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Klaus Berger: SWMS_2D & HYDRUS 2D for Capillary Barriers; HYDRUS Conference Prague 2017
Comparison and Validation of SWMS_2D and HYDRUS 2D/3D for Capillary Barriers
Using Data of a 10-m Tipping Trough
Klaus Berger, University of Hamburg, Institute of Soil Science, Germany
5. HYDRUS Conference30 - 31 March 2017, Prague, Czech Republic
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Outline
1. Introduction
2. Empirical investigations with a 10-m tipping trough (tilt gutter)
3. Simulations with SWMS_2D (1996)
4. Simulations with HYDRUS 2D(/3D) (2017)
5. Comparison of SWMS_2D and HYDRUS 2D/3D results
6. Possible reasons for the mismatch of measured and simulated outflow rates
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 2
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Introduction: What is a Capillary Barrier?
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 3
Capillary layer (e.g. sand)Relatively fine-grained/porous
Capillary block (e.g. gravel)Relatively coarse-grained/porous
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Introduction: Capillary Barriers in Landfill Cover Systems
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 4
Mineral liner / Barrier soil layer
Recultivation layer (for vegetation)
Geomembrane (e.g. PEHD)
Lateral drainage layerGeotextile
Standard design of a cover system Alternative design with an ‘extended‘ capillary barrier (schematic profile)
Vegetation
Recultivation layer
Lateral drainage layerBarrier soil layerGeotextileCapillary layer
Capillary block
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Introduction: How to Dimension Capillary Barriers? (1)
What does ‘dimension’ mean?
Determine suitable materials and maximum distances to the drain dependent on site specific conditions. Relevant parameters are:
1. Soil hydrological properties of materials for capillary layer and capillary block
2. Slope
3. Slope length / Maximum distance to drain
4. Shape of the slope (convex – concave; convergent – divergent): complex, therefore neglected here
5. Infiltration rate into the capillary layer (dependent on climate and the layers above the capillary barrier)
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
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Klaus BergerUniversity of Hamburg, Institute of Soil Science
Introduction: How to Dimension Capillary Barriers? (2)
1. Empirical investigations with large test fields (lysimeters)
Six test fields on the landfill Hamburg-Georgswerder,Germany (50 m long, 10 m wide; profiles see on the right;test field S3 with ‘extended’ capillary barrier)
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
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F1/S1 F2/S2 S3
25
60
20
2540
60
25
F3
75 75
F: 4% slopeS: 20% slope
cmcm
VegetationRecultivation layer / Top soilGeotextileLateral drainage layer; S3: Capillary blockGeomembrane (welded)Geomembrane (not welded)Mineral liner / Barrier soil layerCapillary layer
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Introduction: How to Dimension Capillary Barriers? (3)
2. Empirical investigations with tipping troughs (tilt gutters) in pilot plant scale
10-m tipping trough of the Institute of Soil Science ofthe University of Hamburg
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 7
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Introduction: How to Dimension Capillary Barriers? (4)
Principal methods for dimensioning capillary barriers:
1. Empirical investigations with large test fields (lysimeters)Advantages: Close to reality (field size)Disadvantages: Limited to very few parameter values; time consuming;
very expensive; results not reproducible
2. Empirical investigations with tipping troughs (tilt gutters) in pilot plant scaleAdvantages: Relatively close to reality, results (approximately) reproducibleDisadvantages: Limited to some parameter values; relatively time consuming;
expensive
3. Simulations with 2D or 3D models like SWMS_2D or HYDRUS 2D/3DAdvantages: Many parameter values possible; fast; low costs; reproducibleDisadvantages: Close to reality? Requires sufficient validation of the model!
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 8
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Empirical Investigations in a 10-m Tipping Trough (Tilt Gutter)
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 9
Main characteristics:• 10 m long• 1 m high (capillary barrier)• 0.5 m deep
(0.3 m deep measurement area)• Slope adjustable up to 1:3 (33 %)
by a crank handle• Weighable (empty: ~ 4 t; full: ~ 13 t)• 9 capillary barrier segments,
1 m each, with separate outflows• 1 final capillary layer segment
(1 m long) with separate outflow• Irrigation system on top (uniform
irrigation of the surface)
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Simulations with SWMS_2D (Vs. 1.1) in 1996
Simulations were performed for:• One material combination (capillary layer: ‘METHA’ sand; capillary block:
gravel 1 – 3 mm; both well sorted; assumption: homogeneous and isotropic)• Two slopes: Steep, i.e. 1:5 (20 %); flat, i.e. 1:25 (4 %)• Only periods with (assumed) stationary flow (constant irrigation from top;
maximum weighing difference of the entire tipping trough of 5 kg)Preliminary simulation series to check the impact of the FE net (4 nets from 392 nodes & 347 rectangular elements to 1118 nodes & 1039 rectangular elements).Refinements of the FE nets along the upper boundary, the interface, and the outflows of capillary layer and capillary block (seepage faces).Four simulation series with the same FE net, reflecting the statistical variation of soil hydrological parameters; one outflow each for capillary layer & capillary block.
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 10
Klaus BergerUniversity of Hamburg, Institute of Soil Science
1 10 100 10000.0
0.1
0.2
0.3
0.4
Water content Sand Gravel
Wat
er c
onte
nt θ
(1)
0.0
0.2
0.4
0.6
0.8
Equivalent pore diameter (µm)
Pore density Sand Gravel
Pore density (-d θ(h)/d log10 h)
30000 3000 300 30 3
1 10 100 1000-24
-18
-12
-6
0 0.1
α (cm-1) n Sand 0.0302 5.113 Gravel 0.2057 3.75
Pressure head h (cm)
Hydr
aulic
con
duct
ivity
log 10
(k (
m/s
))
0.1
Simulations with SWMS_2D (2)Van Genuchten Mualem model for METHA sand and 1/3 gravel (average values)
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
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METHA sand Mean 95 % confidence interval
α (cm-1)n (1)
0.030185.11346
0.02834.2778
0.03215.9491
θs (1)θr (1)
0.30560.0400
--
--
ks (m s-1) 1.3 e-4 - -
1/3 gravel
α (cm-1)n (1)
0.205703.75010
0.19723.4224
0.21424.0778
θs (1)θr (1)
0.37460.0330
--
--
ks (m s-1) 1.2 e-2 - -
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Simulations with SWMS_2D: Results
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 12
Validation attempt for SWMS_2D failed!(Possible reasons will be discussed at the end.)
Break for 20 years …
0.0 0.5 1.0 1.50.0
0.5
1.0
1.5
Out
flow
rate
(see
page
face
s) (c
m 2/m
in)
Inflow rate (upper boundary) (cm2/min)
Measured dataSeries of simulation runs:
best fit ks capillary layerbest fit hydrological(separation layer - block)best fit kscapillary blockAverage values of the van-Genuchten-Mualem parameters
0.0 0.5 1.0 1.5
0.0
0.5
1.0
1.5
Slope 1:250.0 0.5 1.0 1.5
0.0
0.5
1.0
1.5 Capillary layer
Slope 1:5
0.0 0.5 1.0 1.50.0
0.5
1.0
1.5 Capillary block
0 5 10 15 20Inflow rate (mm/d)
0 5 10 15 20
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Simulations with HYDRUS 2D/3D (Vs. 2.05) in 2017Possible reason for the mismatch: assumption of homogeneous materials.Due to spatial inhomogeneity, breakthrough of the capillary barrier may occur in fingers.Question: Will HYDRUS 2D/3D with scaling lead to a better match?Three simulation series were performed with a 2D general geometry for the same materials, slopes and periods with stationary flow as 20 years before:1. Preliminary simulation series to check the impact of FE net (1:5, 14.2 mm/d)2. Average values of the van Genuchten Mualem parameters; no scaling3. Scaling option with Miller-Miller similitudeRefinements of the FE nets along the interface and the outflows of capillary layer and capillary block (seepage faces); stretching along the length of tipping trough.Different FE nets compared to SWMS_2D simulations; Slightly different nets for slopes 1:25 and 1:5 generated by HYDRUS.
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 13
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Simulations with HYDRUS 2D/3D: FE net, slope 1:5
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 14
Entire tipping trough
Detail: Sump and seepage faces ofCapillary layer & capillary block (arrows)
FE mesh statistics:• Nodes 367• 1D-elements 115• 2D-elements 670
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Simulations with HYDRUS 2D: Results
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 15
Validation attempt for HYDRUS 2D/3D failed, too!
0.0 0.5 1.0 1.50.0
0.5
1.0
1.5
Out
flow
rate
(see
page
face
s) (c
m 2/m
in)
Inflow rate (upper boundary) (cm2/min)
Measured dataSeries of simulation runs:
Scaling, Miller-Miller similitudeAverage values of the van-Genuchten-Mualem parameters
0.0 0.5 1.0 1.5
0.0
0.5
1.0
1.5
Slope 1:250.0 0.5 1.0 1.5
0.0
0.5
1.0
1.5 Capillary layer
Slope 1:5
0.0 0.5 1.0 1.50.0
0.5
1.0
1.5 Capillary block
0 5 10 15 20Inflow rate (mm/d)
0 5 10 15 20
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Simulations with HYDRUS 2D: Results (2)
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 16
Final water content without scaling
Final water content with scaling (MMS)
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Average relative deviation of simulated and measured outflow rates:
Simulation series:• Avg vGM: with average values of the van Genuchten Mualem parameters• Best fit ks Layer: Best fit of saturated hydraulic conductivity of capillary layer• Best fit ks Block: Best fit of saturated hydraulic conductivity of capillary block• Bfit hydSep Lay – Block: Best fit of the hydrologic separation of capillary layer and
capillary block• Scaling MMS: Scaling with Miller-Miller similitude (parameters 0.125; 0; 0)
Comparison of SWMS_2D and HYDRUS 2D Results
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 17
Slope SWMS_2D HYDRUS 2D/3D
Avg vGMParam
Best fitks Layer
Best fitks Block
Bfit hydSepLay – Block
Avg vGM Scaling MMS
Steep 1:5 0.498 1.39 3.24 3.61 2.63 3.14
Flat 1:25 0.495 1.62 2.69 2.94 1.48 1.48
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Errors in the empirical investigation:• Typical flow pattern with distinct inflow rates designating the effectiveness of
the capillary barrier (specific materials, slope) is well confirmed.
Errors in the application of the models:• Parameters of the interface capillary layer – capillary block: not isotropic• Hysteresis neglected • Parameters of the van Genuchten Mualem model ok? (see also below)• Spatial inhomogeneity of material properties modeled with scaling;
Fingering would require 3D simulation
Errors in the models (incompleteness, unsuitable approaches, FEM problems, …):• Van Genuchten Mualem model suitable for these materials?• FEM: Material properties assigned to the nodes, not to the elements; does not
allow a sharp interface between two layers (Heiberger 1996)
Possible Reasons for the Mismatch of Measured and Simulated Outflow Rates
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 18
Klaus BergerUniversity of Hamburg, Institute of Soil Science
The METHA Sand in the van Genuchten Mualem Model
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 19
1 10 100 10000.0
0.1
0.2
0.3
0.4
0.1
Measured data
Wat
er c
onte
nt θ
(1)
Different fits of the van-Genuchten Mualem modelfor the METHA sand
0.1
1 10 100 1000-18
-12
-6
0
Measured data (IfB) kr(h) characteristic of
10-m tipping trough (tensiometer data)
θr: 0.040, θs: 0.3056 (total pore volume: 0.382)θr: 0.005, θs: 0.34 (TU Berlin)
α n Source0.03018 5.11346 θ(h) fit with RETC0.04895 4.50385 kr(h) fit
(tension infitrometer data)0.069 2.51 kr(h) fit of TU Berlin
(data from transient evaporation experiment)
Pressure head h (cm)
Rela
tive
cond
uctiv
ity lo
g 10 k
r (1)
Klaus BergerUniversity of Hamburg, Institute of Soil Science
FEM: Modeling of the Interface between Two Layers
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 20
From Heiberger 1996, p. 52
Klaus BergerUniversity of Hamburg, Institute of Soil Science
Errors in the empirical investigation:• Typical flow pattern with distinct inflow rates designating the effectiveness of
the capillary barrier (specific materials, slope) is well confirmed.
Errors in the application of the models:• Parameters of the interface capillary layer – capillary block: not isotropic• Hysteresis neglected• Parameters of the van Genuchten Mualem model ok? (see also below)• Spatial inhomogeneity of material properties modeled with scaling;
Fingering would require 3D simulation
Errors in the models (incompleteness, unsuitable approaches, FEM problems, …):• Van Genuchten Mualem model suitable for these materials?• FEM: Material properties assigned to the nodes, not to the elements; does not
allow a sharp interface between two layers (Heiberger 1996)
Possible Reasons for the Mismatch of Measured and Simulated Outflow Rates
SWMS_2D & HYDRUS 2D/3D for Capillary BarriersHYDRUS Conference 2017 30.03.2017
Page 21
Thank you for your attention!
Any idea to overcome the mismatch of measured and simulated outflow rates is welcome!