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Abstract: The subsoil contains many evaporites such as limestone, gypsum, and salt. Such rocks are very sensitive to water. The deposit of evaporites raises questions because of their dissolution with time and the mechanical-geotechnical impact on the neighboring zone. Depending on the configuration of the site and the location of the rocks, the dissolution can lead to surface subsidence and, for instance, the formation of sinkholes and landslides. In this study, we present an approach that describes the dissolution process and its coupling with geotechnical engineering. In the first part we set the physico-mathematical framework, the hypothesis, and the limitations in which the dissolution process is stated. The physical interface between the fluid and the rock (porous) is represented by a diffuse interface of finite thickness. We briefly describe, in the framework of porous media, the steps needed to upscale the microscopic-scale (pore-scale) model to the macroscopic scale (Darcy scale). Although the constructed method has a large range of application, we will restrict it to saline and gypsum rocks. The second part is mainly devoted to the geotechnical consequences of the dissolution of gypsum material. We then analyze the effect of dissolution in the vicinity of a soil dam or slope and the partial dissolution of a gypsum pillar by a thin layer of water. These theoretical examples show the relevance and the potential of the approach in the general framework of geoengineering problems.

岩石溶解的建模与应用

[1]AndersonDM, McFaddenGB, 1998. Diffuse-interface methods in fluid mechanics. Annual Review of Fluid Mechanics, 30:139-165.

[2]BachmatY, BearJ, 1987. On the concept and size of a representative elementary volume (Rev). In: Bear J, Corapcioglu MY (Eds.), Advances in Transport Phenomena in Porous Media. Springer, Dordrecht, the Netherlands, p.3-20.

[3]BellFG, StaceyTR, GenskeDD, 2000. Mining subsidence and its effect on the environment: some differing examples. Environmental Geology, 40(1-2):135-152.

[4]BrinkmanHC, 1949. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Flow, Turbulence and Combustion, 1(1):27-34.

[5]CastellanzaR, GerolymatouE, NovaR, 2008. An attempt to predict the failure time of abandoned mine pillars. Rock Mechanics and Rock Engineering, 41(3):377-401.

[6]CharmoilleA, DaupleyX, 2012. Analyse et Modélisation de L’évolution Spatio-Temporelle des Cavités de Dissolution. Report DRS-12-127199-10107A, INERIS, France (in French).

[7]CollinsJB, LevineH, 1985. Diffuse interface model of diffusion-limited crystal growth. Physical Review B, 31(9):6119-6122.

[8]CooperAH, 1988. Subsidence resulting from the dissolution of Permian gypsum in the Ripon area; its relevance to mining and water abstraction. Geological Society, London, Engineering Geology Special Publications, 5:387-390.

[9]DoneaJ, GiulianiS, HalleuxJP, 1982. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Computer Methods in Applied Mechanics and Engineering, 33(1-3):689-723.

[10]FengJ, HuHH, JosephDD, 1994. Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows. Journal of Fluid Mechanics, 277:271-301.

[11]FreezeRA, CherryJA, 1979. Groundwater. Prentice Hall, Englewood Cliffs, USA, p.604.

[12]GerolymatouE, NovaR, 2008. An analysis of chamber filling effects on the remediation of flooded gypsum and anhydrite mines. Rock Mechanics and Rock Engineering, 41(3):403-419.

[13]GombertP, OrsatJ, MathonD, et al., 2015. Rôle des effondrements karstiques sur les désordres survenus sur les digues de Loire dans le Val D’Orleans (France). Bulletin of Engineering Geology and the Environment, 74(1):‍125-140 (in French).

[14]GuoJW, QuintardM, LaouafaF, 2015. Dispersion in porous media with heterogeneous nonlinear reactions. Transport in Porous Media, 109(3):541-570.

[15]GuoJW, LaouafaF, QuintardM, 2016. A theoretical and numerical framework for modeling gypsum cavity dissolution. International Journal for Numerical and Analytical Methods in Geomechanics, 40(12):1662-1689.

[16]GyselM, 2002. Anhydrite dissolution phenomena: three case histories of anhydrite karst caused by water tunnel operation. Rock Mechanics and Rock Engineering, 35(1):1-21.

[17]HillR, 1958. A general theory of uniqueness and stability in elastic-plastic solids. Journal of the Mechanics and Physics of Solids, 6(3):236-249.

[18]JamesAN, LuptonARR, 1978. Gypsum and anhydrite in foundations of hydraulic structures. Géotechnique, 28(3):249-272.

[19]JeschkeAA, DreybrodtW, 2002. Dissolution rates of minerals and their relation to surface morphology. Geochimica et Cosmochimica Acta, 66(17):3055-3062.

[20]JeschkeAA, VosbeckK, DreybrodtW, 2001. Surface controlled dissolution rates of gypsum in aqueous solutions exhibit nonlinear dissolution kinetics. Geochimica et Cosmochimica Acta, 65(1):27-34.

[21]LaddAJC, SzymczakP, 2021. Reactive flows in porous media: challenges in theoretical and numerical methods. Annual Review of Chemical and Biomolecular Engineering, 12:543-571.

[22]LaddAJC, YuL, SzymczakP, 2020. Dissolution of a cylindrical disk in Hele-Shaw flow: a conformal-mapping approach. Journal of Fluid Mechanics, 903:A46.

[23]LaouafaF, PrunierF, DaouadjiA, et al., 2011. Stability in geomechanics, experimental and numerical analyses. International Journal for Numerical and Analytical Methods in Geomechanics, 35(2):112-139.

[24]LaouafaF, GuoJW, QuintardM, 2021. Underground rock dissolution and geomechanical issues. Rock Mechanics and Rock Engineering, 54(7):3423-3445.

[25]LuoH, LaouafaF, GuoJ, et al., 2014. Numerical modeling of three-phase dissolution of underground cavities using a diffuse interface model. International Journal for Numerical and Analytical Methods in Geomechanics, 38(15):1600-1616.

[26]LuoHS, QuintardM, DebenestG, et al., 2012. Properties of a diffuse interface model based on a porous medium theory for solid-liquid dissolution problems. Computational Geosciences, 16(4):913-932.

[27]LuoHS, LaouafaF, DebenestG, et al., 2015. Large scale cavity dissolution: from the physical problem to its numerical solution. European Journal of Mechanics-B/Fluids, 52:131-146.

[28]MolinsS, SoulaineC, PrasianakisNI, et al., 2021. Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set. Computational Geosciences, 25(4):1285-1318.

[29]PrunierF, LaouafaF, DarveF, 2009. 3D bifurcation analysis in geomaterials: investigation of the second order work criterion. European Journal of Environmental and Civil Engineering, 13(2):135-147.

[30]QuintardM, WhitakerS, 1994a. Convection, dispersion, and interfacial transport of contaminants: homogeneous porous media. Advances in Water Resources, 17(4):221-239.

[31]QuintardM, WhitakerS, 1994b. Transport in ordered and disordered porous media I: the cellular average and the use of weighting functions. Transport in Porous Media, 14(2):163-177.

[32]QuintardM, WhitakerS, 1999. Dissolution of an immobile phase during flow in porous media. Industrial & Engineering Chemistry Research, 38(3):833-844.

[33]SwiftG, ReddishD, 2002. Stability problems associated with an abandoned ironstone mine. Bulletin of Engineering Geology and the Environment, 61(3):227-239.

[34]ToulemontM, 1981. Evolution Actuelle des Massifs Gypseux par Lessivage-Cas des Gypses Lutétiens de la Région Parisienne, France. IFSTTAR, France (in French).

[35]ToulemontM, 1987. Les Risques D’instabilité Liés au Karst Gypseux Lutétien de la Région Parisienne‍–‍Prévision en Cartographie. IFSTTAR, France (in French).

[36]TryggvasonG, BunnerB, EsmaeeliA, et al., 2001. A front-tracking method for the computations of multiphase flow. Journal of Computational Physics, 169(2):708-759.

[37]WalthamT, BellFG, CulshawMG, 2005. Sinkholes and Subsidence: Karst and Cavernous Rocks in Engineering and Construction. Springer, Berlin, Germany.

[38]WangSJ, ChengZC, ZhangY, et al., 2021. Unstable density-driven convection of CO₂ in homogeneous and heterogeneous porous media with implications for deep saline aquifers. Water Resources Research, 57(3):e2020WR028132.

[39]WhitakerS, 1999. The Method of Volume Averaging. Springer, Dordrecht, the Netherlands.

[40]YangJ, YinZY, LaouafaF, et al., 2020. Three-dimensional hydromechanical modeling of internal erosion in dike-on-foundation. International Journal for Numerical and Analytical Methods in Geomechanics, 44(8):1200-1218.