Deriving hydraulic conductivity function from soil column tests
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1 Deriving hydrulic conductivity function from soil column tests Yvonne Lins, Mri Dtchev & Tom Schnz DFG Fo TP 4 Experimentelle und theoretische Untersuchungen teilgesättigter Reibungsmterilien
2 Content Equipment column test device & modified pressure plte pprtus Presenttion of results SWCC & unsturted hydrulic conductivity function Comprison of results Numericl nlysis Inverse Modelling with Comes Geo Conclusions
3 Modified pressure plte device Dil gge Air pressure supply u Wter pressure supply u w Porous stone Soil smple Cermic disk W ter reservior Wter pressure supply u w Schemtic sketch nd photos of modified pressure plte pprtus
4 Column test device 5 dil gge Mini Tensiometer T5 (UMS) TDR T TDR TDR TDR 4 TDR 5 67 x Time Domine Reflectometry sensores 5 Tensiometers T T T 4 TDR Mini Burible Wveguide (Soilmoisture Equipment Corp.) T 5 wter reservior Lyout of the test device Instlltion of sensors
5 Clibrtion TDR & Tensiometer Apprent dielectric constnt [-] void rtio e=.75 void rtio e=.97 Topp et l. (98) 4 5 Vol. wter content [-] Clibrtion TDR θ ( K θ ( K θ ) = 4. 6 ) =.8 Topp et l. (98) K K ,4K 4 ( K ) =.9 4 K 6.57 K K + 4 Lins (BUW) Potentil [cm] K K 5 y = -,8x +,64 y = -,8499x +,78 y = -,859x +,75 y = -,85x +,986 y = -,796x -, K mv Clibrtion tensiometers T6 T6 T6 T6 T64
6 Modified pressure plte device Volumetric wter content [%] -4 m/s] Unsturted hydrulic conductivity [ 5 4 ψ w ev =.8kP θ s =.47 k s SWCC by using Fredlund & Xing eqution Wetting bnd Loose specimen ψ ev =.kp M tric suction [kp] ψ wev ψ ev. Mtric suction [kp] Fredlund nd Xing (994) initil void rtio e =.89 drying (verge vlue) wetting (verge vlue) Drying bnd Wetting bnd θ r =.; ψ r =.8kP Drying bnd Loose specimen Unsturted hydrulic conductivity by using sttisticl model Fredlund & Xing (994) Θ = C( ψ ) ψ ln e + k r ( θ ) = Θ q θr θ s θ θ r n Θ - normlized volumetric wter content ψ - suction C(ψ) - Correction function, n, m - Prmeters Childs & Collis George (95) θ - volumetric wter content m ( θ ζ ) dζ ψ ( ζ ) ( θ s ζ ) dζ ψ ( ζ ) θ r - residul volumetric wter content θ s - residul volumetric wter content ζ - dummy integrtion vrible q - prmeter k r - reltive hydrulic conductivity,
7 Volumetric wter content [%] Volumetric wter content [%] 5 4 Time [min] Column device Exmple of Mesurements TDR Loose specimen Initil void rtio =.89 TDR (top) TDR TDR TDR4 TDR5 (bottom) Drying process SWCC. Mtric suction [kp] Pore - wter pressure [kp] Tensiometer 4 Lyer (top) - drying Lyer (top) - wetting Lyer - drying Lyer - wetting Lyer - drying Lyer - wetting Lyer 4 - drying Lyer 4 - wetting Lyer 5 (bottom) - drying Lyer 5 (bottom) - wetting Time [min] T (top) Mtric suction T T T4 T5 (bottom) Hydrosttic pressure Drying process TDR & Tensiometer mesurements linked to SWCC
8 Volumetric wter content [%] Column device Influence of flow rte Initil drying st nd nd wetting lyer (top) lyer lyer lyer 4 st nd nd drying. Mtric suction [kp] Fredlund nd Xing (994) Initil void rtio e =.89 Flow rte ml/min Flow rte ml/min SWCCs by using Fredlund & Xing eqution resulting from different flow rtes -4 m/s] Unsturted hydrulic conductivity [ st nd nd wetting lyer (top) lyer lyer lyer 4. Mtric suction [kp] Fredlund et l. (994) Initil void rtio e =.89 Flow rte ml/min Flow rte ml/min Initil drying st nd nd drying Unsturted hydrulic conductivity resulting from different flow rtes by using sttisticl model
9 Column device Sttisticl model vs. Instntneous Profile Method Unst. hydrulic conductivity [ -4 m/s]... Mtric suction [kp] Instntneous Profile Method: first drying Sttisticl Model: first drying V A t w ( ψ ) = dhw dz Unsturted hydrulic conductivity resulting from sttisticl model nd instntneous profile method k V w - mount of wter flowing pst point i t time intervl t A - cross sectionl re dh i /dz i - hydrulic hed grdient z - verticl coordinte h w - hydrulic hed i
10 Modified pressure plte versus column device SWCC Volumetric wter content [%] Mtric suction [kp] Fredlund nd Xing (994) Initil void rtio e =.89 Results smll scle tests: Drying bnd Wetting bnd Results lrge scle tests: Initil, st nd nd drying st nd nd wetting Flow rte ml/min Flow rte ml/min SWCC from smll scle nd lrge scle tests
11 Modified pressure plte versus column device Hydrulic conductivity function -4 m/s].5. Fredlund et l. (994) Initil void rtio e =.89 Unsturted hydrulic conductivity [ Results smll scle tests: Drying bnd Wetting bnd. Mtric suction [kp] Results lrge scle tests: Initil, st nd nd drying st nd nd wetting Flow rte ml/min Flow rte ml/min Unsturted hydrulic conductivity from smll scle nd lrge scle tests for
12 Numericl nlysis coupled hydro-mechnicl nlysis of column drying test using the FE code Comes-Geo (University of Pdu) FE with 5 degrees of freedom in ech node: wter pressure - ; gs pressure - ; cpillry pressure - Drcy s lw reltive permebility SWCC liner elstic mteril effective stress
13 Numericl nlysis Inverse nlysis procedure Optimizer k,, n, m, α Comes Geo p c, S, t Experimentl results p c, S, t No Objective Function Minimum Yes End Scheme of inverse nlysis procedure..5 F(x).. p Prticle swrm optimizer (Meier 6)
14 Numericl nlysis Drying of loose specimen: scenrios - Numericl versus experimentl results: fit using only Tensiometer redings (left) nd only TDR redings (right) Pressure hed [kp] Degree of Sturtion [-],8,6,4, Pressure hed [kp] Time [min] Time [min] 5 5 5,8,6,4, Time [min] Numericl nd experimentl results: fit using both Tensiometer redings nd TDR redings Degree of Sturtion [-] Time [min] b
15 Numericl nlysis Comprison predicted & observed vlues Degree of Sturtion Cpillry pressure Predicted vlues Observed vlues Predicted versus observed vlues for the different scenrios Optimized prmeters. Methods k [m ] [/P] n m α.tensiometers only.5e- 7.4e-4.6e+ 8.6e-.98. TDRs only.455e-.6e-4.9e+.687e TDRs nd tensiometers.878e- 4.9e-4.849e+.78e
16 Numericl nlysis SWCC for scenrios 6 Initil void rtio e =.89 5 Volumetric wter content [%] Results smll scle tests 4 Results lrge scle tests Results simultion. Mtric suction [kp] SWCC: numericl nd experimentl results in comprison
17 Summry & conclusions We study the hydrulic behvior of unsturted grnulr mteril in the cse of Hostun snd. New experimentl devices were developed, modified pressure plte pprtus nd column type device. SWCC & hydrulic conductivity function were estblished for loose specimen under vrible loding pth directions utilizing stedy stte & trnsient method. SWCC & hydrulic conductivity function for Hostun snd tkes plce in nrrow rnge of suction. Significnt effect of hysteresis ws found for loose specimen in the drying nd wetting curves of SWCC. Experiments crried out under stedy stte & trnsient method show similr behvior regrding SWCC nd hydrulic conductivity function. Inverse nlysis of drying cycle of snd column test results ws performed in different scenrios.
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