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in equilibrium under principal stresses:. with a pore water pressure:. whose volume = V and Porosity = n. Pore Pressure Coefficients. σ 1. Consider a soil element:. σ 3. u 0. V, n. σ 2. Pore Pressure Coefficient, B. σ 1. σ 1 + σ 3.
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in equilibrium under principal stresses: with a pore water pressure: whose volume = V and Porosity = n Pore Pressure Coefficients σ1 Consider a soil element: σ3 u0 V, n σ2
Pore Pressure Coefficient, B σ1 σ1+ σ3 Then, the element is subjected to an increase in stress in all 3 directions of σ3 which produces an increase in pore pressure of u3 σ3 σ3+ σ3 u0 +u3 u0 V, n σ2 σ2+ σ3
This increase in effective stress reduces the volume of the soil skeleton and the pore space. Pore Pressure Coefficient, B σ1+ σ3 σ3 -u3 As a result, the effective stress in each direction increases by σ3 -u3 σ3 -u3 σ3+ σ3 u0 +u3 V, n σ3 -u3 σ2+ σ3
σ3 -u3 Pore Pressure Coefficient, B σ3 -u3 V, n σ3 -u3 where: Soil Skeleton Vss = the change in volume of the soil skeleton caused by an increase in the cell pressure, σ3 Cs = the compressibility of the soil skeleton under an isotropic effective stress increment; i.e., the fraction of volume reduction per kPa increase in cell pressure
σ3 -u3 Pore Pressure Coefficient, B σ3 -u3 V, n σ3 -u3 where: VPS = the volume reduction in pore space caused by a change in the pore pressure, u3 Pore Space (Voids) CV = the compressibility of the pore fluid; i.e., the fraction of volume reduction per kPa increase in pore pressure Since: Then:
σ3 -u3 the soil particles are incompressible no drainage of the pore fluid Pore Pressure Coefficient, B σ3 -u3 Therefore, the reduction in soil skeleton volume must equal the reduction in volume of pore space V, n σ3 -u3 Assuming: Therefore: or:
σ3 -u3 Pore Pressure Coefficient, B σ3 -u3 V, n σ3 -u3 is called the pore pressure coefficient, B So, u3 = B σ3 Thevalue: If the void space is completely saturated, Cv = 0 and B = 1 In an undrained triaxial test, B is estimated by increasing the cell pressure by σ3 and measuring the resulting change in pore pressure, u3 so that: When soils are partially saturated, Cv > 0 and B < 1 This is illustrated on Figure 4.26 in the text.
Pore Pressure Coefficient, A σ1 σ1+ σ1 What happens if the element is subjected to an increase in axial (major principal) stress of σ1 which produces an increase in pore pressure of u1 σ3 σ3- u1 u0 +u1 u0 V, n σ2 σ2- u1
This change in effective stress also changes the volume of the soil skeleton and the pore space. Pore Pressure Coefficients σ1+ σ1 σ1-u1 As a result, the effective stress in each of the minor directions increases by -u1 -u1 σ3-u1 u0 +u1 V, n -u1 σ2- u1
σ1-u1 Pore Pressure Coefficients -u1 V, n -u3 As before, the change in volume of the pore space: If we assume for a minute that soil is an elastic material, then the Volume change of the soil skeleton can be expressed from elastic theory: Again, if the soil particles are incompressible and no drainage of the pore fluid, then:
σ1-u1 or: Pore Pressure Coefficient, A -u1 V, n -u3 Since soils are NOT elastic, this is rewritten as: u1 = AB σ1 or where A is a pore pressure coefficient to be determined by experiment A value of A for a fully saturated soil can be determined by measuring the pore water pressure during the application of the deviator stress in an undrained triaxial test For different values of σ1 during the test, u1 is measured, although the values at failure are of particular interest:
Normally Consolidated σ1-u1 Figure 4.28 in the text illustrates the variation of A with OCR (Overconsolidation Ratio). Lightly Over-Consolidated Pore Pressure Coefficient, A -u1 V, n Heavily Over-Consolidated -u3 In highly compressible soils (normally consolidated clays), A ranges between 0.5 and 1.0 For lightly overconsolidated clays, 0 < A < 0.5 For heavily overconsolidated clays, A may lie between -0.5 & 0
Pore Pressure Coefficient, B From the two previous effects: u = u3 + u1 If we divide through by σ1 u3 = Bσ3 The third pore pressure coefficient is determined from the response, u to a combination of the effects of increasing both the cell pressure, σ3 and the axial stress (σ1 -σ3) or deviator stress. { u3+ u1 = u = B[σ3+A(σ1-σ3)] { u1 = BA(σ1-σ3) or: or:
Pore Pressure Coefficient, B With no movement of water (undrained) and no change in water table level during subsequent consolidation, u = initial excess pore water pressure in fully saturated soils. Testing under Back Pressure The third pore pressure coefficient is not a constant but depends on σ3 and σ1 This process allows the calculation of the pore pressure coefficient, B. When a sample of saturated clay is extracted from the ground, it can swell thereby decreasing Sr as it breathes in air The pore pressure can be raised artificially (in sync with σ3) to a datum value for excess pore water pressure and then the sample can be allowed to consolidate back to the in situ conditions (saturation, pore water pressure). Values of B 0.95 are considered to represent saturation.