Elastic-Perfectly Plastic Soils

Question 1

What is perfect plasticity?

Answer 1

Yield stress does not change during plastic deformation

Question 2

What are the other 2 types of plasticity than perfect plasticity? What is the collective name for these models?

Answer 2

Hardening and Softening
Elasto-plastic models

Question 3

If soil is perfectly plastic, what is true of elastic strain?

Answer 3

There are no elastic strains after yield

Question 4

What is the flow rule and why is it used?

Answer 4

The ratio of plastic volumetric and deviatoric strains
The total strain vector must always be perpendicular to the yield surface

Question 5

According to the Tresca and Von Mises models, what is plastic volumetric strain?

Answer 5

Zero

Question 6

Where does yield occur for the Von Mises and Tresca models?

Answer 6

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

Question 7

What is the value of Poisson’s ratio for all elastic-perfectly plastic models?

Answer 7

0.5

Question 8

What defines a Mohr-Coulomb yield surface?

Answer 8

Failure is governed by the shear strength and primary axial stress equations

Question 9

What defines a Drucker-Prager yield surface?

Answer 9

Failure is governed by q=d+Mp’

Question 10

When do Mohr-Coulomb and Drucker-Prager yield surfaces agree?

Answer 10

When b = 0 (i.e. on the axis)

Question 11

What are some issues with the M-C and D-P models?

Answer 11

They predict no yield before failure and constant dilation angle, but these are unrealistic
The models do not predict a critical state

Question 12

How are the deviator stress and undrained shear strength related?

Answer 12

q = 2cu

Question 13

What is the equation for the undrained axial strain increment?

Answer 13

ΔεA = 1/Eu * (ΔσA - 2vuΔσR)

Question 14

What is the relationship of the stress and strain ratios for an associated flow rule?

Answer 14

Strain ratio = -1/stress ratio

Question 15

If a soil strains plastically during loading and is then unloaded, how is the unloading strain found?

Answer 15

It is the elastic strain only

Question 16

What is true of strain during unloading?

Answer 16

It is elastic only

Question 17

What is the equation for specific volume at any given point not on the normal compression or critical state lines?

Answer 17

v = N - λlnp’0 + ϰln(p’0/p’)

Question 18

What is the equation for the drained radial strain increment?

Answer 18

ΔεR = 1/E’ * (-v’Δσ’A + (1-v’)ΔσR)

Question 19

What is the factor K0?

Answer 19

σ’h/σ’v

Question 20

How do you calculate p’0 from p’ and q?

Answer 20

p’0 = (q^2/(M^2*p’)) + p’

Question 21

How are the factors Γ and N related?

Answer 21

Γ = N - (λ-κ)ln2

Question 22

What is the relationship between undrained shear strength, vertical effective stress and overconsolidation ratio?

Answer 22

cu = β (n)^Λ σ’v
β & Λ are soil constants based on prior investigation of the soil

Question 23

What types of constitutive models can account for cyclic loading?

Answer 23

Bounding Surface and Nested Yield Surface Models