BACKGROUND
Initial, first-time or "virgin" uniaxial experimental consolidation of disaggregated or highly disturbed (remolded) porous sediments results in the well-known relationship between volume and effective vertical stress (
v') that shows an approximately exponential decrease in volume or vertical strain with increasing
v'. Geotechnical engineers have concluded that there is a linear relationship between void ratio (e) and log
v' for most sediments over a low-stress range,
but this linearity does not extend into higher, geologically pertinent stresses (Bryant et al., 1981; Karig and
Hou, 1992). Tests of a silty clay in our laboratory demonstrated that for v' up to 30
MPa, log v' is more nearly linear with respect to porosity (
) than it is to e (Karig and Morgan, 1994). The constant of proportionality, Ac , in the relationship:
= Ac log v' is a measure of compressibility analogous to the index of compressibility, Cc , when void ratio is used. Ac is a function of
lithology, with clay having a much higher value than sand.
As v' is increased during uniaxial consolidation,
h' also increases, at a ratio with
v' (
h'/v') that is termed Ko . Ko has been shown to be constant for a clay over a geologically applicable stress range in the laboratory, but for sand it increases moderately with stress, probably caused by grain crushing
(Karig and Hou, 1992). Ko ranges between about 0.4 and 0.7, generally increasing with clay content, but with wide variations.
Consolidation is not elastic strain and cannot be described by equations of linear elasticity. Nevertheless, consolidation generates a component of elastic strain in the sample, usually small, that can be measured by reducing
v'. Along such a stress path,
v' is related to vertical strain (
v) by
v' = Ecv. Ec, termed the constrained modulus, is analogous to Young's modulus and increases with increased consolidation. The equations of linear elastic strain lead to the relationship between
h'
and v':
h, = (v/1
– v) v, where v is Poisson's ratio; for an anisotropic sediment such as a mudstone, the correct anisotropic components of v must be used (e.g., Atkinson, 1975; Karig and Morgan, 1994). The elastic stress ratio has a lower value than Ko for the same sediment at a given state of uniaxial consolidation.
Progressive consolidation increases the stress range within which the sediment can behave elastically. For a given state of uniaxial consolidation, this field of elastic behavior can be represented on a plot of effective mean stress (m' = ([1' +
2' +
3']/3) against differential stress ( =
1
– 3), or in geotechnical parlance, the q-p' plane
(Fig. 1). On this plane, the elastic behavior is restricted to within an approximately elliptical area with its major axis along the uniaxial consolidation stress path. This elliptical envelope is determined by yield stresses along a wide variety of test paths (e.g., triaxial tests at different constant q/p' ratios). Uniaxial consolidation to a given state creates a single and unique yield envelope for all stress paths on that sample but is only a specific point on that yield envelope.
Progressive consolidation of a sediment increases the yield strength and enlarges the yield envelope with a geometrically similar shape
(Fig. 1), at least over the lower range of stresses (Graham et al., 1983). A different ratio of p' to q during consolidation will generate a yield envelope with a different orientation on the q-p' plane. Isotropic consolidation, the only other path for which there are significant data, produces a yield envelope that is symmetrical about the p' axis
(Fig. 1). It is thus presumed that yield envelopes in general are symmetric about the stress paths used to create them, at least if those paths have constant q/p' ratios.
Consolidation is associated with porosity reduction, which varies significantly as a function of the stress path during consolidation, especially in clay-rich sediments. In general, the greater the q/p' ratio along the consolidation path, the larger the porosity reduction (e.g., Wood, 1990). The increased ratio is permanently reflected in the sediment by the increased statistical alignment of poles to platy minerals such as clays, which is reflected in the fabric anisotropy (e.g., Morgan and
Karig, 1993). For experimental uniaxially consolidated clay-rich sediments at least, there is a specific relationship among q, p', and porosity (), just as there is among q, p', and yield stress (c').
In the Critical State Theory, the yield condition for an ideal sediment can be described as a point on a three-dimensional surface in
q-p'- (or some other parameter of volume) space (e.g., Wood, 1990; Jones and Addis, 1986). As will be shown later, the relationship between porosity and yield stress may become "uncoupled" for naturally consolidated sediments, for instance, by stress rotation or by
natural cementation. Such decoupling must be understood to interpret most consolidation tests of natural sediments adequately.
