q a = the allowable bearing capacity q ult = the ultimate bearing capacity FS = the factor of safety against bearing capacity failure

Transcription

1 Bearing Caacity There is a limit to the amount of weight that a soil can carry due to alied loads without failing. That failure limit is known as a soil s ultimate bearing caacity. Foundations are not designed on the basis of a soil s ultimate bearing caacity because the closer a soil gets to its ultimate caacity the greater the amount of consolidation and settlement. Allowable Bearing Pressure q a = q ult / FS q a = the allowable bearing caacity q ult = the ultimate bearing caacity FS = the factor of safety against bearing caacity failure Net Bearing Pressure The above equation for allowable bearing caacity does not differentiate on how the soil is loaded. If the footing excavation is backfilled the bearing caacity must be reduced by the ressure caused by the backfill. The resulting bearing caacity is known as a net ultimate bearing caacity or a net allowable bearing caacity. q ult(net) = q ult q q a(net) = q ult(net) / FS q ult(net) = the net ultimate bearing caacity q ult = the ultimate bearing caacity q = the ressure alied by backfilling the footing excavation q a(net) = the net allowable bearing caacity (aka design bearing caacity) q = γ 1 D f γ 1 = the effective unit weight of the soil above the bottom of the footing D f = the distance from the ground surface to the bottom of the footing Page 90 Coyright 2011 by Test Masters. 26 All Rights Reserved. Page 90

2 It is usually assumed that the unit weight of the soil above the footing is close enough to the unit weight of the footing material (concrete) that areciable error will not be introduced into the calculations. General Bearing Caacity Equation Meyerhof s Equations (other solutions: Terzaghi, Hansen) Bearing caacity notation. q ult = c N c s c i c d c + γ 1 D f N q s q i q d q + (1/2) B γ 2 N γ s γ i γ d γ q ult = ultimate bearing caacity (units of stress) N c, N q, N γ = bearing caacity factors c = cohesion s = shae factors i = load inclination factors d = deth factors γ 1 = effective unit weight of the soil above the bottom of the footing D f = deth from the ground surface to the bottom of the footing B = footing width (smallest dimension of the footing contact area) γ 2 = effective unit weight of the soil below the bottom of the footing Page 91 Coyright 2011 by Test Masters. 27 All Rights Reserved. Page 91

3 Shae Factors : L = length of footing into age, The basic bearing caacity equation was derived for a stri footing, which is considered to be infinitely long. In ractical terms, the length of a stri footing is 10 times greater than the width (i.e. L 10B). For stri footing (infinitely long) all shae factors = 1.0 For rectangular footings: s c = 1 + (B/L)( N q /N c ) s γ = 1 0.4(B/L) s q = 1 + (B/L) tan φ For square and circular footings B = L so: s c = 1 + ( N q /N c ) s γ = 0.6 s q = 1 + tan φ Inclined Loading: α = angle of alied load measured from vertical For vertical loads, all inclined load factors = 1.0 i c = [1-(α/90) 2 ] i q = [1-(α/90) 2 ] i γ = 1 if φ = 0 i γ = [1-(α/φ) 2 ] if φ > 0: Page 92 Coyright 2011 by Test Masters. 28 All Rights Reserved. Page 92

4 Schematic showing how α is measured. Embedment Correction: In general, the deeer the footing is below the ground surface the higher the bearing caacity due to the effects of the overburden. d c = K D f /B d q = d γ = 1 if φ = 0 d q = d γ = K (D f /B) if φ > 0: K = tan 2 (45 + φ/2) K = tan (45 + φ/2) D f = deth of footing Secial Case when φ = 0 K = K = 1 Page 93 Coyright 2011 by Test Masters. 29 All Rights Reserved. Page 93

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6 Modification for Eccentricity, e An eccentric load condition occurs when the load is not alied to the center of the footing. One way that eccentric loadings are addressed is to reduce the area of the footing that is available to carry load. Bear in mind that the actual size of the footing is not reduced, there are simly ortions of the footing that are assumed to be unavailable to carry the alied load. B = B - 2e B L = L - 2e L B = the effective width of the footing after the effect of eccentric loading has been removed B = the actual width of the footing e B = the distance from the center of the width that the load is alied L = the effective length of the footing after the effect of eccentric loading has been removed L = the actual length of the footing e L = the distance from the center of the length that the load is alied Eccentric loading can occur in the B and/or the L dimension. Footings with eccentric loadings in both directions are said to be exeriencing double eccentricity. The load must be alied within middle third of footing to avoid ulift on the edge of footing. Modifications for Groundwater The location of the ground water table can affect the unit weights (γ 1 and γ 2 ) of the soils used in the bearing caacity calculation. The following conditions could occur: 1. The to of the ground water table is B below the bottom of the footing. a. Use the total unit weights of the soils in calculations. 2. The footing is comletely submerged (water table is at or above the ground surface). Page 95 Coyright 2011 by Test Masters. 31 All Rights Reserved. Page 95