Increasing Fracture Density Research Articles

Aspects and origins of fractured dip-domain boundaries in folded carbonate rocks

We present comparative field studies in folded areas (Southern France, Moroccan Western Atlas and Abruzzo, Italy) giving new insights into fracture distribution within folded rocks of the shallow brittle crust. We show that the curvature in folds formed in brittle mechanical units is usually accommodated by multiple “dip-domain boundaries” (appearing as curvature discontinuities at fold scale) corresponding to relatively narrow and dense fracture zones, striking parallel or slightly oblique to the fold axis. They separate “dip-domains” where curvature is absent or moderate. It is shown that the dip-domain boundaries (which are obvious in the case of kink folds or box-fold anticlines) are currently present as multiple subtle hinges even when the curvature appears continuous at first sight. The nature of dip-domain boundaries is studied: they often cut through the whole thickness of the mechanical units. Their internal structure varies, and a non-exhaustive typology is proposed. For each type, an interpretative kinematic scenario shows how the dip-domain boundaries could initiate and develop. We suggest two kinds of origins: (1) they could correspond to the reactivation of inherited, along-strike fracture zones (opening-mode fracture concentrations such as big joints, fracture corridors, inherited faults, etc.); (2) they could be created as mechanical instabilities during the fold formation (syn-folding origin), in particular through small reverse faults. In both cases, early zones of weakness localize the dip-domain boundaries, and control the increase in curvature in association with increasing fracture density within the boundary. Because they represent well-defined vertically and axially persistent sub-seismic fracture zones generally limited to the thickness of the folded unit, dip-domain boundaries could enhance the axial permeability of folded and fractured reservoirs.

Dyke emplacement in fractured media: application to the 2000 intrusion at Izu islands, Japan

SUMMARY We use a boundary element approach to study the problem of a large, magma-filled dyke embedded in a fractured, damaged medium. The numerical simulations show that the dyke opening and the crack extension force at the dyke tip increases with increasing fracture density. We show that this behaviour can at moderate fracture densities be predicted by an effective media model. Simple analytical formulae are given for the increasing average opening of the dyke and the decreasing fracture toughness as functions of increasing fracture density. The numerical and the theoretical results are found to be in good agreement. In a first application we tested the model by using GPS deformation and seismicity data from a recent lateral magma intrusion in Izu islands, Japan. This shows that a simple comparison of the distance change and the cumulative earthquake number enables the study of the stability of the dyke intrusion. The method seems to distinguish whether the dyke opening is actively driven by magma influx or passively driven by an expansion due to fracturing.

Geomechanical Properties of Shear Zones in the Eastern Aar Massif, Switzerland and their Implication on Tunnelling

¶Rock zones containing a high fracture density and/or soft, low cohesion materials can be highly problematic when encountered during tunnel excavation. For example in the eastern Aar massif of central Switzerland, experiences during the construction of the Gotthard highway tunnel showed that heavily fractured areas within shear zones were responsible for overbreaks in the form of chimneys several metres in height. To understand and estimate the impact of the shear zones on rock mass behaviour, knowledge concerning the rock mass strength and deformation characteristics is fundamental. A series of laboratory triaxial tests, performed on samples from granite- and gneiss-hosted shear zones revealed that with increasing degree of tectonic overprint, sample strength decreases and rock behaviour shows a transition from brittle to ductile deformation. These trends may be explained by increasing fracture densities, increasing foliation intensity, increasing thickness of fine-grained, low cohesion fracture infill, and increasing mica content associated with the increasing degree of tectonic overprint. As fracture density increases and the influence of discrete, persistent discontinuities on rock mass strength decreases, behaviour of the test samples becomes more and more representative of rock mass behaviour, i.e. that of a densely fractured continuum. For the purpose of numerical modeling calculations, the shear zones may be subdivided with respect to an increasing fracture density, foliation intensity and mica content into a strongly foliated zone, a fractured zone and a cohesionless zone, which in turn exhibit brittle, brittle-ductile and ductile rock mass constitutive behaviour, respectively.

Power‐law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport

Velocity distributions in two‐ and three‐dimensional networks of discrete fractures are studied through numerical simulations. The distribution of 1/v, where v is the velocity along particle trajectories, is closely approximated by a power law (Pareto) distribution over a wide range of velocities. For the conditions studied, the power law exponents are in the range 1.1–1.8, and generally increase with increasing fracture density. The same is true for the quantity 1/bv, which is related to retention properties of the rock; b is the fracture half‐aperture. Using a stochastic Lagrangian methodology and statistical limit theorems applicable to power‐law variables, it is shown that the distributions of residence times for conservative and reacting tracers are related to one‐sided stable distributions. These results are incompatible with the classical advection dispersion equation and underscore the need for alternative modeling approaches.

Evaluation of instability in fractured rock masses using numerical analysis methods: Effects of fracture geometry and loading direction

Numerical modeling, using two‐dimensional distinct element methods, is used to examine the effect of stress on the stability of a fractured rock mass. The critical stress state depends on the differential stress, mean stress, and fluid pressure and is represented by a surface which bounds all stable stress states. By examining the critical stress states under different loading conditions it is possible to define the stability/instability in terms of the far‐field differential stress and effective mean stress. Thus the strength of fractured rock can be represented by a macroscopic frictional component (μz) and a cohesion (Cz), which differ from the corresponding parameters for individual fractures. A series of simulations are used to examine the effects of fracture network geometry, such as fracture density, fracture length, and fracture network anisotropy, on the instability strength. A steady decrease in equivalent frictional strength (μe) with increasing fracture density was found. For the same fracture density, rock masses with fewer, but larger, fractures had lower instability strength. As networks became more anisotropic, the orientation of the fractures in relation to the loading direction had a considerable impact on the instability strength and deformation pattern. The effects of loading direction in relation to fracture set orientation have been examined for two fracture networks with different anisotropy coefficients. Where the directions of the principal stresses were parallel to the fracture sets, extensional deformation was observed. Otherwise, dilational shear deformation modes develop, within which sliding, opening, and block rotation occur.

Interaction between normal faults and fractures and fault scarp morphology

Fault slip and geomorphic surface processes create and modify bedrock normal fault scarps. Our field studies and numerical models show that mechanical interaction between near‐surface fractures and active faults may diminish scarp slopes and broaden deformation near the surface. In our models, increasing fracture density and depth reduces and complicates the scarp's topographic expression. Fracture depth and density, and orientation of the structures control the location and magnitude of zones of positive and negative shear displacements along the fractures. Our field studies of the interaction of active graben bounding normal faults and fractures in Northern Arizona illustrate the mechanical analysis. Reduction in scarp slopes and broadening of the deformation field may cause incorrect interpretations of shallow bedrock scarp morphologies as old, rather than as the result of slip along fractures around the fault.

Numerical study of critical behaviour of deformation and permeability of fractured rock masses

The connectivity of fractures in rock masses is determined using a numerical simulation method. There is a continuous fracture cluster throughout a fractured rock mass if fracture density ( d) is at or above a threshold fracture density d c , Fractal dimension ( D f ) is used to describe the connectivity and compactness of the largest fracture clusters. D f increases with increasing fracture density. Percolation theory is used to determine the universal law, D f = A f ( d− d c ) f, which describes the critical behaviour of connectivity of fractures in rock masses. The results from numerical modeling show that the deformability of fractured rock masses increases greatly with increasing fracture density (i.e., fractal dimension), and the critical behaviour of deformability can be described by B s = A( d− d f ) s. Also, the overall permeability of a fractured rock mass occurs at or above a critical fracture density ( d c ) and increases with increasing fracture density. The critical behaviour of permeability can be described by q = A p ( d− d c ) p. The critical behaviour of connectivity and permeability of naturally fractured rock masses is examined using the universal forms.

P‐to‐S conversion for a thin anisotropic zone produced by vertical fracturing

Point‐source synthetic seismic responses for a thin, fractured bed are generated, interpreted and processed. The synthesis is carried out for a compressional source and multicomponent surface receivers. The anisotropy considered has hexagonal symmetry, with a horizontal symmetry axis, and represents oil‐ and gas‐filled, aligned vertical fractures for a broad range of fracture densities and aspect ratios. P‐to‐S reflected conversions recorded on the horizontal geophones show both kinematic and dynamic anomalies that increase with increasing fracture density and are only weakly dependent on aspect ratio. In contrast, the vertical component P‐wave reflections provide a much poorer diagnostic of fracturing. Analytic expressions for the eigenvalues and eigenvectors of a vertically fractured system are presented, that have the same simplicity as those for transverse isotropy. New linearized expressions for mode‐converted amplitudes are developed for small angles of incidence and are used to interpret the synthetic response.

Gel formation by main-chain fracture of long-chain polymers

The conditions are examined under which the fracture of main-chain bonds in a long-chain polymer, which would normally result in a decrease in average molecular weight, can nevertheless result in formation of a network of infinite extent (gel). It is assumed that the two end-groups produced at a fractured site can attack neighbouring molecules, and link them ­ selves to them. For an initially random distribution it is shown that gel formation will first occur when one molecule in three is thus fractured. The sol fraction is found to equal ( i /3 r ) 2 , where r/i is the average number of fractures per molecule; with increasing fracture density the sol therefore tends to zero. Where only a proportion of the fractures result in linking, the sol fraction decreases to a limiting value. Expressions are derived for many of the parameters of the sol and gel fractions and for the swelling. The results obtained are compared with those for crosslinking of polymers with a similar molecular weight distribution. To distinguish the process considered in this paper from that usually referred to as crosslinking, the term endlinking is proposed.