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Modeling fracture in geomaterials is essential to the understanding of many physical phenomenon which may posses natural hazards e.g. landslides, faults and iceberg calving or man-made processes e.g. hydraulic fracture and excavations. Continuum Damage Mechanics (CDM) models the crack as a solid region with a degraded stiffness. This continuum definition of cracks in CDM allows more feasible coupling with other forms of material non-linearity and eliminates the need to track complicated crack geometry. Using CDM to analyze fracture for the modeling of fracture in geomaterials encounters several challenges e.g.: 1) the need to model the multiple physical processes occurring in geomaterials, typically: coupled fluid flow and solid deformation, 2) the need to consider non-local damage and transport in order to capture the underlying long range interactions and achieve mesh-independent finite element solutions and 3) the elevated computational cost associated with non-linear mixed finite element formulations. The research presented in this thesis aims at improving the CDM formulations for modeling fracture geomaterials. This research can be divided into three main parts. The first is the introduction of a novel non-local damage transport formulation for modeling fracture in poroelastic media. The mathematical basis of the formulation are derived from thermodynamic equilibrium that considers non-local processes and homogenization principles. The non-local damage transport model leads to two additional regularization equations, one for non-local damage and the other for non-local transport which is reduced to non-local permeability. We consider two options for the implementation of the derived non-local transport damage model. The first option is the four-field formulation which extends the (u/P) formulation widely used in poroelasticity to include the non-local damage and transport phenomena. The second option is the three-field formulation, which is based on the coupling of the regularization equations under the assumptions of similar damage and permeability length scales and similar driving local stress/strain for the evolution of the damage and permeability. The three-field formulation is computationally cheaper but it degrades the physical modeling capabilities of the model. For each of these formulations, a non-linear mixed-finite element solution is developed and the Jacobian matrix is derived analytically. The developed formulations are used in the analysis of hydraulic fracture and consolidation examples. In the second part, a novel approach for CDM modeling of hydraulic fracture of glaciers is pretended. The presence of water-filled crevasses is known to increase the penetration depth of crevasses and this has been hypothesized to play an important role controlling iceberg calving rate. Here, we develop a continuum damage-based poro-mechanics formulation that enables the simulation of water-filled basal and/or surface crevasse propagation. The formulation incorporates a scalar isotropic damage variable into a Maxwell-type viscoelastic constitutive model for glacial ice and the effect of the water pressure on fracture propagation using the concept of effective solid stress. We illustrate the model by simulating quasi-static hydro-fracture in idealized rectangular slabs of ice in contact with the ocean. Our results indicate that water-filled basal crevasses only propagate when the water pressure is sufficiently large and that the interaction between simultaneously propagating water-filled surface and basal crevasses can have a mutually positive influence leading to deeper crevasse propagation which can critically affect glacial stability. In the third part, we propose a coupled Boundary Element Method (BEM) and Finite Element Method (FEM) for modeling localized damage growth in structures. BEM offers the flexibility of modeling large domains efficiently while the nonlinear damage growth is accurately accounted by a local FEM mesh. An integral-type nonlocal continuum damage mechanics with adapting FEM mesh is used to model multiple damage zones and follow their propagation in the structure. Strong form coupling, BEM hosted, is achieved using Lagrange multipliers. Since the non-linearity is isolated in the FEM part of the system of equations, the system size is reduced using Schur complement approach, then, the solution is obtained by a monolithic Newton method that is used to solve both domains simultaneously. The method is applied to multiple fractures growth benchmark problems and shows good agreement with the literature.

It has been shown by Neuman [1990], Di Federico and Neuman [1997, 1998a,b] and Di Federico et al. [1999] that observed multiscale behaviors of subsurface fluid flow and transport variables can be explained within the context of a unified stochastic framework, which views hydraulic conductivity as a random fractal characterized by a power variogram. Any such random fractal field is statistically nonhomogeneous but possesses homogeneous spatial increments. When the field is statistically isotropic, it is associated with a power variogram γ(s) = Cs²ᴴ where C is a constant, s is separation distance, and If is a Hurst coefficient (0 < H< 1). If the field is Gaussian it constitutes fractional Brownian motion (fBm). The authors have shown that the power variogram of a statistically isotropic or anisotropic fractal field can be constructed as a weighted integral from zero to infinity of exponential or Gaussian vario grams of overlapping, homogeneous random fields (modes) having mutually uncorrelated increments and variance proportional to a power 2H of the integral (spatial correlation) scale. Low- and high-frequency cutoffs are related to length scales of the sampling window (domain) and data support (sample volume), respectively. Intermediate cutoffs account for lacunarity due to gaps in the multiscale hierarchy, created by a hiatus of modes associated with discrete ranges of scales. In this dissertation, I investigate the effects of domain and support scales on the multiscale properties of random fractal fields characterized by a power variogram using real and synthetic data. Neuman [1994] and Di Federico and Neuman [1997] have concluded empirically, on the basis of hydraulic conductivity data from many sites, that a finite window of length-scale L filters out (truncates) all modes having integral scales λ larger than λ = μL where μ ≃ 1/3. I confii in their finding computationally by generating truncated fBm realizations on a large grid, using various initial values of μ, and demonstrating that μ ≃ 1/3 for windows smaller than the original grid. My synthetic experiments also show that generating an fl3m realization on a finite grid using a truncated power variogram yields sample variograms that are more consistent with theory than those obtained when the realization is generated using a power variogram. Interpreting sample data from such a realization using wavelet analysis yields more reliable estimates of the Hurst coefficient than those obtained when one employs variogram analysis. Di Federico et al. [1997] developed expressions for the equivalent hydraulic conductivity of a box-shaped support volume, embedded in a log-hydraulic conductivity field characterized by a power variogram, under the action of a mean uniform hydraulic gradient. I demonstrate that their expression and empirically derived value of μ ≃ 1/3 are consistent with a pronounced permeability scale effect observed in unsaturated fractured tuff at the Apache Leap Research Site (ALRS) near Superior, Arizona. I then investigate the compatibility of single-hole air permeability data, obtained at the ALRS on a nominal support scale of about 1 m, with various scaling models including fBm, fGn (fractional Gaussian noise), fLm (fractional Lévy motion), bfLm (bounded fractional Lévy motion) and UM (Universal Multifractals). I find that the data have a Lévy-like distribution at small lags but become Gaussian as the lag increases (corresponding to bfLm). Though this implies multiple scaling, it is not consistent with the UM model, which considers a unique distribution. If one nevertheless applies a UM model to the data, one obtains a very small codimension which suggests that multiple scaling is of minor consequence (applying the UM model to permeability rather than log-permeability data yields a larger codimension but is otherwise not consistent with these data). Variogram and resealed range analyses of the log-permeability data yield comparable estimates of the Hurst coefficient. Resealed range analysis shows that the data are not compatible with an fGn model. I conclude that the data are represented most closely by a truncated fBm model.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Sciences, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND LINDGREN. / Vita. / Bibliography: leaves 164-168. / by Teng-Fong Wong. / Ph.D.

This experimental investigation was conducted to assess the effect of zero point of charge (ZPC) environment on fracture behavior of rocks. The material parameters selected for this purpose were fracture toughness and specific work of fracture. These properties were determined for three rock types in five environments. Semi-circular bend specimens of dolomitic limestone, Sioux quartzite and Westerly granite were tested in aqueous solutions of aluminum chloride, calcium chloride and polyethylene oxide, all at ZPC conditions. These rocks were also tested in atmospheric air and distilled deionized water. For every rock type, the results obtained for the tests done in each of the ZPC environment were statistically compared with the results in water. This comparison was also made for air and water. The average fracture toughness in each of the ZPC environments, for all three rock types, was found to be less than the corresponding average in water. The specific work of fracture results also indicated reduction in ZPC environments as compared to water. The statistical analysis of the results, however, showed that this reduction was significant in some but not all of the rock-environment combinations tested in this investigation. / Master of Science

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Fire-cracked rock is often overlooked in archaeology. This study attempted to determine whether or not fire-cracked rock from the surface of an archaeological site located in a cultivated field can be differentiated from other cracked rocks. A study sample of 67 rocks from the surface of a prehistoric site located in a cultivated field and another study sample of 58 rocks from an adjacent area that was sterile of prehistoric human activities was collected. A third sample of 70 fire-cracked rocks excavated from features below the plowzone in a prehistoric site served as a control sample. The fracture surface morphologies of the control sample were examined for distinguishing characteristics, which were then compared to the study samples. Those cracked rocks from the study samples which exhibited similar characteristics were identified as fire-cracked rock. Ten fire-cracked rocks were thus observed within the on-site sample and the offsite sample included only one. / Department of Anthropology

This is an analysis of fractures occurring within the Paloezoic sedimentary rocks in a portion of southeastern Indiana. Fifteen hundred seventy-two fractures were used in analysis of distribution, orientation, pervasiveness, persistence, and intensity. The data collected is representative of eight counties and seventeen different collection sites.All fracture data were given an associated numerical value identifying each variable used for analysis and recorded into computer data files. A computer program was used for statistical analysis and construction of equal area nets which graphically displayed the distribution of variables. The compilation of the fracture data allowed for close interpretative analyses of variables and correlation of the orientation and distribution of the fractures within the study area.This study revealed that two orthogonal fracture systems exist in southeastern Indiana. The fracture set containing the largest percentage of those measured is oriented N11W with its compliment oriented N73W. The orientation of the second largest fracture set is N8E with its compliment oriented N82°W.The effects of the tectonic history as well as contemporary stress on the area are discussed relative to their effects on the overall distribution of fracture sets.Evidence is presented to substantiate a reactivation of the Cincinnati Arch as indicated in the Devonian-Mississippian lithologic units from data collected in the southeastern portion of the study area. Fracture data correlating to these units displays a rotation of the major fracture set maxima 90w. This data is supported by radiometric dates from the Belfast member of the Brassfield Limestone in which Laskouski, et.al., correlated a reactivation of the arch.Also within this study are lithologic descriptions of all the Paleozoic formations used for data collection. These descriptions were developed over a three year period from extensive field observation.A map of the study area is presented displaying the distribution and orientation of the fractures recorded at each data collection site. / Department of Geology

La caractérisation de l'agencement spatial des propriétés hydrauliques est essentielle pour prédire les écoulements et le transport des solutés dans les milieux hétérogènes. Les méthodes de tomographie hydraulique, principalement développées pour estimer les propriétés des milieux poreux, n'ont qu'une faible résolution spatiale qui ne reflète pas la vraie hétérogénéité des distributions de fractures des milieux fracturés. Le principal objectif de cette thèse est de développer une nouvelle méthode d'inversion spécifique pour imager les propriétés hydrauliques et de transport des milieux fracturés à l'échelle du site. Pour atteindre ces objectifs, des expériences in situ ainsi qu'une nouvelle approche de modélisation inverse sont proposées, notamment en utilisant la température comme marqueur des écoulements. Nous proposons tout d'abord la tomographie d'écoulement basée sur des tests séquentiels de débimétrie entre puits, comme une nouvelle approche pour caractériser la connectivité des fractures ainsi que leur transmissivité. À partir de simulations numériques reproduisant des cas d'études synthétiques, nous montrons que l'approche par tomographie réduit significativement l'incertitude sur les paramètres estimés, et fournit une caractérisation détaillée du réseau de fracture sans requérir à l'utilisation d'obturateurs hydrauliques. Nous montrons ensuite comment les mesures de température peuvent être utilisées pour quantifier les écoulements dans les milieux fracturés. Le grand intérêt d'utiliser la température est d'obtenir facilement et de façon continue en puits des profils de température. En utilisant un modèle numérique d'écoulement et de transfert de chaleur à l'échelle du puits, une méthode d'inversion pour estimer les vitesses d'écoulement dans le puits à partir des données de température est proposée. Nous couplons ensuite les deux approches présentées précédemment dans une nouvelle approche expérimentale consistant en des enregistrements séquentiels de température dans un puits dans des conditions de pompage entre puits. L'application de cette approche de tomographie en température sur le site de Stang er Brune montre des résultats encourageants pour l'identification du réseau global de connectivité et des zones d'écoulement principales. Enfin, nous discutons de l'intérêt d'utiliser la chaleur comme traceur par rapport à l'utilisation de traceurs classiques. Nous montrons que réaliser des tests de traçage thermiques en milieu fracturé fournit des contraintes supplémentaires importantes sur les propriétés de transport du milieu. / The accurate characterization of distribution of hydraulic properties and connectivity distribution is essential to predict flow and transport in fractured media. Classical approaches were developed for homogeneous aquifers and result in smooth tomograms that often do not match true heterogeneity distribution of fractured media. The main goal of this thesis is to develop new inverse approaches specifically for imaging hydraulic and transport properties in fractured media at the field-scale. To attain this objective new in situ measurement methods as well as new inverse modelling frameworks are proposed.We first propose flow tomography (i.e., sequential cross-borehole flowmeter tests) as a new approach for characterizing fracture connectivity and transmissivities. Based on a discrete fracture network approach, we present a general method to invert flow tomography data. From synthetic case studies, we show that the tomographic approach reduces significantly the uncertainty on the parameter estimation. Flow tomography approach provides detailed characterization on fracture networks without the necessity of using packers. We then study the contribution of temperature measurements for quantifying flow in fractured media. The advantage of using temperature data is that temperature profiles can be obtained more easily and continuously in space, compared to flowmeter profiles. Using a numerical model of flow and heat transfer at the borehole scale, a method to invert temperature measurements to derive borehole flow velocities was proposed. We then couple the two previously proposed approaches in a new experimental approach which we call temperature tomography. This experiment consists of sequential borehole temperature logging under cross-borehole flow conditions. The full inverse framework is then presented to interpret temperature tomography experiments. Application of the temperature tomography approach to Stang er Brune field site showed encouraging results for the identification of general connectivity patterns and transmissivities of the main flowpaths. Finally, we explore the interest of using push-pull thermal tracer tests. Through field experiments and numerical modelling, we demonstrate that conducting push-pull heat tracer tests provide important constraints on the effective transport behavior.