dimensional threshold for fracture linkage and hooking fracture connectivity in rocks depends on spatial properties of the pattern including length abundance and orientation when fractures form a single strike set they hardly cross cut each other and the connectivity is limited linkage probability increases with increasing fracture abundance and length as small fractures connect to each other to form longer ones a process for parallel fracture linkage is the hooking where two converging fracture tips mutually deviate and then converge to connect due to the interaction of their crack tip stresses quantifying the processes and conditions for fracture linkage in single strike fracture sets is crucial to better predicting fluid flow in naturally fractured reservoirs for 1734 fractures in permian shales of the lodeve basin se france we measured geometrical parameters in 2d characterizing three stages of the hooking process underlapping overlapping and linkage we deciphered the threshold values shape ratios and limiting conditions to switch from one stage to another one the hook set up depends on the spacing s and fracture length lh with the relation s 0 15 lh once the hooking is initiated with the fracture deviation length l l 0 4 lh the fractures reaches the linkage stage only when the spacing is reduced to s 0 02 lh and the convergence c is 0 1 l these conditions apply to multi scale fractures with a shape ratio l s 10 and for fracture curvature of 10 20

hydraulic sealing due to pressure solution contact zone growth in siliciclastic rock fractures thermo hydro mechanical chemical simulations at the pore scale are conducted to study the hydraulic sealing of siliciclastic rock fractures as contact zones grow driven by pressure dissolution the evolving fluid saturated three dimensional pore space of the fracture results from the elastic contact between self affine randomly rough surfaces in response to the effective confining pressure a diffusion reaction equation controls pressure solution over contact zones as a function of their emergent geometry and stress variations results show that three coupled processes govern the evolution of the fracture s hydraulic properties 1 the dissolution driven convergence of the opposing fracture walls acts to compact the pore space 2 the growth of contact zones reduces the elastic compression of the pore space and 3 the growth of contact zones leads to flow channeling and the presence of stagnant zones in the flow field the dominant early time compaction mechanism is the elastic compression of the fracture void space but this eventually becomes overshadowed by the irreversible process of pressure dissolution growing contact zones isolate void space and cause an increasing disproportion between average and hydraulic aperture this results in the loss of hydraulic conductivity when the mean aperture is a third of its initial value and the contact ratio approaches the characteristic value of one half convergence rates depend on small wavelength roughness initially and on long wavelength roughness in the late time the assumption of a characteristic roughness length scale therefore leads to a characteristic time scale with an underestimation of dissolution rates before and an overestimation thereafter

estimating flow heterogeneity in natural fracture systems abstract examples of small to medium scale fault systems have been mapped in jurassic sedimentary rocks in north somerset england these examples include contractional and dilational strike slip oversteps as well as normal faults these maps form the basis of calculations performed to investigate heterogeneity in natural fracture systems with the aim of predicting fluid flow localisation in different fault styles as there is no way to measure fracture aperture directly we use vein thickness to represent an integrated flow path or palaeo aperture from which we derive a representation of the flow distribution three different methods are used to estimate flow heterogeneity based on 1 fracture density the ratio of fracture length to area 2 fracture aperture fracture porosity and 3 hydraulic conductance fracture permeability normalised to the pressure gradient and fluid properties our results show that fracture density and hydraulic conductance are poorly correlated and that fracture density does not fully represent the natural heterogeneity of fracture systems fracture aperture and hydraulic conductance indicate stronger degrees of flow localisation different types of structures also seem to display characteristic and predictable patterns of heterogeneity normal fault systems show the highest magnitude of localisation along the faults rather than in the relay ramps while contractional and dilational strike slip systems show very strong localisation in the faults and oversteps respectively in all cases the amount of damage in the oversteps can modify such patterns of heterogeneity

multiscale fracture network characterization and impact on flow a case study on the latemar carbonate platform a fracture network arrangement is quantified across an isolated carbonate platform from outcrop and aerial imagery to address its impact on fluid flow the network is described in terms of fracture density orientation and length distribution parameters of particular interest is the role of fracture cross connections and abutments on the effective permeability hence the flow simulations explicitly account for network topology by adopting discrete fracture and matrix description the interior of the latemar carbonate platform dolomites italy is taken as outcrop analogue for subsurface reservoirs of isolated carbonate build ups that exhibit a fracture dominated permeability new is our dual strategy to describe the fracture network both as deterministic and stochastic based inputs for flow simulations the fracture geometries are captured explicitly and form a multiscale data set by integration of interpretations from outcrops airborne imagery and lidar the deterministic network descriptions form the basis for descriptive rules that are diagnostic of the complex natural fracture arrangement the fracture networks exhibit a variable degree of multitier hierarchies with smaller sized fractures abutting against larger fractures under both right and oblique angles the influence of network topology on connectivity is quantified using discrete fracture single phase fluid flow simulations the simulation results show that the effective permeability for the fracture and matrix ensemble can be 50 to 400 times higher than the matrix permeability of 1 0 10 14 m2 the permeability enhancement is strongly controlled by the connectivity of the fracture network therefore the degree of intersecting and abutting fractures should be captured from outcrops with accuracy to be of value as analogue

connectivity permeability and channeling in randomly distributed and kinematically defined discrete fracture network models a major use of dfn models for industrial applications is to evaluate permeability and flow structure in hardrock aquifers from geological observations of fracture networks the relationship between the statistical fracture density distributions and permeability has been extensively studied but there has been little interest in the spatial structure of dfn models which is generally assumed to be spatially random i e poisson in this paper we compare the predictions of poisson dfns to new dfn models where fractures result from a growth process defined by simplified kinematic rules for nucleation growth and fracture arrest davy et al 2010 2013 this so called kinematic fracture model is characterized by a large proportion of t intersections and a smaller number of intersections per fracture several kinematic models were tested and compared with poisson dfn models with the same density length and orientation distributions connectivity permeability and flow distribution were calculated for 3d networks with a self similar power law fracture length distribution for the same statistical properties in orientation and density the permeability is systematically and significantly smaller by a factor of 1 5 to 10 for kinematic than for poisson models in both cases the permeability is well described by a linear relationship with the areal density p32 but the threshold of kinematic models is 50 larger than of poisson models flow channeling is also enhanced in kinematic dfn models this analysis demonstrates the importance of choosing an appropriate dfn organization for predicting flow properties from fracture network parameters

three dimensional characterization of a fractured granite and transport properties a three dimensional fracture network in a granite block is reconstructed from a series of experimental serial sections it is visualized and its most important geometrical characteristics are studied namely the orientation of the fractures the connectivity of the fractures the number of cycles per unit volume the distributions of surface areas and of the intersection lengths and the number of finite solid blocks isolated in the solid matrix by the network though the network mostly consists of two families of fractures it is interesting to note that a simple model of randomly oriented monodisperse hexagons often yields a good order of magnitude for the various geometrical properties which have been measured on the real block the flow properties are then studied examples of velocity field are provided as well as histograms of velocities the permeability tensor is determined and is found to be in good agreement with snow s formula finally dispersion is analyzed by means of a random walk method histograms of arrival times are provided and interpreted in terms of dispersion tensor

formation and interpretation of dilatant echelon cracks the relative displacements of the walls of many veins joints and dikes demonstrate that these structures are dilatant cracks we infer that dilatant cracks propagate in a principal stress plane normal to the maximum tensile or least compressive stress arrays of echelon crack segments appear to emerge from the peripheries of some dilatant cracks breakdown of a parent crack into an echelon array may be initiated by a spatial or temporal rotation of the remote principal stresses about an axis parallel to the crack propagation direction near the parent crack tip a rotation of the local principal stresses is induced in the same sense but not necessarily through the same angle incipient echelon cracks form at the parent crack tip normal to the local maximum tensile stress further longitudinal growth along surfaces that twist about axes parallel to the propagation direction realigns each echelon crack into a remote principal stress plane the walls of these twisted cracks may be idealized as helicoidal surfaces an array of helicoidal cracks sweeps out less surface area than one parent crack twisting through the same angle thus many echelon cracks grow from a single parent because the work done in creating the array as measured by its surface area decreases as the number of cracks increases in cross sections perpendicular to the propagation direction echelon cracks grow laterally each crack overlapping its neighbors until the mechanical interaction of adjacent cracks limits this growth dilation of each crack pinches the tips of adjacent cracks into an asymmetrical form and introduces local stresses that can cause lateral growth along a curving sigmoidal path sigmoidal echelon cracks may link at tip to plane intersections leaving a step in the through going crack wall the geometry of dilatant echelon cracks may be used to infer spatial or temporal changes in the orientation of principal stresses in the earth

stress effects on permeability in a fractured rock mass with correlated fracture length and aperture the effect of stress on permeability and fluid flow patterns in fractured rock masses is studied when distributed fracture aperture is correlated with fracture trace length using a discrete elemen

the initiation and growth of en echelon veins abstract numerical models are used to understand the evolution of mode i opening fractures from spatially random distributions in a brittle elastic material en echelon arrays commonly develop because mechanical fracture interaction promotes growth for this geometry this provides a new mechanism for en echelon vein formation in rock which is distinctly different than previously proposed mechanisms it is suggested that some macroscopic en echelon vein arrays may have served as zones of weakness that localized later shear zone development in a manner analogous to that observed by experimentalists examining micro cracking and subsequent shear rupture of rocks loaded under compression sigmoidally shaped veins and vein fillings are explicitly modeled showing that they can form in response to the mechanical interaction of neighboring fractures which redirects the propagation path numerical comparison of sigmoidal veins formed by brittle fracture and by ductile shear zones demonstrates some of the pitfalls of failing to correctly identify the mechanism of formation

the control of stress history and flaw distribution on the evolution of polygonal fracture networks abstract we use boundary element models of fracture propagation and linkage to investigate the factors controlling the development of two dimensional multi directional polygonal fracture networks characterised by a large number of abutting intersections between fractures the position and orientation of a number of fracture seeds are prescribed in the model which propagate when the applied stress reaches a critical value according to linear elastic fracture mechanics theory the applied boundary condition is a remote isotropic horizontal tension where the stress is increased at a steady rate throughout each model to simulate continued fracture growth realistic polygonal systems are developed with the boundary element model simulations which are comparable with those observed in natural systems such as those found within eocene and oligocene mudrocks in the north sea and on the surface of mars if conditions exist where a small number of fracture seeds propagate and develop significant structures before others then these will dominate the resulting fracture network geometry not only do such early structures represent the largest fractures in the system they also significantly modify the stress field around them preventing some other seeds from developing and influencing the propagation paths of nearby fractures fracture seeding distribution and the rate at which the stress is increased are found to be the most significant parameters affecting the development of fracture network geometry these results suggest that the geometry of evolving fracture networks should be considered not only in terms of the mechanical properties of the deforming material but also in terms of the stress rate driving deformation

hydrologic issues associated with nuclear waste repositories significant progress in hydrology especially in subsurface flow and solute transport has been made over the last 35 years because of sustained interest in underground nuclear waste repositories the present paper provides an overview of the key hydrologic issues involved and to highlight advances in their understanding and treatment because of these efforts the focus is not on the development of radioactive waste repositories and their safety assessment but instead on the advances in hydrologic science that have emerged from such studies work and results associated with three rock types which are being considered to host the repositories are reviewed with a different emphasis for each rock type the first rock type is fractured crystalline rock for which the discussion will be mainly on flow and transport in saturated fractured rock the second rock type is unsaturated tuff for which the emphasis will be on flow from the shallow subsurface through the unsaturated zone to the repository the third rock type is clay rich formations whose permeability is very low in an undisturbed state in this case the emphasis will be on hydrologic issues that arise from mechanical and thermal disturbances i e on the relevant coupled thermo hydro mechanical processes the extensive research results especially those from multiyear large scale underground research laboratory investigations represent a rich body of information and data that can form the basis for further development in the related areas of hydrologic research

measurement and characterisation of spatial distributions of fractures abstract a variety of line sample 1 d and map 2 d datasets of faults and joints has been used to investigate the spatial distributions of fractures and to test techniques of fractal analysis the natural fracture datasets have been supplemented by synthetic datasets with known characteristics the fault datasets investigated range in scale from regional to outcrop and the joint datasets are derived from outcrop 1 d datasets were analysed by the spacing population interval counting and fracture number interval counting techniques 2 d datasets were analysed by box counting and fracture number box counting techniques results indicate that fracture spacing can be characterised in line samples using either the 1 d interval counting technique or more simply by measuring the spacing population as the cumulative frequency distribution of spaces between adjacent fractures tectonic faults frequently show a power law spacing population indicating fractal dimensions of between 0 4 and 1 0 but except for outcrop data truncation effects degrade the analysis unrefined joint datasets commonly show negative exponential or lognormal spacing cumulative frequency distributions however single orientation joint sets are characterised by a regular spacing and are therefore non fractal for both fault and joint map data box counting techniques do not yield the power law relationship between box size and the number of boxes that is expected of fractal geometries it is concluded that 2 d box counting techniques are too insensitive to characterise the many different parameters of a fracture array the fracture density technique appears not to discriminate between very different fracture patterns and therefore does not provide useful results a fracture pattern incorporates several attributes e g size distribution orientation linkage density roughness each of which may scale independently and each of which may be fractal with its own fractal dimension full characterisation of fracture patterns will therefore require independent analysis of each of these attributes

measurement of rock fracture toughness under modes i and ii and mixed mode conditions by using disc type specimens rock fracture mechanics has been widely applied to blasting hydraulic fracturing mechanical fragmentation rock slope analysis geophysics earthquake mechanics hot dry rock geothermal energy extraction and many other practical problems but a standard method to accurately determine fracture toughness of rocks one of the most important parameters in fracture mechanics as an intrinsic property of rock has not been yet well established to obtain rock fracture toughness disc type specimens were used in this study rock fracture toughness under mixed mode conditions was measured by using the straight through crack assumption stca applied to the cracked chevron notched brazilian disc ccnbd specimen and the semicircular bend scb specimen size effects in terms of specimen thickness diameter and notch length on fracture toughness were investigated from the mixed mode test results fracture envelopes were obtained by applying various regression curves the mixed mode test results were also compared with the three well known mixed mode failure criteria

numerical simulation of fracture set formation a fracture mechanics model consistent with experimental observations a physically based model for the evolution of a single set of planar parallel fractures subject to a constant remote stress is presented the model simulates the mechanical interaction between fractures using a recently developed approximation technique for stress analysis in elastic solids with many fractures a comparison between experimental and numerical results shows that the model can accurately simulate the development of experimentally generated fracture sets once the flaw geometry is specified only one parameter controls the geometric evolution of the fracture set this parameter the velocity exponent relates fracture propagation velocity to stress concentration at the fracture tip monte carlo sensitivity analyses suggest that this parameter also controls the extent to which fracture growth is concentrated within zones or clusters similar analyses suggest that the extent of fracture clustering is less sensitive to the flaw density

inferring paleostresses from natural fracture patterns a new method we introduce a method to infer the remote differential stress magnitude from the curvature of overlapping echelon fracture traces the curving paths of overlapping echelon cracks imply the predominance of local crack induced stresses over remote stresses during propagation nearly straight crack paths imply the controlling influence of a remote compressive crack parallel differential stress this method is used to interpret complex joint patterns mapped in sedimentary rock it is also applied to the problem of fracture pattern generation using computer models

volatile contents of obsidian clasts in tephra from the taupo volcanic zone new zealand implications to eruptive processes obsidian clasts in 6500 20 000 year old rhyolitic tephra deposits from the taupo volcanic zone new zealand contain variable h2o 0 2 2 5 wt and ci 0 12 0 18 wt contents these are elevated compared to degassed obsidian from rhyolitic domes 0 1 wt h2o2 0 1 wt cl which quenched at the surface major and trace element compositions of obsidian from tephra deposits suggest that they are co genetic with associated pumice the clear glassy appearance of the obsidian their high h2o release temperatures and 18o of 7 show that the water is magmatic and was not absorbed into the obsidian after tephra deposition based on analysis of melt inclusions recent primary taupo volcanic zone rhyolitic magmas contain 4 3 wt h2o and 0 18 wt cl the obsidian in the tephra deposits therefore represents partially degassed quenched primary magma water and cl contents correlate in the obsidian suggesting that the magmatic cl partitioned into a h2o rich fluid phase during eruptive degassing the partitioning of cl between the water rich vapor phase and the residual magma can be modelled as open system rayleigh fractionation using a pre eruptive h2o content of 4 3 wt and burnham s 1979 water solubility model the pressure and depth of initial vesiculation of the taupo magma is calculated to occur at about 0 9 kbar or 3 5 km depth initial fragmentation assumed to occur at a vapor melt ratio of 3 1 began at 0 1 kbar or 500 m depth obsidian in most tephra deposits contains less than 1 wt h2o and are calculated to have formed at 0 1 kbar or 500 m depth therefore some obsidian in these tephra deposits may have formed from fragmented magma the variable water contents of obsidian fragments in a single deposit indicates that quenching occurred over a range of depths this and the strong alignment of microphenocrysts in obsidian suggests that fragmented magma was welded onto the conduit walls during eruption cooled to form obsidian then incorporated into the tephra the 2000 year old hatepe phreatoplinian tephra contains many obsidian fragments with 2 wt h2o the meteoric water which caused this eruption to be phreatomagmatic may have caused obsidian to quench at unusually great depths resulting in higher h2o contents

orientation of late precambrian sutures in the arabian nubian shield recent tectonic models have resulted in conflicting descriptions of how the late precambrian sutures of the arabian nubian shield extend into northeast africa the hamisana shear zone in northeastern sudan is critical to this discussion because it truncates and disrupts two sutures the allagi heiani and the onib sol harried analysis of field structural data thematic mapper imagery and rb sr and u pb geochronology suggests that the allagi heiani suture is the western extension of the onib sol harried suture and that both make up the exposed parts of a far traveled polydeformed ophiolitic nappe complex subsequent deformation localized in the hamisana shear zone disrupted this nappe and displaced the suture between 660 and 550 ma during regional deformation associated with the najd fault system these results indicate that at least one suture extends westward into the interior of northern africa

the impact of in situ stress and outcrop based fracture geometry on hydraulic aperture and upscaled permeability in fractured reservoirs abstract aperture has a controlling impact on porosity and permeability and is a source of uncertainty in modeling of naturally fractured reservoirs this uncertainty results from difficulties in accurately quantifying aperture in the subsurface and from a limited fundamental understanding of the mechanical and diagenetic processes that control aperture in the absence of cement bridges and high pore pressure fractures in the subsurface are generally considered to be closed however experimental work outcrop analyses and subsurface data show that some fractures remain open and that aperture varies even along a single fracture however most fracture flow models consider constant apertures for fractures we create a stress dependent heterogeneous aperture by combining finite element modeling of discrete fracture networks with an empirical aperture model using a modeling approach that considers fractures explicitly we quantify equivalent permeability i e combined matrix and stress dependent fracture flow fracture networks extracted from a large outcropping pavement form the basis of these models the results show that the angle between fracture strike and 1 has a controlling impact on aperture and permeability where hydraulic opening is maximum for an angle of 15 at this angle the fracture experiences a minor amount of shear displacement that allows the fracture to remain open even when fluid pressure is lower than the local normal stress averaging the heterogeneous aperture to scale up permeability probably results in an underestimation of flow indicating the need to incorporate full aperture distributions rather than simplified aperture models in reservoir scale flow models

stochastic simulation of radionuclide migration in discretely fractured rock near the aspo hard rock laboratory we study the migration of sorbing tracers through crystalline rock by combining relatively simple transport measures with particle tracking in a discrete fracture network the rock volume is on a 1

formation and growth of extensional fracture sets naturally occurring extension fractures including some joints and veins form sets consisting of numerous subparallel fractures each with well defined ends in order to correctly interpret these fractures in the field it is necessary to determine which factors control the geometries of fracture sets this requires consideration of the conditions leading to both the initiation and the cessation of fracture propagation a fracture begins to propagate when the crack extension force reaches a critical value which is a property of the rock and of environmental conditions after propagation initiates the crack extension force varies owing to 1 increase in crack length 2 change in remote strain 3 elastic interaction with nearby cracks 4 change in internal fluid pressure and 5 stress relaxation due to growth of cracks in the surrounding rock each fracture continues to propagate as long as its crack extension force exceeds the critical value and terminates when this condition is no longer met neglecting fluid effects the final geometry of the fracture set is a function of the remote strain history and the initial crack geometry which can be characterized by the initial crack density for low initial densities large increases in crack length occur with little or no increase in remote strain however for large initial densities crack lengths increase only if the applied strain increases this analysis is used to estimate the variation in remote strain during formation of a fracture set in granitic rock from observations of the final fracture geometry

a model of fracture nucleation growth and arrest and consequences for fracture density and scaling 1 in order to improve discrete fracture network dfn models which are increasingly required into groundwater and rock mechanics applications we propose a new dfn modeling based on the evolution of fracture network formation nucleation growth and arrest with simplified mechanical rules the central idea of the model relies on the mechanical role played by large fractures in stopping the growth of smaller ones the modeling framework combines in a time wise approach fracture nucleation growth and arrest it yields two main regimes below a certain critical scale the density distribution of fracture sizes is a power law with a scaling exponent directly derived from the growth law and nuclei properties above the critical scale a quasi universal self similar regime establishes with a self similar scaling the density term of the dense regime is related to the details of arrest rule and to the orientation distribution of the fractures the dfn model so defined is fully consistent with field cases former studied unlike more usual stochastic dfn models ours is based on a simplified description of fracture interactions which eventually reproduces the multiscale self similar fracture size distribution often observed and reported in the literature the model is a potential significant step forward for further applications to groundwater flow and rock mechanical issues

a three dimensional model to simulate jointnetworks in layered rocks modelling the discontinuity network of fractured reservoirs may be addressed 1 by purely stochastic means 2 with a fractal approach or 3 using mechanical parameters describing the spatial organisation of fracture systems our paper presents an approach where the geometrical properties of the fracture networks are incorporated in the form of both statistical and mechanical rules this type of approach is particularly suitable to model stratified fractured rock masses comprising two orthogonal families of joints and a family of sedimentary discontinuities their geometrical arrangement is governed by two kinds of rules based on 1 statistical parameters such as the mean standard deviation of joint length and of bed thickness both determined by field observations and 2 geometrical parameters that result from genetic processes inferred from field observations and analogue experiments on the nucleation and propagation mechanisms of joints using these parameters we generate realistic networks in