A one-dimensional finite-strain formulation [developed by Jeeravipoolvarn (2010)] was used. The model was based on the following form of the slurry consolidation equation (Somogyi 1980) that used depth coordinate (z) along with material properties [unit weight of water (γ
w
), specific gravity of solids (G
s
) void ratio (e), and hydraulic conductivity (k)] as well as excess pore pressure (u) and time (t):
$$\frac{\partial }{\partial z}\left[ { - \frac{k}{{\gamma_{w} (1 + e)}}\frac{\partial u}{\partial z}} \right] + \frac{de}{d\sigma '}\left[ {\left( {G_{s} - 1} \right)\gamma_{w} \frac{{d\left( {\Delta z} \right)}}{dt} - \frac{\partial u}{\partial t}} \right] = 0$$
(1)
An implicit finite difference method, that yielded a set of linear equations, was employed to solve the above governing equation. A 10 m deep deposit was simulated for 1 year duration using material properties [reported by Owolagba and Azam (2015a)] along with appropriate field conditions. The model output was selected to be in the form of effective stress (\(\sigma '\)) profile.
Material properties of treated MFT included specific gravity (G
s
= 2.4), solids content (s = 60%), void ratio (e = 1.5) and non-linear constitutive relationships. The above initial conditions (s and e) meant negligible sedimentation thereby precluding the capture of this phase of dewatering (Azam et al. 2009). This provided the rationale to use Eq. (1) for simulating slurry consolidation along with the coefficients of the volume compressibility relationship (e = 13.6 \(\sigma '^{ - 0.3}\)) and the hydraulic conductivity relationship (k = 1.3 × 10−10 e
2.3): where \(\sigma '\) is effective stress and k is hydraulic conductivity.
The hydraulic boundary included atmospheric conditions on top of the deposit and, as such, the surface could be affected by precipitation and evaporation. However, the climatic conditions in northern Alberta ensure that surface evaporation is negligible during eight months of the year and intermittent rainfall can offset the influence of desiccation during the summer months (Owolagba and Azam 2015b). Furthermore, the low hydraulic conductivity of the slurry means minimal storm water ingress into the deposit thereby resulting in surface runoff. Likewise, seepage at the bottom of the deposit was considered to be negligible because of the dominance of clays in the supporting soils (Morgenstern and Scott 1997). Therefore, most of the water flow through the slurry is in the upward direction.