CE 333 Geotechnical Engineering II Sultan Mohammad Farooq Sheikh Sharif Ahmed Department of Civil Engineering Chittagong University of Engineering & Technology Bearing Capacity of Shallow Foundation The General Bearing Capacity Equation can be written in the following formπ ππ = ππ΅π πππ πππ πππ + ππ΅π πππ πππ πππ + πΈπ©π΅πΈ ππΈπ ππΈπ ππΈπ π Where, ππ’ = πππ‘ππππ‘π π΅ππππππ πΆππππππ‘π¦ π = ππβππ πππ π = ππππππ‘ππ£π π π‘πππ π ππ‘ π‘βπ πππ£ππ ππ π‘βπ πππ‘π‘ππ ππ π‘βπ πππ’ππππ‘πππ πΎ = π’πππ‘ π€πππβπ‘ ππ π πππ π΅ = π€πππ‘β ππ πππ’ππππ‘πππ = ππππππ‘ππ πππ π πππππ’πππ πππ’ππππ‘πππ πΉππ , πΉππ , πΉπΎπ = π βπππ ππππ‘πππ πΉππ , πΉππ , πΉπΎπ = ππππ‘β ππππ‘πππ πΉππ , πΉππ, πΉπΎπ = ππππ ππππππππ‘πππ ππππ‘πππ ππ , ππ , ππΎ = πππππππ πππππππ‘π¦ ππππ‘πππ Bearing Capacity of Shallow Foundation Bearing Capacity Factors π΅π = (π΅π −π) πππ∅ ∅ π πππ§ ∅ π π΅π = πππ ππ + π π π΅πΈ = π΅π − π πππ§ π. π ∅ (Meyerhof) π΅πΈ = π. π π΅π − π πππ§ ∅ (Hansen) π΅πΈ = π π΅π + π πππ§ ∅ (Vesic) Bearing Capacity of Shallow Foundation ∅ Nc Nq π΅πΈ (M) π΅πΈ (V) π΅πΈ (H) ∅ Nc Nq π΅πΈ (M) π΅πΈ (V) π΅πΈ (H) 0° 1° 2° 3° 4° 5° 6° 7° 8° 9° 10° 11° 12° 13° 14° 15° 16° 17° 18° 19° 20° 21° 22° 23° 24° 5.10 5.38 5.63 5.90 6.19 6.49 6.81 7.16 7.53 7.92 8.34 8.80 9.28 9.81 10.37 10.98 11.63 12.34 13.10 13.93 14.83 15.81 16.88 18.05 19.32 1.00 1.09 1.20 1.31 1.43 1.57 1.72 1.88 2.06 2.25 2.47 2.71 2.97 3.26 3.59 3.94 4.34 4.77 5.26 5.80 6.40 7.07 7.82 8.66 9.60 0.00 0.00 0.01 0.02 0.04 0.07 0.11 0.15 0.21 0.28 0.37 0.47 0.60 0.74 0.92 1.13 1.37 1.66 2.00 2.40 2.87 3.42 4.07 4.82 5.72 0.00 0.07 0.15 0.24 0.34 0.45 0.57 0.71 0.86 1.03 1.22 1.44 1.69 1.97 2.29 2.65 3.06 3.53 4.07 4.68 5.39 6.20 7.13 8.20 9.44 0.00 0.00 0.01 0.02 0.05 0.07 0.11 0.16 0.22 0.30 0.39 0.50 0.63 0.78 0.97 1.18 1.43 1.73 2.08 2.48 2.95 3.50 4.13 4.88 5.75 25° 26° 27° 28° 29° 30° 31° 32° 33° 34° 35° 36° 37° 38° 39° 40° 41° 42° 43° 44° 45° 46° 47° 48° 49° 20.72 22.25 23.94 25.80 27.86 30.14 32.67 35.49 38.64 42.16 46.12 50.59 55.63 61.35 67.87 75.31 83.86 93.71 105.11 118.37 133.87 152.10 173.64 199.26 229.93 10.66 11.85 13.20 14.72 16.44 18.40 20.63 23.18 26.09 29.44 33.30 37.75 42.92 48.93 55.96 64.20 73.90 85.37 99.01 115.31 134.87 158.50 187.21 222.30 265.50 6.77 8.00 9.46 11.19 13.24 15.67 18.56 22.02 26.17 31.15 37.15 44.43 53.27 64.07 77.33 93.69 113.99 139.32 171.14 211.41 262.74 328.73 414.33 526.46 674.92 10.88 12.54 14.47 16.72 19.34 22.40 25.99 30.21 35.19 41.06 48.03 56.31 66.19 78.02 92.25 109.41 130.21 155.54 186.53 224.64 271.75 330.34 403.66 496.00 613.15 6.76 7.94 9.32 10.94 12.84 15.07 17.69 20.79 24.44 28.77 33.92 40.05 47.38 56.17 66.76 79.54 95.05 113.96 137.10 165.58 200.81 244.65 299.52 368.67 456.41 Bearing Capacity of Shallow Foundation Author Factor Condition πππ ∅ = 0° Relationship πΉππ = 1 + 0.2 πΉππ = πΉπΎπ = 1.0 Shape πππ ∅ ≥ 10° πΉππ = 1 + 0.2 π΅ πΏ Meyerhof πΉππ = πΉπΎπ = 1 + 0.1 πππ ∅ = 0° π‘ππ2 45 + π΅ πΏ ∅ 2 π‘ππ2 45 + πΉππ = 1 + 0.2 ∅ 2 π·π π΅ πΉππ = πΉπΎπ = 1.0 Depth πππ ∅ ≥ 10° πΉππ = 1 + 0.2 π·π πππ πππ¦ ∅ π‘ππ 45 + π΅ πΉππ = πΉπΎπ = 1 + 0.1 Inclination π΅ πΏ π·π π΅ πΉππ = πΉππ = 1 − π‘ππ 45 + πΌ° 2 90° πΌ° 2 ∅° πππ ∅ > 0° πΉπΎπ = 1 − πππ ∅ = 0° πΉπΎπ = 0 ∅ 2 ∅ 2 Bearing Capacity of Shallow Foundation Author Factor Condition Relationship πΉππ = 1 + Shape πππ πππ ∅ ππ π΅ πΏ ππ π΅ πΉππ = 1 + tan ∅ πΏ π΅ πΉπΎπ = 1 − 0.4 πΏ Hansen & Vesic π·π π·π πππ ≤ 1.0 π΅ Depth π·π πππ > 1.0 π΅ & πππ πππ ∅ πΉππ = 1 + 0.4 πππ ∅ = 0° π΅ 1 − πΉππ πΉππ = πΉππ − πππ ∅ > 0° ππ tan ∅ πππ πππ ∅ π·π πΉππ = 1 + 2 tan ∅ 1 − π ππ∅ 2 π΅ πΉπΎπ = 1.0 πΉππ = 1 + 0.4 π‘ππ−1 πΉππ = 1 + 2 tan ∅ 1 − π ππ∅ 2 π·π π΅ π‘ππ −1 πΉπΎπ = 1.0 Note: πππ−π π«π π© is in radians π·π π΅ Bearing Capacity of Shallow Foundation Hansen Author Factor Condition Relationship πππ ∅ > 0° 1 − πΉππ πΉππ = πΉππ − ππ − 1 πππ ∅ = 0° Inclination ππ» πΉππ = 0.5 1 − π΄π ππ πΉππ = 1 − πππ πππ¦ ∅ 0.5 0.5ππ» ππ +π΄π ππ cot ∅ 5 0.7ππ» πΉπΎπ = 1 − ππ + π΄π ππ cot ∅ 5 Bearing Capacity of Shallow Foundation Author Factor Condition Vesic πππ ∅ > 0° πππ ∅ = 0° Inclination πππ πππ¦ ∅ Relationship πΉππ = πΉππ − 1 − πΉππ ππ − 1 πππ» πΉππ = 1 − π΄π ππ ππ 0.5 ππ» πΉππ = 1 − ππ + π΄π ππ cot ∅ ππ» πΉπΎπ = 1 − ππ + π΄π ππ cot ∅ π π+1 Bearing Capacity of Shallow Foundation In the above charts ππ» = βππππ§πππ‘ππ πππππππππ‘ ππ π‘βπ ππππππππ ππππ ππ = π£πππ‘ππππ πππππππππ‘ ππ π‘βπ ππππππππ ππππ ππ = π’πππ‘ ππβππ πππ ππ π‘βπ πππ π ππ π‘βπ ππππ‘πππ π΄π = ππππππ‘ππ£π ππππ‘πππ‘ ππππ ππ π‘βπ ππππ‘πππ π΅ 2+ πΏ π= π΅ 1+ πΏ Bearing Capacity of Shallow Foundation Total Overburden Pressure οΆ The intensity of total overburden pressure due to the weight of both soil and water at the base level of the foundation. Effective Overburden Pressure οΆ The effective overburden pressure at the base level of the foundation. οΆ In bearing capacity equation it is usually expressed as q. Bearing Capacity of Shallow Foundation The Ultimate Bearing Capacity of Soil, qu qu is the maximum bearing capacity of soil at which the soil fails by shear. The Net Ultimate Bearing Capacity, qu(net) qu(net) is the bearing capacity in excess of the effective overburden pressure and expressed asππ(πππ) = ππ − π = ππ − πΈπ«π Bearing Capacity of Shallow Foundation Gross Allowable Bearing Pressure, qallow qallow is expressed asππππππ Where, FS= factor of safety ππ = ππΊ Net Allowable Bearing Pressure, qallow(net) qallow(net) is expressed asππ − πΈπ«π ππ(πππ) ππππππ(πππ) = = ππΊ ππΊ Bearing Capacity of Shallow Foundation Safe Bearing Pressure, qsafe qsafe is defined as the net safe bearing pressure which produces a settlement of the foundation which does not exceed a permissible limit. Note: In the design of foundations, one has to use the least of the two values of qallow(net) and qsafe. Bearing Capacity of Shallow Foundation οΆ The theoretical equations developed for computing the ultimate bearing capacity qu of soil are based on the assumption that the water table lies at a depth below the base of the foundation equal to or greater than the width B of the foundation or otherwise the depth of the water table from ground surface is equal to or greater than (π«π + π©). οΆ In case the water table lies at any intermediate depth less than the depth (π«π + π©), the bearing capacity equations are affected due to the presence of the water table and the terms q and πΈ in bearing capacity equations need to be modified. Bearing Capacity of Shallow Foundation CASE 1: d = 0 For d = 0, the term π = πΈπ«π associated with Nq should be changed to π = πΈ′π«π (πΈ′ = πΈ − πΈπ = ππππππ‘ππ£π π’πππ‘ π€πππβπ‘ ππ π πππ). Also, the term πΈ associated with π΅πΈ should be changed to πΈ′ . Bearing Capacity of Shallow Foundation CASE 2: 0 < d ≤ π«π For this case, q will be equal to πΈπ + (π«π − π )πΈ′, and the term πΈ associated with π΅πΈ should be changed to πΈ′ . Bearing Capacity of Shallow Foundation CASE 3: π«π ≤ π ≤ π«π + π© This condition is one in which the groundwater table is located at or below the bottom of the foundation. In such case, π = πΈπ«π and the last term πΈ should be replaced by an average effective unit weight of soil πΈ , or π − π«π πΈ=πΈ + π© ′ πΈ − πΈ′ Bearing Capacity of Shallow Foundation CASE 4: π > π«π + π© For π > π«π + π©, π = πΈπ«π and the last term should remain πΈ. This implies that the groundwater table has no effect on the ultimate capacity.
