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**Pore Pressure Coefficients**

in equilibrium under principal stresses: whose volume = V and Porosity = n Consider a soil element: with a pore water pressure: Pore Pressure Coefficients σ1 σ3 u0 V, n σ2

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**Pore Pressure Coefficient, B**

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 σ1 σ1 + σ3 σ3 σ3 + σ3 u0 +u3 u0 V, n σ2 σ2 + σ3

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**Pore Pressure Coefficient, B**

This increase in effective stress reduces the volume of the soil skeleton and the pore space. As a result, the effective stress in each direction increases by σ3 -u3 σ1 + σ3 σ3 - u3 σ3 - u3 σ3 + σ3 u0 +u3 V, n σ3 - u3 σ2 + σ3

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**Pore Pressure Coefficient, B**

Soil Skeleton σ3 - u3 V, n σ3 - u3 where: 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

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**Pore Pressure Coefficient, B**

Pore Space (Voids) σ3 - u3 V, n σ3 - u3 where: VPS = the volume reduction in pore space caused by a change in the pore pressure, u3 CV = the compressibility of the pore fluid; i.e., the fraction of volume reduction per kPa increase in pore pressure Since: Then:

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**Pore Pressure Coefficient, B**

Assuming: the soil particles are incompressible no drainage of the pore fluid σ3 - u3 Therefore, the reduction in soil skeleton volume must equal the reduction in volume of pore space V, n σ3 - u3 Therefore: or:

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**Pore Pressure Coefficient, B**

The value: σ3 - u3 V, n σ3 - u3 is called the pore pressure coefficient, B So, u3 = B σ3 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.

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**Pore Pressure Coefficient, A**

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 σ1 σ1 + σ1 σ3 σ3 - u1 u0 +u1 u0 V, n σ2 σ2 - u1

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**Pore Pressure Coefficients**

This change in effective stress also changes the volume of the soil skeleton and the pore space. As a result, the effective stress in each of the minor directions increases by -u1 σ1 + σ1 σ1 - u1 - u1 σ3 -u1 u0 +u1 V, n -u1 σ2 - u1

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**Pore Pressure Coefficients**

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: - u1 V, n - u3 As before, the change in volume of the pore space: Again, if the soil particles are incompressible and no drainage of the pore fluid, then:

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**Pore Pressure Coefficient, A**

V, n - u3 Since soils are NOT elastic, this is rewritten as: u1 = AB σ1 or For different values of σ1 during the test, u1 is measured, although the values at failure are of particular interest: 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

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**Pore Pressure Coefficient, A**

Normally Consolidated σ1 - u1 Figure 4.28 in the text illustrates the variation of A with OCR (Overconsolidation Ratio). Lightly Over-Consolidated - u1 V, n Heavily Over-Consolidated - u3 In highly compressible soils (normally consolidated clays), A ranges between 0.5 and 1.0 For heavily overconsolidated clays, A may lie between -0.5 & 0 For lightly overconsolidated clays, 0 < A < 0.5

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**Pore Pressure Coefficient, B**

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. From the two previous effects: u = u3 + u1 If we divide through by σ1 u3 = Bσ3 { u3 + u1 = u = B[σ3+A(σ1-σ3)] { u1 = BA(σ1-σ3) or: or:

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**Pore Pressure Coefficient, B**

The third pore pressure coefficient is not a constant but depends on σ3 and σ1 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 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.

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