Sinking of anhydrite blocks within a Newtonian salt diapir#
This section was contributed by Cedric Thieulot.
The setup for this experiment originates in Burchardt et al. [2012]. Similar experiments are conducted by the same authors in Burchardt et al. [2011] and Burchardt et al. [2012].
Based on the principal structural configurations of the Main Anhydrite segments within the Gorleben diapir, as shown in Fig. 181, the authors set up three series of models.
Fig. 181 NW–SE cross-section through the Gorleben diapir. Taken from Burchardt et al. [2012].#
Each model analyses the deformation associated with the gravity-driven sinking of one anhydrite block. The block geometry was simplified to rectangular shapes of different aspect ratios which vary from 10:1 to 1:10, with a 1:1 ratio corresponding to a \(100 \times 100~\text{ m}\) block as shown in the fifth panel of Fig. 182.
Fig. 182 Scaled sketches of model set-ups. Taken from Burchardt et al. [2012].#
In the article the authors consider three cases A,B,C with potentially different domain sizes or viscosity stratification. We focus here on experiment C with a domain of size \(L_x=2500~\text{ m}\) and \(L_y=5000~\text{ m}\). The gravity is not specified in the paper but it is set to \(g=9.81~\text{ m s}^{-2}\). Boundary conditions are free slip on all four sides. Simulations are run up to about \(500~\text{ ka}\). There are three materials in the domain as shown in Fig. 183. The full input file that contains these modifications and that was used for the simulations can be found at cookbooks/sinking_anhydrite_block.prm.
Fig. 183 Geometry, density and viscosity values of the three compositions in the case of a block of aspect ratio 1:1, i.e. \(b_x=b_y=100~\text{ m}\). Note that the top edge of the block is always at distance \(h=100~\text{ m}\) below the surface at the beginning of the simulation.#
In all three articles the authors use the Finite Differences code FDCON from Weinberg and Schmeling [1992]. In the current case the original resolution of the experiment is \(200 \times 400\) cells, i.e. cells of \(12.5 \times 12.5~\text{ m}\) in size. The particles are located every 10 to \(12.5~\text{ m}\) in vertical and horizontal direction, i.e. about 100,000 particles in total. We here make use of adaptive mesh refinement with a criterion based on the compositions interface and seed the system with 2,000,000 randomly distributed particles. Elements of the finest are then \(5 \times 5~\text{ m}\) in size. Unfortunately the authors fail to mention the type of averaging that they use for the density and viscosity carried by the particles. We here choose the harmonic one, keeping in mind that it may affect the dynamics of the system somewhat (e.g. Schmeling et al. [2008]).
Rather importantly, the authors add that their models are based on a number of assumptions and simplifications:
All materials are homogeneous and isotropic, neglecting any stratigraphic heterogeneities within the salt formations or the anhydrite.
The materials used are incompressible and entirely viscous, that is, no elastic behavior of, for example, the anhydrite is enabled.
The salt rheology in the models is Newtonian. However, salt rheology is a complex product of, for example, composition, grain size, fluid content, temperature and strain rate (e.g. Urai et al. [1986], van Keken et al. [1993], Jackson et al. [1994]).
The models are isothermal, neglecting temperature effects on the rheology.
Limitations regarding geometry include the simplified, rectangular shape of the anhydrite blocks with thicknesses of 100 m (instead of 70 m in case of the Main Anhydrite) and the perfectly straight interface between the two salt types. Hence, pre-existing deformation caused by salt ascent and emplacement along with the entrainment of the Main Anhydrite layer is neglected.
On Fig. 184, the panels of Fig. 6 of the paper are placed next to ASPECT’s results at three different times. We find a reasonable agreement between both codes, again acknowledging that the size of the sinking block probably requires an even higher resolution that what is here used and that material averaging is also likely to change results.
Fig. 184 Results obtained at three different times: a) \(t=104~\text{ ka}\); b) \(t=228~\text{ ka}\); c) \(t=352~\text{ ka}\). Blue-green panels are from the original paper while black & white plots are obtained with aspect. The last panel on the right shows the mesh and highlights Adaptive Mesh Refinement working optimally to capture the materials interface.#