Swelling Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 191

The rate of water uptake is governed by the access to water, that is, the permeability of the
surrounding rock mass and the seepage fl ow in the discontinuities, since the rock cannot
absorb more water than it is provided by seepage fl ow. On the other hand, water uptake is
limited and controlled by the water absorption capacity of the rock (Wittke 2003).
In order to describe the interaction between seepage fl ow and water uptake the corre-
sponding equations (6.49b) and (8.6) must be modifi ed as follows:

(8.8)

(8.9)

where the exchange water volume q e is the sum of all water volumes V WB per time
and unit volume absorbed by the blocks of intact rock from the discontinuities, while
q e serves as a sink for seepage fl ow and as a source for water uptake. Therefore it is
introduced in the seepage fl ow equation with a negative sign and in the water uptake
equation with a positive sign (Wittke 2003).

Equations (8.8) and (8.9), in a simplifi ed manner, describe the convective and diffusive
transport of ions taking place during swelling of corrensite and the transformation
of anhydrite into gypsum. Alternatively, these transport processes may be modeled by
means of mass balance equations for the involved constituents (Alonso & Olivella 2008,
Alonso & Ramon 2011).

8.4 Swelling

The one-dimensional swelling law (Fig. 8.5) has turned out to be valid also if the rock is
not fully water saturated (Wittke 2003). Then the swelling strain is dependent on ω , that

is, on the supply of water (Fig. 8.7, right):

(8.10)

The swelling parameter K q was found to be almost independent of ω while σ q0 increases

linearly with ω (Fig. 8.7, right):

(8.11)

where σ q0 in Fig. 8.5 (Wittke 2003).

Figure 8.9 (left) shows the result of a long-term swelling pressure test (

σ q0 ( ω = 1) corresponds to

= 0) on a small
specimen of unleached Gypsum Keuper with a test duration of 6 years. The extrapola-
tion of the measured vertical stress

ε

σ over a time period of 20 years leads to a value of

9.6 MPa. Since after that time σ does not increase anymore, this value can be assumed

to be equal to σ q0 ( ω = 1).