1 Foundations and retaining walls

Foundations and retaining walls If you have any doubts, you can check your textbook, pp. 90-91

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

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

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

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

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, 15500 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

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)

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:

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:

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:

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

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

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:

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

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: