geotechnical engineering_chapter 2 - critical state soil mechanics

8/10/2019 geotechnical engineering_Chapter 2 - Critical State Soil Mechanics

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CEGB 333GEOTECHNICAL ENGINEECHAPTER 1: CRITICAL STATE SOIL MEC

MISS INTAN NOR ZULIANA BIN

INTAN@


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CONTENTS OF MODULE 2

Critical State Concept. State Boundary Surface. Critical State Line and Stress Paths. Soil Yielding.


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Is used to interpret soil behaviour

The concept is that soil and other granular materials, if continuodistorted and sheared until they flow as a frictional fluid, will cowell-defined critical state.


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CRITICAL STATE THEORY

The particulate nature and porosity of soil leads to volume chansignificant magnitude under compressive and shearing loadingbecause of the wide range of permeabilities

, the rate of volumesome sands is so fast as to be almost instantaneous, whereas incould be 10 million times slower. It is therefore necessary to relachanges in stress state to the consequent short-term and long-tchanges in volume.

The parameter phi and c, evaluated from a stress-state analysisMohr-Coulomb criterion, are valid for a given soil only at a partiand may vary considerably at different volumes. The undrainedstrength, su is directly related to the water content of the soil.


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The critical state theory provides a unified model of soil behaviothe stress state and volume states are interrelated. The concepproposed in 1958 by Roscoe, Scholfield and Worth in a paper onof soils and further work followed mainly in the University of Ca

A model is proposed in which the soil will yield i.e. pass from pu

to elasto-plastic behaviour, at a critical specific volume (vc = 1+e

Yielding or shear slipping is then considered to be occurring as tcombination of effective stress (1,2 ,3) and the specific volucoincides with a state boundary surface. This state boundary surseen as a three-dimensional analogue of a failure envelope such

Coulomb criterion.


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Consider a series of a six triaxial compression tests on specimens of th

normally consolidated clay in which pairs of specimens are consolidatsame value of isotropic stress (po) before the major principal stress isto the yield point. Figure 1 shows the stress paths for the six test in q/

Consolidation stages: O>C1, O>C2, O>C3

Undrained specimens : O>U1, O>U2, O>U3

Drained specimens : O>D1, O>D2, O>D3

At respective yield points the stress paths each terminate on the samenvelope (qf= Mpf). However, during uniaxial stages of the drained tin volume takes place, whereas in the undrained tests the volume remconstant.

For example a complete model of the stress-strain behaviour, therefovolume associated with changes in stress must be incorporated.


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During consolidation under isotropic stress (po) the volume chamove along the normal consolidation line (NCL), as shown in Fivolume/stress paths are drawn in v/p space, where v= specific v(=1+e). The drained paths CD indicate a decrease in volume aundrained paths C indicate constant volume. The curve passi

points U1, D1, U2, D2, U3 and D3 represents the failure criterion inwhich is projection of the failure criterion in q/p space.


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Figure 1: q/v/p plots of triaxial test results


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Thus Figure 1(a) and 1(b) are respectively an elevation and a pladimensional failure criterion line in q/v/p space: this is called thstate line (CSL).

The critical state line (CSL) is a curve drawn on a three dimensio

boundary surface which represents the yielding of soil, i.e. it is tbetween elastic and plastic behaviour.

For convenience in mathematical interpretations the plan view often shown as v/ln p (Fig 1 (c))


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The critical state model was developed using remoulded saturait may be assumed sufficiently representative of naturally occurprovide a generalised model of behaviour.

The defining equations and other relevant relationships must n

established.

The CSL line is shown in a three-dimensional projection in Figur

For analytical purposes it is convenient to use the q/p elevationp plan.


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Figure 2 : A three-dimensional projection of the critical state line


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The normal consolidation and swelling linesfor isotropic and one-dimensionalconsolidation may be assumed parallel andto have same slopes ( and ).

However, the intercepts of the specificvolume axis for one-dimensionalconsolidation are lower (Fig 3) and areparallel to compression curve drawn in e/logp space. Figure 3 : Consol

swelling lines in v


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Figure 4: critical state line and stress paths for undrained loading on anormally consolidated clay


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Referring to Fig 1, the families of CU and CD stress paths arhave similar shapes.

These paths in fact traverse a three-dimensional surface whoseare the CSL and the NCL.

This is clearly part of the state boundary surface and is called Rosurface. The position of the stress path on the Roscoe surface isby the consolidation pressure (p0).


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In the case of lightly overconsolidated soil, the stress path will con the swelling line at point (L) between the NCL and the CSL (fat a volume greater than critical and at a moisture content wettcritical.

Under undrained loading, the path will be LD.


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Figure 5: critical state plot for lightly overconsolidated soil


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A heavily overconsolidated soil will have been consolidated to a

on the swelling line below the CSL (point H in Figure 6). Under uloading, with the volume remaining constant, the stress path wwhere UH is a point above the projection of the CSL passing thrq/p origin.

After yielding, the stress path will continue with further straininstraight line (TS) to meet the CSL in S.

The critical state is only likely to be reached in part of the soil adslip surfaces that may develop.

The greater the degree of overconsolidation, the greater is the required to bring the soil to its critical state.


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Figure 6: critical state plot for heavily overconsolidated soil

U d d i d l di diti h il lid t d


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Under undrained loading conditions heavily overconsolidated sexpand and the volume will continue to increase after yielding. path will be HDH, where DH is a failure point also on the TS li

After yielding, the increase in volume causes the stresses to fallresidual value (RH) which may be on or below the projected CSL

soil adjacent to slip planes will be affected to a much greater dethus become weaker.

The line TS therefore represents that part of the state boundarywhich governs the yielding of heavily overconsolidated soils andHvorslev surface.

The third part of the state boundary surface lies between O andspace. This represents the condition of zero tensile stress whichassumed limit for soils and is called the no tension cut-off. Fig 7constant volume section of the complete state boundary surfac


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Figure 7: critical state boundary surface Figure 8: three- dimensional critical state b


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It is important to distinguish between the behaviour of normally conoverconsolidated soils. The stress paths for a normally consolidated the Roscoe surface, whereas stress paths for overconsolidated soil lieprogressively further way as the degree of consolidation increases.

In the case of overconsolidated soils, critical states are preceded by pother) states; the overconsolidation ratio has a significant effect on s

Normally consolidated soil the stress paths traverse the Roscoe surfathe CSL at S.

With overconsolidation and so the stress paths start between E and

Lightly overconsolidated soils are less dense and wetter than criticalstress path (LS) reach the CSL from below.

Heavily overconsolidated soils are more dense and drier than criticalstress paths commence between O and E before curving slightly in tdirection as they rise toward Hvorslev surface. They then follow the surface if straining continues undrained or fall back slightly when dra


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It is important to recognise the three significant stress states inheavily overconsolidated soils. The peak stress shear is reachedstress path reaches the Hvorslev surface, whereas the critical stat the CSL.

After large strains, especially along slip surfaces, the ield stress back to a lower residual value.

geotechnical engineering_chapter 2 - critical state soil mechanics

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