Section 3

Question 1

Shear Stress (𝜏)

Answer 1

shear-Force / Area

Question 2

Shear Strain (γ-xz)

Answer 2

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)

Question 3

Normal Stress

Answer 3

force applied perpendicular to an area/surface

Question 4

Normal Strain

Answer 4

Change in shape (in Geotech we focus on a change in height) of an object

Question 5

Shear Stress

Answer 5

Force applied parallel to an area/surface

Question 6

Shear Strain

Answer 6

deformation (angular) as a result of a parallel force applied to a surface

Question 7

What directions are we focused on in geotech for analyzing stress and strain?

Answer 7

• 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)

Question 8

What kind of reactions does soil have under compression?

Answer 8

• linear elastic: increase and decrease linearly
• non-linear elastic response: increase and decrease non-linear elastically

Question 9

How does soil behave under loading an unloading?

Answer 9

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.

Question 10

Elastic response

Answer 10

applied stress→ deformation
remove stress→ back to original shape
(hair tie example)

Question 11

Plastic response

Answer 11

applied stress → deformation
remove stress→ retains deformation caused by applied stress
(car bumper example)

Question 12

What do we assume about soil in regards to stresses and strains?

Answer 12

We assume that most soils are linear, isotropic, and elastic, so stresses and strains can be related through Hooke’s Law

Question 13

Hooke’s Law

Answer 13

G = E / [2*(1+v)]

E: Young’s Modulus
v: poissons ratio
G: Shear modulus

Question 14

Why is appropriate to assume that soils are linear, isotropic, and elastic?

Answer 14

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.

Question 15

How does soil behave in reaction to small strains?

Answer 15

Soil behaves elastically in response to small strains

Question 16

How does soil behave in reaction to large strains?

Answer 16

Soil behaves plastically in response to large strains

Question 17

What sign convention is used for compression and tension in geotech?

Answer 17

compression: (+)
tension: (-)
Why: compression states are more common in soil behavior and geotech likes to make things easier

Question 18

What is the plain strain condition?

Answer 18

some value of stress (σ) in the x and z-direction, and no stress (0) or strain in y-direction

Question 19

What is the axial symmetric condition?

Answer 19

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.

Question 20

What are the axis for drawing Mohrs Circle?

Answer 20

x-axis: Normal force applied (σ, normal stress)
y-axis: Shear stress (τ, shear force)

Question 21

How are points generated for the Mohrs Circle?

Answer 21

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

Question 22

What are the major and minor principle stress on Mohrs Circle?

Answer 22

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

Question 23

How do you draw the pole on Mohrs Circle?

Answer 23

• 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

Question 24

How do you draw the major principle stress plane?

Answer 24

Draw a line from the pole to the major principle stress (σ1: largest value on the circle where τ:shear force equals zero)

Question 25

Effective stress only applies to soils that have what saturation level?

Answer 25

100% saturation, completely saturated

Question 26

What is total stress (σ)?

Answer 26

Total stress (σ) is the combination (sum) of inter-particle forces and pore water pressure

Question 27

What is effective stress (σ-bar)?

Answer 27

Effective stress (σ-bar) removes the effect of pore water pressure

Question 28

If you don’t have pore water pressure what is the only stress you are dealing with?

Answer 28

effective stress (σ-bar)