Critical state soil mechanics
Forces are applied to soils in a number of ways, for example when they are loaded by foundations, or unloaded by excavations.
The basic concept is that soil and other granular materials, if continuously distorted until they flow as a frictional fluid, will come into a well-defined critical state.
In practical terms, the critical state can be considered a failure condition for the soil.
It's the point at which the soil cannot sustain any additional load without undergoing continuous deformation, in a manner similar to the behaviour of fluids.
Certain properties of the soil, like porosity, shear strength, and volume, reach characteristic values.
[1] The Critical State concept is an idealization of the observed behavior of saturated remoulded clays in triaxial compression tests, and it is assumed to apply to undisturbed soils.
, in uniaxial tension according to the von Mises yielding criterion), or specific volume
occupied by unit volume of flowing particles will decrease as the logarithm of the mean effective stress increases.
In an attempt to advance soil testing techniques, Kenneth Harry Roscoe of Cambridge University, in the late forties and early fifties, developed a simple shear apparatus in which his successive students attempted to study the changes in conditions in the shear zone both in sand and in clay soils.
In 1958 a study of the yielding of soil based on some Cambridge data of the simple shear apparatus tests, and on much more extensive data of triaxial tests at Imperial College London from research led by Professor Sir Alec Skempton at Imperial College, led to the publication of the critical state concept (Roscoe, Schofield & Wroth 1958).
[2] Subsequent to this 1958 paper, concepts of plasticity were introduced by Schofield and published in his textbook.
Prof. Baker's theories strongly influenced Schofield's thinking on soil shear.
Prof. Baker's views were developed from his pre-war work on steel structures and further informed by his wartime experiences assessing blast-damaged structures and with the design of the "Morrison Shelter", an air-raid shelter which could be located indoors (Schofield 2006).
The name cam clay asserts that the plastic volume change typical of clay soil behaviour is due to mechanical stability of an aggregate of small, rough, frictional, interlocking hard particles.
[3] The Original Cam-Clay model is based on the assumption that the soil is isotropic, elasto-plastic, deforms as a continuum, and it is not affected by creep.
A limitation of this model is the possibility of negative specific volumes at realistic values of stress.
The difference between the Cam Clay and the Modified Cam Clay [4] (MCC) is that the yield surface of the MCC is described by an ellipse and therefore the plastic strain increment vector (which is perpendicular to the yield surface) for the largest value of the mean effective stress is horizontal, and hence no incremental deviatoric plastic strain takes place for a change in mean effective stress (for purely hydrostatic states of stress).
[5] In their note, Drucker and Prager also demonstrated how to use their approach to calculate the critical height of a vertical bank using either a plane or a log spiral failure surface.
Their approach was subsequently extended by Kenneth H. Roscoe and others in the soil mechanics department of Cambridge University.
The key factor driving the criticism is primarily the implicit assumption that soils are made of isotropic point particles.
Real soils are composed of finite size particles with anisotropic properties that strongly determine observed behavior.
Consequently, models based on a metals based theory of plasticity are not able to model behavior of soils that is a result of anisotropic particle properties, one example of which is the drop in shear strengths post peak strength, i.e., strain-softening behavior.
Further, elasto-plastic models describe the entire element as a whole and not specifically conditions directly on the failure plane, as a consequence of which, they do not model the stress-strain curve post failure, particularly for soils that exhibit strain-softening post peak.
Additional criticisms are that the theory is "only descriptive," i.e., only describes known behavior and lacking the ability to either explain or predict standard soil behaviors such as, why the void ratio in a one dimensional compression test varies linearly with the logarithm of the vertical effective stress.
For these reasons, critical-state and elasto-plastic soil mechanics have been subject to charges of scholasticism; the tests to demonstrated its validity are usually "conformation tests" where only simple stress-strain curves are demonstrated to be modeled satisfactorily.
The critical-state and concepts surrounding it have a long history of being "scholastic," with Sir Alec Skempton, the “founding father” of British soil mechanics, attributed the scholastic nature of CSSM to Roscoe, of whom he said: “…he did little field work and was, I believe, never involved in a practical engineering job.”[6].In the 1960s and 1970s, Prof. Alan Bishop at Imperial College used to routinely demonstrate the inability of these theories to match the stress-strain curves of real soils.
Joseph (2013) has suggested that critical-state and elasto-plastic soil mechanics meet the criterion of a “degenerate research program” a concept proposed by the philosopher of science Imre Lakatos, for theories where excuses are used to justify an inability of theory to match empirical data.
[7] The claims that critical state soil mechanics is only descriptive and meets the criterion of a degenerate research program have not been settled.
[10] Separation of Plane Strain Stress State Matrix into Distortional and Volumetric Parts:
The following data were obtained from a conventional triaxial compression test on a saturated (B=1), normally consolidated simple clay (Ladd, 1964).
