Elastic-Perfectly Plastic Soils Flashcards
What is perfect plasticity?
Yield stress does not change during plastic deformation
What are the other 2 types of plasticity than perfect plasticity? What is the collective name for these models?
Hardening and Softening
Elasto-plastic models
If soil is perfectly plastic, what is true of elastic strain?
There are no elastic strains after yield
What is the flow rule and why is it used?
The ratio of plastic volumetric and deviatoric strains
The total strain vector must always be perpendicular to the yield surface
According to the Tresca and Von Mises models, what is plastic volumetric strain?
Zero
Where does yield occur for the Von Mises and Tresca models?
VM: yield occurs when b = 0.5
T: yield can occur when 0<b<1, except on the corners of the yield surface due to the undefined direction of the strain vector
What is the value of Poisson’s ratio for all elastic-perfectly plastic models?
0.5
What defines a Mohr-Coulomb yield surface?
Failure is governed by the shear strength and primary axial stress equations
What defines a Drucker-Prager yield surface?
Failure is governed by q=d+Mp’
When do Mohr-Coulomb and Drucker-Prager yield surfaces agree?
When b = 0 (i.e. on the axis)
What are some issues with the M-C and D-P models?
They predict no yield before failure and constant dilation angle, but these are unrealistic
The models do not predict a critical state
How are the deviator stress and undrained shear strength related?
q = 2cu
What is the equation for the undrained axial strain increment?
ΔεA = 1/Eu * (ΔσA - 2vuΔσR)
What is the relationship of the stress and strain ratios for an associated flow rule?
Strain ratio = -1/stress ratio
If a soil strains plastically during loading and is then unloaded, how is the unloading strain found?
It is the elastic strain only
What is true of strain during unloading?
It is elastic only
What is the equation for specific volume at any given point not on the normal compression or critical state lines?
v = N - λlnp’0 + ϰln(p’0/p’)
What is the equation for the drained radial strain increment?
ΔεR = 1/E’ * (-v’Δσ’A + (1-v’)ΔσR)
What is the factor K0?
σ’h/σ’v
How do you calculate p’0 from p’ and q?
p’0 = (q^2/(M^2*p’)) + p’
How are the factors Γ and N related?
Γ = N - (λ-κ)ln2
What is the relationship between undrained shear strength, vertical effective stress and overconsolidation ratio?
cu = β (n)^Λ σ’v
β & Λ are soil constants based on prior investigation of the soil
What types of constitutive models can account for cyclic loading?
Bounding Surface and Nested Yield Surface Models
