Pile Foundations question

Pile Foundations question - Example 1 Calculate the...

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Example 1 Calculate the ultimate bearing capacity of a 12m pile with a diameter 1.3m driven into a soft clay with γ sat =17kN/m3. The unit weight of the pile 27 kN/m3. The water table is 1m below the ground. The undrained shear strength of the soil is shown in the diagraph. 2m 0 c u z L= 12m D=1.3m 40 kPa 20 kPa Cu= 20+4(z-2) kPa P u Step1 (decide the equation? Bearing capacity of a single pile in soft clay with c u is given.) The bearing capacity can be worked out by P u =P s +P b -W The bearing capacity is calculated as follows with the effect of the pile weight and that of overburden pressure on P b balanced. Thus P u =f s A s +f b A b Step 2 (decide the method for f s and f b ) The soil is soft clay with c u given. Undrained analysis is used to calculate f s and f b . Step 3 (Find out P s ) Find out P s (Three different ways can be used and anyone of the ways is ok. Different way has different accuracy) Way 1: treat the soil as one uniform layer with a constant c u , the average c u The average undrained shear strength along the pile shaft can be estimated as At the top: c u =40 kPa At z=2m, c u =20 kPa At the base, c u =20+4(12-2)=60 kPa c u(ave) =(40+20+60)/3=40 kPa From the α ~ c u curve, For c u =40 kPa, α =1 Therefore P s =f s π DL= α c u π DL =1*40*3*1.3*12=1900 kN. Way 2: divide the soil into three layers and treat the soil as possessing constant c u in every individual layer. The soil is divided into three layers. They are, z=0~2m, 2~7m, 7~12m. The undrained shear strengths at these depths are: c u(0m) =40 kPa, c u(2m) =20 kPa,
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u(7m) =40 kPa c u(12m) =60 kPa The average c u and α for the three layers. z=0~2m, c u,ave =(40+20)/2=30 kPa, α =1 z=2~7m, c u,ave =(20+40)/2=30 kPa, α =1 z=7~12m, c u,ave =(40+60)/2=50 kPa, α =0.88 P s = α∑ c u π D Δ L =1*30*3*1.3*2+1*30*3*1.3*5+0.88*50*3*1.3*5 = 1700kN. Way 3: by integral As both undrained shear strength and α change with depth z, then α π + α π = 12 2 2 0 dz c D dz c D P u u s The variation of c u with z is linear, but α with z is more complicated. Step 4 (Find out f b A b part of P b ) Find out f b A b c u(base) =60 kPa L/D=12/1.3>4, It is a long pile, N c = 9 f b A b =N c c u π (D/2) 2 =9*60*3*(1.3/2) 2 = 700 kN Step 5 (find out the bearing capacity of the pile) The bearing capacity of the pile L= 12m D=1.3m P u P u =P s +f b P b By Way 1 (soil divided into one layer) P u =1900+700=2600 KN By Way 2 (soil divided into three layers) P u =1700+700=2400 KN By Way 3 (integral) P u =??+700 KN Example 2 Calculate the ultimate capacity of a 12m pile with a diameter 1.33m driven into a uniform soft clay. Soil with γ sat =17kN/m3 has an undrained shear strength of 60 kPa. The unit weight of the pile 27 kN/m3. The water table is 1m below the ground. Step1 (decide the equation? Bearing capacity of a single pile)
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Pile Foundations question - Example 1 Calculate the...

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