Hydro-Mechanical Properties of an Unsaturated Frictional Material

Appendix A
Details Zou’s Model (2003, 2004)
During a main imbibition process of a soil, first all the contact regions are at the same time
filled with water from the position angle α = 0 to α = αmax (Fig. 2.22(a)). For α = αmax
some adjacent capillary menisci contact with each other, and some frustum-shaped pores are
formed. Then, all the frustum-shaped pores are at the same time filled with water from y = 0
to y = rs gradually (Fig. 2.22(b)). During a main drainage process of a soil, first a part of
the frustum-shaped pores begins to drain gradually from y = rs to y = 0. Then another part
begins to drain and one after another. Subsequently the contact regions begin to drain from
α = αmax to α = 0, and a part of frustum-shaped pores with the number µ · nf0 (where µ is a
percentage) is just drained during the drainage process of the contact regions. If in a soil all
the contact regions have been filled with water to α = αmax and all the frustum-shaped pores
have been filled with water to y = y1 < rs during a previous main imbibition process, and
now the soil begins to dry, then the drainage process is called as secondary drainage process.
Similar to the main drainage process, during the secondary drainage process, first a part of
the frustum-shaped pores that have been filled with water to y = y1 previously begins to
drain gradually. Then another part begins to drain and one after another. Subsequently the
contact regions begin to drain from α = αmax to α = 0, and a part of frustum-shaped pores
with the number µ·nf0 is also just drained during the drainage process of the contact regions.
If in a soil only a part of the frustum-shaped pores has been drained to y = y2 < rs during a
previous main drainage process, the other parts are still filled with water to y = rs, and now
the soil begins to be wetted again, then the imbibition process is called secondary imbibition
process. During the secondary imbibition process only the part of the frustum-shaped pores
that have been drained to y = y2 previously are at the same time wetted again.
The volume Vw1(α) of the pore water in a contact region between two tangent particles
(spheres) with the same radius rs, depending on α, can be expressed approximately as:
Vw1(α)
r 3 s
�
= 2π (1 − cos α) sin 2 (α) −
213
�
(1 − cos α)(2 + cos α)
3
(A.1)