Factors controlling normal fault offset in an ideal brittle layer (original) (raw)
Related papers
Journal of Structural Geology, 2003
The influence in space and time of viscous layers on the deformation pattern of brittle layers is investigated using wet clay/silicone putty analogue models in extension. Brittle and brittle-viscous experiments at various extension velocities are compared. Numerical models are also performed to confirm the results and to control the boundary conditions. Our results show that: (i) the presence of a basal viscous layer localizes the deformation by creating faults with very large throw. This kind of deformation distribution constrains the location of small faults, with scattered orientations, in the vicinity of the larger, in particular in relay zones. (ii) A lower strength of the viscous layer (i.e. a low extension velocity) enhances this localization of the deformation. (iii) The displacement -length relationship and the spatial distribution of small-scale faults are strongly influenced by both the rheology of the model and the amount of extension. This study shows that they are important parameters, especially when characterizing the whole fault network evolution and the relationship between large and small faults. q
On strike‐slip faulting in layered media
Geophysical Journal …, 2002
We study the effects of structural inhomogeneities on the stress and displacement fields induced by strike-slip faults in layered media. An elastic medium is considered, made up of an upper layer bounded by a free surface and welded to a lower half-space characterized by different elastic parameters. Shear cracks with assigned stress drop are employed as mathematical models of strike-slip faults, which are assumed to be vertical and planar. If the crack is entirely embedded within the lower medium (case A), a Cauchy-kernel integral equation is obtained, which is solved by employing an expansion of the dislocation density in Chebyshev polynomials. If the crack is within the lower medium but it terminates at the interface (case B), a generalized Cauchy singularity appears in the integral kernel. This singularity affects the singular behaviour of the dislocation density at the crack tip touching the interface. Finally, the case of a crack crossing the interface is considered (case C). The crack is split into two interacting sections, each placed in a homogeneous medium and both open at the interface. Two coupled generalized Cauchy equations are obtained and solved for the dislocation density distribution of each crack section. An asymptotic study near the intersection between the crack and the interface shows that the dislocation densities for each crack section are bounded at the interface, where a jump discontinuity is present. As a corollary, the stress drop must be discontinuous at the interface, with a jump proportional to the rigidity contrast between the adjoining media. This finding is shown to have important implications for the development of geometrical complexities within transform fault zones: planar strike-slip faults cutting across layer discontinuities with arbitrary stress drop values are shown to be admissible only if the interface between different layers becomes unwelded during the earthquake at the crack/interface junction. Planar strike-slip faulting may take place only in mature transform zones, where a repetitive earthquake cycle has already developed, if the rheology is perfectly elastic. Otherwise, the fault cannot be planar: we infer that strike-slip faulting at depth is plausibly accompanied by en-echelon surface breaks in a shallow sedimentary layer (where the stress drop is lower than prescribed by the discontinuity condition), while ductile deformation (or steady sliding) at depth may be accommodated by multiple fault branching or by antithetic faulting in the upper brittle layer (endowed with lower rigidity but higher stress).
Tectonophysics, 2010
The mechanical coupling between brittle and ductile layers in the continental lithosphere produces rheological contrasts, which are supposed to trigger localized or distributed mode of faulting. A plane-strain 2D finite-element model is used to highlight the mechanical role of the brittle-ductile coupling in defining the patterns of fracturing. The coupling is performed through the shortening of a Von Mises elastoviscoplastic layer rimmed by two ductile layers behaving as Newtonian incompressible fluids. By varying the viscosity of the ductile layers or the amount of softening in the brittle layer, the fracturing mode evolves from localized to distributed. The mechanics of brittle-ductile coupling is explained by the limitation of the fault displacement rate imposed by both brittle and ductile rheologies. On these bases, an analytical approach is presented in order to estimate the maximum velocity along each fault permitted by both brittle and ductile media. This velocity is then compared to the velocity required by the boundary shortening rate. If the velocity in the fault is not large enough, the development of new faults is necessary. From this analysis, we define four fracturing modes in a brittle-ductile media: the localized mode with the onset of a few large faults, the distributed mode with very dense fault patterns, and finally, the ductile-control mode and the brittle-control mode, where the number of faults increases with an increase in the ductile viscosity and a decrease in the brittle softening respectively.
A dynamic model for fault nucleation and propagation in a mechanically layered section
Tectonophysics, 2009
When a mechanically layered section of rock is subject to a horizontal strain, faults often nucleate preferentially in one or more layers before propagating through the rest of the section. The result is a high density of small, low-throw faults within these layers, and a much smaller number of large, through-cutting faults which nevertheless accommodate most of the strain due to their much larger displacement. A dynamic model of fault nucleation and propagation has been created by combining analytical and finite element techniques to calculate the energy balance of these propagating faults. This model shows that: 1) faults may nucleate in either mechanically weak layers, or in stiff layers with a high differential stress; 2) fault propagation may be halted either by strong layers (in which the sliding friction coefficient is high), or by layers which deform by flow and thus have low differential stress. This model can predict quantitatively the horizontal strain required for faults to nucleate, and to propagate across mechanical layer boundaries. The model is able to explain the complex pattern of fault nucleation and propagation observed in a mechanically layered outcrop in Sinai, Egypt.
J. Geophys. Res, 2003
1] We use a two-dimensional (2-D) finite element code to investigate how mechanical properties and boundary conditions influence progressive strain localization during extension of a 2-D elastoplastic layer. The deforming medium is modeled using a strain softening Von Mises rheology, with a Gaussian heterogeneity in yield strength distributed randomly in space. Specifically, we examine the effects of changing (1) the thickness of the deforming layer, (2) the basal boundary condition, (3) the range of strengths in the deforming layer, (4) the strength loss on failure, and (5) the total accommodated strain. Discrete zones of plastic shear strain are observed to nucleate and grow progressively during each experiment. In order to quantify and thus discriminate between the deformation patterns produced under differing conditions, we calculate the size-frequency distributions of the shear band populations. Size is defined as the total plastic strain represented by each discrete structure. A wide range of size-frequency distributions is observed, including both power law and exponential as well as distributions that show breaks in scaling with a transition from power law (at small sizes) to exponential (at large sizes). We show that these variations in population statistics are directly reflecting a change in strain localization in space and time caused by changing model parameters. Furthermore, by making an analogy between the model shear bands and tectonic faults, we provide insights into key features of fault size-frequency distributions that have been measured in continental and oceanic extensional settings and also observed in analogue experiments.
Influence of the structural framework on the origin of multiple fault patterns
Journal of Structural Geology, 1995
We demonstrate that the general equation for three-dimensional strain by slip on orthorhombic faults can be rearranged to take a form that applies to two-dimensional strain due to slip on pre-existing planes of weakness. Therefore, either two-dimensional or three-dimensional strain may result from the same stress state. We deduce that the kinematic interaction between planes of weakness in a body is a fundamental factor to determine the type of strain produced by a stress state. Whether deformation occurs by forming new fractures or by slip on existing planes depends upon which requires a lower stress difference. The stress difference necessary to initiate slip along a plane is highly sensitive to variations in orientation, cohesion and depth. We propose a model for crustal deformation composed of an anisotropic body with existing planes of weakness that interact kinematically.
Interactions and Growth of Normal Faults: Comparison of Model with Observations
We have developed a numerical model of crack growth in a brittle layer extended over a ductile substrate which successfully reproduces the statistics of crack populations and their evolution with brittle strain. Here we study the crack interactions in the model and compare them with geological observations of systems of sub-parallel normal faults. Most of the geological examples are found in the model, but because we can observe their temporal (or strain) evolution in the model a deeper understanding can be obtained than that from geological observations or static crack models. We observe, in end pinning, a progressive increase in the crack tip tapers and slowing of crack propagation with progressive overlap. Cracks pinned at both ends become increasingly sessile and accrue strain by accumulating slip with little or no lengthening. Small offset cracks attract, then pin one another, eventually developing echelon segmented arrays with sessile cracks in the interior. Cracks become inactive when bypassed and stress shadowed by a neighbor. When cracks coalesce, they may develop saddles in their slip distributions which can be quite persistent throughout additional growth, as observed on real normal faults. Complex slip distributions may result from multifault interactions in regions of high brittle strain, such as in the Afar rift region, and the systematic asymmetry of the slip distributions there may be explained by a strain rate gradient.
Journal of Structural Geology, 2006
This work is a 2D numerical contribution to the problem of fault and fracture interaction in layered rocks, focusing on fracture aperture. We investigate the influence of an underlying normal fault on the aperture of open fractures in bonded multilayers submitted to vertical shortening and horizontal lengthening. The tests are carried out using the finite element code Franc 2D under plane strain conditions. It is first shown that the presence of a straight normal fault affects the aperture of the above fractures. The fractures located in two very local areas near the upper tip of the fault, one in the hanging wall and one in the footwall, tend to open, whereas the neighboring fractures tend to close. The increases in aperture are systematically greater in the footwall than in the hanging wall. Furthermore, the two areas with increased fracture aperture move towards the footwall when the dip of the fault increases. Second, the case of more complex underlying faults with restraining/releasing bends is studied. These models have similar results to those observed in the case of the straight underlying fault, with two areas of increased fracture aperture. The increases in fracture aperture are comparable with the case of the straight fault in the hanging wall, but are larger in the footwall. The contrasting behaviors of fractures described in the experiments are interpreted as a consequence of changes in the stress field in the central fractured layer caused by the presence of the underlying fault. They may provide a guide to explain fluid flow in fault tip areas. Finally, the case of fracture corridors (swarms of closely spaced fractures) is addressed. It is shown that, whatever the characteristics of the underlying fault, the total aperture of a corridor formed by three equally spaced fractures is equal to 1.41-1.69 times the aperture of a single fracture located at the same place in the fractured layer. This strongly suggests that these structures may act as preferential geological drains, with important consequences in terms of fluid flow. q
Fault growth in brittle-ductile experiments and the mechanics of continental collisions
Journal of Geophysical Research, 1993
Using laboratory models of continental collisions, we study the mechanisms responsible for large-scale deformation and the nature of the penetrative deformation, localized or homogeneous, and its characteristic scales and structure. In order to focus the study, one of the most •poctacular cases of continental collisions, namely the India-Asia collision, is considered. Different models with varying theologies are analyzed which attempt to respect the brittle-ductile stratification corresponding to the crust and mantle structure in the Earth. Each experiment is quantified by studying the strain field and the fault pattern as a function of the position P of the indenter within the system. The strain field is characterized by (1) the second invariant of the two-dimensional strain tensor and its variation with position for a fixed P, the evolution of its average as a function of P, (2) the evolution with P of the participation ratio S. z, which quantifies the fraction of the system surface area which participates in the deformation, O) the evolution of the 'escape ratio,' calculated as the surface increase gained by the system during its eastward lateral escape divided by the surface covered by the indenter penetration. Qualitatively, we find that the deformation first spreads out but later on undergoes localization. Once the fault pattern is 'mature' (the cumulative fault length does not increas• anymore), we observe that the strain field is essentially controlled by the kinematics of the larger faults. Each fault pattern is quantified by studying the histograms of fault orientations, (2) the 'capacity' and barycenter fractal dimensions, O) the 'multifractal' generalized dimensions, and (4) the distribution of fault lengths. The fractal dimension D/is found to almost constant within experimental uncertainty (D/= 1.7+0.1) and thus appears rather insensitive to the particular chosen theology. We find a correlation b•tween the generalized multifractal dimensions and two exponents, the barycenter fractal dimension 'b' and the exponent 'a' of the fault length distribution. This shows that the scaling properties of fault patterns can be characterized by the knowledge of only two exponents 'b' and 'a' of the spatial and length distributions of faults. Our main results are (1) observation of the growth of self-similar fault patterns, (2) complete characterization of the fault patterns with two scaling exponents 'a' and 'b,' (3) wide distribution of undeteriorated domains and large heterogeneity of the deformation field, (4) maturation of the fault structure corresponding to a localization of the deformation on a few large faults in the late stage of the deformation. continental deformation, it is often observed that the deformation does not remain localized in the neighborhood of the plate boundaries and can occur several hundreds or even thousands of kilometers within continental plates, as shown from the complex fault systems and the seismic activity. How can one characterize the strain field (diffuse or homogeneous) and the observed complex fault patterns? Is the deformation really so diffuse or is it in reality controlled by the kinematics of a few large faults? What is the origin of the observed diffuse deformation? What is the relative importance of the theology of the crust and of the boundary conditions? These are the main questions that we attempt to address in this paper. We report a set of laboratory experiments which explore a large sample of different theologies. We focus the study on the case of asymmetric collisions in presence of a free lateral boundary (see Figure 1), best exemplified in nature by the collision between India and Asia [Windley, 1988]. This is the archetype of the indentation of a small rigid continent penetrating within a larger continent, whose left or right side is not confined. In this case one expects and observes two principal modes of deformations (1) thickening in front of the indenter and (2) large-scale lateral extrusion of continental blocks. This problem is found in several geological contexts, foremost in two spectacular active collisions, the India-Asia collision [Tapponnier and Molnar, 1977] and the Anatolia-Arabia collision [e.g., Dewey et al., 1986; McKenzie and Jackson, 1986; P. Davy and P. Suzanne, unpublished manuscript, 1991]. Many studies of the mechanical behavior of such continental collisions with asymmetric boundary 12,111 12,112 SORNETFE ET AL.: FAULT GROWTH IN BRITIZE-DUCTILE EXPERIMENTS zoo 550 secondary faults may be due to the relaxation of strain in the vicinity of a large active fault, in order to maintain kinematic compatibility. Another example (among many) is provided by the complex fault structure in Asia resulting from the India-Asia collision [CobboM and Davy, 1988]. The first model is of course inappropriate in order to predict the formation of fault structures. These studies rather tried to predict the strain field, i.e., the location and nature of major zones of deformation, and it was assumed that fault dimensions can be neglected at the scale considered. On the other hand, the basic assumption of Tapponnier et al. [1986] is that the largest faults account for most of the deformation. This hypothesis is SORNETFE ET AL.: FAULT GROWTH IN BRITtLE-DUCTILE EXPERIMENTS 12,113 12,114 SORNETrE ET AL.: FAULT GROWTH IN BRrFrLE-DUCTR.E EXPERIMENTS
Role of the brittle–ductile transition on fault activation
Physics of the Earth and Planetary Interiors 184, 160–171., 2011
We model a fault cross-cutting the brittle upper crust and the ductile lower crust. In the brittle layer the fault is assumed to have stick–slip behaviour, whereas the lower ductile crust is inferred to deform in a steady-state shear. Therefore, the brittle–ductile transition (BDT) separates two layers with different strain rates and structural styles. This contrasting behaviour determines a stress gradient at the BDT that is eventually dissipated during the earthquake. During the interseismic period, along a normal fault it should form a dilated hinge at and above the BDT. Conversely, an over-compressed volume should rather develop above a thrust plane at the BDT. On a normal fault the earthquake is associated with the coseismic closure of the dilated fractures generated in the stretched hangingwall during the interseismic period. In addition to the shear stress overcoming the friction of the fault, the brittle fault moves when the weight of the hangingwall exceeds the strength of the dilated band above the BDT. On a thrust fault, the seismic event is instead associated with the sudden dilation of the previously over-compressed volume in the hangingwall above the BDT, a mechanism requiring much more energy because it acts against gravity. In both cases, the deeper the BDT, the larger the involved volume, and the bigger the related magnitude. We tested two scenarios with two examples from L’Aquila 2009 (Italy) and Chi-Chi 1999 (Taiwan) events. GPS data, energy dissipation and strain rate analysis support these contrasting evolutions. Our model also predicts, consistently with data, that the interseismic strain rate is lower along the fault segment more prone to seismic activation.