arXiv subjects

Bettina Detmann

Publications and source records attributed to Bettina Detmann.

3 recordsLinked to original sources

arXiv2026

Analytic description of the moving moisture front in soils

The fact that moisture propagates in soils at a finite speed is confirmed by natural everyday experience as well as by controlled laboratory tests. In this text, we rigorously derive analytical upper bounds for the speed of moisture front propagation under gravity for the solution to the Richards equation with compactly supported initial data. The main result is an explicit criterion describing a competition between gravity and capillarity, where the dominant effect is determined by the characteristics of the soil. If capillarity prevails, the initially wet regions remain wet for all times, while if gravity is dominant, moisture travels downward at a speed that is asymptotically bounded from below and above. As a by-product, we prove the existence and uniqueness of a solution to an initial value problem for the degenerate Richards equation on the whole space. Numerical simulations based on the proposed model confirm the theoretical predictions, with results that closely match experimental observations.

math.AP↗

arXiv2024

How to identify earth pressures on in-service tunnel linings: Insights from Bayesian inversion to address non-uniqueness

Identifying earth pressures on in-service transportation tunnel linings is essential for their health monitoring and performance prediction, particularly in structures that exhibit poor performance. Due to the high costs associated with pressure gauges, pressure inversion based on easily observed structural responses, such as deformations, is preferred. A significant challenge lies in the non-uniqueness of inversion results, where various pressures can yield similar structural responses. Existing approaches often overlook detailed discussions on this critical issue. In addressing this gap, this study introduces a Bayesian approach. The proposed statistical framework effectively quantifies the uncertainty induced by non-uniqueness. Further analysis identifies the uniform component in distributed pressures as the primary source of non-uniqueness. Insights into mitigation strategies are provided, including increasing the quantity of deformation data or incorporating an observation of internal normal force within the tunnel lining -- the latter proving to be notably more effective. A practical application in a numerical case study demonstrates the effectiveness of this approach. In addition, our investigation recommends maintaining deformation measurement accuracy within the range of [-1, 1] mm to ensure satisfactory outcomes. Finally, deficiencies and potential future extensions of this approach are discussed.

stat.AP↗

arXiv2021

A model for lime consolidation of porous solids

We propose a mathematical model describing the process of filling the pores of a building material with lime water solution with the goal to improve the consistency of the porous solid. Chemical reactions produce calcium carbonate which glues the solid particles together at some distance from the boundary and strengthens the whole structure. The model consists of a 3D convection-diffusion system with a nonlinear boundary condition for the liquid and for calcium hydroxide, coupled with the mass balance equations for the chemical reaction. The main result consists in proving that the system has a solution for each initial data from a physically relevant class. A 1D numerical test shows a qualitative agreement with experimental observations.

math.AP↗