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CE 394K.2 Hydrology Infiltration Reading AH Sec 5.1 to 5.5 Some slides were prepared by Venkatesh Merwade Slides 2-6 come from http://biosystems.okstate.edu/Home/mkizer/C%20Soil%20Water%20Relationships.ppt Soil Water Measurement • Neutron scattering (attenuation) – Measures volumetric water content (v) – Attenuation of high-energy neutrons by hydrogen nucleus – Advantages: • samples a relatively large soil sphere • repeatedly sample same site and several depths • accurate – Disadvantages: • high cost instrument • radioactive licensing and safety • not reliable for shallow measurements near the soil surface • Dielectric constant – – – – A soil’s dielectric constant is dependent on soil moisture Time domain reflectometry (TDR) Frequency domain reflectometry (FDR) Primarily used for research purposes at this time Soil Water Measurement Neutron Attenuation Soil Water Measurement • Tensiometers – Measure soil water potential (tension) – Practical operating range is about 0 to 0.75 bar of tension (this can be a limitation on medium- and fine-textured soils) • Electrical resistance blocks – Measure soil water potential (tension) – Tend to work better at higher tensions (lower water contents) • Thermal dissipation blocks – Measure soil water potential (tension) – Require individual calibration Tensiometer for Measuring Soil Water Potential Water Reservoir Variable Tube Length (12 in- 48 in) Based on Root Zone Depth Porous Ceramic Tip Vacuum Gauge (0-100 centibar) Electrical Resistance Blocks & Meters Infiltration • General – Process of water penetrating from ground into soil – Factors affecting • Condition of soil surface, vegetative cover, soil properties, hydraulic conductivity, antecedent soil moisture Saturation Zone Transition Zone Transmission Zone Wetting Zone – Four zones • Saturated, transmission, wetting, and wetting front Wetting Front depth Richard’s Equation • Recall – Darcy’s Law – Total head • So Darcy becomes D K h z h z q z K z z K K z D K z q z K Soil water diffusivity • Continuity becomes t q z K q D K z z z K z Philips Equation • Recall Richard’s Equation D K t z z – Assume K and D are functions of , not z • Solution – Two terms represent effects of • Suction head • Gravity head • S – Sorptivity – Function of soil suction potential – Found from experiment F (t ) St1/ 2 Kt 1 1/ 2 f (t ) St K 2 Infiltration into a horizontal soil column Θ = Θo for x = 0, t > 0 Boundary conditions Θ = Θn for t = 0, x > 0 x 0 Equation: D t x z Measurement of Diffusivity by Evaporation from Soil Cores Air stream q x q = soil water flux = evaporation rate qD x Measurement of Diffusivity by Evaporation from Soil Cores http://www.regional.org.au/au/asa/2006/poster/water/4521_deeryd.htm Numerical Solution of Richard’s Equation (Ernest To) http://www.ce.utexas.edu/prof/maidment/GradHydro2007/Ex4/Ex4Soln.doc Implicit Numerical Solution of Richard’s Equation t (j) j j -1 x (i) i-1 i i+1 Implicit Numerical Solution of Richard’s Equation Matrix solution of the equations Θ f F Definitions V gross volume of element Vv volume of pores Element of soil, V (Saturated) Pore with water solid Vs volume of solids Vw volume of water Vv n porosity V Vw S saturation; 0 S 1 Vv V w nS moisture content; 0 n V Pore with air Element of soil, V (Unsaturated) Infiltration • Infiltration rate f (t ) – Rate at which water enters the soil at the surface (in/hr or cm/hr) • Cumulative infiltration – Accumulated depth of water infiltrating during given time period t F (t ) f ( )d 0 f (t ) dF (t ) dt Infiltrometers Single Ring Double Ring http://en.wikipedia.org/wiki/Infiltrometer Infiltration Methods • Horton and Phillips – Infiltration models developed as approximate solutions of an exact theory (Richard’s Equation) • Green – Ampt – Infiltration model developed from an approximate theory to an exact solution Hortonian Infiltration • Recall Richard’s Equation – Assume K and D are constants, not a function of or z • Solve for moisture diffusion at surface D K t z z 2 K D 2 t z z 2 D 2 t z 0 f (t ) f c ( f 0 f c )e kt f0 initial infiltration rate, fc is constant rate and k is decay constant Hortonian Infiltration 3.5 f0 3 Infiltration rate, f 2.5 k1 2 k1 < k2 < k3 1.5 k2 1 k3 fc 0.5 0 0 0.5 1 Time 1.5 2 Philips Equation • Recall Richard’s Equation D K t z z – Assume K and D are functions of , not z • Solution – Two terms represent effects of • Suction head • Gravity head • S – Sorptivity – Function of soil suction potential – Found from experiment F (t ) St1/ 2 Kt 1 1/ 2 f (t ) St K 2 Green – Ampt Infiltration L Depth to Wetting Front i Initial Soil Moisture Ponded Water h0 Ground Surface F (t ) L( i ) L Wetted Zone dF dL f dt dt Wetting Front h q z K f z i h z f K K z n z Dry Soil L Green – Ampt Infiltration (Cont.) f K Ground Surface Wetted Zone K z Wetting Front • Apply finite difference to the derivative, between – Ground surface z 0, 0 – Wetting front z L, f f 0 f K K K K K K z z L0 F (t ) L F L f K F f 1 i z Dry Soil f K K z L Green – Ampt Infiltration (Cont.) f K F f 1 f Ground Surface Wetted Zone dL dt i f dL K 1 dt L f dL K dt dL f L Integrate K t L f ln( f L) C L Wetting Front F (t ) L z Dry Soil Evaluate the constant of integration L 0 @t 0 C f ln( f ) Kt L f ln( f f L ) Green – Ampt Infiltration (Cont.) Kt L f ln( f f L Ground Surface Wetted Zone Wetting Front ) i F Kt f ln(1 f K F f 1 F f ) z Dry Soil Nonlinear equation, requiring iterative solution. See: http://www.ce.utexas.edu/prof/mckinney/ce311k/Lab/Lab8/Lab8.html L Soil Parameters • Green-Ampt model requires – Hydraulic conductivity, Porosity, Wetting Front Suction Head – Brooks and Corey se r e e n r Effective saturation Soil Class Porosity Effective Porosity n e Effective porosity (1 se ) e Sand Loam Clay 0.437 0.463 0.475 0.417 0.434 0.385 Wetting Front Suction Head (cm) 4.95 9.89 31.63 Hydraulic Conductivity K (cm/h) 11.78 0.34 0.03 Ponding time • Elapsed time between the time rainfall begins and the time water begins to pond on the soil surface (tp) • Up to the time of ponding, all rainfall has infiltrated (i = rainfall rate) Potential Infiltration Rainfall i F i *t p f K F f 1 f i K 1 i *t p f tp K i (i K ) Actual Infiltration Accumulated Rainfall Cumulative Infiltration, F f i Infiltration rate, f Ponding Time Time Infiltration Fp i * t p tp Time Example • Silty-Loam soil, 30% effective saturation, rainfall 5 cm/hr intensity e 0.486 16.7 cm K 0.65 cm / hr se 0.30 (1 se ) e (1 0.3)(0.486) 0.340 16.7 * 0.340 tp K f i (i K ) 0.65 5.68 0.17 hr 5.0(5.0 0.65)(i K )