Modelo Elasto-Plástico Del Suelo

Elastic-Plastic Soil Model
Assoc. Prof. Dr. Mohd. Jamaludin Md. Noor / Dr. SONG KI IL mohdjamaludinmdnoor@yahoo.com Geotechnical, Highway & Survey Eng. Division Faculty of Civil Engineering Universiti Teknologi MARA Shah Alam, MALAYSIA

Is soil a plastic or elastic material ?

Problem base / outcome base teaching approach.
At the end of this lecture the student should be able to answerthese questions. 1. Plastic behaviour is considered as soil irrecoverable deformation while elastic is taken the behaviour when deformation is recoverable. Illustrate using the relevant graphs that soil behave elastically within the yield limit and plastic when the stress exceeded the yield limit. 2. Differentiate the meaning of yield and failure. Explain the meaning of failure at peak strength andfailure at critical state. 3. By referring to the changes undergo by the solid particles when being compressed explain how the soil able to behave plastic and elastic manner. With the aid of v – log p’ curve differentiate the path which is elastic and plastic and show how their magnitude can be calculated. 4. The yield limit can be define by the pre-consolidation pressure in clay and the pastmaximum deviator stress in sand. Explain these. 5. Show that the yield limit is the past maximum mobilised shear strength whether it is clay or sand. Explain how that mobilised shear strength governs the elastic and plastic behaviour of sand. 6. Mobilised shear strength envelope define the yield limit or the yield locus. In other words the mobilised shear strength represents a certain deformationparameter. Explain this. 7. With the aid of graphs of q-p’ and v-p’ explain how the different sizes of the yield locus is achieved and relate them to the soil elastic and plastic behaviour. 8. Using the behaviour of a specimen in CID triaxial test explain the principal governing factor that influence the specimen’s deformation. Emphasize your answer by considering 3 identical specimens sheared atdifferent effective stress. 9. Explain the uniqueness of the critical state line (CSL) by the sketching the line in 3-dimensional space of q-p’-v. Differentiate the stress path that lead to the CSL when the test specimens are normally consolidated, lightly consolidated and over-consolidated clay. 10. With the aid of sketches of the relevant graphs show that it is not the critical state strength thatgoverns soil volume change behaviour but it is in fact the mobilised shear strength.

DEFINITION OF Mean stress, p’, Deviatoric or shear stress, q, Volumetric strain, εp, Shear strain, εq.
σ1
p

σ2
q

σ3
Mean stress represented by space diagonal

p=

σ1 + σ 2 + σ 3
3

Volume change

Volumetric strain

εp

Deviatoric stress or shear stress

ε p = ε1 + ε 2 + ε 3

1 (σ 1 −σ 2 )2 + (σ 2 − σ 3 )2 + (σ 3 − σ 1 )2 q= 2

[

]

1

2

Distortion or shearing

Deviatoric strain

εq

2 (ε 1 − ε 2 )2 + (ε 2 − ε 3 )2 + (ε 3 − ε 1 )2 εq = 3

[

]

1

2

TWO COMMON CONDITIONS OF STRESS AND STRAIN IN GEOTECHNICAL ENGINEERING Triaxial condition/ σ1 σ 2 = σ 3 ε2 = ε3 Axisymmetric

p =

'

σ 1' + 2σ 3'
3

' q = σ 1' − σ 3

ε p = ε 1 + 2ε 3Volumetric strain

2 ε q = (ε 1 − ε 3 ) 3
Shear strain

σ3

σ2

Plane strain

ε2 = 0
' 3

p =

'

σ +σ +σ
3

' 1

' 2

1 (σ 1 − σ 2 )2 + (σ 2 − σ 3 )2 + (σ 3 − σ 1 )2 q= 2

[

]

1

2

ε p = ε1 + ε 3

2 2 ε q = ε 1 + ε 32 − ε 1ε 3 3

[

]

1

2

Soil elastic response to stress
BULK MODULUS, K’, SHEAR MODULUS, G’ AND ELASTIC MODULUS, E’.

1 ε = p' K' 1e εq = q 3G
e P

p '  K ' 0  ε e    p  =  ε e   q   0 3G   q   
Shear stress do not cause volume changes and net mean stress do not cause shear deformation. Shear stress only produce shear deformation and net mean stress only produce volume changes.

Effective bulk modulus Shear modulus modulus

E' K '= 3(1 − 2υ ')

Poisson ratio as a function of K’ and G’

E'...