Swelling Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 188

8.3 Water Uptake

Water uptake of argillaceous rocks has been described by a diffusion equation (Gat-
termann 1998, Gattermann et al. 2001), the one-dimensional formulation of which is

(8.1)

where D H is the so-called “hydraulic diffusion coeffi cient”, is the so-called “dimension-

less water content” defi ned as the ratio of absorbed water to maximum absorbable water:

ω

(8.3)

in which w is the current water content, w i is the initial or natural water content, w s is
the water content at saturation and S r is the degree of saturation defi ned as

(8.3)

and ω can vary between 0 and 1. In the case of ω = 1 the rock does not absorb any ad-

ditional water (S r = 1) while = 0 characterizes the in-situ state (w = w i ).

Water uptake of rocks containing clay and anhydrite is driven by the same phenomenon
but is delayed by the dissolution of anhydrite and subsequent crystallization from this
solution into gypsum (cf. Section 8.2). The transformation of anhydrite into gypsum is
thus governed by transport processes such as convection of ions within the groundwater
and diffusion driven by ionic concentration gradients in the solution (Anagnostou et al.
2010). It is therefore reasonable to describe water uptake of argillaceous rocks containing
clay and anhydrite also by a diffusion equation as was successfully done for the water
uptake of argillaceous rocks (Wittke 2003). This gave rise to the defi nition of a diffusion
coeffi cient D W describing water uptake of the unleached Gypsum Keuper. D W is depen-
dent on the anhydrite and corrensite content of the rock, which can vary considerably.

ω

To obtain a formulation by a diffusion equation that is independent of the percentage
of anhydrite and corrensite content of the rock, (8.1) is converted into

(8.4)

in which D W is referred to as the “water uptake coeffi cient” and S W is the relative wa-
ter volume required for the water consumption of the swelling clay and the complete
transformation of anhydrite into gypsum (Wittke 2003). As follows from the volume
balance, in relation to the volumetric anhydrite fraction A of the rock, an amount of
78% of water is required for complete transformation of anhydrite into gypsum:

(8.5)