of the resources required for the tasks of Control & Preservation of heritage buildings. It proposed a three steps approach: i) the design of the HBIM to collect the information on the structure and to export them in computational models; ii) the integration of a Structural Health Monitoring (SHM) system to ensure the steady flow of structural information and its updating through Bayesian inference; iii). the definition of robust computational models for the Joint Vulnerability Assessment of the structure and the works of art inside. In this context, the Pieve of Sant'Andrea in Pistoia (Italy) and its masterpiece, the Pulpit of Giovanni Pisano, represents an emblematic case study to meet the challenges of the research. In this paper the preliminary stages of the project are reported and discussed together with the expected results.

ABSTRACT Three-point bending test is a widely used laboratory test for the estimation of the flexural force-displacement response of the material. It is well known that the results of the three-point bending test are sensitive to the specimen and the loading. In this work, the impact of the boundary effects on a single notch three-point bending test is studied using LANL's combined finite-discrete element method (FDEM) based code, the Hybrid Optimization Software Suite (HOSS). To this goal, a series of virtual experiments with different specimens and boundary conditions are conducted. The influence of the notch location, and fixture shape are studied. Results clearly show that these boundary conditions greatly influence on the fracture initiation and propagation behaviors as well as the flexural force-displacement response. INTRODUCTION Three-point bending test is a long-used technique applied mainly in the oil and gas industry to estimate the fracture toughness of rocks in the laboratory. In this test, the vertical tension is applied to the convex side of a sheet or plate specimen placed on two supporting fixtures with a set distance apart. A variety of numerical approached have been proposed to analyze the crack initiation and growth behavior of three-point bending test in the past several decades (Fakhimi, 2005; Kokot, G., Binkowski, 2011; Ramos, 2015; Klasztorny, 2018: Sauvage, 2020). However, the effect of boundary conditions is still lacking consideration in the previous studies. Motivated by the prior works and the knowledge gaps remaining in effect of boundary conditions, a finite-discrete element method (FDEM) model is applied here to interpret three-point bending experiment results in order to characterize dependence of rock fracture behavior on boundary conditions and notch location. The present study therefore aims to capture the crack initiation and propagation behavior for laboratory experiments using material properties and traction-separation law that has been calibrated by comparing the simulation results with lab experiments provided by Jiang et al. (2021) and Jiang et al. (2022), regardless of notch location. This study aims to revisit the effect of boundary conditions on crack initiation and growth behavior under three-point bending test. For this purpose, a 2D plane-strain model is developed using HOSS, a combined finite-discrete element method (FDEM) based code. Different boundary conditions and notch locations are considered for lab-scale simulations. Indeed, simulation results indicated that the crack initiation location and crack growth behavior can vary with different boundary conditions and notch locations, which can challenge the general belief that the crack initiation and propagation behavior should not be affected by the boundary conditions greatly.

ABSTRACT: Numerical modeling of the Earth’s response to underground explosions poses longstanding challenges in relating seismic signal measurements to source yield and emplacement conditions, where complex responses of the earth near to the source affect the propagation of seismic signals. In simulations, assumptions and approximations are necessarily made, e.g., there is often need to make decisions regarding an inherent trade-off between model fidelity and computational expense. It is thus important to be able to justify approximations and understand their limitations. In this work, sequentially more complex constitutive models are introduced into the finite element analysis of underground explosions, starting from simple small-strain elastic models and progressing to elastoplastic models, including large-strain hyper-elastoplasticity. Various model geometry assumptions, such as choices of approximate boundary conditions are also compared. The results show how different modeling assumptions affect the predicted seismic signals and are compared to gauge measurements for a large chemical explosion underground test. Boundary value problems are set up in a variety of configurations in order to assess their effects on model predictions. The outcomes of this work provide insight into the effect of modeling approximations in simulation of underground explosions where decisions pertaining to trade-offs between fidelity and computation speed may be necessary. 1 INTRODUCTION Numerical modeling of the Earth’s response to Under-Ground explosions (UGX) can be used to estimate the source yield (Bache, 1982) and potentially discriminate whether the source is nuclear or chemical (Kamm and Bos, 1995). However, the Earth exhibits a complex response to the shock in the region immediately surrounding the explosion which affects the propagation of seismic signals through the ground (Johnson and Sammis, 2001a). These complex responses involve a number of processes that occur as the energy density of the shock wave decreases with distance from the explosion. In the immediate vicinity of the explosion, described sometimes as the "hydrodynamic region," the rock behaves as a fluid as it is vaporized and melts (Ford, 2020). Within the hydrodynamic region, the shock front precedes the "temperature front" (cf. Stroujkova and Richards), so inelastic deformation such as dislocation based plasticity and extensive fracture likely occur; however, measurements in this region are sparse because the high stresses and temperatures result in very brief survival of instruments. Outside the hydrodynamic region but still within the so-called "elastic-radius" (where the rock response transitions to purely elastic), inelastic deformation mechanisms are well documented (e.g., Johnson and Sammis, 2001b; Zhang and Zhao, 2014), notably with damage and fracture occurring on a wide range of scales (with cracks ranging from micrometers to many meters in length) (Swanson et al., 2018; Bennett, 2020). The shock wave decays with distance; eventually, the motions are small enough to be described by linear elastic waves (e.g., Harris, 2001).

Two >130-meter-diameter impact craters formed on Mars during the later half of 2021. These are the two largest fresh impact craters discovered by the Mars Reconnaissance Orbiter since operations started 16 years ago. The impacts created two of the largest seismic events (magnitudes greater than 4) recorded by InSight during its 3-year mission. The combination of orbital imagery and seismic ground motion enables the investigation of subsurface and atmospheric energy partitioning of the impact process on a planet with a thin atmosphere and the first direct test of martian deep-interior seismic models with known event distances. The impact at 35°N excavated blocks of water ice, which is the lowest latitude at which ice has been directly observed on Mars.

ABSTRACT: Numerical modeling techniques using the combined finite-discrete element method have been utilized to explore the relationship between stress, damage, and crack propagation in concrete. Obtaining post-peak behavior from the Brazilian tension test is difficult because failure occurs abruptly. An experimental test method is described which enables monitoring of the post-peak cracking behavior in the Brazilian tension test by slowing the crack propagation. Experimental testing with this technique proved its capabilities in slowing crack propagation. The combined finite-discrete element method is used to further examine the stress states during this test and to understand the damage evolution present in this test prior to the peak strength. The method also allows for interpretation into the type of damage present throughout the entire test and the zones in which that damage initiates. A comparison is also performed between the numerical results and experimental observations to determine how well the numerical method captures the experimental results. This work enables a good understanding of how fractures form in the Brazilian tension test as well as a comparison between experimental and numerical technique results. 1. INTRODUCTION 1.1. Combined Finite Discrete Element Method In an effort to model inelastic behavior and predict the deformation and failure of materials, the combined finite discrete element method has been employed. The finite-discrete element method (FDEM) is an innovative numerical computation method that combines the efficiency of the finite element method (FEM) with the discontinuity framework of the discrete element method (DEM) to create a highly powerful and efficient system (Munjiza et al., 1999; Rougier et al., 2014). The comparison of DEM and FEM with a schematic visualization of FDEM is shown in Fig. 1. At the contact interfaces of the FDEM framework, there is bonding. The bonding is numerically represented with cohesion points along the boundaries of the deformable particles (Rougier, Knight, Lei, et al., 2014). The cohesion of these bonds is a combination of normal cohesion and tangential cohesion. When the material is exposed to significant stress, these bonds become strained and can become unbonded (Rougier, Knight, Lei, et al., 2014).

Permeability measurements were made on sandstone during confined Brazilian strength tests. The test involves 50 mm diameter disk-shaped, jacketed samples that are subjected to confining stresses while they are diametrically loaded. Specially designed end caps allow for concurrent gas flow measurements. The test configuration allows for the samples to be subjected to a range of stresses, with the confining stress as the intermediate principal stress. The majority of the tests measured permeability during loading to failure in the confined extension region. The permeability of the sandstone sample increases significantly well before the peak load is reached due to newly formed microcracks that continue to coalesce and dilate with further loading. Permeability increases are inversely proportional to the intermediate principal stress as increased confining pressures suppress growth, coalescence, and dilation of microcracks. Additional testing includes unloading and reloading cycles prior to failure. With each unloading–reloading cycle, permeability at comparable stresses is increased compared to the previous cycle, consistent with increasing damage in the form of an expanding microcrack network.

This research experimentally studies coupled hydro-mechanical relationships using flattened Brazilian disks under confinement, with concurrent permeability measurements and acoustic emission monitoring. A series of tests are performed on concrete, as representative samples of brittle geo-materials, under a range of confining stresses between 2.76 and 13.79 MPa. Acoustic emission data is used to quantify damage and identify damage thresholds. Damage is then correlated to pre-peak changes in permeability. The advancement of models that couple transport properties to mechanical responses are of interest in the fields of carbon sequestration, hydrofracking, production of geothermal energy, induced seismicity, and underground nuclear waste storage, and these experiments validate a novel experimental approach towards investigating hydro-mechanical relationships.

Most of the surface of Mars is covered with unconsolidated rocky material, known as regolith. High‐fidelity models of the dynamics of impacts in such material are needed to help with the interpretation of seismic signals that are now recorded by SEIS, the seismometer of InSight. We developed a numerical model for impacts on regolith, using the novel Hybrid Optimization Software Suite (HOSS), which is a Lagrangian code mixing finite and discrete element formulations. We use data from hypervelocity impact experiments performed on pumice sand at the NASA Ames Vertical Gun Range to identify and calibrate key model parameters. The model provides insight into the plastic‐elastic transition observed in the data and it also demonstrates that gravity plays a key role in the material response. Waveforms for receivers situated vertically below the impact point are correctly modeled, while more research is needed to explain the shallow receivers' signals.

It has been shown experimentally that under mixed tensile and compressive stress states, a corresponding mixed-mode fracture will occur. In this paper, the formation of mixed-mode fractures is investigated using the combined finite–discrete element method. A series of simulations with confining pressures ranging from 7.5 to 150 MPa generate a spectrum of mixed-mode failure conditions. These stress states at failure span the transition from the tensile to compressive failure. The models reproduce previous experiments on Carrara marble using a dog-bone geometry, and a comparison shows good qualitative agreement with the experimental observations. This paper demonstrates that mixed-mode fracture can be captured via numerical simulations and identifies areas where further research is required to better understand mixed-mode fracture processes.

The presence and growth of micro-cracks degrade the strength of brittle solids, greatly impacting the overall material response. Hence, the evolution of these micro-cracks must be accounted for in models describing the relationship between stress and strain so that accurate predictions of material failure can be made. The evolution of individual cracks and crack networks can be simulated with high-fidelity microscale models utilizing highly resolved meshes that can be computationally expensive to a point in which it limits the simulation scale. Hence, for many engineering applications that require simulations of large components, continuum-scale models, which cannot explicitly resolve individual cracks and thus lose important physical information, are required. In this work, we bridge these two scales by developing and implementing a continuum-scale effective moduli constitutive model that is informed by crack statistics generated from a high-fidelity model resolved using a finite-discrete element method (FDEM) implementation. Using statistical information describing the evolution of crack lengths and orientations, this model can capture the effects of brittle damage evolution without the need to resolve individual cracks. We have successfully captured the stress-strain behavior of the high-fidelity simulations using the statistics-based constitutive model shown through direct comparison of stress-strain curves. The curves match within error bars present in the strain-softening portions of the stress-strain curve of the high-fidelity results due to the statistical variation of the initial pre-existing crack network. The stress-strain curves are also compared to experimental results for similar loading conditions and show good qualitative agreement.

Fracture coalescence is a critical phenomenon for creating large, inter-connected fractures from smaller cracks, affecting fracture network flow and seismic energy release potential. In this paper, simulations are performed to model fracture coalescence processes in granite specimens with pre-existing flaws. These simulations utilize an in-house implementation of the combined finite–discrete element method (FDEM) known as the hybrid optimization software suite (HOSS). The pre-existing flaws within the specimens follow two geometric patterns: (1) a single-flaw oriented at different angles with respect to the loading direction, and (2) two flaws, where the primary flaw is oriented perpendicular to the loading direction and the secondary flaw is oriented at different angles. The simulations provide insight into the evolution of tensile and shear fracture behavior as a function of time. The single-flaw simulations accurately reproduce experimentally measured peak stresses as a function of flaw inclination angle. Both the single- and double-flaw simulations exhibit a linear increase in strength with increasing flaw angle while the double-flaw specimens are systematically weaker than the single-flaw specimens.

In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible to incorporate in upscaling and uncertainty quantification frameworks. The goal of this paper is to provide a fast heuristic to reasonably estimate quantities such as failure path and damage in the process of brittle failure. Towards this goal, we first present a method to predict failure paths under tensile loading conditions and low-strain rates. The method uses a k-nearest neighbors algorithm built on fracture process zone theory, and identifies the set of all possible pre-existing cracks that are likely to join early to form a large crack. The method then identifies zone of failure and failure paths using weighted graphs algorithms. We compare these failure paths to those computed with a high-fidelity model called the Hybrid Optimization Software Simulation Suite (HOSS). A probabilistic evolution model for average damage in a system is also developed that is trained using 150 HOSS simulations and tested on 40 simulations. A non-parametric approach based on confidence intervals is used to determine the damage evolution over time along the dominant failure path. For upscaling, damage is the key QoI needed as an input by the continuum models. This needs to be informed accurately by the surrogate models for calculating effective modulii at continuum-scale. We show that for the proposed average damage evolution model, the prediction accuracy on the test data is more than 90%. In terms of the computational time, the proposed models are ≈𝒪(10^6) times faster compared to high-fidelity HOSS.

In this paper, five different approaches for reduced-order modeling of brittle fracture in geomaterials, specifically concrete, are presented and compared. Four of the five methods rely on machine learning (ML) algorithms to approximate important aspects of the brittle fracture problem. In addition to the ML algorithms, each method incorporates different physics-based assumptions in order to reduce the computational complexity while maintaining the physics as much as possible. This work specifically focuses on using the ML approaches to model a 2D concrete sample under low strain rate pure tensile loading conditions with 20 preexisting cracks present. A high-fidelity finite element-discrete element model is used to both produce a training dataset of 150 simulations and an additional 35 simulations for validation. Results from the ML approaches are directly compared against the results from the high-fidelity model. Strengths and weaknesses of each approach are discussed and the most important conclusion is that a combination of physics-informed and data-driven features are necessary for emulating the physics of crack propagation, interaction and coalescence. All of the models presented here have runtimes that are orders of magnitude faster than the original high-fidelity model and pave the path for developing accurate reduced order models that could be used to inform larger length-scale models with important sub-scale physics that often cannot be accounted for due to computational cost.

Shale gas is an unconventional fossil energy resource that is already having a profound impact on United States (US) energy independence and is projected to last for at least 100 years. Production of methane and other hydrocarbons from low permeability shale involves hydraulically fracturing rock, establishing fracture connectivity, and multiphase fluid-flow and reaction processes, all of which are poorly understood. The result is highly inefficient extraction that also raises many environmental concerns. A science-based capability is required to quantify the governing mesoscale fluid-solid interactions, including microstructural control of fracture patterns, and the interaction of engineered fluids with hydrocarbon flow that is required for increasing efficiency and decreasing the potential of environmental impacts. These interactions depend on several complex coupled thermo-hydro-mechanical-chemical (THMC) processes over scales ranging from nanometers to kilometers. Determining the key mechanisms in subsurface THMC systems has been impeded due to the lack of sophisticated experimental methods to measure fracture aperture and connectivity, permeability, and chemical exchange capacities at the high temperature, pressure, and stresses present in the subsurface. In this chapter, we describe innovative experimental techniques and simulation methodologies to address these issues. We use high-pressure microfluidic and triaxial core flood experiments on shale to better constrain fracture-permeability relations and the extraction of hydrocarbon. These data are integrated with simulations including lattice Boltzmann modeling of pore-scale processes, finite-element/discrete element approach for fracture initiation and propagation in the near-well environment, discrete fracture network modeling at the reservoir-scale for modeling transport through large-scale fractures, and system-scale models to assess the economics of alternative fracturing fluids. The ultimate goal is to make the critical measurements needed to develop models that can be used to determine the reservoir operating conditions necessary to gain a degree of control over fracture generation, fluid flow, and interfacial processes over a range of in situ subsurface conditions.

Within the context of rock mechanics, the Combined Finite-Discrete Element Method (FDEM) has been applied to many complex industrial problems such as block caving, deep mining techniques (tunneling, pillar strength, etc.), rock blasting, seismic wave propagation, packing problems, dam stability, rock slope stability, rock mass strength characterization problems, etc. The reality is that most of these were accomplished in a 2D and/or single processor realm. In this work a hardware independent FDEM parallelization framework has been developed using the Virtual Parallel Machine for FDEM, (V-FDEM). With V-FDEM, a parallel FDEM software can be adapted to different parallel architecture systems ranging from just a few to thousands of cores.

A full-scale 3D analysis of a Split Hopkinson Pressure Bar experiment on granite material using a 3D combined Finite-Discrete Element Method (FDEM) is shown. Previous efforts to simulate Split Hopkinson Pressure Bar experiments using the 2D FDEM had obtained a very good match for the loading portion of the experiment. This work extends those efforts by modeling the entire 3D Split Hopkinson Pressure Bar experimental setup, and reproducing the softening behavior of the sample after breakage. This modeling effort introduces the effect of a compliant interface between the bars and the sample.