Fractured Poroelastic Media in the Limit of Vanishing Aperture
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914180021354496 |
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| author | Hörl, Maximilian Kumar, Kundan Rohde, Christian |
| author_facet | Hörl, Maximilian Kumar, Kundan Rohde, Christian |
| contents | We consider a poroelastic medium with a thin heterogeneity, also referred to as a fracture. Fluid flow and mechanical deformation inside both bulk and fracture are governed by the quasi-static Biot equations. The fracture's material parameters, such as hydraulic conductivity and elasticity, are assumed to scale with powers of the width-to-length ratio $\varepsilon$ of the fracture. Based on a priori estimates, we rigorously derive limit models as $\varepsilon \rightarrow 0$ and identify different limit regimes. We obtain five regimes for the hydraulic conductivity and two for the elasticity. While many cases yield discrete fracture models, others result in two-scale limit problems dominated by normal flow or deformation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_04978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractured Poroelastic Media in the Limit of Vanishing Aperture Hörl, Maximilian Kumar, Kundan Rohde, Christian Analysis of PDEs 35B40, 35B45, 74F10, 74R99, 76S05 We consider a poroelastic medium with a thin heterogeneity, also referred to as a fracture. Fluid flow and mechanical deformation inside both bulk and fracture are governed by the quasi-static Biot equations. The fracture's material parameters, such as hydraulic conductivity and elasticity, are assumed to scale with powers of the width-to-length ratio $\varepsilon$ of the fracture. Based on a priori estimates, we rigorously derive limit models as $\varepsilon \rightarrow 0$ and identify different limit regimes. We obtain five regimes for the hydraulic conductivity and two for the elasticity. While many cases yield discrete fracture models, others result in two-scale limit problems dominated by normal flow or deformation. |
| title | Fractured Poroelastic Media in the Limit of Vanishing Aperture |
| topic | Analysis of PDEs 35B40, 35B45, 74F10, 74R99, 76S05 |
| url | https://arxiv.org/abs/2512.04978 |