Experimental Investigation on Transport Properties of Cement-Based Materials Incorporating 2D Crack Networks

Abstract

This paper investigates the correlation between the geometry of crack networks and the altered transport properties of cement-based porous materials. Cracks were artificially introduced into slice specimens to obtain bidimensional (2D) crack networks, and the network was characterized by the crack density, orientation, connectivity and crack opening aperture. For the permeability, the water vapor sorption isotherms were measured and an algorithm was established to solve the intrinsic permeability of cracked specimens with the help of moisture transport modeling and the data of drying tests. The electrical conductivity of cracked specimens was measured using an alternative current method. The study on the specimens with percolated cracks shows that: (1) the pertinent geometry parameters for altered transport properties include average-based crack density, crack opening and local crack connectivity; (2) the water permeability of cracked specimens is correlated to the combination $b^{1.7}\rho f$ and electrical conductivity to $b^{0.45}\rho f$; (3) the different exponents on the crack opening/length ratio reflect the resistance of tortuosity of crack paths to the water and current flow and this resistance is stronger for current flow.

Appendix: Moisture Transport Model

The multi-phase transport model was developed by Baroghel-Bouny et al. (1999a) to describe the moisture transport in cement-based porous materials under isothermal condition. The porous medium was idealized as the superposition of three continuous phases: the solid/rigid skeleton, the liquid phase (l) and the gas phase (g) in pores. The gas phase includes the dry air (a) and the water vapor (v), and assumed to be an ideal mixture. The volumetric mass $m_{j=l,v,a}$ can be expressed as a function of the pore liquid saturation s and the mass density $\rho _{j=l,v,a}$:

$$\begin{aligned} m_{\mathrm{l}}=\phi \rho _{\mathrm{l}} s,\quad m_{\mathrm{v}}=\phi \rho _{\mathrm{v}} (1-s),\quad m_{\mathrm{a}}=\phi \rho _{\mathrm{a}}(1-s) \end{aligned}$$

(10)

where $\phi _{\mathrm{l}}=\phi s$ and $\phi _{\mathrm{g}}=\phi (1-s)$ represent the porosities occupied by the liquid and the gas phases respectively. The mass conservations for moisture (liquid water+vapor) and dry air write,

$$\begin{aligned} \begin{aligned} \dfrac{\partial m_{\mathrm{l}}}{\partial t}+\dfrac{\partial m_{\mathrm{v}}}{\partial t}&=-\text {div}(w_{\mathrm{l}})-\text {div}(w_{\mathrm{v}}) \\ \dfrac{\partial m_{\mathrm{a}}}{\partial t}&=-\text {div}(w_{\mathrm{a}}) \end{aligned} \end{aligned}$$

(11)

where $w_i$ is the mass flow rate of phase i. The flow rate of liquid phase $w_{\mathrm{l}}$ can be expressed through Darcy’s law and the flow rate of gas phases considers contribution from both pressure-induced flow, via Darcy’s law, and diffusion flow, via Fick’s law. These flow rates writes (Li et al. 2016),

$$\begin{aligned} \begin{aligned} w_{\mathrm{l}}&=-\,\rho _{\mathrm{l}} \frac{K_{\mathrm{int}}}{\eta _{\mathrm{l}}}K_{\mathrm{rl}}\nabla p_{\mathrm{l}} \\ w_{\mathrm{a,v}}&=-\,\rho _{\mathrm{a,v}} \frac{K_{\mathrm{int}}}{\eta _{\mathrm{g}}}K_{\mathrm{rg}}\nabla p_{\mathrm{g}} - f(\phi , s)D_{\mathrm{va}}\left[ \frac{E_{\mathrm{a}}E_{\mathrm{v}}(M_{\mathrm{v,a}}-M_{\mathrm{a,v}})}{RT}\nabla p_{\mathrm{g}} + \rho _{\mathrm{g}} \nabla E_{\mathrm{a,v}}\right] \end{aligned} \end{aligned}$$

(12)

Here $K_{\mathrm{int}}$ is the intrinsic permeability and $K_{\mathrm{rg,rl}}$ are the relative gas and liquid permeability, $\eta _{\mathrm{g,l}}$ are the dynamic viscosity for gas and liquid, $M_{\mathrm{v,a}}$ are the molar mass for vapor and dry air, $p_{\mathrm{g,l}}$ are the gas and liquid pressures and $E_{\mathrm{v,a}}$ the mass fraction of vapor and dry air in the gas mixture. The vapor and dry air are assumed to be ideal gas, observing

Table 6 Main parameters and functions used in the moisture transport model

$$\begin{aligned} p_jM_j=RT\rho _j,\quad j=v,a \end{aligned}$$

(13)

and the mass fraction $E_{\mathrm{v,a}}$ and gas pressure $p_{\mathrm{g}}$ observe,

$$\begin{aligned} E_{\mathrm{v,a}}=\frac{\rho _{\mathrm{v,a}}}{\rho _{\mathrm{v}} + \rho _{\mathrm{a}}} \quad \text {and} \quad p_{\mathrm{g}}=p_{\mathrm{v}} + p_{\mathrm{a}} \end{aligned}$$

(14)

The local thermodynamic equilibrium between the liquid water and vapor phase writes,

$$\begin{aligned} \dfrac{\hbox {d}p_{\mathrm{v}}}{\rho _{\mathrm{v}}}-\dfrac{\hbox {d}p_{\mathrm{l}}}{\rho _{\mathrm{l}}}=0 \end{aligned}$$

(15)

Last, the liquid and gas pressures at the liquid–gas interface keep mechanical balance with the pore capillary pressure $p_{\mathrm{c}}$,

$$\begin{aligned} p_{\mathrm{g}}-p_{\mathrm{l}}=p_{\mathrm{c}} \end{aligned}$$

(16)

and the capillary pressure $p_{\mathrm{c}}$ can be expressed in terms of pore saturation through the moisture characteristic curve, $p_{\mathrm{c}}=p_{\mathrm{c}}(s)$, cf. Eq. (6). Actually, the multi-phase moisture transport model is described completely through Eqs. (11)–(16), with pore saturation s and pressures of gas and liquid phases $p_{\mathrm{l,g,a,v}}$ as basic variables.

To use this model, some physical properties should be implemented, including the gas diffusivity $D_{\mathrm{va}}$, the gas resistance function $f(\phi , s)$ and the relative gas/liquid permeability $K_{\mathrm{rg,rl}}$. The detailed expressions for these properties are omitted here, and the sources of these expressions are given in Table 6. Some main parameters are also given in the same table.