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Mechanical and/or chemical removal of material from the subsurface may generate large subsurface cavities, the destabilisation of which can lead to ground collapse and the formation of sinkholes. Numerical simulation of the interaction of cavity growth, host material deformation and overburden collapse is desirable to better understand the sinkhole hazard but is a challenging task due to the involved high strains and material discontinuities. Here, we present 2-D distinct element method numerical simulations of cavity growth and sinkhole development. Firstly, we simulate cavity formation by quasi-static, stepwise removal of material in a single growing zone of an arbitrary geometry and depth. We benchmark this approach against analytical and boundary element method models of a deep void space in a linear elastic material. Secondly, we explore the effects of properties of different uniform materials on cavity stability and sinkhole development. We perform simulated biaxial tests to calibrate macroscopic geotechnical parameters of three model materials representative of those in which sinkholes develop at the Dead Sea shoreline: mud, alluvium and salt. We show that weak materials do not support large cavities, leading to gradual sagging or suffusion-style subsidence. Strong materials support quasi-stable to stable cavities, the overburdens of which may fail suddenly in a caprock or bedrock collapse style. Thirdly, we examine the consequences of layered arrangements of weak and strong materials. We find that these are more susceptible to sinkhole collapse than uniform materials not only due to a lower integrated strength of the overburden but also due to an inhibition of stabilising stress arching. Finally, we compare our model sinkhole geometries to observations at the Ghor Al-Haditha sinkhole site in Jordan. Sinkhole depth ∕ diameter ratios of 0.15 in mud, 0.37 in alluvium and 0.33 in salt are reproduced successfully in the calibrated model materials. The model results suggest that the observed distribution of sinkhole depth ∕ diameter values in each material type may partly reflect sinkhole growth trends.
The Postmasburg Manganese Field (PMF), Northern Cape Province, South Africa, once represented one of the largest sources of manganese ore worldwide. Two belts of manganese ore deposits have been distinguished in the PMF, namely the Western Belt of ferruginous manganese ores and the Eastern Belt of siliceous manganese ores. Prevailing models of ore formation in these two belts invoke karstification of manganese-rich dolomites and residual accumulation of manganese wad which later underwent diagenetic and low-grade metamorphic processes. For the most part, the role of hydrothermal processes and metasomatic alteration towards ore formation has not been adequately discussed. Here we report an abundance of common and some rare Al-, Na-, K- and Ba-bearing minerals, particularly aegirine, albite, microcline, banalsite, sérandite-pectolite, paragonite and natrolite in Mn ores of the PMF, indicative of hydrothermal influence. Enrichments in Na, K and/or Ba in the ores are generally on a percentage level for most samples analysed through bulk-rock techniques. The presence of As-rich tokyoite also suggests the presence of As and V in the hydrothermal fluid. The fluid was likely oxidized and alkaline in nature, akin to a mature basinal brine. Various replacement textures, particularly of Na- and K- rich minerals by Ba-bearing phases, suggest sequential deposition of gangue as well as ore-minerals from the hydrothermal fluid, with Ba phases being deposited at a later stage. The stratigraphic variability of the studied ores and their deviation from the strict classification of ferruginous and siliceous ores in the literature, suggests that a re-evaluation of genetic models is warranted. New Ar-Ar ages for K-feldspars suggest a late Neoproterozoic timing for hydrothermal activity. This corroborates previous geochronological evidence for regional hydrothermal activity that affected Mn ores at the PMF but also, possibly, the high-grade Mn ores of the Kalahari Manganese Field to the north. A revised, all-encompassing model for the development of the manganese deposits of the PMF is then proposed, whereby the source of metals is attributed to underlying carbonate rocks beyond the Reivilo Formation of the Campbellrand Subgroup. The main process by which metals are primarily accumulated is attributed to karstification of the dolomitic substrate. The overlying Asbestos Hills Subgroup banded iron formation (BIF) is suggested as a potential source of alkali metals, which also provides a mechanism for leaching of these BIFs to form high-grade residual iron ore deposits.