Evaluating the Condition of Sandstone Rock-Hewn Cave-Temple Façade Using In Situ Non-invasive Techniques

Appendix

Formulas for calculating sorptivity ($S)$ and capillary saturated moisture content ($\theta_{\text{cap}}$)

$$x\left( t \right) = R_{\text{wet}} \left( t \right) - R_{e}$$

(1)

$$V_{\text{wet}} \left( t \right) = \frac{2}{3}\pi \left( {x\left( t \right)^{3} + R_{e} x\left( t \right)} \right) + \pi R_{e}^{2} x\left( t \right)$$

(2)

$$\theta_{\text{cap}} = \frac{{V_{\text{abs}} \left( t \right)}}{{V_{\text{wet}} \left( t \right)}}$$

(3)

$$V_{\text{abs}} \left( t \right) = \pi R_{e}^{2} S\sqrt t + \frac{{\pi R_{e} \gamma S^{2} }}{{\theta_{\text{cap}} }}t$$

(4)

$x\left( t \right)$: penetration distance of wet front at time t. $R_{\text{wet}} \left( t \right)$: radius of wetting area at time t. $V_{\text{wet}} \left( t \right)$: wetted volume of stone at time t. $R_{e}$: radius of effective contact zone. θ_cap: capillary saturated moisture content. $V_{\text{abs}}$: absorbed water volume, i.e. decrease in volume of water observed in Karsten tube. $\gamma$: constant, 0.75. $S$: sorptivity, capacity to absorb water by capillarity.