CE/ENVE 320 CE/ENVE 320 ––VadoseVadoseZone Hydrology/Soil PhysicsZone Hydrology/Soil PhysicsSpring 2004Spring 2004Copyright © Markus Tuller and Dani Or 2002Copyright © Markus Tuller and Dani Or 2002--20042004Soil Texture, Particle Size Distribution and Soil ClassificationHillel, pp. 63-69 3Copyright© Markus Tuller and Dani Or2002-2004Soil TextureSOIL TEXTURE is defined by size distribution or mass fractions of soil primary particles (individual grains and particles).● Primary mineral particles formed through physical and chemical weathering of parent material and refractory organic substances make up the solid phase. ● Particle size distribution and shape are the most important characteristics affecting:- pore geometry- total pore volume (porosity)- pore size distribution- solid surface areaCopyright© Markus Tuller and Dani Or2002-2004Methods to Determine Particle Size Distribution• Sieving methods – soil particles ≥ 0.05 mm (sand fraction) we use Sieving methods.• Sedimentation methods Pipette Hydrometer X-ray attenuation• Particle counting methods Light, SEM Microscopy Coulter method• Laser/Light diffractionmethodsCopyright© Markus Tuller and Dani Or2002-2004Sieving MethodsFor particles ≥ 0.05 mm (sand fraction) we apply SIEVING methods.Results are expressed as particle diametersNote - particles are rarely spherical, hence these diameters should be regarded as effective diameters based on sieve opening size.Sieve ShakerCopyright© Markus Tuller and Dani Or2002-2004Particle Size Distribution - Sedimentation• For particles ≤ 0.05 mm (silt and clay fractions) sedimentation methods based on Stokes law are used to deduce particle size distribution.• Soil particles settle in aqueous solution attaining terminal velocities proportional to their mass and size.• The amount of suspended soil after a given settling time is used to determine particle size fractions.• The amount of soil in suspension is determined by either extracting a sample by the pipette method or from a direct hydrometer reading.Copyright© Markus Tuller and Dani Or2002-2004Stokes LawGravitational ForceBuoyancy Force(weight of displaced liquid)Drag Force (exerted bythe surrounding liquid)g)3r4(F3sgπρ=g)3r4(F3lbπρ=Vr6Fdηπ=ρl....density liquid [kg/m3] ρs...density solid [kg/m3] r.....radius sphere [m] g ....acceleration of gravity [m/s2] V....settling velocity [m/s] η dynamic viscosity [kg/m s] • Three forces acting on a spherical particle. • Buoyancy and drag forces act against the gravitational force. • A spherical soil particle D=5 um reaches 99% of its terminal velocity in aqueous solution within 0.017 ms, and for D=1 mm the time is 0.68 s.Copyright© Markus Tuller and Dani Or2002-2004The three forces acting upon the settling particle quickly equilibrate and the particle reaches a constant settling velocity.We can solve the force balance equation to obtain the settling velocitySince we know that velocity equals length per time we can calculate the time particles of a certain size need to settle through a distance h:t is the time required for particles of a certain size to settle below a certain depth h.Stokes Law∑−−==dbgiFFF0F()ηρρηππρπρ18gdVVr6g3r4g3r402ls3l3s−=⇒−−=()gd)(h18t18gdthV2ls2lsρρηηρρ−=⇒−==Copyright© Markus Tuller and Dani Or2002-2004Stokes Law - LimitationsWhen applying STOKES law we need to be aware of a number of simplifying assumptions:- Particles are large enough to be unaffected by the thermal (Brownian) motion of the fluid molecules- All particles are rigid, spherical, and smooth- All particles have the same density- The suspension is dilute enough that particles do not interfere with each other- Fluid flow around the particles is laminar. That means no particle exceeds the critical velocity for the onset of turbulenceIn practice we know that soil particles are neither spherical nor smooth.Hence the diameter calculated from STOKES law does not necessarily correspond to the actual dimensions of the particles.We rather receive an effective or equivalent settling diameterCopyright© Markus Tuller and Dani Or2002-2004Soil particles are not spherical• Relative settling velocities of triaxial ellipsoids (L=long, I=intermediate, & S=short axis) relative to spherical particle of equal volume (Matthews, 1991).Copyright© Markus Tuller and Dani Or2002-2004Sedimentation – Pipette Methodgd)(h18t2lsρρη−=Typical experimental setup for the pipette method Cylinder withsuspended sampleCopyright© Markus Tuller and Dani Or2002-2004Sedimentation – Hydrometer MethodThe concentration (density) of suspended particles is measured directly with a calibrated Hydrometer at certain time intervals. The hydrometer settling depth h’ is dependent on the concentration R in g/l of the pure Sodium pyrophosphate solution and the shape and design of the hydrometer.For the ASTM 152H Hydrometer h’=-0.164R+16.3 [cm]. When h’ is known we can calculate settling times as:gd)('h18t2lsρρη−=Copyright© Markus Tuller and Dani Or2002-2004Sedimentation – Hydrometer MethodAll particles arein suspensionOnly Silt and Clayparticles arein suspensionOnly Clayparticles arein suspensionStartAfter 11.6 hrsAfter 67 secCopyright© Markus Tuller and Dani Or2002-2004Settling Times - Example23l3so2sm81.9gmkg1000mkg2650m2.0h)C25at(ssmkg00089.0sPam89.0======ρρη[][][][]tMttMtMtMtLLLMLttLMskgsskgskgskgsmmmkgmssmkg222232222232=⋅==⋅⋅⋅⋅⋅=⋅==⋅⋅⋅⋅⋅Use Stokes' law to calculate the time needed for: (a) sand particles (diameter >50µm) and (b) silt particles (>2µm) to settle to a depth of 0.2 m in an aqueous suspension at 25oC.gd)(h18t2lsρρη−=Sand d > 0.00005 ms7981.9)00005.0()10002650(00089.02.018t2=⋅⋅−⋅⋅=Units Dimensional AnalysisCopyright© Markus Tuller and Dani Or2002-2004Settling Times - Examplegd)(h18t2lsρρη−=Silt d > 0.000002 mhr74.13s4948581.9)000002.0()10002650(00089.02.018t2==⋅⋅−⋅⋅=Stokes LawCopyright© Markus Tuller and Dani Or2002-2004Modern methods for particle size analysesNew methods are now available (powder technology, etc.) - Optical Microscopy- Transmission/Scanning Electron Microscopy- X-ray attenuation- Particle counting (Coulter method)- Light Scattering and Laser Diffraction MethodsCopyright© Markus Tuller