# unsat5 - Flow in Unsaturated Soil Requirements for Flow...

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Flow in Unsaturated Soil Requirements for Flow Laws Requires a law relating the diffusion or flow rate with the driving potential. For diffusion, the driving potential is either due to a chemical, thermal or electrical gradient. For flow, it is necessary to consider what the fundamental driving potential is. Fundamental Driving Potential The following gradients have been suggested as the cause for flow in unsaturated flow: water content, matric suction and total or hydraulic head. Water content cannot be the driving potential because it is unrelated to the state of energy of the water. Matric suction cannot be the driving potential because it does not include all the energy of the water. Total or hydraulic head accounts for all the energy. UNSAT5 - 1

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Total or Hydraulic Head An expression for the total head is obtained from energy considerations: Total Energy = Gravitational + Pressure + Velocity E = M w g y + ww w Mu Mv ρ + 2 2 Dividing by the weight, g M w , and ignoring the velocity potential gives the energy per unit weight in units of length: h = y + w w u g w w u g y Datum h For an unsaturated soil with u a = 0, the matric suction is equal to the pore water pressure. The pressure head does not account for the elevation head. The fundamental law for flow is that flow is due to differences in total head. UNSAT5 - 2
Flow Law for Unsaturated Soil Observations From Unsaturated Flow Water flows through the soil pore volume occupied by water only. The flow rate is affected by the water condition, e. g. volumetric water content, of the soil. For constant volumetric water content, the flow rate is directly proportional to the total head gradient in the w a t e r . Statement of Darcy's Law for Water s h K g s h k v w w w w w w = = µ ρ k w = coefficient of permeability (hydraulic conductivity) µ w = absolute (dynamic) viscosity of water K = intrinsic permeability UNSAT5 - 3

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Unsaturated Coefficient of Permeability Since the water flows through the pore space occupied by water, the permeability of unsaturated soil is affected as this volume of water changes. The permeability is affected by combined changes in the void ratio and the soil degree of saturation (water content).
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## unsat5 - Flow in Unsaturated Soil Requirements for Flow...

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