G MS THESIS_final version_Maxim Prokudin.pdf - Digital Repository ...

170APPENDIXSample CalculationsUltimate bearing capacity for single pierLong Aggregate Pier (Table 25)σ' v = H shaft γ dry loess = 0.1m x 1,556kg/m 3 x 9.81m/s 2 / 1000 = 1.5kPaσ' r.lim = σ' r.o + C u (1+In(E/(2C u (1+µ)))) = 2σ' v + 5.2C u =2 x 1.5kPa + 5.2 x 33kPa == 175kPaq ult AGGREGATE PIER = σ' r.lim tan 2 (45+ φ p AGGREGATE PIER /2) = 175kPa x tan 2 (45+44/2) == 970kPaShort Aggregate Pier (Table 26)f 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) = (25mm+305mm/2) /1,000 x 1,588kg/m 3 x tan(30) x tan 2 (45+30/2) = 489kg/m 2q shaft = 4f s d shaft H shaft /d 2 nominal = 4 x 489kg/m 2 x 9.81m/s 2 / 1,000 x 305mm x 84mm / 76 2 mm 2 =85kPaq tip =C u N c + 0.5d shaft γN γ + σ' v N q = 40kPa x 37 + 0.5 x 84mm / 1,000 x 9.81m/s 2 x1,588kg/m 3 x 19 / 1000 + 0.305m x 1,588kg/m 3 x 9.81m/s 2 / 1,000 x 22.5 = 1,480kPa +12.4kPa + 107kPa = 1,606kPaq ult = q shaft + q tip = 85kPa + 1,606kPa = 1,690kPaLoess (Table 26)q u =1.3c’N c + σ' v N q + 0.3d steel cap γN γ = 1.3 x 40kPa x 37.2 + 1,550kg/m 3 x 0.0254m x9.81m/s 2 / 1,000 + 0.3 x 76mm / 1,000 x 1,550 kg/m 3 x 9.81m/s 2 / 1,000 x 19 = 1,451kPa +0.4kPa + 6.6kPa = 1,460kPa