Hydro-Mechanical Properties of an Unsaturated Frictional Material

10.1. GENERAL 197
where: α is a parameter similar to κ in Eq. 10.2, ξc is a shape factor due to cohesion and
ξγ is a shape factor due to unit weight. Before reaching the air-entry value the contribution
of the suction to the bearing capacity is linear. This is considered by the following equation
given by (Vanapalli & Mohamed 2007):
qu = [c ′ + (ua − uw)aev(1 − S α ) tan φ + (ua − uw)avrS α tan φ] · Ncξc + 0.5BNγγξγ (10.4)
where: (ua − uw)aev is equal to the air-entry value and (ua − uw)avr is the average suction
measured in the stress bulb below the foundation. In Eqs. 10.3 and 10.4 the influence of
overburden pressure is set to zero because unsaturated bearing capacity was tested on surface
footings. Following factors were proposed by Vesic (1973) to account for the different shape
of footings:
ξc = 1 + Nq
·
Nc
B
L
ξγ = 1 − 0.4 · B
L
where: B is the width and L the length of the foundation.
(10.5)
(10.6)
When investigating bearing capacity 2 main failure mechanisms are available. Gussmann’s
(1986) study shows typical failure patterns below strip foundation with rough and smooth
surfaces respectively (see Fig. 10.1 and 10.2). The failure pattern with a rough footing is
different from a smooth footing. A rough footing typically offers more resistance in comparison
to a smooth footing. The ultimate bearing capacity for rough footing is twice the value in
comparison to a smooth footing (Gussmann 1986). Therefore the bearing capacity qu derived
in Eq. 10.4 (this equation is based on Eq. 10.1, that considers failure mechanism as given in
Fig. 10.1) is reduced to qu/2, when estimating the bearing capacity for smooth footings.
Figure 10.1: Mechanism of failure below rough footing (Gussmann 1986, reprint with permission
from P. Gussmann)