Isotropic material for moisture transport based on Bazant and Najjar - BazantNajjarMoisture

This is a specific model for nonlinear moisture transport in isotropic cementitious materials, based on [2]. The governing equation

$$\frac{\partial h}{\partial t} = \nabla \cdot \left( C(h) \nabla h \right)$$ (237)

is a special case of Eq. (239), valid under the assumption that the slope of the sorption isotherm is linear, i.e. the moisture capacity is constant. In Eq. (237), $h$ is the relative humidity and $C(h)$ is the humidity-dependent diffusivity approximated by

$$C (h) = C_1 \left( \alpha_0 + \frac{1-\alpha_0}{1+\left(\frac{1-h}{1-h_c}\right)^n} \right)$$ (238)

where $C_1$ is the diffusivity at saturation (typical value for concrete $\approx 30$ mm$^2/$day), $\alpha_0$ is the dimensionless ratio of diffusivity at low humidity to diffusivity at saturation (typical value $\approx 0.05$), $h_c$ is the humidity “in the middle” of the transition between low and high diffusivity (typical value $\approx 0.8$), and $n$ is dimensionless exponent (high values of $n$, e.g. 12, lead to a rapid transition between low and high diffusivity). Optionally, it is possible to specify the moisture capacity. This property is not needed for solution of the diffusion equation (237), but it is needed if the computed change of relative humidity is transformed into water content loss (mass of lost water per unit volume).

The model parameters are summarized in Tab. 55.

Table 55: Nonlinear isotropic material for moisture transport - summary.

Description	Nonlinear isotropic material for moisture transport
Record Format	BazantNajjarMoistureMat num(in) # d(rn) # c1(rn) # n(rn) # alpha0(rn) # hc(rn) # [ capa(rn) #]
Parameters	- num material model number
	- d material density
	- c1 moisture diffusivity at full saturation [m$^2$ s$^{-1}$]
	- n exponent [-]
	- alpha0 ratio between minimum and maximum diffusivity [-]
	- hc relative humidity at which the diffusivity is exactly between its minimum and maximum value [-]
	- capa moisture capacity (default value is 1.0)
Supported modes	_2dHeat