Critical state soil mechanics
Encyclopedia
Critical State Soil Mechanics is the area of Soil Mechanics
that encompasses the conceptual models that represent the mechanical behavior of saturated remolded soils based on the Critical State concept.
occur without any further changes in mean effective stress 
, deviatoric stress 
(or yield stress, 
, in uniaxial tension according to the von Mises yielding criterion), or specific volume 
:
where,
However, for triaxial conditions
. Thus,
All critical states, for a given soil, form a unique line called the Critical State Line (CSL) defined by the following equations in the space
:
where
, 
, and 
are soil constants. The first equation determines the magnitude of the deviatoric stress 
needed to keep the soil flowing continuously as the product of a frictional constant 
(capital 
) and the mean effective stress 
. The second equation states that the specific volume 
occupied by unit volume of flowing particles will decrease as the logarithm of the mean effective stress increases.
from research led by Professor Sir Alec Skempton at the Imperial Geotechnical Laboratories
, led to the publication of the critical state concept .
Roscoe obtained his undergraduate degree in mechanical engineering and his experiences trying to create tunnels to escape when held as a prisoner of war by the Nazis during WWII introduced him to soil mechanics. Subsequent to this 1958 paper, concepts of plasticity were introduced by Schofield and publa classic text book . Schofield was taught at Cambridge by Prof. John Baker
, a structural engineer who was a strong believer in designing structures that would fail "plastically". 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 .
, and it is not affected by creep. The yield surface of the Cam clay model is described by a log arc.
of Imperial College
who worked with Professor Roscoe is credited with the development of the modified version of the original model. The difference between the Cam Clay and the Modified Cam Clay (MCC) is that the yield surface of the MCC is described by an ellipse and therefore the plastic strain increment vector (which is vertical 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. This is very convenient for constitutive modelling in numerical analysis, especially finite element analysis, where numerical stability issues are important (as a curve needs to be continuous in order to be differentiable).
Soil mechanics
Soil mechanics is a branch of engineering mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids and particles but soil may also contain organic solids, liquids, and gasses and other...
that encompasses the conceptual models that represent the mechanical behavior of saturated remolded soils based on the Critical State concept.
Formulation
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. It states that soils and other granular materials, if continuously distorted (sheared) until they flow as a frictional fluid, will come into a well-defined critical state. At the onset of the critical state, shear distortions occur without any further changes in mean effective stress , deviatoric stress (or yield stress, , in uniaxial tension according to the von Mises yielding criterion), or specific volume :where,
However, for triaxial conditions
. Thus,All critical states, for a given soil, form a unique line called the Critical State Line (CSL) defined by the following equations in the space
:where
, , and are soil constants. The first equation determines the magnitude of the deviatoric stress needed to keep the soil flowing continuously as the product of a frictional constant (capital ) and the mean effective stress . The second equation states that the specific volume occupied by unit volume of flowing particles will decrease as the logarithm of the mean effective stress increases.History
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 LondonImperial College London
Imperial College London is a public research university located in London, United Kingdom, specialising in science, engineering, business and medicine...
from research led by Professor Sir Alec Skempton at the Imperial Geotechnical Laboratories
Imperial College Civil & Environmental Engineering
The Department of Civil and Environmental Engineering at Imperial College London is located in the Skempton Building at the South Kensington Campus in London. It is one of the 9 main academic departments of the Faculty of Engineering. The current Head of the Department is Professor David A...
, led to the publication of the critical state concept .
Roscoe obtained his undergraduate degree in mechanical engineering and his experiences trying to create tunnels to escape when held as a prisoner of war by the Nazis during WWII introduced him to soil mechanics. Subsequent to this 1958 paper, concepts of plasticity were introduced by Schofield and publa classic text book . Schofield was taught at Cambridge by Prof. John Baker
John Baker, Baron Baker
John Fleetwood Baker, Baron Baker OBE was a British scientist and structural engineer.-Early life:Baker was born in Liscard, Cheshire, a son of J.W. Baker and Emily Fleetwood...
, a structural engineer who was a strong believer in designing structures that would fail "plastically". 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 .
Original Cam-Clay Model
The Original Cam-Clay model is based on the assumption that the soil is isotropic, elasto-plastic, deforms as a continuumContinuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modelled as a continuous mass rather than as discrete particles...
, and it is not affected by creep. The yield surface of the Cam clay model is described by a log arc.
Modified Cam-Clay Model
Professor John BurlandJohn Burland
John Boscawen Burland CBE, DSc, FREng, FRS is an Emeritus Professor and Senior Research Investigator at the Department of Civil and Environmental Engineering of Imperial College London.-Early education:...
of Imperial College
Imperial College London
Imperial College London is a public research university located in London, United Kingdom, specialising in science, engineering, business and medicine...
who worked with Professor Roscoe is credited with the development of the modified version of the original model. The difference between the Cam Clay and the Modified Cam Clay (MCC) is that the yield surface of the MCC is described by an ellipse and therefore the plastic strain increment vector (which is vertical 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. This is very convenient for constitutive modelling in numerical analysis, especially finite element analysis, where numerical stability issues are important (as a curve needs to be continuous in order to be differentiable).