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SOIL STRESS *TOTAL STRESS, *PORE PRESSURE, U *EFFECTIVE

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SOIL STRESS *TOTAL STRESS, *PORE PRESSURE, U *EFFECTIVE Prepared by: Dr. Hetty STRESS 2 (kN/m )= .z where: = unit weight of soil (kN/m3) z = depth / thickness from ground surface (m) 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) multiplied by soil thickness or depth. Denoted as , v, Po The unit weight of soil is in natural condition and the water influence is ignored. Total stress increases with depth and with unit weight: Vertical total stress at depth z .z t z = The depth of point EXAMPLE 1 : Total stress in multi-layered in soil The total stress at depth z (i.e. Point D) is the sum of the weights of soil in each layer thickness above. 1 m 3 A = t,1 x 1 m t,1 = 17 kN/m 3 m A · = 17 kN/m2 B · B = t,1 x 3 m 2 3 = 51 kN/m t,2 = 18 kN/m 4 m = x 3 m + x 4 m C C t,1 t,2 · 2 = 123 kN/m 2 m 3 t,3 = 18 kN/m 4 m D · D = t,1 x 3 m + t,2 x 4 m + t,3 x 2 m = 159 kN/m2 Pore water pressure (u) Under hydrostatic conditions (no water flow) the pore pressure at a given point is given by the hydrostatic pressure: u = w .hw Where 3 3 w = unit weight of water (9.81kN/m 10 kN/m ) hw = depth below water table or overlying water surface Negative pore pressure - Below the water table, pore pressures are positive. - In dry soil, the pore pressure is zero. - Above the water table, when the soil is saturated, pore pressure will be negative. u = -(w .hw) EFFECTIVE STRESS Defined as soil stress which not 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 ' u EFFECTIVE STRESS u .z t .z w @ ' (t w ).z '.z ' u EXAMPLE 2 h1 = 2 m Sand MAT 3 sat = 18.0 kN/m h2 = 2.5 m 3 d = 13.1 kN/m Clay h3 = 4.5 m 3 sat = 19.80 kN/m x EXAMPLE Total Stress = d,1 . h1 + t,1 . h2 + t,2 . h3 = 13.1 . 2 + 18 . 2.5 + 19.8 . 4.5 = 160.3 kN/m2 Pore Water Pressure u = w . (h2+h3) u = 10 . 7 = 70 kN/m2 Effective Stress 2 ’ = - u = 90.3 kN/m ’ = d,1 . h1 + (t,2 - w) . h2 + (t,2 - w) . h3 ’ = 13.1 . 2 + (18-10) . 2.5 + (19,8-10) . 4.5 = 90.3 kN/m2 EXAMPLE Total Stress () Pore Water Pressure (u) Effective Stress (’) 26.2 kPa 26.2 kPa -2.0 71.2 kPa 25 kPa 46.2 kPa -4.5 -9.0 160.3 kPa 70 kPa 90.3 kPa Profile of Vertical Stress / Stress distribution Diagram EXAMPLE 3 For the soil profile shown here, plot the stress distribution diagram including total stress, pore pressure and effective stress 3 d= 18 kN/m 1 m Dry sand 3 d= 19 kN/m 0.5 m Silty sand 3 sat= 22 kN/m 2 m Clay EXAMPLE 3 (answer) Total Stress () Pore Water Pressure (u) Effective Stress (’) 18 kPa 18 kPa -1.0 27.5 kPa 0 kPa 27.5 kPa -1.5 -3.5 71.5 kPa 19.62 kPa 51.88 kPa Profile of Vertical Stress / Stress distribution Diagram .
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