Analytical Chem Soil HW Solutions 74

Analytical Chem Soil HW Solutions 74 - Vt = Vs Vv e = Vv/Vs...

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74 V t = V s + V v ; e = V v /V s ; so V t = V s .(1 + e) = V s .v and Δ V t = V s . Δ v The first sample at a cell pressure of 300 kPa (q = 0) has a total volume V t given by V t = ( π × 38 2 mm 2 /4) × 80 mm = 90729 mm 3 It is saturated, so e = w.G s (main text Equation 1.10); w = 0.572 and G s = 2.61 so e = 1.493 Hence the volume of solids V s = V t /(1 + e) = 90729 mm 3 ÷ 2.493 = 36393.5 mm 3 (constant) When the cell pressure was increased to 320 kPa, the change in total volume Δ V t was -618 mm 3 giving a change in specific volume Δ v of –618 mm ÷ 36393.5 mm = -0.017. The slope of the isotropic normal compression line on a graph of v against lnp' is - λ , where λ = - Δ v/ Δ (lnp'). Hence λ = 0.017 ÷ (ln320-ln300) = 0.017/0.0645 λ = 0.26 The same change in specific volume occurs on swelling from p' = 320 kPa to p' = 229 kPa, which is along a swelling line on the graph of v against lnp' which has slope -
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