Bunger, A.P. (CSIRO Earth Science and Resource Engineering) | Jeffrey, R.G. (CSIRO Earth Science and Resource Engineering) | Kear, J. (CSIRO Earth Science and Resource Engineering) | Zhang, X. (CSIRO Earth Science and Resource Engineering) | Morgan, M. (Newcrest Mining Limited)
Spacings between hydraulic fractures placed during preconditioning of orebodies for cave mining methods and used between stages in horizontal shale gas wells for stimulation continues to be reduced. The question of the effect of the interaction between a new hydraulic fracture and one or more nearby hydraulic fractures is important for both of these applications. Here we present experimental data from both mine-through and laboratory investigations aimed at verifying model predictions of the deflection of the path of a hydraulic fracture that is influenced by a previously placed, propped hydraulic fracture. In one laboratory case, the minimum stress was zero and, consistent with the model prediction, the fracture path curved toward and coalesced with the previously-placed fracture. In another laboratory case and in the mine-through case, the stress, injection, and propping conditions were such that the model predicted that curving could be neglected. This prediction is consistent with both the laboratory and mine-through data, where in the mine-through subparallel fractures were mapped, growing at 1.25 m separation for a distance of over 15 m.
The creation of arrays of closely spaced hydraulic fractures is an emerging technique for stimulation of horizontal wells in unconventional gas reservoirs [1, 2] and for preconditioning orebodies for block/panel caving operations . In the unconventional gas applications, which are now most commonly related to shale gas plays, an array of hydraulic fractures is created from multiple perforation clusters that are placed along a horizontal well. In some cases injection is made into several or all of the perforation clusters at the same time (simultaneous fracturing), while in other cases the perforation clusters are sequentially isolated so that injection proceeds into one cluster at a time (sequential or “zipper” fracturing). The horizontal well is typically drilled sub-parallel to the minimum horizontal stress direction, thus promoting hydraulic fracture growth orthogonal to the wellbore axis. These gas industry fractures are usually driven by water containing friction reducing additives to enable high flow rates through the injection system. In light of the low viscosity fracturing fluid, proppant (typically sand) concentrations in the injected water/sand slurry are typically lower than in conventional hydraulic fracturing, but the rate of injection is usually higher and treatment duration is longer so that the total volume of proppant that is placed can be greater than for conventional hydraulic fractures .
Like their gas industry counterparts, arrays of hydraulic fractures that are created for preconditioning orebodies for block/panel caving operations are typically water driven. However, these fractures are most often unpropped because their eventual conductivity to fluid flow is not a primary consideration and placing proppant increases the operational complexity and costs. Often the hydraulic fractures are placed from uncased cored boreholes using inflatable packers. As in the gas industry applications, boreholes that are sub-parallel to the minimum stress direction are favored because these will experience hydraulic fracture growth that is orthogonal to the wellbore axis, in principle enabling a more closely spaced array and allowing the greatest volume of rock to be treated per borehole.
This paper presents a re-evaluation of a case study of an instrumented test drift in the Kiirunavaara mine. A 20 m long section of the test drift, located at the 514 m level in the Kiirunavaara mine, was instrumented in 1983, with the objective of studying the interaction of grouted rock bolts and hard rock masses subjected to changes in stresses induced by mining. During the test a large rock wedge was observed in the footwall side of the drift. Borehole extensometers, distometers, telescopic tube extensometers and rockbolts with strain gauges recorded the movement of the rock mass during the whole field measurement time. However, the actual failure process of the large wedge was not addressed in the original study. In this paper, this case was re-evaluated with the aim of increasing knowledge regarding of failure process of a large wedge in terms of deformation. A global-local numerical modeling approach was employed to reproduce the in situ conditions using the finite element program Phase2 and Universal Distinct Element Code (UDEC) software. The global approach was used to calculate the stresses induced during sublevel caving in the mine. The stresses from the global model were applied to the local model which simulated the test drift behavior, and in which geological structures were explicitly modeled. The deformation experienced by the rock mass due to the wedge in the drift was calculated in the local model and compared to the measured deformation in the field. The field measurement results showed that a small fallout occurred close to the large wedge. The small fallout acted as initiator of the large wedge movement. The numerical modeling results showed that the large wedge did not fall out. The large wedge was characterized by shear displacements.
1.1. Problem description
Rock wedges are formed by the intersection of discontinuities in a jointed rock mass and the free surface of the opening. The wedges are volumes of rock that may fall or slide into the opening. In underground excavations with wedges falling from the roof and/or sliding from the sidewalls the consequences are significant. Sudden sliding or fallout of large wedges may injure people and cause property damage, safety hazards, and interrupt the tunneling and mining activities. Therefore, the failure process of a wedge should be assessed to understand the stability of the construction, and thus to improve the design and performance of underground excavations in jointed rock. The work presented in this paper is part of a research project concerned with Eurocode 7: Geotechnical designs . Based on geotechnical design rock behavior with acceptable limits should be established to assess the stability of a construction. A section of a test drift in the Kiirunavaara mine was instrumented in 1980 to study the interaction of grouted rock bolts and the hard rock mass subjected to mininginduced stresses. During the test a large wedge was observed in the footwall side of the test drift. Instrumentation located near the wedge recorded the movement of the rock mass.
Kim, H.M. (Korea Institute of Geoscience and Mineral Resources (KIGAM)) | Rutqvist, J. (Lawrence Berkeley National Laboratory (LBNL)) | Ryu, D.W. (Korea Institute of Geoscience and Mineral Resources (KIGAM)) | Synn, J.H. (Korea Institute of Geoscience and Mineral Resources (KIGAM)) | Song, W.K. (Korea Institute of Geoscience and Mineral Resources (KIGAM))
We carried out a numerical modeling study of coupled thermodynamic, multiphase fluid flow and geomechanical processes associated with underground compressed air energy storage (CAES) in lined rock caverns. The simulation results showed that a concrete lining with a permeability of 1.0x10-18 m2 could reduce air leakage to an acceptable leakage rate of less than 1% using an operational pressure range between 5 and 8 MPa at a depth of 100 m. It was also noted that initial saturation of the lining was very important, and air leakage could be effectively prevented when the lining is kept at a high moisture content. The geomechanical simulation results showed that substantial tensile stress may develop in the concrete lining, which could lead to the formation of radial fractures and increased air leakage. However, our analysis indicated that even if such fracturing would occur, the magnitude of air leakage may be insignificant, if the surrounding rock is sufficiently tight.
With the worldwide demand for wind and solar power generation, as well as for a ‘Smart Grid’ modernization movement, large-scale energy-storage technologies are attracting increasing attention. This is because renewable energy sources of wind and solar have an intermittent nature—they cannot steadily provide power, subject as they are to daily cycles and weather conditions. Thus, energy storage is critical to making renewable energy more practical. Along with pumped hydroelectric storage, compressed air energy storage (CAES) can be one of the most promising large-scale electric energy storage technologies. CAES systems convert surplus electricity into compressed air, store the compressed air in an underground cavern, and then utilize the stored compressed air in generating electricity at the time of demand (Figure 1). The first commercial CAES projects were a 290 MW unit built in Huntorf, Germany in 1978, and a 110 MW unit built in McIntosh, Alabama in 1991. Recently, plans have been made for construction of a 2700 MW plant in Norton, Ohio. Solution-mined caverns in salt rock were used for compressed air storage in first two cases, and an abandoned limestone mine cavern is planned to be used at the Norton site . Usually, the storage facility for CAES is located in the subsurface, for safety and economic reasons. The principal requirements for any underground rock caverns used in CAES include air tightness, stability, and acceptable surface subsidence. These requirements are subject to geomechanical design parameters, such as cavern geometry and volume, cavern depth, operational pressure of cavern, groundwater table level, as well as other parameters such as strength, permeability, and degree of saturation of concrete lining and surrounding rock mass. Existing commercial underground CAES systems are located in solution-mined salt caverns, whereas pilot tests have been conducted in old mined rock caverns in Japan [2, 3]. These facilities were constructed at deep depths, from 200 to 500 m, in order to have relatively high surrounding groundwater pressure and thereby prevent stored air from leaking. However, underground lined rock caverns reinforced by concrete linings and steel plates can be located at a shallow depth, provide more flexibility in site selection for CAES, and consequently reduce construction costs.
Fully coupled, 3d discontinuum, hydromechanical simulation is becoming more commonplace for mine based and oil and gas geotechnical problems. The focus of simulation for the two industries overlaps, but is balanced differently; mining focuses more often on deformation and damage and has opportunities for calibration at a high resolution, while oil and gas simulation often focuses more on aspects of the fluid and gas flow but has more opportunities for calibration of the fluid simulation. As both industries share similar rock and hydro mechanical problems, as far as the governing physics is concerned, rapid improvement across the fields may come from collaboration between the industries and potentially, as computing power makes multi-scale hydromechanical simulation more common, from shared tools. It does not make sense to use separate solution procedures and develop parallel technologies when the capacity and sufficiency requirements are converging As a numerical experiment, an existing explicit Finite Element, discontinuum tool used in non-linear analysis for open pit slope and underground hydromechanical problems was modified to allow simulation of additional phases and used to simulate fluid extraction and injection for multiple wells across a faulted, folded and expansive multi-layered oul and gas deposit. This reflects an attempt at such a process by mining researchers; a reciprocal technology transfer to mining from oil and gas is of course the essential task for mutually beneficial collaboration. The simulation of hydrological aspects of the mining problems shown as examples already benefits from the oil and gas industry, by way of the particular hydromechanical functionality of the FE tool used which has been developed mostly for oil and gas problems. The example model results were then interpreted using the direct measures frequently employed for mine simulations: plastic strain for damage, vertical movement for subsidence and dissipated plastic energy for seismic potential. The main benefit is that the closely calibrated and refined small scale rock mass behavior derived from the mining analysis might allow some similitude benefits for the oil and gas problem.
Displacement realistic, non-linear, fully coupled, hydro mechanical (HM) simulation is at the leading edge of simulation for the mining and oil and gas industries but is undertaken regularly. Commercial Finite Element (FE) and Finite Difference packages, including some discontinuum tools are now available, or are HM ready for problem solution using 3rd party and in-house constitutive frameworks. There are a sufficient number of packages that are HM ready that the specific brands and applications need not be listed. The effort involved in developing a sufficient constitutive framework for these problems is a significant expert task, but has yielded important benefits for several operations. The main effort for this area of simulation in both industries is generally different. Oil and gas HM simulation is more often focused on resource recovery and less frequently focused on deformation though this is a significant, important and well servived field. Mining simulation is almost entirely undertaken to estimate aspects of stability, but managing water is a main consideration for safe and sustainable mining. At this time, HM simulation for mining is a niche at the high end for simulation projects, even though it is now specified as the minimum standard of analysis for critical decisions in many mines.
Surface deformations generated as a result of oil production, waste or water reinjection can be applied to model reservoir deformations. This is referred to as inverse modeling. Inverse models presented in the literature are mostly based on the nucleus of strain approach, and apply one deformation data type (i.e., vertical displacements) as input. In this study, a new numerical model was developed based on the unidirectional deformation technique. In order to solve the inverse ill-posed problem, a regularization technique was developed. The main objective of this research was to study the effects of monitoring strategies on inverse simulation by applying combinations of surface deformation measurements as input. A detailed sensitivity analysis was therefore performed in order to optimize the data collection procedure. The sensitivity of the inverse simulation was examined based on the following parameters: observation area; geometry and number of benchmarks; and measurement error. The results indicated that adding benchmarks after a certain number did not significantly affect the simulation. The distribution pattern of benchmark points was also found to significantly affect the inverse simulation.
Ground surface deformations generated as a result of fluid/material injection or withdrawal, into or from the subsurface are easy to monitor and sensitive to subsurface pressure changes [1, 2, 3]. Induced surface deformation data can therefore be used to indirectly monitor subsurface deformations. This approach has considerable potential use in fast-paced projects, where continuous monitoring of reservoir deformation is vital: steam injection/steam-assisted gravity drainage, where the objective of screening is to monitor steam concentration zones in the subsurface; waste injection projects, in order to track and model induced deformations and fracture movements; general reservoir monitoring and optimization, where the objective is to monitor the behaviour of the reservoir with respect to production and reinjection processes. Applying surface deformation measurements in order to model subsurface deformation sources is referred to as solving for the inverse case. Direct and inverse models have been previously studied and reported on in the literature [4, 5, 6, 7, 8, 9, 10, 11, 12]. Previous studies on inverse modeling in the hydrocarbon industry are mostly based on the nucleus of strain approach , where subsurface deformation sources are simulated as point sources that expand or compact in all directions, representing expansion or compaction (e.g. [6, 10, 14, 15]). Most inverse simulations are developed based on one type of deformation data (i.e. vertical displacement measurements). Very few studies have focused on inverse simulation based on different combinations of surface displacement measurements (i.e., vertical displacements/tilt measurements) . It has been revealed that tilt measurements are more appropriate for inverse modeling compared to vertical displacements . The main focus of this paper was therefore, to numerically study the effect of the data collection procedure on reservoir inverse simulation, using combinations of surface tilt measurements.
Sands in the Gulf of Mexico (GoM) are in general highly compressible. In this paper we develop methods to predict compressibility in the GoM from parameters derivable from logs. . All the compressibility data are corrected for creep using the method of step and hold tests presented in an earlier paper. Attempts to use log data to predict formation compressibility have met with limited success. Correlations between compressibility and individual variables such as age, temperature, or depth have significant limitations. This effort has centered on the two primary variables that impact compressibility: velocity and porosity. The following examples are methods used to correlate various rock property variables with easily measured geologic properties. Although many of these methods are commonly used to estimate compressibility, the cross plot of static compressibility, velocity, and porosity provides the most accurate correlation. In this paper we develop such a cross plot and relate it to physically justified parameters.
PREDICTION OF GOM PROPERTIES AT INSITU STRESS
In Fig. (1) we show a general overview of measurements performed for GOM sediments. They span a range of over almost two orders of magnitude in pore volume compressibility. The sands generally show an initially increasing compressibility with increasing stress. Thinsection studies show that the grain cracking and ductile deformation is the dominant mechanism responsible for this initial increase. Post the peak in compressibility grain rearrangement and sliding cause a more rigid framework to form which causes the compressibility to decrease.
DEPENDENCE OF VELOCITY ON POROSITY
In Fig. 2 we show the stress velocity with stress in these samples with the velocity increasing with decreasing porosity as expected. The velocity is show a linear dependence with porosity for these data within experimental error. This may be a key understanding as to what the curvature means in more lithified rocks. We will use this dependence as a key parameter in determining compressibility in the GOM porosity dependence for the samples in Fig. 1. compressibility
Cross plot of Static Compressibility, Velocity, and Porosity
We therefore show the regression formed to predict Cm the uniaxial compaction coefficient from compressional velocity and porosity in Figure 4. This cross plot has the advantages of the previous regressions combined. Here we regress the velocity to a functional form which at least has physical. When the porosity approaches 20% the compressibility approaches a physically realistic value of a 2.0 μ sips. When the velocity approaches 7000 ft/sec the compressibility diverges as the sands approach the properties of a suspension.
DEPENDENCE OF VELOCITY ON COMPRESSIBILITY
It is common to attempt to predict the static compressibility from velocity. A plots velocity versus compressibility is shown Fig. 3. We see that there is a correlation between the velocity and compressibility but it is not very robust. There is obviously more to the story.
This work investigates the opening of two fractures symmetrically located at the edge of a wellbore in a shale formation subjected to a uniform wellbore pressure and remote anisotropic in-situ stresses. Detailed fracture opening profiles (fracture aperture) for various values of in-situ stresses and fracture length to wellbore radius ratios are obtained using a finite element method. An approximate, closed-form solution for the crack mouth opening displacement (CMOD) with the fracture surfaces subjected to either the wellbore pressure or pore pressure is derived based on a dimensional analysis and the superposition principle of linear elastic fracture mechanics. It is found that the closed form, approximate CMOD solutions agree well with the finite element results for the fracture length to the wellbore radius ratio in the range of L/R = 1 to 4, and for the maximum to minimum in-situ stress ratio in the range of SH/Sh = 1 to 2.
The mud-weight window serves as a critical design factor for the design of both the well and drilling fluid system. It defines the range between the minimum weight to avoid well collapse (compressive failure) and the maximum mud weight to avoid formation breakdown (tensile fracturing). The mud-weight window may be very narrow under certain conditions, thereby requiring expensive design changes or rendering drilling impractical.
A common example is drilling through a depleted producing formation, where pore pressures have dropped since the start of production and the formation total stresses have decreased. At the same time, the neighboring shale layers may have maintained their pore pressure. As a result, the difference between the minimum mud weight required in the shales to prevent collapse and the maximum mud weight in the depleted interval to prevent formation breakdown and lost circulation may be insufficient for the drilling operation. In such cases, the wellbore strengthening technique is one that has been employed to increase the breakdown limit of the depleted formation and allow the well to be drilled safely and economically [1-4].
Knowledge of opening of fractures at a wellbore edge is the key information required for selecting the appropriate wellbore strengthening material blends and suitable concentration in wellbore stability applications. Alberty and McLean proposed a simple empirical formula for fracture aperture based on the line crack solution which does not take the wellbore-fracture interaction and anisotropy of in-situ stresses into account . They also performed a finite element analysis (FEA) of fracture aperture and found that their empirical solution agrees with the FEA results under near-isotropic remote in-situ stresses but the empirical fracture aperture is significantly smaller than their FEA result under anisotropic remote in-situ stresses. Moreover, the line crack solution will lead to significant errors when the fracture length compares to wellbore radius. The purposes of the present work are to perform a detailed finite element analysis for two fractures symmetrically located at the edge of a wellbore subjected to anisotropic remote in-situ stresses (Fig. 1) and to develop an approximate closed-form solution of crack mouth opening displacement (CMOD) based on linear elastic fracture mechanics. The fractures are in the direction of the maximum remote stress. The fracture surfaces are subjected to either the wellbore pressure or the pore pressure.
McGuire, T.P. (Department of Energy and Mineral Engineering and G3 Center, Pennsylvannia State University) | Elsworth, D. (Department of Energy and Mineral Engineering and G3 Center, Pennsylvannia State University) | Karcz, Z. (ExxonMobil Upstream Research Company: Stratigraphic and Reservoir Systems Division)
We explore how fracture permeability in confined carbonates evolves due to flow of reactive fluids. Core plugs the Capitan Massive Limestone are saw-cut to form a consider axial fracture that is subsequently roughened to simulate a natural fracture with controlled topography. Either distilled water or 0.176M NH4Cl solutions are circulated while initial fracture roughness, influent fluid pH, and confining stresses are controlled. Throughout the experiment we measure the fluid flow rate and chemical composition of the effluent fluid. The cubic law is used to infer the retreat or advance rate of the fracture walls from the evolution of permeability. By taking measurements in regimes of both increasing and decreasing permeability we quantitatively constrain the transition between fracture-gaping and fracture-closing modes of behavior. We parameterize this transition using the ratio of mechanically-to-chemically-controlled dissolved mass fluxes and compare it to the effective hydraulic aperture velocity. The transition value of unity for the mass flux ratio logically coincides with a predicted net effective hydraulic aperture velocity that asymptotes to zero. These results offer a first opportunity of constraining the transition between stress-dominated and dissolution-dominated mechanisms of permeability evolution for stress-sensitive fractures.
Prediction of fracture permeability evolution during reactive fluid flow is becoming increasingly important with the development of tight (<10-17 m2)  carbonate reservoirs. These predictions commonly require complex calculations that take into account the rates of free-face dissolution [2-9], precipitation [4,6], and pressure solution . The relative rates of these processes and their extent exert a key control of whether fracture permeability decreases [2,3,5,7-9] or increases [4,6] through time. Models the integrate mechanical, chemical, and fluid dynamics aspects of flow through reservoir-scale fractures may yield good predictions, but are extremely taxing computationally . Simplified models can be used to simulate larger fracture domains and networks but often overlook important factors such as effects of fracture effective stress [2,3,6-8]. Dimensionless parameters such as the Damkohler number [3,5,6,9] and the peclet number [2-8], have been used to represent the evolution of reactive flow through fractures. However, focusing on chemical effects may neglect important influences of mechanically mediated dissolution-the focus of this work here we explore the complex interaction of chemical and mechanical processes in prescribing fracture hydraulics by measuring permeability evolution in fractured samples, where fracture roughness, fluid reactivity, and confining stress are independently monitored.
2. EXPERIMENTAL METHODS
We report on flow-through experiments on artificially fracture cylindrical plugs (1”diameter and 2” long) of Capitan Massive Limestone (CML), a massive vuggy limestone. The artificial fracture is a saw-cut fracture is a saw cut that was subsequently roughened with either a “rough” 60 grit ceramic (average grain size of 423 μm) or a “fine” 150 grit ceramic (average grain size of 169 μm). The initial effective permeabilities of the fractured plugs was ~174mD and ~4.0 mD respectively and the matrix permeability was << 1mD. Fractured plugs are placed between two stainless steel end platens faced with flow distributors within a flow-through apparatus capable of applying constant pressure differential across the sample.
A new method is proposed for locating free methane accumulation sites. The basis for this method is the concept of change in the stressed state of coal seam in the process of its mining, as well as volume density of fractures filled with gas and elastic properties of fractured zones. Repeated seismic soundings of the seam allow us to reveal such unstable sections by disturbances of wave travel times. The calculated relations and results of numerical experiments carried out with the use of transversally isotropic model for the fractured zones of coal seam are presented. The areas of variation in parameters of seismic-wave velocity anisotropy are determined applying a tomographic approach.
The modern history of underground coal mining in Russia shows an increased hazard of disastrous methane outbursts, which is associated with bringing deeper levels into production. As a consequence, gas content of producing seams, mechanical stresses acting in them, as well as degree and rate of their technogenic changes increased.
It is known that the sites of gas dynamic phenomena are inherent in the fractured zones of geological dislocations. They form permeable channels which can connect a coal seam with fractured-cavernous methane traps at the underlying levels of mine field [1, 2]. A possibility to accumulate considerable reserves of gas in such traps  is explained by its generation by scattered organic matter in sedimentary rocks . In the fractured zones, coal is in disintegrated state and begins avalanche-like failing when methane outburst is high-volume and transient. This creates conditions for gas-and-dust mixture explosion .
The detection of small fractured zones by exploratory boreholes is random in character. Thus, in the Karaganda coal basin, approximately 75% of dislocations comparable in amplitude to the seam thickness are unexpectedly revealed in performing preparatory work .
Surface seismic methods are not sensitive to small anisotropic inclusions in the geological medium. The arrangement of sources and receivers in the coal seam ensures higher resolution. The seam is sounded by seismic waves at small distances. In a number of methods, the scattered and reflected components of wave field are used. Sources and receivers are arranged closely to each other, which makes it possible to apply a set of simple models (such as a homogeneous medium, unit dislocation, etc.) instead of a complex inhomogeneous model for the extended area of the seam. The correspondence between the medium area under investigation and the concrete model is established by dynamic characteristics of waves with complex polarization . Unfortunately, the employment of such signs is not always possible for the following reasons:
This research study investigates the cracking processes associated with inclusion pairs of varying shape, orientation and inclusion materials. Specifically, this study summarizes a series of uniaxial compression tests on gypsum specimens with varying inclusion pair configurations. The inclusions consisted of differing materials, of contrasting Young’s Modulus (higher and lower than the matrix), shapes (hexagon, diamond, ellipse), and relative pair orientations (bridging angle). Similar cracking sequences were seen in the newly introduced inclusion pairs as in previous studies. Slightly increased debonding (usually corresponding to increased interface shearing) occurred as inclusion pairs with inclined interfaces were introduced. Coalescence behavior trended from indirect or no coalescence, to direct shear coalescence, to combined direct tensile-shear coalescence as the inclusion bridging angle was increased, similar to past studies on circular and square inclusion pairs and flaw pairs. Also, the coalescence related to inclusion interface inclination and bridging angles resembled the actual coalescence of flaw pairs with similar inclination and bridging angles.
The cracking processes in a brittle material consisting of a matrix with inclusions are important mechanisms for both natural materials (rocks) as well as synthetic composite materials (e.g. concrete). There have been many past studies regarding the cracking processes in brittle materials, which contain pre-existing cracks (called flaws) both analytically [1, 2], as well as experimentally [2, 3, 4]. Also, the cracking processes in brittle materials, which contain inclusions have been studied both analytically [6, 7, 8] and experimentally [7, 9, 10, 11, 12]. Only recently have experiments been performed with the technology capable of capturing high speed imagery to fully describe the crack propagation and coalescence behavior in a brittle material. The majority of the previous research performed on brittle materials with inclusions investigated the fracturing patterns associated with circular or rectangular (square) inclusions. The present research was conducted to develop a more detailed description of the coalescence patterns of uniaxially loaded gypsum specimens with inclusion pairs of varying shape, stiffness and orientation. Emphasis was placed on the coalescence behavior associated with the effects of varying these inclusion pair configurations.
2. PREVIOUS STUDIES
2.1 Flaw Coalescence Studies Amongst the many experimental studies regarding flaws in brittle materials, experimental work done by Wong and Einstein  is particularly significant because it incorporated the use of a high speed camera to follow crack propagation and coalescence. One of the most important contributions of Wong and Einstein’s study was a proposed set of coalescence categories for different co-planar and stepped flaw pairs (Figure 2.1). These coalescence patterns will later serve as a basis for comparing the coalescence patterns seen in brittle materials containing inclusions pairs.
2.2 Inclusion Coalescence Studies Extending on the macro-scale flaw testing techniques used in the Massachusetts Institute of Technology (MIT) Rock Mechanics Laboratory, brittle material with inclusions was investigated with high speed imagery by Janeiro and Einstein . That study tested 1” single square, circle, diamond, and hexagon inclusion shapes as well as 1/2" circular and square inclusions with varying inclusion material stiffness (Figure 2.2).