Distinct element geomechanical modelling of the formation of sinkhole clusters within large-scale karstic depressions

The 2-D distinct element method (DEM) code (PFC2D_V5) is used here to simulate the evolution of subsidence-related karst landforms, such as single and clustered sinkholes, and associated larger-scale depressions. Subsurface material in the DEM model is removed progressively to produce an array of cavities; this simulates a network of subsurface groundwater conduits growing by chemical/mechanical erosion. The growth of the cavity array is coupled mechanically to the gravitationally loaded surroundings, such that cavities can grow also in part by material failure at their margins, which in the limit can produce individual collapse sinkholes. Two end-member growth scenarios of the cavity array and their impact on surface subsidence were examined in the models: (1) cavity growth at the same depth level and growth rate; (2) cavity growth at progressively deepening levels with varying growth rates. These growth scenarios are characterised by differing stress patterns across the cavity array and its overburden, which are in turn an important factor for the formation of sinkholes and uvala-like depressions. For growth scenario (1), a stable compression arch is established around the entire cavity array, hindering sinkhole collapse into individual cavities and favouring block-wise, relatively even subsidence across the whole cavity array. In contrast, for growth scenario (2), the stress system is more heterogeneous, such that local stress concentrations exist around individual cavities, leading to stress interactions and local wall/overburden fractures. Consequently, sinkhole collapses occur in individual cavities, which results in uneven, differential subsidence within a larger-scale depression. Depending on material properties of the cavity-hosting material and the overburden, the larger-scale depression forms either by sinkhole coalescence or by widespread subsidence linked geometrically to the entire cavity array. The results from models with growth scenario (2) are in close agreement with surface morphological and subsurface geophysical observations from an evaporite karst area on the eastern shore of the Dead Sea

The geomorphology and radar facies of Kaitorete Spit, Canterbury, New Zealand

Kaitorete Spit is a mixed sand and gravel barrier beach complex that is located at the northeastern end of the Canterbury Bight. Kaitorete Spit was examined during this study using a combination of ground penetrating radar surveys, sedimentological and geomorphological examinations of the barrier beach complex. The geomorphology formed on Kaitorete has developed in three different environments. At the northeastern end of Kaitorete low elevation spit recurves are formed. South of these are numerous parallel beach ridges, formed by the tops of prograded storm berms. Lacustrine geomorphic features have developed over the marine geomorphology. Small scale cuspate ridges have formed in shallow lake water and associated with lake bottom sediments. Lacustrine beach ridges, lacustrine beach ridge plains and lacustrine spit complexes all formed along the shore of a higher lake. Nine different radar facies were found developed in the radar profiles collected on Kaitorete Spit. The facies are defined on the basis of their internal reflector patterns. Generally, the reflector patterns could be predicted by interpreting the geomorphic features over which the radar profiles ran. Three of the radar facies revealed reflector patterns that could not be predicted using geomorphology alone. At the eastern end of Kaitorete Spit, the radar profiles revealed that the marine spit recurves comprise a spit beach overlying a spit platform. It also reveals that the distal end of the spit platform was reworked by tidal currents into a series of seaward prograding foresets. The radar profiles also revealed that immediately the barrier beach reached the edge of the spit platform, a rise in the elevation of the beach crest occurred due to an increase in the wave energy expended on the beach. In the centre of the barrier beach complex the radar profiles revealed that two long overwash barriers developed, which fill two long (up to 12 km), thin lake outlet lagoons. These lagoons developed as a result of breaching due to a large river overfilling the lake basin. After the initial breach, the longshore drift and lake outflow developed a dynamic equilibrium, resulting in the progressive eastward dislocation of the outlet mouth. The large volume of lake water acted to buffer the high flows of the river thereby, maintaining flow conditions at the outlet channel which were conducive to lagoon elongation. Associated with the lacustrine spit complexes are scarp-like ridges which have steep reflectors which dip away from the lake. These developed in a similar way to shore-parallel bars, with material moving up the stoss side and avalanching down the lee side. The combined application of ground penetrating radar and geomorphology reveals a much more complete geological history of an area where outcrop is sparse

Gradual caldera collapse at Bárdarbunga volcano, Iceland, regulated by lateral magma outflow

Large volcanic eruptions on Earth commonly occur with a collapse of the roof of a crustal magma reservoir, forming a caldera. Only a few such collapses occur per century, and the lack of detailed observations has obscured insight into the mechanical interplay between collapse and eruption.We usemultiparameter geophysical and geochemical data to show that the 110-squarekilometer and 65-meter-deep collapse of Bárdarbunga caldera in 2014-2015 was initiated through withdrawal of magma, and lateral migration through a 48-kilometers-long dike, from a 12-kilometers deep reservoir. Interaction between the pressure exerted by the subsiding reservoir roof and the physical properties of the subsurface flow path explain the gradual, nearexponential decline of both collapse rate and the intensity of the 180-day-long eruption.</p

Reconciliation of contrasting theories for fracture spacing in layered rocks

Natural and man-made brittle layers embedded in a weaker matrix and subjected to layer-parallel extension typically develop an array of opening-mode fractures with a remarkably regular spacing. This spacing often scales with layer thickness, and it decreases as extension increases until fracture saturation is reached. Existing analytical one-dimensional (1-D) 'full-slip' models, which assume that interfacial slip occurs over the entire length of the fracture-bound blocks, predict that the ratio of fracture spacing to layer thickness at saturation is proportional to the ratio of layer tensile to interface shear strength (T/s). Using 2-D discontinuum mechanical models run for conditions appropriate to layered rocks, we show that fracture spacing at saturation decreases linearly with decreasing T/s ratio, as predicted by 1-D models. At low T/s ratios (ca. <3.0), however, interfacial slip is suppressed and the heterogeneous 2-D stress distribution within fracture-bound blocks controls further fracture nucleation, as predicted by an existing 2-D 'fracture infill criterion'. The applicability of the two theories is hence T/s ratio dependent. Our models illustrate that fracture spacing in systems permitting interfacial slip is not necessarily an indicator of fracture system maturity. Fracture spacing is expected to decrease with increasing overburden pressure and decreasing layer tensile strength.Science Foundation IrelandAssociated movies require QuickTime to vie

Geometrical analysis of the refraction and segmentation of normal faults in periodically layered sequences

Normal faults contained in multilayers are often characterised by dip refraction which is generally attributed to differences in the mechanical properties of the layers, sometimes leading to different modes of fracture. Because existing theoretical and numerical schemes are not yet capable of predicting the 3D geometries of normal faults through inclined multilayer sequences, a simple geometric model is developed which predicts that such faults should show either strike refraction or fault segmentation or both. From a purely geometrical point of view a continuous refracting normal fault will exhibit strike (i.e. map view) refraction in different lithologies if the intersection lineation of fault and bedding is inclined. An alternative outcome of dip refraction in inclined multilayers is the formation of segmented faults exhibiting en échelon geometry. The degree of fault segmentation should increase with increasing dip of bedding, and a higher degree of segmentation is expected in less abundant lithologies. Strike changes and associated fault segmentation predicted by our geometrical model are tested using experimental analogue modelling. The modelling reveals that normal faults refracting from pure dip-slip predefined faults into an overlying (sand) cover will, as predicted, exhibit systematically stepping segments if the base of the cover is inclined.Irish Research Council for Science, Engineering and TechnologyEnterprise Irelan

Two-dimensional distinct element modeling of the structure and growth of normal faults in multilayer sequences

The distinct element method is used for modeling the growth of normal faults in layered sequences. The models consist of circular particles that can be bonded together with breakable cement. Size effects of the model mechanical properties were studied for a constant average particle size and various sample widths. The study revealed that the bulk strength of the model material decreases with increasing sample size. Consequently, numerical lab tests and the associated construction of failure envelopes were performed for the specific layer width to particle diameter ratios used in the multilayer models. The normal faulting models are composed of strong layers (bonded particles) and weak layers (nonbonded particles) that are deformed in response to movement on a predefined fault at the base of the sequence. The modeling reproduces many of the geometries observed in natural faults, including (1) changes in fault dip due to different modes of failure in the strong and weak layers, (2) fault bifurcation (splaying), (3) the flexure of strong layers and the rotation of associated blocks to form normal drag, and (4) the progressive linkage of fault segments. The model fault zone geometries and their growth are compared to natural faults from Kilve foreshore (Somerset, United Kingdom). Both the model and natural faults provide support for the well-known general trend that fault zone width increases with increasing displacement.Irish Research Council for Science, Engineering and TechnologyEnterprise Irelan

Two-dimensional distinct element modeling of the structure and growth of normal faults in multilayer sequence

The growth of normal faults in periodically layered sequences with varying strength contrast and at varying confining pressure is modeled using the Distinct Element Method. The normal faulting models are comprised of strong layers (bonded particles) and weak layers (non-bonded particles) that are deformed using a predefined fault at the base of the sequence. The model results suggest that faults in sequences with high strength contrast at low confining pressure are highly segmented due to different types of failure (extension vs. shear failure) in the different layers. The degree of segmentation decreases as the strength contrast decreases and confining pressure increases. Faults at low confining pressure localize as extension (Mode I) fractures within the strong layers and are later linked via shallow dipping faults in the weak ones. This leads to initial staircase geometries that, with increasing displacement, cause space problems that are later resolved by splaying and segmentation. As confining pressure increases the modeled faults show a transition from extension to hybrid and to shear fracture and an associated decrease in fault refraction, with a consequent decrease in fault surface irregularities. Therefore the mode of fracture, which is active in the strong layers of a mechanical multilayer at a particular confining pressure, exerts an important control on the final fault geometry.Irish Research Council for Science, Engineering and TechnologyEnterprise Irelan

Localisation of normal faults in multilayer sequences

Existing conceptual growth models for faults in layered sequences suggest that faults first localise in strong, and brittle, layers and are later linked in weak, and ductile, layers. We use the Discrete Element Method (DEM) for modelling the growth of a normal fault in a brittle/ductile multilayer sequence. The modelling reveals that faults in brittle/ductile sequences at low confining pressure and high strength contrast localise first as Mode I fractures in the brittle layers. Low amplitude monoclinal folding prior to failure is accommodated by ductile flow in the weak layers. The initially vertically segmented fault arrays are later linked via shallow dipping faults in the weak layers. Faults localise, therefore, as geometrically and kinematically coherent arrays of fault segments in which abandoned fault tips or splays are a product of the strain localisation process and do not necessarily indicate linkage of initially isolated faults. The modelling suggests that fault tip lines in layered sequences are more advanced in the strong layers compared to weak layers, where the difference in propagation distance is most likely related to strength and/or ductility contrast. Layer dependent variations in fault propagation rates generate fringed rather than smooth fault tip lines in multilayers.Not applicableEnterprise Irelan