Shallow Foundations

I've decided to jump to shallow foundations. I'll come back to phase relationships and compaction later.

What do we mean by shallow foundation?
In simple terms, a foundation with depth to width ratio less than or equal to one typically, i.e. Df/B <= 1 ; however, it may be more.(Bowles, 5th Ed.)

Sources of uncertainties in foundation design:
1. Load estimation
2. Variability of soil conditions at the site
3. Evaluation of engineering properties of soil and rock at the site
4. uncertainties in modeling

The bearing capacity of shallow foundation (strip footing) can be evaluated with the use of Terzaghi's equation:

Ultimate Bearing Capacity, T(ult) = cNc + qNq + 0.5ByNy

or in words, T(ult) = contribution for cohesion + contribution from overburden (and surcharge) + contribution from soils (failure zone) below the footing.

c = cohesion, psf
y = unit weight, pcf
B = width of the footing, ft
q = yDf where Df is the depth of the footing below the ground level.
Nc, Nq, Ny = bearing capacity factors

The coefficients of each term in the equation changes with the shape of foundation, e.g. for square footing,

T(ult) = 1.3cNc + qNq + 0.4ByNy

Sand: There is negligible cohesion in sands, so we can remove the cohesion term from the equation to calculate the bearing capacity of a shallow foundation in sand.
T(ult) = qNq + 0.5ByNy (assuming strip footing)

Saturated clay: For phi = 0, we'll have Ny = 0. Therefore,
T(ult) = cNc + qNq (assuming strip footing)
one of the implications of the above equation is:

for angle of internal friction, phi = 0, Nc = 5.7, Nq = 1.0 (refer to Table 36.2 in CERM 11th edition)
T(ult) = 5.7c + yDf
Net bearing capacity, T(net) = T(ult) - yDf ...apply overburden correction to get net bearing capacity.
Therefore,
T(net) = 5.7c
Allowable Bearing Capacity, T(all) = T(net)/Factor of safety, assume FS = 2.5, we get
T(all) = 5.7c/2.5 = 2.3c ~ 2c (for practical purposes)

Hence, we see that the allowable bearing capacity of shallow foundation on saturated clay is approximately twice the cohesive strength of the soil.

Also, since c = qu/2 ... qu = unconfined compressive strength,
T(all) = qu ...for practical purposes

I hope you enjoyed the start. We'll solve a problem tomorrow...