Section 3 Flashcards
Shear Stress (𝜏)
shear-Force / Area
Shear Strain (γ-xz)
tan^-1( Δx / z)
Δx: displacement in the x-direction
z: height (vertical distance)
γ-xz: angle formed due to shear force (which is what strain is - deformation)
Normal Stress
force applied perpendicular to an area/surface
Normal Strain
Change in shape (in Geotech we focus on a change in height) of an object
Shear Stress
Force applied parallel to an area/surface
Shear Strain
deformation (angular) as a result of a parallel force applied to a surface
What directions are we focused on in geotech for analyzing stress and strain?
- z and x directions, because we assume that x and y are equal
- x is horizontal and z is vertical
- z values increase positively with depth (0 at the top, largest value at the bottom)
What kind of reactions does soil have under compression?
- linear elastic: increase and decrease linearly
- non-linear elastic response: increase and decrease non-linear elastically
How does soil behave under loading an unloading?
Elasto-plastic: Soil has elastic and plastic tendancies. Under loading, the soil will experience stress up to a point and when unloaded back to no load, the soil will hold some strain - it will not have the same initial strain (0) it had before loading, instead, it will be greater than 0 due to the plastic deformation.
Elastic response
applied stress→ deformation
remove stress→ back to original shape
(hair tie example)
Plastic response
applied stress → deformation
remove stress→ retains deformation caused by applied stress
(car bumper example)
What do we assume about soil in regards to stresses and strains?
We assume that most soils are linear, isotropic, and elastic, so stresses and strains can be related through Hooke’s Law
Hooke’s Law
G = E / [2*(1+v)]
E: Young’s Modulus
v: poissons ratio
G: Shear modulus
Why is appropriate to assume that soils are linear, isotropic, and elastic?
Because a lot of times, the stresses and strains we apply to soils are so small that soil does mostly behave in a linear elastic way.
So, for very large stresses and strains it is not appropriate to make this assumption.
How does soil behave in reaction to small strains?
Soil behaves elastically in response to small strains
How does soil behave in reaction to large strains?
Soil behaves plastically in response to large strains
What sign convention is used for compression and tension in geotech?
compression: (+)
tension: (-)
Why: compression states are more common in soil behavior and geotech likes to make things easier
What is the plain strain condition?
some value of stress (σ) in the x and z-direction, and no stress (0) or strain in y-direction
What is the axial symmetric condition?
Assuming that stresses in the x and y direction are equal so we use a cylinder (instead of a cube for infinitesimally small particle) and use r for radius instead of x or y.
can be used for tanks, pools, any cylindrical shaped thing sitting on the ground.
What are the axis for drawing Mohrs Circle?
x-axis: Normal force applied (σ, normal stress)
y-axis: Shear stress (τ, shear force)
How are points generated for the Mohrs Circle?
x and y coordinates are the corresponding normal and shear forces applied at each face of an infinitesimally small particle
So, a particle experiencing normal forces on two sides will generate two separate points for our Mohrs circle
What are the major and minor principle stress on Mohrs Circle?
Major principle stress (σ1): largest value on the circle where τ (shear force) equals zero
Minor principle stress (σ3): smallest value on the circle where τ (shear force) equals zero
How do you draw the pole on Mohrs Circle?
- identify the vertical force
- identify the plane the vertical force is acting on
- draw a line in the same direction as the plane the vertical force is acting on and through the point representing the forces acting on that plane
- NEXT, identify the horizontal force
- identify the plane the horizontal force acts on
- draw a line in the same direction as the plane the horizontal force is acting on and through the point representing the forces acting on that plane
How do you draw the major principle stress plane?
Draw a line from the pole to the major principle stress (σ1: largest value on the circle where τ:shear force equals zero)
Effective stress only applies to soils that have what saturation level?
100% saturation, completely saturated
What is total stress (σ)?
Total stress (σ) is the combination (sum) of inter-particle forces and pore water pressure
What is effective stress (σ-bar)?
Effective stress (σ-bar) removes the effect of pore water pressure
If you don’t have pore water pressure what is the only stress you are dealing with?
effective stress (σ-bar)
