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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Dating Melt Rock 63545 By Rb-Sr and Sm-Nd: Age of Imbrium; Spa Dress Rehearsal

Apollo 16 sample 63545 was initially described as one of a group of 19 generally rounded, fine-grained, crystalline rocks that were collected as rake samples [1]. This 16 g "rocklet" was collected at Station 13 on the ejecta blanket of North Ray Crater at the foot of Smoky Mountain [2]. Originally classified as a Very High Alumina (VHA) basalt on geochemical grounds [3], it was later argued to be an impact melt rock [4]. Here we report a Rb-Sr and Sm-Nd isotopic study that shows that some portions of the rock failed to reach isotopic equilibrium on last melting in agreement with the impact melt rock interpretation. Nevertheless, by omitting mineral fractions that are discordant with the majority of the data, we arrive at the time of last melting as 3.88 plus or minus 0.05 Ga ago. This age is in agreement with the Ar-39/Ar-40 plateau age of 3839 plus or minus 23 Ma [5], if the latter is adjusted for the ~1.4-1.8% revision in the age of the hornblende monitor [6]. This investigation was undertaken in part as proof-of-concept for SPA-basin sample return.

Nyquist, L. E.↗
NASA NTRS2013

Robotic Ankle for Omnidirectional Rock Anchors

Future robotic exploration of near-Earth asteroids and the vertical and inverted rock walls of lava caves and cliff faces on Mars and other planetary bodies would require a method of gripping their rocky surfaces to allow mobility without gravitational assistance. In order to successfully navigate this terrain and drill for samples, the grippers must be able to produce anchoring forces in excess of 100 N. Additionally, the grippers must be able to support the inertial forces of a moving robot, as well gravitational forces for demonstrations on Earth. One possible solution would be to use microspine arrays to anchor to rock surfaces and provide the necessary load-bearing abilities for robotic exploration of asteroids. Microspine arrays comprise dozens of small steel hooks supported on individual suspensions. When these arrays are dragged along a rock surface, the steel hooks engage with asperities and holes on the surface. The suspensions allow for individual hooks to engage with asperities while the remaining hooks continue to drag along the surface. This ensures that the maximum possible number of hooks engage with the surface, thereby increasing the load-bearing abilities of the gripper. Using the microspine array grippers described above as the end-effectors of a robot would allow it to traverse terrain previously unreachable by traditional wheeled robots. Furthermore, microspine-gripping robots that can perch on cliffs or rocky walls could enable a new class of persistent surveillance devices for military applications. In order to interface these microspine grippers with a legged robot, an ankle is needed that can robotically actuate the gripper, as well as allow it to conform to the large-scale irregularities in the rock. The anchor serves three main purposes: deploy and release the anchor, conform to roughness or misalignment with the surface, and cancel out any moments about the anchor that could cause unintentional detachment. The ankle design contains a rotary DC motor that can drag the microspine arrays across the surface to engage them with asperities, as well as a linear actuator to disengage the hooks from the surface. Additionally, the ankle allows the gripper to rotate freely about all three axes so that when the robot takes a step, the gripper may optimally orient itself with respect to the wall or ground. Finally, the ankle contains some minimal elasticity, so that between steps, the gripper returns to a default position that is roughly parallel to the wall.

Parness, Aaron↗
NASA NTRS2013

Memory-Efficient Onboard Rock Segmentation

Rockster-MER is an autonomous perception capability that was uploaded to the Mars Exploration Rover Opportunity in December 2009. This software provides the vision front end for a larger software system known as AEGIS (Autonomous Exploration for Gathering Increased Science), which was recently named 2011 NASA Software of the Year. As the first step in AEGIS, Rockster-MER analyzes an image captured by the rover, and detects and automatically identifies the boundary contours of rocks and regions of outcrop present in the scene. This initial segmentation step reduces the data volume from millions of pixels into hundreds (or fewer) of rock contours. Subsequent stages of AEGIS then prioritize the best rocks according to scientist- defined preferences and take high-resolution, follow-up observations. Rockster-MER has performed robustly from the outset on the Mars surface under challenging conditions. Rockster-MER is a specially adapted, embedded version of the original Rockster algorithm ("Rock Segmentation Through Edge Regrouping," (NPO- 44417) Software Tech Briefs, September 2008, p. 25). Although the new version performs the same basic task as the original code, the software has been (1) significantly upgraded to overcome the severe onboard re source limitations (CPU, memory, power, time) and (2) "bulletproofed" through code reviews and extensive testing and profiling to avoid the occurrence of faults. Because of the limited computational power of the RAD6000 flight processor on Opportunity (roughly two orders of magnitude slower than a modern workstation), the algorithm was heavily tuned to improve its speed. Several functional elements of the original algorithm were removed as a result of an extensive cost/benefit analysis conducted on a large set of archived rover images. The algorithm was also required to operate below a stringent 4MB high-water memory ceiling; hence, numerous tricks and strategies were introduced to reduce the memory footprint. Local filtering operations were re-coded to operate on horizontal data stripes across the image. Data types were reduced to smaller sizes where possible. Binary- valued intermediate results were squeezed into a more compact, one-bit-per-pixel representation through bit packing and bit manipulation macros. An estimated 16-fold reduction in memory footprint relative to the original Rockster algorithm was achieved. The resulting memory footprint is less than four times the base image size. Also, memory allocation calls were modified to draw from a static pool and consolidated to reduce memory management overhead and fragmentation. Rockster-MER has now been run onboard Opportunity numerous times as part of AEGIS with exceptional performance. Sample results are available on the AEGIS website at http://aegis.jpl.nasa.gov.

Burl, Michael C.↗
NASA NTRS2014

Alteration of Lunar Rock Surfaces through Interaction with the Space Environment

Space weathering occurs on all ex-posed surfaces of lunar rocks, as well as on the surfaces of smaller grains in the lunar regolith. Space weather-ing alters these exposed surfaces primarily through the action of solar wind ions and micrometeorite impact processes. On lunar rocks specifically, the alteration products produced by space weathering form surface coatings known as patina. Patinas can have spectral reflectance properties different than the underlying rock. An understanding of patina composition and thickness is therefore important for interpreting re-motely sensed data from airless solar system bodies. The purpose of this study is to try to understand the physical and chemical properties of patina by expanding the number of patinas known and characterized in the lunar rock sample collection.

Frushour, A. M.↗
NASA NTRS2017

Resolving Orbital and Climate Keys of Earth and Extraterrestrial Environments with Dynamics (ROCKE-3D) 1.0: A General Circulation Model for Simulating the Climates of Rocky Planets

Resolving Orbital and Climate Keys of Earth and Extraterrestrial Environments with Dynamics (ROCKE-3D) is a three-dimensional General Circulation Model (GCM) developed at the NASA Goddard Institute for Space Studies for the modeling of atmospheres of solar system and exoplanetary terrestrial planets. Its parent model, known as ModelE2, is used to simulate modern Earth and near-term paleo-Earth climates. ROCKE-3D is an ongoing effort to expand the capabilities of ModelE2 to handle a broader range of atmospheric conditions, including higher and lower atmospheric pressures, more diverse chemistries and compositions, larger and smaller planet radii and gravity, different rotation rates (from slower to more rapid than modern Earth's, including synchronous rotation), diverse ocean and land distributions and topographies, and potential basic biosphere functions. The first aim of ROCKE-3D is to model planetary atmospheres on terrestrial worlds within the solar system such as paleo-Earth, modern and paleo-Mars, paleo-Venus, and Saturn's moon Titan. By validating the model for a broad range of temperatures, pressures, and atmospheric constituents, we can then further expand its capabilities to those exoplanetary rocky worlds that have been discovered in the past, as well as those to be discovered in the future. We also discuss the current and near-future capabilities of ROCKE-3D as a community model for studying planetary and exoplanetary atmospheres.

Astrobiology↗
NASA NTRS2019

Near-Infrared Reflectance Spectroscopy of Venus-Analog Rocks at Venus Surface Temperatures

Venus’ surface can be viewed in emission through the relatively opaque atmosphere via a few spectral ‘windows’ in the near-infrared (NIR, most near 1 μm). Venus’ surface appears to show emissivities that correlate with surface geology, and these emissivity variations are interpreted as differences in surface rock type (mafic vs. silicic) and/or extent of weathering (Fe(2+) silicates vs. Fe(3+)-oxide-coated). To understand and quantify the observed variations in NIR emissivity, laboratories are measuring high-T NIR emissivity directly. For example, the measured emissivities of basalts in the wavelength range 0.85 – 1.2 μm are ~0.9. This value can be tested by measurement of reflectance, because Kirchoff’s Law holds that emissivity (e) = 1 – reflectance (r). The r of basalt in the NIR is ~0.1 so its e should be ~0.9. However, high-T NIR e’s of silicic igneous rocks (granitic, rhyolite) are reported to be 0.8-0.9, which is inconsistent with r values of 0.3-0.7 of such rocks at room-T. For both datasets to be correct, the r values of silicic igneous rock would have to decrease precipitously between room and Venus surface temperatures. This seems unlikely.

Treiman, A. H.↗
NASA NTRS2020

Cerium Stable Isotope Analysis of Synthetic and Terrestrial Rock Reference Materials by MC-ICPMS

Cerium is the most abundant rare earth element (REE) in the solar photosphere, CI chondrites, and the Earth. It has four main stable isotopes (masses: 136,138,140, and 142), with 138Ce being the most studied species, used in geochronology and petrogenesis. In addition, more abundant 140Ce and 142Ce are suggested to be potentially applicable in geochemical investigations. In this work, we developed a modified four-step ion chromatography procedure for Ce chemical separation. Using a MC-ICPMS, we designed a cup configuration to measure 142Ce/140Ce ratio of the samples with an optimized Nd correction equation. A 0.03‰ (2SD) reproducibility was obtained for Ce Ames metal standard. We analyzed ten different igneous and one sedimentary geochemical reference materials. Mean δ142Ce range from −0.07 to 0.32‰. Most of the samples show a heavier Ce isotopic composition than the Ce Ames standard. The majority of rocks have a homogenous δ142Ce. The δ142Ce does not show any correlation with rock chemical composition including their Ce content or rock types. A carbonatite (SARM 40) has a mean δ142Ce of −0.07 ± 0.13‰ (2SD), lower than the other rocks, suggesting the possibility of a pronounced isotopic fractionation. Our work demonstrates the applicability of the developed methodology and the potential of Ce stable isotopes for future geochemical studies. Production of a larger database of δ142Ce values is required to obtain a clearer view on the similarities and differences between different geological material and explaining Ce stable isotope dynamics.

Cerium↗
NASA NTRS2004

Intensity-based rock detection for acquiring onboard rover science

Missions to Mars already under study call for very long autonomous traverses (on the order of hundreds of meters per sol) during which there will be limited contact with Earth. The onboard Autonomous Science Investigation System (OASIS) is a technology for increasing science return during rover traverses by prioritizing science opportunities. By prioritizing data for downlink onboard, it is expected that the set of images selected for downlink by OASIS will have a consistently higher scientific interest then any set of equal number of images of the same traverse obtained using random or periodic sampling. Thus, OASIS can be used to increase the science returned from a long traverse. OASIS prioritizes data and identifies science opportunities by extracting information from image data and then using this information to prioritize the data and identify potential new science opportunities. Currently, the information extracted from the images is the location of the rocks in the image and several properties of these rocks such as size, albedo, texture and shape, In this paper we give an overview of the role of rock detection in the OASIS system and describe the functionality of the rock detector. We then present results on representative images

Judd, Michele↗
NASA NTRSDate not supplied

Comparing the Volatile Contents of Basaltic Rocks Through the Inner Solar System

Volatiles in planetary interiors play important roles in magma genesis, crust formation, eruption style, and even habitability of planetary surfaces. Allan Treiman’s career has touched on volatiles in the Moon, Mars, HED-parent body, the Earth, Venus, and other planetary bodies through studies of igneous rocks, volatile-bearing igneous minerals within these rocks, and the secondary alteration products produced from these rocks and minerals. His seminal work in many of these fields has inspired our careers and many others in our field. Here, we will build on and summarize what we know of the volatile content of basaltic rocks in the inner solar system. Specifically, this talk will focus on using volatile-bearing minerals (amphibole and apatite) along with bulk compositions to constrain the pre-eruptive, and potentially predegassed, volatile content of the magma and their source regions. We will then use these estimates to compare the volatile content of the Earth, Moon, Mars, Venus, and Mercury and what open questions there are for each planetary body.

Justin Filiberto↗
NASA NTRSDate not supplied

Impact of Stress-Activated Positive Holes on the Redox Timing in Organisms Living at the Surface of Rocks: Unlocking Nature's Secrets

Squeezing and deforming igneous and/or high-grade metamorphic rocks activates electronic charge carriers known as positive holes, h•, that are defect electrons in the O2– sublattice. Similar to h• in semiconductors the h• in rocks affect electrical and thermal properties. They produce electrochemical reactions, localized electrical signals, and currents. In this study, we explore the effects of positive holes on the electron flow in the electron transport chain (ETC) of organisms living at the surface of rocks such as gabbro or granite. We found that positive holes, h•, disrupt the temporal coordination in vivo governed by oscillating reduction-oxidation reactions, known as the redox cycle. Positive holes affect the timing of the redox cycle by interacting with molecules in vivo, leading to the formation of superoxide anions and hydroxyl radicals. Thus, we observed that positive holes significantly impede the growth of yeast Saccharomyces cerevisiae (i.e., colony size) and delay the sprouting of broccoli and chia seeds. Additionally, positive holes were found to exert discernible impacts on plant development such as stem length and leaf size. Our findings highlight the intricate interplay between positive holes, redox timing, and biological processes, shedding light on the potentially significant role of positive holes in influencing the growth and development of organisms in tectonically stressed rock environments. Understanding these effects has implications for a broader understanding of redox biology and of how environmental factors can influence cellular development in natural settings.

Redox Timing in Organisms↗
DOE OSTI2017

ESTABLISHING ROCK OUTCROP TIME SERIES AT VARIOUS DEPTHS IN A NONLINEAR SOIL COLUMN

Nonlinear soil-structure interaction (NLSSI) analysis methods are currently being developed at Idaho National Laboratory (INL). Appendix B in ASCE 4 (2016) includes a framework for performing NLSSI analysis. For NLSSI analysis to be widely implemented in industry, it is important to demonstrate that accurate response in a dynamically loaded, nonlinear soil column can be produced. In performing NLSSI analysis, one approach is to consider vertically propagating shear and compressive waves that pass through a nonlinear soil column and into a structure. Using finite element techniques, the structure can be placed in a finite volume of nonlinear soil with a rock outcrop seismic time series applied to the bottom of the nonlinear soil. The necessary depth of the nonlinear soil mesh is dependent on the vertical soil stiffness when the model is in static and dynamic equilibrium. Run time, and therefore size of the meshed soil domain, is an important consideration when developing the NLSSI model. An approach is presented in this paper that establishes compatible rock outcrop seismic time series for reduced nonlinear soil mesh depths. To apply the approach, an example is developed using a reasonable soil column with a reasonable top-of-soil response spectrum. The approach is an iterative method which is applied in two steps. The first step is used to establish a reasonable rock outcrop time series at the highest depth considered. The second step is used to establish compatible rock outcrop time series at shallower depths.

42 ENGINEERING↗
DOE OSTI2019

Anisotropic breakage mechanics: From stored energy to yielding in transversely isotropic granular rocks

The microstructure of geological solids is affected by their deposition history, which generates complex systems of grain contacts and damage patterns able to induce mechanical anisotropy. Here this paper aims to disclose the connection between energy storage and the yield surface of cross-anisotropic granular rocks, with the goal to simplify the representation of their mechanical anisotropy. For this purpose, a reformulation of Continuum Breakage Mechanics (CBM) is proposed to introduce material symmetries associated with energy storage processes. It is shown that, due to the thermodynamic consistency of the selected approach, the energy release resulting from comminution is influenced by the anisotropic characteristics of the elastic energy potential. As a result, the model is able to capture naturally and without additional fitting parameters the dependence of the yielding envelope on the relative orientation between bedding planes and loading direction. The performance of the new CBM model has been tested by performing parametric analyses which elucidate the role of cross-anisotropic elastic properties on the yield surface of a granular rock. Furthermore, its accuracy has been assessed against laboratory results available for two sandstones exhibiting dependence of the yield stress on the orientation of the bedding planes. Despite the simplicity of the selected model, the results emphasize that the proposed approach captures the salient features of the deformation response of anisotropic granular rocks, thereby disclosing an intimate connection between grain-scale energy release and cataclastic yielding which greatly simplifies the mathematical description of intrinsic inelastic anisotropy.

58 GEOSCIENCES↗
DOE OSTI2016

Zapping Rocks on Mars

Better understanding Mars means better understanding its geology. That’s why, sitting atop NASA’s Curiosity rover, is ChemCam, an instrument built by Los Alamos National Laboratory that shoots lasers at Martian rocks and analyzes the data. After nearly 1,500 rock zaps, ChemCam has uncovered some surprising facts about the Red Planet, including the discovery of igneous rocks. Soon, a new Los Alamos-built instrument—the SuperCam—will ride aboard the Mars 2020 rover and bring with it enhanced capabilities to unlock new secrets about the planet.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Experimental Investigation of Elastodynamic Nonlinear Response of Dry Intact, Fractured and Saturated Rock

Nonlinear elastodynamic response of fractured rocks carries crucial information on fracture features that can be exploited to forecast flow properties, friction constitutive behavior and poromechanical response. Well-controlled laboratory experiments are designed to measure the nonlinear elastodynamic response of Westerly granite in three states: dry intact, dry fractured and saturated fractured. We study the effect of fracturing and saturation in modifying the elastodynamic response of the rock. Each sample is tested at a normal stress level of 15 MPa. We measure the elastodynamic response of an intact L-shaped sample of Westerly Granite subjected to normal stress oscillations of prescribed amplitudes (0.2–1 MPa) and frequencies (0.1, 1, 10 Hz). Ultrasonic waves transmitted across the sample are used to monitor the evolution of wave velocity before, during and after dynamic stressing. Furthermore, the nonlinearity of the elastodynamic response is measured in terms of: (1) the offset in normalized wave velocity; (2) the amplitude of wave velocity fluctuation during the oscillations; and (3) recovery rate of the wave velocity post-oscillation. We observe that the three nonlinearity parameters show a similar trend. Irrespective of the parameter, the nonlinearity measures higher for sample in dry-intact condition than that for dry-fractured and the saturated-fractured sample exhibits smaller nonlinearity than the dry-fractured sample. As expected, the saturated sample exhibits less nonlinearity than the dry intact and fractured samples due to the presence of interstitial fluid and the resulting increased interface stiffness. Conversely, the dry intact rock shows a higher nonlinearity than the dry fractured. We use numerical simulations to show that the presence of fracture significantly alters the strain distribution across the bulk of the sample and only the contacting asperities are highly strained, thus resulting in a decrease in the measured elastodynamic nonlinearity.

58 GEOSCIENCES↗
DOE OSTI2022

Microscale THMC Modeling of Pressure Solution in Salt Rock: Impacts of Geometry and Temperature

Abstract Pressure solution, a mechanism that involves tight coupling between the geometry and thermal-hydro-mechanical-chemical (THMC) processes, plays an important role in diagenesis. In this study, we make the first attempt to conduct microscale THMC modeling to understand and quantify the impacts of geometry and temperature on pressure solution, taking natural salt rock as an example. This modeling capability is achieved by expanding a novel MC code that we developed previously (Hu et al. J Geophys Res: Solid Earth 126:e2021JB023112, 2021) to include temperature effects. We first conduct a simulation of an example that involves a single brine inclusion within a single halite grain and find that the temperature impact is limited for that case. We then extract geometry from an image of a natural salt rock and conduct simulations with different cases: (A) only temperature and no stress, (B) only stress and no temperature, and (C) with both stress and temperature. These different cases result in quite different phenomena. In case A, dissolution and precipitation occur across the entire system due to isolated pore space reaching a localized mass balance between dissolution, precipitation, and diffusion. In case B, intense geometric features (e.g., major asperities, inclusions) in one area undergo stress concentration, thus dominating pressure solution in that area. In case C, pressure solution is spread out at contacting highly stressed geometric features close to the hotter side. We conclude that geometric features dominate stress distribution, thus dominating pressure solution in a natural salt rock that may be affected by the temperature if a sufficient temperature gradient is applied.

58 GEOSCIENCES↗
DOE OSTI2020

The role of the spatial heterogeneity and correlation length of surface wettability on two-phase flow in a CO 2 -water-rock system

This study characterized and modeled heterogeneous surface wettability in sandstone and investigated the role of spatial heterogeneity and correlation length of surface wettability on relative permeability in a supercritical CO 2 (scCO 2 )-brine-rock system. Understanding the role of wettability heterogeneity on relative permeability is essential to geological CO 2 sequestration, oil and gas recovery, and contaminated groundwater remediation. Although numerous studies have attempted to understand the influences of surface wettability, capillary number (Ca), and viscosity ratio, the role of the spatial variation and correlation length of surface wettability on two-phase flow in three-dimensional (3D) porous media has not been unraveled due to the challenges in the measurement and representation of realistic rock surface wettability. In this work, we conducted in-situ measurements of surface contact angle (CA) in a Bentheimer sandstone after CO 2 flooding using micro-computed tomography (micro-CT), and found that the pore-scale CA distribution on rock surfaces followed a log-normal distribution associated with a spatial correlation length. Based on the statistical information from CT scanning, a Gaussian random field was used to model CA distributions that had desired standard deviations and spatial correlation lengths, which were then adjusted within a certain range of values for sensitivity analyses to study their combined effects on the two-phase flow in the porous medium using the lattice Boltzmann (LB) method. The LB two-phase flow simulation was accelerated using hybrid, multicore parallel computing to overcome the challenges in simulating multiphase flow in a large 3D domain having 800 × 800 × 600 nodes. The simulation results showed that the surface wettability heterogeneity (i.e., standard deviation of CA) had a lesser effect on the relative permeability of the wetting fluid (water) but a more significant impact on the relative permeability of the non-wetting fluid (scCO 2 ). The Corey model was used to fit the LB-simulated relative permeability curves of water and scCO 2 and showed that the variations in the relative permeability curves for both water and scCO 2 increased as the standard deviation and spatial correlation length of CA increased. This study illustrated that the assumption of homogeneous surface wettability may cause errors in multiphase flow simulations. Furthermore, the impacts of both the standard deviation and spatial correlation length of CAs should be accounted for. This is the first study that explored the spatial correlation lengths associated with CA distributions on sandstone surfaces and comprehensively investigated the roles of both spatial variation and correlation length of CA on two-phase flow properties in 3D porous media. The optimized LB multiphase flow model was proved a powerful tool to study the interplays and combined effects of these statistical parameters, which had critical applications in numerous natural and engineering processes that involved multiphase flow in porous media.

58 GEOSCIENCES↗
DOE OSTI2020

Computational thermomechanics for crystalline rock. Part II: Chemo-damage-plasticity and healing in strongly anisotropic polycrystals

We present a thermal–mechanical–chemical-phase field model that captures the multi-physical coupling effects of precipitation creeping, crystal plasticity, anisotropic fracture, and crack healing in polycrystalline rock at various temperature and strain-rate regimes. This model is solved via a fast Fourier transfer solver with an operator-split algorithm to update displacement, temperature and phase field, and chemical concentration incrementally. In nuclear waste disposal in salt formation, brine inside the crystal salt may migrate along the grain boundary and cracks due to the gradient of interfacial energy and pressure. This migration has a significant implication on the permeability evolution, creep deformation, and crack healing within rock salt but is difficult to incorporate implicitly via effective medium theories compared with computational homogenization. As such, we introduce a thermodynamic framework and a corresponding computational implementation that explicitly captures the brine diffusion along the grain boundary and crack at the grain scale. Meanwhile, the anisotropic fracture and healing are captured via a high-order phase field that represents the regularized crack region in which a newly derived non-monotonic driving force is used to capture the fracture and healing due to the solution–precipitation. Numerical examples are presented to demonstrate the capacity of the thermodynamic framework to capture the multiphysics material behaviors of rock salt.

42 ENGINEERING↗
DOE OSTI2017

Mechanical specific energy versus depth of cut in rock cutting and drilling

The relationship between Mechanical Specific Energy (MSE) and the Rate of Penetration (ROP), or equivalently the depth of cut per revolution, provides an important measure for strategizing a drilling operation. This study explores how MSE evolves with depth of cut, and presents a concerted effort that encompasses analytical, computational and experimental approaches. A simple model for the relationship between MSE and cutting depth is first derived with consideration of the wear progression of a circular cutter. This is an extension of Detournay and Defourny's phenomenological cutting model. Wear is modeled as a flat contact area at the bottom of a cutter referred to as a wear flat, and that wear flat in the past is often considered to be fixed during cutting. But during a drilling operation by a full bit that consists of multiple circular cutters, the wear flat length may increase because of various wear mechanisms involved. The wear progression of cutters generally results in reduced efficiency with either increased MSE or decreased ROP. Also, an accurate estimate of removed rock volume is found important for the evaluation of MSE. The derived model is compared with experiment results from a single circular cutter, for cutting soft rock under ambient pressure with actual depth measured through a micrometer, and for cutting high strength rock under high pressure with actual cutting area measured by a confocal microscope. Lastly, the model is employed to interpret the evolution of MSE with depth of cut for a full drilling bit under confining pressure. The general form of equation of the developed model is found to describe well the experiment data and can be applied to interpret the drilling data for a full bit.

42 ENGINEERING↗