Swelling Rock - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 192

This test result can be interpreted with respect to the water uptake coeffi cient D W as-
suming a linear relationship between = 1

after 20 years of test duration, the solution of the one-dimensional diffusion equation
leads to a water uptake coeffi cient of D W = 1.5 · 10 -12 m 2 /s (Fig. 8.9, left).

σ (t) and ω (t) (Fig. 8.9, right). Assuming ω

Figure 8.9 Interpretation of a long-term swelling pressure test with respect to the water uptake
coeffi cient D W (Wahlen 2009)

The extension of the one-dimensional swelling law (8.10) to three-dimensional stress-
strain states was formulated by Wittke (2003) on the basis of the approach of Kiehl
(1991a) for isotropic swelling behavior at full saturation (

ω = 1):

(8.12a)

ε i q ( with i = 1, 2, 3 and σ i are the principal swelling strains and principle normal

stresses, respectively. Thus, the directions of

ω ) and

ε i q (

ω ) coincide with the directions of σ i .

This equation can also be formulated in a more compact form:

(8.12b)

with the abbreviation