Hydro-Mechanical Properties of an Unsaturated Frictional Material

2.5. CONSTITUTIVE MODELS FOR HYDRAULIC FUNCTIONS 49
responsible for the geometry of the frustums, the parameter nf0 describes the number
of the frustums, and the parameter µ describes the drainage process of some residual
frustums, thus they are responsible for the volume of water in the frustum-shaped pores,
and influence mainly the saturated and the unsaturated zone.
Maximum contact angle αmax: The maximum contact angle αmax is reached, when ad-
joining contractile skins are in contact and the frustum-shaped pores are filled with wa-
ter. As smaller the contact angle αmax as higher the suction, which has to be applied for
draining the contact regions. With decreasing contact angle αmax the unsaturated zone
is increasing and the residual zone is decreasing during drainage process (see Fig. 2.23).
Frustum number nf0 per sphere: When αmax is reached, the frustum-shaped pore be-
tween the grains is filled with water. The remaining pore volume is taken into account
by a function, describing the volume of a frustum. The largest volume of water is lo-
cated in these pores. Thus the number of frustums nf0 is influencing the shape of the
curve significantly in the saturated zone as well as unsaturated zone. With increasing
nf0 the saturated zone and unsaturated zone is shifting to higher suction values during
drainage process. Same behavior can be observed for the imbibition process. As larger
nf0 as larger the air-entry value ψaev and the water-entry value ψwev (see Fig. 2.24).
Form parameter ξ: The form parameter ξ defines the geometry of the frustum and
estimates the upper diameter of the frustum. With increasing ξ the curve becomes
flatter for drainage and imbibition process. As smaller ξ as more distinct the air-entry
value ψaev. The saturated zone is shifting to higher suction values for decreasing ξ while
wetting the specimen (see Fig. 2.25).
Material parameter ζ: The material parameter ζ is responsible for the form of the
meniscus in the frustum-shaped pores and thus it influences the suction (ua − uw)
Contact points
A
Pore water in
“contact regions”
r s
α
Capillary menisci
A
y
Frustum-shaped
pores
r 1
y
β 0
r 1 + ξ r s
β(y)
r
r s
particle water air
a) b)
A - A
Figure 2.22: Pore spaces and pore water (Zou 2003)