1. 1
Foundations
and retaining walls

2. Foundations and retaining walls
If you have any doubts, you can check your textbook, pp

3. Foundations and retaining walls
Lesson 1
Shallow foundations Spread footings, foundation beams, slabs on grade
Deep foundations Piles, drilled shafts, caissons, sheet piles
Limit load
where: c = cohesion g = apparent specific weight
B = width of the foundation
q = pressure at the level of the foundation base
Nc, Ng, Nq = dimensionless coefficients function of the angle of internal
friction ϕ
The coefficients ξc = ξcf ⋅ ξci ⋅ ξct ξg =ξgf ⋅ ξgi ⋅ ξgt ξq = ξqf ⋅ ξqi ⋅ ξqt
can be computed in function of the shape of the foundation and of the inclination of the load and of the level of the foundation base (see PRONT).
Breaking limit load Qlim = qlim ∙ B

4. Foundations and retaining walls
Lesson 2
Spread footing: central concentrated load
Spread footing: load with small eccentricity (e < H/6)
Spread footing: load with large eccentricity (e > H/6)
Spread footing: shear test

5. Foundations and retaining walls
Lesson 3
Rigid spread footing
A spread footing can be considered rigid
if its height exceeds
1.75 times its projection:
where: F = resultant of the major forces acting on half of the base
of the spread footing
c = distance between F and the base of the spread footing
h = height of the spread footing

6. Foundations and retaining walls
Lesson 4
Flexible spread footing
A spread footing can be considered flexible if its height is less than 1.75 times its projection. Testing of the reinforcement is done with an equivalent rectangular section:
Testing of resistance to punching shear stress
Fp =0,5(4B* · h*) · fctd
where: resistance of reinforced concrete to tensile stress

7. Foundations and retaining walls
Lesson 5
Foundation beams
Rigid foundation if
where: J = moment of inertia of the foundation beam in m4
B = width of the beam in m
l = maximum distance between two adjoining piers in m
n = 6500 for non-cohesive soils, for cohesive soils
Extreme loads
where: R = total resultant of the loads
L = total length of the beam
e = eccentricity of the resultant with respect to the centroid
of the beam

8. Foundations and retaining walls
Lesson 8
Rankine theory
Horizontal pressure of the soil at depth z: po = gt ⋅ z ⋅ Ka
where: gt = specific weight of the soil
z = depth
= coefficient of active pressure
Total pressure (without excess load):
Magnitude:
Direction: horizontal
Line of action: (h = height of the wall; y = distance from the base of
the wall)

9. Foundations and retaining walls
Lesson 8
Rankine theory
Total pressure (with excess load d):
Magnitude:
where: = fictitious height of the soil
Direction: horizontal
Line of action:

10. Foundations and retaining walls
Lesson 9
Generalized Coulomb theory
Total pressure
Magnitude:
ϕ = angle of internal friction of soil
β1= inclination with respect to the internal horizontal face of the wall
δ = angle of friction between wall and soil
ε = inclination with respect to the horizontal surface of the soil
Direction: inclined at angle δ with respect to the perpendicular to the internal face of the wall
Line of action:

11. Foundations and retaining walls
Lesson 13
Overturning test
Allowable stress method:
Limit state method:
Actions: Coeff. (EQU)
Geotechnical parameters: Coeff. M2
Resistance: Coeff. gR =1
Test:

12. Foundations and retaining walls
Lesson 14
Sliding test
Allowable stress method:
Horizontal base
Inclined base
where: f = tanδ; δ = angle of friction between wall and soil or wall and wall
V = vertical component of pressure
W = weight of the wall
G = weight of possible soil on a higher ground level above the footing
Q = horizontal component of pressure
α = inclination of the base with respect to the horizontal

13. Foundations and retaining walls
Lesson 14
Sliding test
Limit state method:
Actions: Coeff. A1
Geotechnical parameters: Coeff. M1
Resistance: Coeff. gR = 1,1
Test:
Horizontal base
Inclined base

14. Foundations and retaining walls
Lesson 15
Bearing capacity failure test
Distance between the resultant and the overturning point:
where: MS = stabilizing moment; MR = overturning moment;
N = V + W + G resultant of vertical loads
Eccentricity: where: H = width of the base
Allowable stress method:
Maximum stresses:

15. Foundations and retaining walls
Lesson 15
Bearing capacity failure test
Ultimate stress:
where:
c = cohesion
g = specific weight of soil
D = depth of the foundation
with respect to the lower
ground level

16. Foundations and retaining walls
Lesson 15
Bearing capacity failure test
Limit state method:
Actions: Coeff. A1
Geotechnical parameters: Coeff. M1
Resistance: Coeff. gR = 1,4
Limit load: Test: