Soils Final

Difficulties with soils are not due to soils themselves, but....

to the water contained in their voids (no water=no soil machanics)

Total Stress at a point (σ)

the stress resulting from the weight of everything above this point. SUM of the effective stress and pore water pressure.

Pore Water Pressure (u)

is the stress carried by the water in the soil pores in the cross section

Effective Stress (σ')

is the inter-granular or contact force between soil particles

Pore Water Pressure depends…

if the water is flowing through the soil or not

Static (Not flowing through soil) = u = γwZw

Flowing through soil = u = γwhp

Final Stress

σf = σi + Δσ

Stress Increase (Δσ) due to Point Load

(Increase in vertical stress Δσ at a point at a distance r from a point load, and depth z from the level where force is applied.

Δσ = P *I1 /z2

Δσ due to Rectangular Footing

(under the corner of a uniformly loaded rectangular area)

Δσ = q * I4 (m = B/z, n= L/z)

Δσ due to Circular Footing

The increase in vertical stress (Δσ) at a point under the center of a uniformly loaded circular area (R = Raduis)

Δσ = q * I

Δσ due to Infinitely Long New Soil Layer (Embankment)

The increase in vertical stress (Δσ) applied at the surface

Δσ = γ *z

Stress Decreases...

the farther the point is from the foundation

Mohr Circle and Soil Stresses

if a soil element is subjected to normal stresses σx and σy and shear stresses of txy

In soil mecahnics....

compression stress is positive,

counter-clockwise shear is negative

Principal Stresses

where mohr circle intersects x axis, intersection points are called principal stress (σ1, major and σ3, minor )

Principal Planes

Planes that have zero shear

Origin of Planes

Point on the Mohr Circle that is used as a reference point to find the stresses on any plane on a soil element or soil sample.

Mohr circle can be plotted using

total stresses or effective stresses

soil fails due to

shear

shear strength of soil is the...

maximun resistance that the soil offers to resist shear stresses along any plane in the soil mass

soil shear strength and behavior depends on....

effective stress

Coulomb assumed a linear relationship between strength and normal stress

t = c + σ' tan Φ

Failure Envelope

tangent to mohr circles

points on this line represents stresses on the failure planes of soil samples

Shear Strength for Sands

σ1 = σ3 tan (45+ Φ/2)^2 + 2c tan (45+Φ/2)

Normally consolidated Soil

c ~ 0

Over Consolidated Soil

t = c + σ' tan Φ

Dry Soils

effective stress = total stress