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15The bearing capacity accredited to the fiction of the pier shaft can be estimated throughEquation 6:Equation 6: Bearing capacity due to shaft frictionq shaft = 4f s d shaft H shaft /d nominal2(Equation 6)The next parameter to be evaluated is f s or average unit friction. The following formula wasadopted for the purpose of estimating average unit friction:Equation 7: Average unit frictionf s = σ' v avg tan(φ s )k p,s = (d f +H shaft /2)γtan(φ p loess )tan 2 (45+φ p loess /2) (Equation 7)Footing depth, friction angle, and shaft length parameters had to be considered in order forthe average unit friction to be calculated. Typically, the concrete footing of d f thickness ispoured on top of compacted piers. Friction angle of the matrix loess material can be assumedto be 30 degrees as per Lohnes and Kjartanson (2007). and σ' v or the effective vertical stressparameter can be calculated in the same manner as for the bulging piers outlined in Equation4. However the depth is taken not to the level where bulging is to occur but at a length of piershaft.The other component of the ultimate bearing capacity for plunging piers is attributed to thetip resistance (Terzaghi, 1943):Equation 8: Bearing capacity due to tip resistanceq tip =C u N c + 0.5d shaft γ dry loessN γ + σ' v N q (Equation 8)A classic Terzaghi-Buisman approach is typically used and the dimensionless N c , N γ and N qparameters can be found in table provided by Kumbhojkar, 1993 for a 30 degree angle ofloess frictional resistance.