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_Journal of Structural Geology 33 (2011) 145-153_ Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com/locate/jsg Strain pattern within and around denser blocks sinking within Newtonian salt structures Stef? Burchardt a,*, Hemin Koyi a, Harro Schmeling b a Department of Earth Sciences, University of Uppsala, Villav?gen 16, 75236 Uppsala, Sweden b Faculty of Earth Sciences, J. W. Goethe University, Altenh?ferallee 1, 06438 Frankfurt am Main, Germany Article info Article history: Received 16 June 2010; Received in revised form 5 November 2010; Accepted 17 November 2010; Available online 27 November 2010 Keywords: Salt Anhydrite Deformation Rheology Gorleben Abstract Blocks of dense material, such as anhydrite, entrained in salt structures have been proposed to sink through their host material. Here, we present the results of numerical models that analyse strain patterns within and around initially horizontal anhydrite blocks (viscosity 1021 Pa s) sinking through Newtonian salt with a viscosity of 1017 Pa s. In addition, the influence of the block aspect ratio (thickness to width ratio; AR) is analysed. The model results show that the blocks are folded and marginally sheared to approach streamlined shapes. The effectiveness of this process is a function of the block AR and influences the sinking velocity of the blocks significantly. Final sinking velocities are in the range of ca. 1.7-3.1 mm/a. Around the block in the salt, an array of folds and shear zones develops during block descent, the structure of which is principally the same independent of the block AR. However, the size and development of the structures is a function of the block size. Monitoring of strain magnitudes demonstrates that the salt is subject to extremely high strains with successively changing stress regimes, resulting in closely-spaced zones of high adjacent to low strain. In comparison to the anhydrite blocks, strain magnitudes in the salt are up to one order of magnitude higher. ? 2010 Elsevier Ltd. All rights reserved. 1. Introduction Dense inclusions surrounded by a less viscous matrix occur in a variety of geological settings on practically all scales. Examples include anhydrite and limestone layers in salt structures (e.g., Bornemann, 1991), stoped blocks in magma chambers (Clarke et al., 1998), phenocrysts in magma (Arbaret et al., 2000), and englacial-morain material in glaciers (Talbot and Pohjola, 2009). The contrast in mechanical properties, such as density and viscosity, of these inclusions and their matrix has a strong influence on the strain pattern within the inclusion and the matrix. Dense inclusions of synsedimentary anhydrite and limestone, as well as of extrusive and intrusive igneous rocks in salt structures are known from many locations worldwide, e.g., the salt diapirs in the North Sea and the North German Basin (Bornemann, 1991; Schleder et al., 2008), the Zagros Mountains, Iran (Kent, 1979; Gansser, 1992; Weinberg, 1993), Oman (Peters et al., 2003; Reuning et al., 2009), and Yemen (Davison et al., 1996a, b). These dense inclusions (or “stringers”) have in most cases been entrained into salt diapirs during salt ascent (e.g., Jackson et al., 1990; Chemia et al., 2008). Consequently, they have been subjected to deformation as a result of the complex strain field inside rising salt (Talbot and Jackson, 1987; Koyi, 2001). Recent investigations focus on the potential of some of these stringers as reservoirs for oil and gas (e.g., Al-Siyabi, 2005) as well as on their impact on the strain history of a salt structure. Following Weinberg’s (1993) hypothesis that dense inclusions in salt may start to sink when the ascent rate of the salt is no longer sufficient to support their weight, Koyi (2001) and Chemia et al. (2009) demonstrated that sinking anhydrite slabs can reactivate the internal dynamics of a salt diapir, based on analogue and numerical modelling. This may have undesired effects on the long-term stability of disposal sites of hazardous waste, a number of which are planned in salt structures. Evidence that recent deformation around anhydrite blocks actually takes place comes from acoustic emissions recorded at the interface between anhydrite blocks and the surrounding rock salt in a German salt diapir (Spies and Eisenbl?tter, 2001). These acoustic signals may indicate the relative movement between the denser anhydrite blocks and their host salt diapir. In this paper, we present results of numerical models that focus on the deformation produced by the sinking of a dense block through a less viscous matrix, particularly on the resulting structures within and around the block on block-scale. In order to get a basic understanding of the mechanical interaction of anhydrite blocks of different sizes and the surrounding salt, we analysed the strain associated with the gravity-driven descent of anhydrite blocks of different size through a body of salt representing a diapir. 146 S. Burchardt et al. Journal of Structural Geology 33 (2011) 145-153 2. Model setup and methodological background 2.1. Scaling considerations and model setup The models are not scaled to any particular case. However, the model setup and the material properties are based on natural examples. Dense inclusions in salt diapirs are in most cases of synsedimentary origin, including intraformational evaporites (e.g., anhydrite deposited as gypsum), carbonate layers and platforms, synsedimentary psammites, and even contemporaneous volcanic rocks (e.g., Gansser, 1992) with preserved sedimentary or igneous layering. Consequently, they are often characterised by tabular shapes (e.g., Gansser, 1960, 1992; Kent, 1979; Jackson et al., 1990), even though they have usually been deformed during salt ascent. The thickness and width of these inclusions is thus highly variable. A well-studied example of a salt diapir containing dense inclusions is the Gorleben salt diapir in Northern Germany that served as scaling constraint for our models. This diapir is 3 km wide and approximately 3 km thick in cross section (NWeSE). The original stratigraphic sequence building the diapir consists mainly of halite and potassium salt of Permian age (Zechstein, Stabfurt (z2) to Aller (z4) formations; Bornemann, 1991). The so-called Main Anhydrite (z3HA) is a sequence of anhydrite with minor carbonates and a thickness of up to 70 m. During ascent of the salt diapir the Main Anhydrite was entrained within the salt and subject to intense strain that resulted in folding, boudinage, and shearing. Consequently, the Main Anhydrite forms elongate boudins of approximately 100 to more than 1000 m length, partly folded into isoclinals folds together with the surrounding salt (Bornemann, 1991). Each two-dimensional model consists of a 2000 m wide and 4000 m deep rectangular salt structure (Fig. 1). All sides of the model are defined as free-slip boundaries, i.e., displacement along the boundaries is enabled. Since all sides of the model represent symmetry planes and the model is lateral symmetric, only half of the model, i.e., a 1000 m wide and 4000 m deep rectangle, was modelled. At a depth of 100 m below the top of the model, a rectangular block with a higher density and viscosity, simulating a denser inclusion (e.g., anhydrite), is placed within the salt. The boundaries between the block and its matrix are adherent. The thickness of the block is 100 m, so that the block bottom is at an initial depth of 200 m. In order to understand the basic processes that control the mechanical interaction between blocks of denser material (anhydrite) and a viscous matrix (salt), we focus on one parameter: the size, and more specifically, the aspect ratio (AR; thickness to width ratio) of the anhydrite block. During ten successive model runs, the width of the block is varied from 100 m to 1000 m (thickness to width AR 1:1 to 1:10 respectively). The salt is assigned a density of 2200 kg/m3, while the density of anhydrite is defined as 2900 kg/m3, considering a slightly lower density as compared to pure anhydrite (density 3000 kg/m3), e.g., due to minor amounts of limestone. In each model, the block is allowed to sink within the salt structure driven by gravity alone due to the density contrast of 700 kg/m3. Experimental studies of rock salt subject to high strain rates show that salt rheology can vary from Newtonian to power-law behaviour depending on the interaction of various parameters, such as grain size, strain rate, brine content, the presence of impurities within the salt, and deviatoric stress (e.g., Urai et al., 1986, 2008; Van Keeken et al., 1993; Jackson et al., 1994). However, the rheological behaviour of salt at scales, temperatures, strain rates etc. relevant to natural systems is still not well understood and cannot be extrapolated from experimental results (cf. Urai et al., 1986). Estimations of salt rheology on diapir scale from natural examples conclude that salt may behave as a Newtonian fluid with viscosities in the range of 1015-1021 Pa s (Mukherjee et al., 2010). In our models, we therefore assigned the matrix material a linear viscosity of 1017 Pa s. We do not consider the influence of temperature, rheological contrasts or structural variations within the salt; i.e., the block sinks through an isotropic and homogeneous matrix of salt. Despite a few studies on the rheology of anhydrite under experimental conditions (e.g., M?ller and Siemes, 1974; M?ller et al., 1981; Zulauf et al., 2009), little is known about the viscosity and deformation behaviour of anhydrite subject to natural strain rates and temperatures. Chemia et al. (2009) assumed a viscosity contrast between anhydrite and the surrounding salt of 102-104, while Zulauf et al. (2009) estimated it to be on the order of 101._ Ключевые слова: process, diapir, journal structural, block sink, chemia, talbot, ramsay, geology, viscosity contrast, nearest neighbour, rigid particle, relative, dense inclusion, interlimb angle, parameter, zulauf, point, function, grid, folding, matrix, structural, alsop, burchardt journal, salt rheology, marginal, scale, jackson, ?nal, association, velocity prole, schmeling, rheology, ars, kent, ?ow, grid point, strain shadow, maximum distance, siyabi, structure, surrounding, block descent, contrast, model setup, anhydrite, rate, burchardt, magnitude, geological, shape, nature, focus, lateral, higher, horizontal, development, width, higher density, davison, material, block strain, model demonstrate, sinking process, areal extent, model result, geoarabia, entrainment, evenly distributed, gure legend, mesh plot, strain magnitude, structural geology, fold, sinking velocity, koyi, salt body, mechanical interaction, model, surrounding salt, magma, stokes, linear viscosity, block corner, velocity, zone, inclusion, strain, high, deformation, geological setting, natural, high strain, subject, sspx cardozo, gorleben, marker, pattern, internal dynamic, journal structural geology, channel, nal shape, dense block, germany, internal, dense, weinberg, journal, bornemann, descent, crystal settling, strong inuence, thickness, cruden, settling crystal, shear zone, grid spacing, crystal, in?uence, entrainment channel, marker point, boundary, internal deformation, denser block, block, numerical, van keeken, ha, m?ller, characterised, closely-spaced zone, rheological behaviour, block width, shear, order, result, numerical modelling, body, high adjacent, ar, numerical model, fth row, size, tectonophysics, mesh display, area, density, salt, sinking block, viscosity, earth, strain rate, salt ascent, salt diapir, wa, magmatic fabric, viscous, effective viscosity, marginal shear, sink, vertically shortened, block ars, matrix material, increasing, isoclinal fold, sinking, salt structure, rock, comparison, velocity proles, streamlined shape, gansser, depth, mass, function block, anhydrite block, urai, gravitational sinking, deformation experiment, strain pattern, velocity block, marker eld, society, newtonian