Title 20 Ultimate Bearing Capacity.pdf ✅

Geotech 08: Ultimate Bearing Capacity 1. Terzaghi’s Ultimate Bearing Capacity Equations Figure 1. Shallow Strip Footing The failure mechanism assumed by Terzaghi for determining the ultimate soil bearing capacity (general shear failure) for a rough strip footing located at a depth D௙ measured from the ground surface is shown below. Figure 2. Terzaghi's bearing capacity analysis The zones are described as the following:  Zone I - elastic zone  Zone II - radial shear zones  Zone III - Ranking Passive Zones Terzaghi’s Bearing Capacity Equation - Considers the effects of the unit weight of soil, cohesion, and surcharge
Strip Footing q௨ = q௖ + q௤ + qఊ = c ᇱN௖ + qN௤ + 1 2 γBNఊ Where: q௨ = ultimate bearing capacity q௖ = contribution of cohesion to the ultimate bearing capacity q௤ = contribution of surcharge to the ultimate bearing capacity qఊ = contribution of unit weight of the soil to the ultimate bearing capacity c′ = cohesion q = surcharge load B = width of footing N௖ , N௤, Nఊ = bearing capacity factors Figure 3. Terzaghi's Bearing Capacity Factors Square Footing q௨ = 1.3c ᇱN௖ + qN௤ + 0.4γBNఊ Circular Footing
q௨ = 1.3c ᇱN௖ + qN௤ + 0.3γBNఊ 2. Effect of Groundwater Table Case 1 If the groundwater table is located at a distance D above the bottom of the foundation, Figure 4. Case 1 location of groundwater table The magnitude of q in the second term of the bearing capacity equation should be calculated as: q = γ൫D௙ − D൯ + γ ᇱD Where: γ ᇱ = γ௦௔௧ − γ௪ Also, the unit weight of the soil, γ, that appears in the third term of the bearing capacity equations should be replaced by γ′. Case 2 If the groundwater table coincides with the bottom of the foundation, Figure 5. Case 2 location of groundwater table q = γD௙
However, the unit weight γ in the third terms of the bearing capacity equations should be replaced by γ′. Case 3 When the groundwater table is at a depth D below the bottom of the foundation, Figure 6. Case 3 location of groundwater table q = γD௙ The magnitude of γ in the third term of the bearing capacity equations should be replaced by γ௔௩. γ௔௩ = 1 B [γD + γ ᇱ(B − D)] for D ≤ B γ௔௩ = γ for D > B 3. Factor of Safety Generally, a factor of safety, FS, of about 3 or more is applied to the ultimate soil-bearing capacity to arrive at the value of the allowable bearing capacity. An FS of 3 or more is not considered too conservative due to uncertainty of soil in nature. Gross Allowable Bearing Capacity - The allowable load per unit area to which the soil under the foundation should be subjected to avoid any change of bearing capacity failure q௔௟௟ = q௨ FS q௔௟௟ = W஽ା௅ + Wி + Wௌ A Where: W஽ା௅ = dead and live loads above the ground surface Wி = self-weight of the foundation Wௌ = weight of the soil located immediately above the foundation