SOIL MECHANICS AND FOUNDATION ENGINEERING-II (CE 311)

BEARING CAPACITY Bearing Capacity: Supporting /power of a soil or rock is referred to as its bearing capacity. Gross Bearing Capacity (q): the total pressure at the base of the footing due to the weight of the superstructure, self weight of the footing and the earth fill if any. Net Bearing Capacity (qn): Excess pressure or the difference in intensities of the gross pressure after the construction of the structure and the original overburden pressure. qn = q – gD Ultimate Bearing Capacity (qf): the minimum gross pressure intensity at the base of the foundation at which the soil fails in shear. Net Ultimate Bearing Capacity (qnf): the minimum net pressure intensity causing shear failure.

BEARING CAPACITY qf = qnf + 𝜎 Or qnf = qf - 𝜎 Net Safe Bearing Capacity (qns): the net ultimate bearing capacity divided by a factor of safety F. 𝑞 𝑛𝑠 = 𝑞 𝑛𝑓 𝐹 Safe Bearing Capacity (qs): The maximum pressure which the soil can carry safely without risk of shear failure. 𝑞 𝑠 = 𝑞 𝑛𝑠 +𝛾𝐷= 𝑞 𝑛𝑓 𝐹 +γ𝐷 Allowable Bearing Capacity (qa): Net loading intensity at which neither the soil fails in shear nor there is excessive settlement detrimental the structure.

Terzaghi’s Theory

Terzaghi’s Theory Parameter General Shear Failure Local/ Punching Shear Failure Strain Rate < 5% 10% to 20% Angle of shearing resistance > 36º <28º Penetration Test N≥30 N≤5 Plate Load Test Depends on Shape Density Index >70 < 20 Equation Parameters Cohesion Friction c tan f 2 3 c 2 3 tan f

Terzaghi’s Equations For Strip footing 𝑞 𝑓 =𝑐 𝑁 𝑐 + 𝜎 𝑁 𝑞 +0.5𝛾𝐵 𝑁 𝛾 For circular footing 𝑞 𝑓 =1.3 𝑐 𝑁 𝑐 + 𝜎 𝑁 𝑞 +0.3𝛾𝐵 𝑁 𝛾 For square footing 𝑞 𝑓 =1.3 𝑐 𝑁 𝑐 + 𝜎 𝑁 𝑞 +0.4𝛾𝐵 𝑁 𝛾 For rectangular footing 𝑞 𝑓 =𝑐 𝑁 𝑐 1+0.3 𝐵 𝐿 + 𝜎 𝑁 𝑞 +0.5𝛾𝐵 𝑁 𝛾 1−0.2 𝐵 𝐿

Effect of Water Table 𝑅 𝑤1 =0.5 1+ 𝐷 𝑓 −𝑎 𝐷 𝑓 to be applied in second term of equation 𝑅 𝑤2 =0.5 1+ 𝑏 𝐵 to be applied in third term of the equation

Terzaghi’s Bearing Capacity Factors

Terzaghi’s Bearing Capacity Factors (Degrees) General Shear Failure Local Shear Failure Nc Nq Ng 𝑁 𝑐 ′ 𝑁 𝑞 ′ 𝑁 𝛾 ′ 5.7 1.0 0.0 5 7.3 1.6 0.5 6.7 1.4 0.2 10 9.6 2.7 1.2 8.0 1.9 15 12.9 4.4 2.5 9.7 0.9 20 17.7 7.4 5.0 11.8 3.9 1.7 25 25.1 12.7 14.8 5.6 3.2 30 37.2 22.5 19.7 19.0 8.3 34 52.6 36.5 35.0 23.7 11.7 9.0 35 57.8 41.4 42.4 25.2 12.6 10.1 40 95.7 81.3 100.4 34.9 20.5 18.8 45 172.3 173.3 297.5 51.2 35.1 37.7 48 258.3 287.9 780.1 66.8 50.5 60.4 50 347.5 415.1 1153.2 65.6 87.1

PROBLEMS A square footing 2.5m x 2.5m is built in a homogenous bed of sand of unit weight 20 kN/m3 and having an angle of shearing resistance of 350. The depth of the base of footing is 1.5m below the ground surface. Calculate the safe load that can be carried by a footing with a factor of safety of 3 against complete shear failure. Use Terzaghi’s analysis. What will be the maximum safe load for problem 1 if the soil is loose sand of unit weight 16 kN/m3 and the angle of shearing resistance is 250. A strip footing, 1m wide at its base is located at a depth of 0.8m below the ground surface. The properties of the foundation soil are g=18kN/m3, c=30kN/m2 and f=200. Determine the safe bearing capacity using a factor of safety of 3. Assume soil fails by local shear.

PROBLEMS Solve problem 3 if the water table is located at the base of the footing. Assume saturated unit weight of the soil as equal to 19.5kN/m3. A strip footing 2m wide carries a load intensity of 400kN/m2 at a depth of 1.2m in sand. The saturated unit weight of sand is 19.5 kN/m3 and unit weight above water table is 16.8 kN/m3. The shear strength parameters are c=0 and f=350. Determine the factor of safety with respect to shear failure for the following cases of location of water table: water table is 4m below GL Water table is 1.2m below GL Water table is 2.5m below GL Water table is 0.5m below GL Water table is at GL itself.

PROBLEMS Design a strip footing to carry a load of 750 kN/m at a depth of 1.6m in c-f soil having a unit weight of 18kN/m3 and shear strength parameters as c=20kN/m2 and f=250. Determine the width of footing using factor of safety of 3 against shear failure. A rectangular footing 2m x 3m rests on a c-f soil, with its base at 1.5m below the ground surface. Calculate the safe bearing capacity using a factor of safety of 3 on (i) net ultimate bearing capacity, and (ii) ultimate bearing capacity. The soil has following parameters: g=18kN/m3, c=10kN/m2, f=300.