CE%203400%20HW14-Solution%20Fall%202009

CE%203400%20HW14-Solution%20Fall%202009 - CE 235 - Homework...

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CE 235 - Homework No. 15 - SOLUTION Settlement of a Footing and a Pumping Station Problem 1 : Stress due to footing, () Q 150000 q 1500 A1 0 1 0 == = psf Initial stresses : Layer 1: ( ) 114 4.17 475 σ= = ( ) u 62.4 4.17 5 52 =− = ' u 527 σ=σ− = Layer 2: ( ) 114 12.5 1425 = ( ) u 62.4 12.5 5 468 = ' u 957 Layer 3: ( ) 114 20.83 2375 = ( ) u 62.4 20.83 5 988 = ' u 1387 Increase in stress, ∆σ : Use solution for the stresses at the corner or a rectangle and superimpose stresses. B' B/2 10/2 5 = Layer 1: z = 4.17 5 m1 . 2 z4 . 1 7 = 3 I 0.194 = (from Chart) ( ) 3 ' 4I q 4 0.194 1500 1164 ∆σ = ∆σ = = =
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Layer 2: z = 12.5 B' 5 m0 . 4 z 12.5 == = I 3 = 0.06 (from Chart) () ( ) 3 ' 4I q 4 0.06 1500 360 ∆σ = ∆σ = = = Layer 3: z = 20.83 5 . 2 4 z 20.83 = I 3 = 0.023 (from Chart) ( ) 3 ' 4I q 4 0.023 1500 138 ∆σ = ∆σ = = = Change in void ratio, e: Layer 1: 10 10 1581 1691 e 0.19 log 0.73 log 0.112 527 1581 ⎛⎞ ∆= + = ⎜⎟ ⎝⎠ Layer 2: 10 1317 e 0.19 log 0.026 957 = Layer 3: 10 1525 e 0.19 log 0.008 1387 = Computations of settlement are summarized below : Layer σ ' i σ ' max ∆σ ' σ ' f e S 1 527 1581 1164 1691 0.112 0.45 2 957 2871 360 1317 0.026 0.11 3 1387 4161 138 1525 0.008 0.03 Total settlement = 0.45 + 0.11 + 0.03 = 0.59 feet
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Problem 2 : Calculations of unit weights : For Sand: sr w GS e 1e + γ= γ + above water table: () 2.65 0.25 0.38 62.4 124.1 10 . 3 8 + = + below water table: ( ) 2.65 1.0 0.38 62.4 137.0 . 3 8 + = +
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CE%203400%20HW14-Solution%20Fall%202009 - CE 235 - Homework...

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