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Mathematical modelling of the water absorption properties for historical lime-based mortars from Catania (Sicily, Italy)

Gabriella Bretti, Cristina M. Belfiore

Abstract

In this paper we propose a mathematical model of the capillary and permeability properties of lime-based mortars from the historic built heritage of Catania (Sicily, Italy) produced by using two different types of volcanic aggregate, i.e. ghiara and azolo. In order to find a formulation for the capillary pressure and the permeability as functions of the saturation level inside the porous medium we calibrate the numerical algorithm against imbibition data. The validation of the mathematical model was done by comparing the experimental retention curve with the one obtained by the simulation algorithm. Indeed, with the proposed approach it was possible to reproduce the main features of the experimentally observed phenomenon for both materials.

Mathematical modelling of the water absorption properties for historical lime-based mortars from Catania (Sicily, Italy)

Abstract

In this paper we propose a mathematical model of the capillary and permeability properties of lime-based mortars from the historic built heritage of Catania (Sicily, Italy) produced by using two different types of volcanic aggregate, i.e. ghiara and azolo. In order to find a formulation for the capillary pressure and the permeability as functions of the saturation level inside the porous medium we calibrate the numerical algorithm against imbibition data. The validation of the mathematical model was done by comparing the experimental retention curve with the one obtained by the simulation algorithm. Indeed, with the proposed approach it was possible to reproduce the main features of the experimentally observed phenomenon for both materials.

Paper Structure

This paper contains 14 sections, 25 equations, 9 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Materials and methods
  3. The laboratory experiment belfiore
  4. MIP experiment
  5. The mathematical model of suction of pure water
  6. The absorption function $B'$ Clarelli2010
  7. A new formulation of absorption function $B'$ for Darcy's law
  8. Calibration and validation of the mathematical model: statement of the inverse problem and results
  9. Calibration of imbibition parameters in \ref{['BkP']} against data
  10. Validation of the calibration procedure using MIP data
  11. Sensitivity analysis
  12. Discussion of results and methodology
  13. Conclusions and future perspectives
  14. Acknowledgements.

Figures (9)

  • Figure 1: Laboratory experiment for the measurement of water absorption for azolo and ghiara mortars.
  • Figure 2: Left panel: Plot of functions $B(s)$ and $B'(s)$ defined in \ref{['NN']} and obtained for $s_R=0.1, s_S=0.9$ and $D=$5e-03. Right Panel: Plot of functions $B(s)$ and $B'(s)$ defined in \ref{['BkP']} and obtained for $s_R=0.1, s_S=0.9, \alpha=0.25, c=$1.35e+05, $K_s=$ 8e-10,$\gamma=1.45$ with $D_{kP}=$5e-03.
  • Figure 3: Plot of permeability function \ref{['perm_fun']} for $K_s=$1e-10 and of capillary function \ref{['Pc']} for fixed $c=$1e+06, assuming different values of $\alpha$.
  • Figure 4: Left panel: Plots of the imbibition curve for ghiara mortar obtained numerically by the mathematical model \ref{['pb-water']}-\ref{['bc1']}-\ref{['bc2']}-\ref{['BkP']} (green line) VS experimental data (red diamonds). Right panel: Plot of $B'$ function (\ref{['BkP']}) for ghiara mortar (blue line).
  • Figure 5: Left panel: Plot of the imbibition curve for azolo mortar obtained numerically by the mathematical model \ref{['pb-water']}-\ref{['bc1']}-\ref{['bc2']}-\ref{['BkP']} (green line) VS experimental data (red diamonds). Right panel: Plot of $B'$ function (\ref{['BkP']}) for azolo mortar (blue line).
  • ...and 4 more figures

Theorems & Definitions (2)

  • Remark 1
  • Remark 2