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TOPIC 3 SOIL STRESS Course: S0705 – Soil Mechanic Year: 2008

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Bina Nusantara CONTENT TOTAL STRESS EFFECTIVE STRESS STRESS DISTRIBUTION

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Bina Nusantara TOTAL NORMAL STRESS Generated by the mass in the soil body, calculated by sum up the unit weight of all the material (soil solids + water) multiflied by soil thickness or depth. Denoted as , v, Po The unit weight of soil is in natural condition and the water influence is ignored. z = The depth of point

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Bina Nusantara EXAMPLE 3 m 4 m t,1 = 17 kN/m 3 d,1 = 13 kN/m 3 t,2 = 18 kN/m 3 d,2 = 14 kN/m 3 t,3 = 18 kN/m 3 d,3 = 15 kN/m 3 ·A·B·C·D·A·B·C·D 1 m 2 m A = t,1 x 1 m = 17 kN/m 2 B = t,1 x 3 m = 51 kN/m 2 C = t,1 x 3 m + t,2 x 4 m = 123 kN/m 2 D = t,1 x 3 m + t,2 x 4 m + t,3 x 2 m = 159 kN/m 2

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Bina Nusantara EFFECTIVE STRESS Defined as soil stress which influenced by water pressure in soil body. Published first time by Terzaghi at 1923 base on the experimental result Applied to saturated soil and has a relationship with two type of stress i.e.: –Total Normal Stress ( ) –Pore Water Pressure (u) Effective stress formula

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Bina Nusantara EFFECTIVE STRESS

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Bina Nusantara EXAMPLE MAT Sand t = 18.0 kN/m 3 d = 13.1 kN/m 3 Clay t = 19.80 kN/m 3 h 1 = 2 m h 2 = 2.5 m h 3 = 4.5 m x

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Bina Nusantara EXAMPLE Total Stress = d,1. h 1 + t,1. h 2 + t,2. h 3 = 13.1. 2 + 18. 2.5 + 19.8. 4.5 = 160.3 kN/m 2 Pore Water Pressure u = w. (h 2 +h 3 ) u = 10. 7 = 70 kN/m 2 Effective Stress ’ = - u = 90.3 kN/m 2 ’ = d,1. h 1 + ( t,2 - w ). h 2 + ( t,2 - w ). h 3 ’ = 13.1. 2 + (18-10). 2.5 + (19,8-10). 4.5 = 90.3 kN/m 2

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Bina Nusantara EXAMPLE -2.0 -4.5 -9.0 26.2 kPa 71.2 kPa 160.3 kPa 25 kPa 70 kPa 26.2 kPa 46.2 kPa 90.3 kPa Total Stress ( ) Pore Water Pressure (u) Effective Stress ( ’) Profile of Vertical Stress

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Bina Nusantara SOIL STRESS CAUSED BY EXTERNAL LOAD External Load Types –Point Load –Line Load –Uniform Load

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Bina Nusantara LOAD DISTRIBUTION PATTERN

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Bina Nusantara STRESS CONTOUR

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Bina Nusantara STRESS DISTRIBUTION Point Load P z 2 1 zz

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Bina Nusantara STRESS DISTRIBUTION Uniform Load z B L B+z L+z

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Bina Nusantara BOUSSINESQ METHOD Point Load z P r zz

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Bina Nusantara BOUSSINESQ METHOD ]

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Bina Nusantara BOUSSINESQ METHOD Line Load z q r zz x

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Bina Nusantara Uniform Load –Square/Rectangular –Circular –Trapezoidal –Triangle BOUSSINESQ METHOD

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Bina Nusantara BOUSSINESQ METHOD Rectangular z x y qoqo m = x/z n = y/z

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Bina Nusantara BOUSSINESQ METHOD Rectangular

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Bina Nusantara BOUSSINESQ METHOD Circular z x zz 2r At the center of circle (X = 0) For other positions (X 0), Use chart for finding the influence factor

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Bina Nusantara BOUSSINESQ METHOD Circular

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Bina Nusantara BOUSSINESQ METHOD Trapezoidal

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Bina Nusantara BOUSSINESQ METHOD Triangle

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Bina Nusantara EXAMPLE The 5 m x 10 m area uniformly loaded with 100 kPa Question : 1.Find the at a depth of 5 m under point Y 2.Repeat question no.1 if the right half of the 5 x 10 m area were loaded with an additional 100 kPa Y A B C D E F G H I J 5 m 5 m 5 m 5 m

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Bina Nusantara EXAMPLE ItemArea Y ABC- Y AFD- Y EGC Y EHD x15 105 y 555 z5555 m = x/z3321 n = y/z2111 I0.2380.2090.2060.18 zz 23.8- 20.9-20.618.0 z total = 23.8 – 20.9 – 20.6 + 18 = 0.3 kPa Question 1

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Bina Nusantara EXAMPLE Question 2 ItemArea Y ABC- Y AFD- Y EGC Y EHD x15 105 y 555 z5555 m = x/z3321 n = y/z2111 I0.2380.2090.2060.18 zz 47.6- 41.9-43.838.6 z total = 47.6 – 41.9 – 43.8 + 38.6 = 0.5 kPa

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Bina Nusantara NEWMARK METHOD Where : q o = Uniform Load I = Influence factor N = No. of blocks

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Bina Nusantara NEWMARK METHOD Diagram Drawing 1.Take z /q o between 0 and 1, with increment 0.1 or other, then find r/z value 2.Determine the scale of depth and length Example : 2.5 cm for 6 m 3. Calculate the radius of each circle by r/z value multiplied with depth (z) 4. Draw the circles with radius at step 3 by considering the scale at step 2

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Bina Nusantara NEWMARK METHOD Example, the depth of point (z) = 6 m z /q o r/zRadius (z=6 m)Radius at drawingOperation 0.10.271.62 m0.675 cm1.62/6 x 2.5 cm 0.20.402.40 m1 cm2.4/6 x 2.5 cm 0.30.523.12 m1.3 cm3.12/6 x 2.5 cm 0.40.643.84 m1.6 cm3.84/6 x 2.5 cm And so on, generally up to z /q o 1 because if z /q o = 1 we get r/z =

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Bina Nusantara NEWMARK METHOD

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Bina Nusantara EXAMPLE A uniform load of 250 kPa is applied to the loaded area shown in next figure : Find the stress at a depth of 80 m below the ground surface due to the loaded area under point O’

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Bina Nusantara EXAMPLE v = 250. 0.02. 8 = 40 kPa Solution : –Draw the loaded area such that the length of the line OQ is scaled to 80 m. –Place point O’, the point where the stress is required, over the center of the influence chart –The number of blocks are counted under the loaded area –The vertical stress at 80 m is then indicated by : v = q o. I. N

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Bina Nusantara WESTERGAARD METHOD Point Load = 0

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Bina Nusantara WESTERGAARD METHOD ]

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Bina Nusantara WESTERGAARD METHOD Circular Uniform Load

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Bina Nusantara WESTERGAARD METHOD

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Bina Nusantara BOUSSINESQ VS WESTERGAARD

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Bina Nusantara BOUSSINESQ VS WESTERGAARD

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Bina Nusantara BOUSSINESQ VS WESTERGAARD

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