Hydro-Mechanical Properties of an Unsaturated Frictional Material

10 CHAPTER 2. STATE OF THE ART
soil is governed mainly by the soils pore size distribution, grain-size distribution, density, the
surface area and cation exchange capacity. Different phenomena are caused in a soil due to
the presence of suction. Considering a fine grained soil, it undergoes collapse and is subjected
to shrinkage as well as swelling phenomenon when changing water content in the soil. The
soil-water characteristic curve occurs in a wide range of suction. Coarse grained soils undergo
collapse and the soil-water characteristic curve occurs in a narrow range of suction.
The two important relationships describing the hydraulic behavior are the soil-water char-
acteristic curve and the unsaturated hydraulic conductivity function. The influence of water
content on the mechanical behavior of soils is reflected in their stress-strain behavior, e.g.
volume change and shear strength.
2.2.1 Stress State in Unsaturated Soils
The mechanical behavior of a soil, e.g. volume change or shear strength, are described using
the state of stress in the soil. Several combinations of the state of stress in a soil exists and
are referred to stress state variables. Stress state variables have to be independent of the soil
properties.
Soil mechanic is historically focused on the study of saturated soils. Effective stress is
considered to be a fundamental variable for describing the mechanical effects due to a change
in stress in the soil. The effective stress is applicable to all types of soil (e.g. sand, silt, clay),
because it is independent of the soil properties. Fundamental principles and the concept of
effective stress are suggested by Terzaghi (1943). In saturated soils the effective stress σ ′ is
defined as difference between the total stress σ and the pore pressure uw. The effective stress
sits exclusively in the solid skeleton of the soil and is given by:
σ ′ = σ − uw
(2.1)
The effective stress can be defined at any point in a soil if total stress and pore pressure are
known. The validity of Terzaghi’s effective stress equation for saturated soils is well accepted
(Rendulic 1936, Skempton 1961).
In unsaturated soils it has to be considered that stress is acting in the air phase as pore
air pressure as well as matric suction, which is defined as difference between air pressure and
water pressure (ua − uw), where ua is the pore-air pressure and uw is the pore-water pressure.
Thus the state of stress in unsaturated soils is fundamentally different from the state of stress
in saturated soils. Saturated soils are two phase systems composed of either solids and liquid
(e.g. water saturated soil) or solids and gas (e.g. dry soil). Unsaturated soils are three phase
systems comprised of solids (soil particles), liquid (pore water), and gas (pore air) (Lambe &
Whitman 1969). As fourth phase Fredlund & Morgenstern (1977) introduced the contractile
skin. Changes in pore water phase and pore-air phase directly influence the state of stress
acting on the soil skeleton. Thus Bishop (1959) expanded Terzaghi’s classical effective stress
equation and suggested an effective stress equation, later named after him, for unsaturated