3d)
COMPARISON AND VALIDATION OF SWMS_2D AND HYDRUS (2D/3D) FOR CAPILLARY BARRIERS USING DATA OF A 10-M TIPPING TROUGH K. BERGER* * Universität Hamburg, Institute of Soil Science, Allende-Platz 2, 20146 Hamburg, Germany
SUMMARY: Capillary barriers are an interesting alternative component for cover systems of landfills and contaminated sites. Soil hydrologic models could be fast and powerful tools for dimensioning of capillary barriers provided they are sufficiently validated. Outflow rates measured in a 10 m long tipping trough for one material combination and two slopes from stationary periods were compared to simulation results of SWMS_2D (Vs. 1.1) in 1995 and of HYDRUS (2D/3D) (Vs. 2.05) in 2017. The measured outflow rates show a typical pattern with threshold values indicating the efficiency of the capillary barrier. This flow pattern could neither be reproduced with SWMS_2D nor with HYDRUS (2D/3D). Both models produced smooth patterns without thresholds. Four validation series were run with SWMS_2D with different parametrizations assuming homogeneous and isotropic materials. Two validation series were run with HYDRUS (2D/3D), one assuming homogeneous material, the second assuming heterogeneous material simulated by stochastically distributed scaling factors with Miller-Miller similitude. Possible sources of error explaining the mismatch of measured and simulated outflow patterns could exist in the empirical investigation, the application of the models or in the models themselves. However, essential errors could not be identified yet. Currently, SWMS_2D and HYDRUS (2D/3D) should not be used for dimensioning of capillary barriers in engineering practice.
1. INTRODUCTION Capillary barriers are two-layer systems consisting of an upper layer made of a relatively fine-grained and fine-porous material (e.g. sand), the so-called ‘capillary layer’, underlain by a lower layer made of a relatively coarse-grained and coarse-porous material (e.g. gravel), the socalled ‘capillary block’. Between the two layers is a sharp interface that is sloped. Water that is percolating through the capillary layer under unsaturated conditions is hold at the interface due to capillary forces (capillary barrier effect). If the inflow into the capillary layer is not too high, nearly no water breaks through the interface into the capillary block; instead, the water is moving in the capillary layer downward along the interface (wick(ing) effect or capillary diversion), see e.g. Oldenburg & Pruess (1993), and Yeh et al. (1994). This type of flow is called ‘funneled flow’ (Kung 1990). However, if the inflow into the capillary layer is too high, water is
Proceedings Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium/ 2 - 6 October 2017 S. Margherita di Pula, Cagliari, Italy / © 2017 by CISA Publisher, Italy
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
breaking through the interface. Capillary barriers are not only a curious soil hydrologic phenomenon; they are also an interesting component for cover systems of landfills and contaminated sites. Cover systems are multi-layer systems consisting of layers that perform specific tasks. Especially on steep slopes capillary barriers can be used as a component of the liner, if necessary overlain by a layer to limit the inflow into the capillary layer (so-called ‘extended capillary barrier’). For the use in cover systems, capillary barriers have to be dimensioned; that means suitable material combinations for the capillary layer and capillary block and suitable maximum distances to the drain that removes the water from the systems have to be determined dependent on site-specific conditions. Relevant are the following parameters: § Soil hydrological properties of the materials for the capillary layer and capillary block; § Slope; § Slope length / Maximum distance to the drain; § Shape of the slope (convex – concave; convergent – divergent); § Infiltration rate into the capillary layer; it depends on the climate of the site and on the layers above the capillary barrier. There are several methods available for dimensioning capillary barriers that have specific advantages and disadvantages, especially empirical investigations with large test fields (lysimeters), empirical investigations with tipping troughs in pilot plant scale, and simulations with two- or three-dimensional soil hydrological models like HYDRUS (2D/3D) (Sejna et al. 2016; see also Radcliffe and Simunek 2010). Empirical investigations with large test fields were performed e.g. on the landfill Georgswerder in Hamburg, Germany, using six test fields, each 50 m long and 10 m wide, one having an extended capillary barrier (Melchior 1993, Berger et al. 2009). Compared to empirical investigations simulations with a 2D or 3D model have major advantages in terms of required time and costs. However, the model has to be sufficiently validated for the type of application to assure that the simulation results are close to reality and can be transferred into the field. Validation is a complex procedure (see e.g. Berger 1999). However, most important are output comparisons of simulation and measurement results. Such an output comparison was performed using outflow data of a capillary barrier constructed in a 10 m long tipping trough.
2. EXPERIMENTS WITH A 10 M LONG TIPPING TROUGH Design, experiments and measurement results with the tipping trough are described in detail in Steinert et al. (1997a, 1997b) and Steinert (1999). Just the main characteristics are given here. The tipping trough (see Figure 1) was 10 m long; the capillary barrier constructed inside had a height of 1 m (0.3 m capillary block, 0.7 m capillary layer), the trough was 0.5 m deep with a central measurement area of 0.3 m depth and two margins at the front and on the back of 0.1 m depth each, separated by steel panels. The slope was continuously adjustable by a crank handle up to 1:3 (33 %). The entire trough stood on weighing cells with a resolution of 1 kg. The empty trough weighted about 4 t; the trough filled with materials and irrigated weighted around 13 t depending on the mass of the water in the trough. There were 9 capillary barrier segments, each 1 m long with a separate outflow, and 1 final capillary layer segment, also 1 m long with a separate outflow. Outflow rates were measured with a maximum resolution of 0.1 l. On the top
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
of the trough was an irrigation system that allowed a uniform irrigation of the surface of the capillary layer with a continuously adjustable irrigation rate between 0.1 and 30 mm/d. Experiments with a material combination for the capillary layer and capillary block took several months without interruption. The evaluation was focussed on the outflow rates of the capillary layer and the capillary block at different inflow rates.
Figure 1. Front view to the filled 10-m tipping trough (dark brown material: capillary block; lightcoloured material: capillary layer and collection sump; on the left side a dye tracer experiment with a red tracer is depicted; Photo: Jens Heisterkamp, Institute of Soil Science, Universität Hamburg). 3. SIMULATION WITH SWMS_2D 3.1 Material and Methods In 1995 simulations with SWMS_2D (Vs. 1.1, Simunek et al. 1992) were performed for one material combination, two slopes and only for periods where stationary flow could be assumed. The capillary layer was constructed from medium sand that was recycled from dredged material of the river Elbe in a mechanical treatment plant for harbour sediments (called ‘METHA’, see Berger et al. 2017). The capillary block consisted of gravel with main grain diameters of 1 to 3 mm. Both materials were well sorted. In the simulation they were assumed to be homogeneous and isotropic. Two slopes were investigated, steep, i.e. 1:5 (20 %) and flat, i.e. 1:25 (4 %), respectively. Only periods with a constant irrigation rate from the top and a maximum weighing difference of the entire tipping trough of 5 kg were simulated in separate simulation runs. The simulation period was set to 34,560 minutes (24 days) to assure a steady state at the end of each simulation run. Outflows of the capillary layer and capillary block were modelled as seepage faces. The evaluation was focussed on the outflow rates at the end of each simulation run. Water content–pressure head relationships and saturated hydraulic conductivities were measured and evaluated with RETC (van Genuchten et al. 1991).
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
Two groups of simulation series were performed: 1. A preliminary simulation series to check the impact of the FE mesh (for one stationary period
with slope 1:25 and inflow rate 21.3 mm/d); 2. Four validation series for all inflow rates and the two slopes; one series with the average
values of the van Genuchten-Mualem parameters and the saturated hydraulic conductivity, and three series considering the spatial heterogeneity of these parameters using that FE mesh from the preliminary series with a good match of measured and simulated outflow rates. In the preliminary simulation series nine FE meshes from 392 nodes and 347 rectangular elements to 1118 nodes and 1039 rectangular elements were used. All FE meshes had refinements the along the upper boundary (irrigation), the interface between the two layers, and the outflows of the capillary layer and the capillary block (seepage faces). The four validation simulation series were performed with that FE mesh from the preliminary series that led to a reasonable compromise of robustness (avoidance of run-time errors), exactness (small water balance errors) and computing time (mesh with 536 nodes and 483 rectangular elements). One simulation series was run with the average soil hydrological parameters of both layers (van Genuchten-Mualem parameters α and n (van Genuchten 1980), and saturated hydraulic conductivity ks) and three series with soil hydrological parameters reflecting the statistical variation of these parameters. In these three series the simulated outflow rates were calibrated to the measured outflow rates for the same stationary period as in the preliminary series (slope 1:25, inflow rate 21.3 mm/d), and afterwards the obtained parameters were used to simulate all other stationary periods (extrapolation). Actuating variables of the calibration were the saturated hydraulic conductivities ks of the capillary layer (simulation series ‘Best fit ks of capillary layer’) and of the capillary block (simulation series ‘Best fit ks of capillary block’), respectively, and the van Genuchten-Mualem parameters α and n (set to the upper values of the 95 % confidence interval for the capillary layer and to the lower values for the capillary block, respectively), slightly boosted by the ks of both layers (simulation series ‘Best fit of hydrological separation of capillary layer and capillary block’); see Table 1. Table 1. Soil hydrological parameters of the four validation simulation series with SWMS_2D. Simulations series
Average values Best fit ks capillary layer Best fit ks capillary block Best fit hydrological separation of capillary layer and cap. block
Capillary layer (METHA sand) α n ks -1 (cm ) (1) (cm/min) 0.03018 5.11346 0.78 0.03018 5.11346 0.41 0.03018 5.11346 0.78 0.0321 5.9491 0.6975
Capillary block (1/3 gravel) α n ks -1 (cm ) (1) (cm/min) 0.20570 3.75010 72.0 0.20570 3.75010 72.0 0.20570 3.75010 800 0.1972 3.4224 80.0
3.2 Results and Discussion The outflow rates of the nine FE meshes of the preliminary simulation series differ for less than 10 %. The finest FE mesh led to the largest balance error (0.493 %, the minimum balance error was 0.232 %, the average balance error 0.323 %). The measured and simulated outflow rates dependent on the inflow rates of the four validation series are shown in Figure 2, in the left column for the slope 1:25, in the right column for the slope 1:5, in the upper row for the capillary layer and in the lower row for the capillary block. Each pair of outflow rates of the capillary layer and the capillary block belonging to an
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
inflow rate sum up to the inflow rate (steady state). For illustration the inflow rate is shown at the bottom in mm/d. The measured data show a typical flow pattern: At small inflow rates (almost) all infiltrating water is moving laterally downward in the capillary layer along the interface, no outflow is measured in the capillary block. At a first threshold of the inflow rate water is breaking through the interface into the capillary block leading to an increase of the capillary block outflow. At a second higher threshold of the inflow rate the very most (slope 1:25) or all (slope 1:5) of the additional water infiltrating into the capillary layer is breaking through into the capillary block and the outflow rates of the capillary layer increase only slightly (slope 1:25) or remain constant (slope 1:5). Objective of the simulations was to reproduce this flow pattern and to identify the two thresholds. However, the simulated outflow rates show a different flow pattern with a smooth increase of the outflow rates of the capillary layer as well as of the capillary block without any thresholds. The simulation series with the average values of the van Genuchten-Mualem parameters reproduced the outflow rates at small inflow rates well. However, especially for the steep slope (20 %) at high inflow rates SWMS_2D overestimated the outflow rate of the capillary layer and underestimated that of the capillary block. Thus the model overestimated the efficiency of the capillary barrier just for that condition (steep slopes) where capillary barriers shall be used. The three simulation series with different calibrations for the stationary period with the highest inflow rate at a slope of 1:25 show a similar smooth flow pattern, too. Thus, the validation attempt failed for SWMS_2D. Slope 1:5
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Figure 2. Comparison of measured and with SWMS_2D simulated outflow rates of the capillary layer and the capillary block dependent on the inflow rates (four validation series, symbols mark stationary periods).
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
4. SIMULATION WITH HYDRUS (2D/3D) 4.1 Material and Methods A possible reason for the mismatch of the measured and simulated outflow rates obtained with SWMS_2D is the assumption of homogeneous materials. Actually, homogeneity is a concept that cannot be found in pure form in nature. Due to spatial inhomogeneity the breakthrough of the capillary barrier may occur in fingers that are self-reinforcing with increasing inflow flow rates. HYDRUS (2D/3D) allows the stochastically distribution of scaling factors that can be used to model spatial heterogeneity. Therefore, in 2017 three simulation series were performed with HYDRUS (2D/3D) (Vs. 2.05; Sejna et al. 2016) with a 2D general geometry for the same materials, slopes and periods with stationary flow as formerly with SWMS_2D: 1. A preliminary simulation series to check the impact of the FE mesh (for one stationary period with slope 1:5 and inflow rate 14.2 mm/d) 2. Simulation series for all inflow rates and the two slopes with the average values of the van Genuchten-Mualem parameters and without scaling using the FE mesh from the preliminary series with a good match of measured and simulated outflow rates that, moreover, resulted in the smallest relative water balance error at the end of the simulation (0.001 %). 3. Simulation series as series 2, but with the scaling option of HYDRUS (2D/3D) and stochastic distribution of scaling factors with Miller-Miller similitude (MMS, using default parameters of the GUI except for the standard deviation of the hydraulic conductivity scaling factor, which was set after some tests to 0.125 instead of the default of 0.25). The FE meshes were defined with refinements along the interface of the capillary layer and capillary block and along the upper boundary (inflow). In some FE meshes stretching along the length of the tipping trough was applied (default stretching factor in x-direction of 3). HYDRUS (2D/3D) generated slightly different meshes for the slopes 1:25 and 1:5, respectively. In the simulation series with scaling the same stochastically distribution of scaling factors was applied for all simulation runs of a slope (i.e. the distribution was not recalculated for each steady state period). Note that the FE meshes generated by HYDRUS (2D/3D) and generated for SWMS_2D are different. 4.2 Results and Discussion The measured and simulated outflow rates dependent on the inflow rates of the two validation series are shown in Figure 3 analogously to Figure 2. Similar to the results of the SWMS_2D simulations, the outflow rates simulated with HYDRUS (2D/3D) show a smooth increase for the capillary layer as well as for the capillary block without any thresholds. The outflow rates of the simulation without and with scaling are close together. This means, if fingering occurs in the simulation, it does not play the assumed important role. Thus, the validation attempt failed for HYDRUS (2D/3D), too.
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
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Figure 3. Comparison of measured and with HYDRUS (2D/3D) simulated outflow rates of the capillary layer and the capillary block dependent on the inflow rates (two validation series, symbols mark stationary periods) 5. POSSIBLE REASONS FOR THE MISMATCH OF MEASURED AND SIMULATED OUTFLOW RATES Due to the systematic measurement and simulation results, the mismatch of measured and simulated outflow rates is very probably caused by systematic and not by random errors. There are three groups of possible reasons to explain the mismatch of measured and simulated outflow rates. 1.) Errors in the empirical investigation The 10-m tipping trough is a well-defined but large device, and there may be many sources of error and uncertainties in the experiments, like spatial heterogeneous materials e.g. due to the filling of the device or the impact of temperature on the water flow. Furthermore, in the assumed stationary periods there might have been no stationary flow, but redistribution of water inside the tipping trough without impact on the outflow rates. However, the typical measured flow pattern with distinct threshold values of the inflow rates indicating the effectiveness of the capillary barrier and depending on the material combination and the slope is well confirmed (Steinert 1999). 2.) Errors in the application of the models The simulation task is quite well defined, for example the shape of the tipping trough and of the capillary barrier inside. However, some material properties were not considered in the simulations due to missing measurement data, like hysteresis of the soil hydrologic functions and the anisotropy of the hydraulic conductivity of the capillary layer material at the interface. Both materials (METHA-sand and 1/3 gravel) were technically pre-treated and therefore had a specific grain-size and pore-size distribution. This may be one reason why the parametrization
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
of the van Genuchten-Mualem model for the soil hydrologic functions was not unique (see below in 3.). The spatial inhomogeneity of material properties was modelled with scaling. If fingering plays an important role in the flow across the interface of capillary layer and capillary block, twodimensional simulations are not sufficient because they reflect constant conditions along the depth of the slope. Fingers as separate three-dimensional entities require three-dimensional simulations. 3.) Errors in the models like incompleteness, unsuitable approaches and FEM problems This is a broad and complex field. Only a few topics will be addressed here. The van Genuchten-Mualem model may not be suitable to describe the soil hydrologic relationships of the technical pre-treated materials used in the capillary barrier. The fitting of the van Genuchten-Mualem model to three different measured data sets for the METHA-sand resulted in significantly different parameter values for α, n, θs and θr. These data sets comprise water content - pressure head data from pressure cells (used in the simulations), and, obtained only after the simulations with SWMS_2D, unsaturated hydraulic conductivity data from tensioninfiltrometer measurements, and unsaturated hydraulic conductivity data from a transient evaporation experiment; the latter results, however, are uncertain. In the regular HYDRUS (2D/3D) version material properties are assigned to the nodes, not to the elements of the FE mesh. According to Heiberger (1996, p. 52) this approach does not allow a sharp interface between two layers, but leads to an interface layer with alternating intermediate material properties. An alternative HYDRUS version is available on request that assigns the material properties to the elements instead of the nodes of the FE mesh. Simulations with this version are under way. In the author’s opinion none of the reasons mentioned in this brief discussion is essential to explain the mismatch of measured and simulated flow patterns of the capillary barrier. The simulation results of the alternative HYDRUS version, however, have to be awaited. 6. CONCLUSIONS The model application described in this paper is quite simple: The shape of the tipping trough and of the capillary barrier inside are well defined, the two materials are quite well defined, and only stationary periods are simulated. The critical point of modelling capillary barriers is the flow process along and across the interface of the capillary layer and the capillary block. Neither SWMS_2D nor HYDRUS (2D/3D) could reproduce the measured outflow patterns and could identify the threshold values indicating the effectiveness of the capillary barrier. Possible sources of error explaining the mismatch of measured and simulated outflow patterns were discussed; errors could exist in the empirical investigation, the application of the models or in the models themselves. However, in the author’s opinion the essential reason(s) for the mismatch of simulated and measured outflow rates could not be identified yet. Additional simulations with the alternative HYDRUS version assigning material properties to the FE elements are under way. Due to the unsuccessful validation attempts of SWMS_2D and HYDRUS (2D/3D) both models should currently not be used in engineering practice for the dimensioning of capillary barriers.
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
ACKNOWLEDGEMENTS The empirical investigation in the tipping trough and the simulations with SWMS_2D were funded by the German Federal Ministry for Education, Science, Research and Technology (BMBF) within the integrated research project ‘Advanced Landfill Liner Systems’ under the project number 1440 569A-39. The author thanks Dr. habil. Stefan Melchior and Prof. Dr. Günter Miehlich, who led the empirical investigation, and Dr. Bernd Steinert, Matthias Türk, Karin Burger and all involved staff members for their work. The author also thanks Prof. Jirka Simunek (Ph.D.) and all other developers of SWMS_2D and HYDRUS (2D/3D). REFERENCES Berger K. (1999). Validation of the Hydrologic Evaluation of Landfill Performance (HELP) model for simulating the water balance of cover systems. Environmental Geology, Springer, 39 (11), 1261-1274. Berger K., Melchior S., Sokollek V., Steinert B. and Vielhaber B. (2009). Water Balance and Effectiveness of Landfill Cover Systems: 20 Years Measurements at the Landfill HamburgGeorgswerder. Sardinia 2009 / Twelfth International Waste Management and Landfill Symposium / 5 - 9 October 2009. CISA, Padova, Italy. Paper 316. Berger K., Groengroeft A., Gebert J., Harms C. and Eschenbach A. (2017). 20 years of longterm water balance measurements of a landfill cover system with components constructed from pre-treated dredged material. Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017. CISA, Padova, Italy. Paper 226. Heiberger T. S. (1996). Simulating the effects of a capillary barrier using the two-dimensional variably saturated flow model SWMS_2D / HYDRUS-2D. Master thesis, Oregon State University, 124 pp. Kung K.-J.S., (1990). Preferential Flow in a Sandy Vadose Zone: 2. Mechanism and Implications. Geoderma, 46 (1-3), 59-71. Melchior S. (1993). Wasserhaushalt und Wirksamkeit mehrschichtiger Abdecksysteme für Deponien und Altlasten. Dissertation, Universität Hamburg. Hamburger Bodenkundliche Arbeiten 22, 330 pp. [in German] Oldenburg C.M., Pruess K. (1993). On Numerical Modeling of Capillary Barriers. Water Resour. Res., 29 (4), 1045-1056. Radcliffe D. E. and Simunek J. (2010). Soil Physics with HYDRUS. Modeling and Applications. CRC Press, Boca Raton, FL, 372 pp. Sejna M., Simunek J. and van Genuchten M. Th. (2016). The HYDRUS Software Package for Simulating the Two- and Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Porous Media. User Manual, Version 2.05. PC Progress, Prague, Czech Republic, 306 pp. Simunek J., Vogel T. and van Genuchten M. T. (1992). The SWMS_2D code for simulating water flow and solute transport in two-dimensional variably saturated media. Vs. 1.1. Research report 126, U.S. Salinity Lab., Riverside, CA, 169 pp. Steinert B., Melchior S., Burger K., Berger K., Türk M. and Miehlich G. (1997a). Dimensionierung von Kapillarsperren zur Oberflächenabdichtung von Deponien und Altlasten. Hamburger Bodenkundliche Arbeiten 32, 420 pp. [in German] Steinert B., Melchior S., Burger K., Berger K., Türk M. and Miehlich G. (1997b). Design of capillary barriers for capping of landfills and contaminated sites. In: August H., Holzlöhner U.
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
and Meggyes T. (Eds.): Advanced Landfill Liner Systems. Th. Telford, London, pp. 286-301. Steinert B. (1999). Kapillarsperren für die Oberflächenabdichtung von Deponien und Altlasten Bodenphysikalische Grundlagen und Kipprinnenuntersuchungen. Dissertation, Universität Hamburg. Hamburger Bodenkundliche Arbeiten 45, 250 pp. [in German] van Genuchten M.Th. (1980). A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Sci. Soc. Am. J., 44, 892-898. van Genuchten M.Th., Leij F.J. and Yates S.R. (1991). The RETC Code for Quantifying the Hydraulic Functions of Unsaturated Soils. EPA Report No. 600/2-91/065, U.S. Salinity Laboratory, Riverside, California, 83 pp. Yeh T.-C.J., Guzman A., Srivastava R. and Gagnard P.E. (1994). Numerical Simulation of the Wicking Effect in Liner Systems. Ground Water, 32 (1), 2-11.
SUMMARY: Capillary barriers are an interesting alternative component for cover systems of landfills and contaminated sites. Soil hydrologic models could be fast and powerful tools for dimensioning of capillary barriers provided they are sufficiently validated. Outflow rates measured in a 10 m long tipping trough for one material combination and two slopes from stationary periods were compared to simulation results of SWMS_2D (Vs. 1.1) in 1995 and of HYDRUS (2D/3D) (Vs. 2.05) in 2017. The measured outflow rates show a typical pattern with threshold values indicating the efficiency of the capillary barrier. This flow pattern could neither be reproduced with SWMS_2D nor with HYDRUS (2D/3D). Both models produced smooth patterns without thresholds. Four validation series were run with SWMS_2D with different parametrizations assuming homogeneous and isotropic materials. Two validation series were run with HYDRUS (2D/3D), one assuming homogeneous material, the second assuming heterogeneous material simulated by stochastically distributed scaling factors with Miller-Miller similitude. Possible sources of error explaining the mismatch of measured and simulated outflow patterns could exist in the empirical investigation, the application of the models or in the models themselves. However, essential errors could not be identified yet. Currently, SWMS_2D and HYDRUS (2D/3D) should not be used for dimensioning of capillary barriers in engineering practice.
1. INTRODUCTION Capillary barriers are two-layer systems consisting of an upper layer made of a relatively fine-grained and fine-porous material (e.g. sand), the so-called ‘capillary layer’, underlain by a lower layer made of a relatively coarse-grained and coarse-porous material (e.g. gravel), the socalled ‘capillary block’. Between the two layers is a sharp interface that is sloped. Water that is percolating through the capillary layer under unsaturated conditions is hold at the interface due to capillary forces (capillary barrier effect). If the inflow into the capillary layer is not too high, nearly no water breaks through the interface into the capillary block; instead, the water is moving in the capillary layer downward along the interface (wick(ing) effect or capillary diversion), see e.g. Oldenburg & Pruess (1993), and Yeh et al. (1994). This type of flow is called ‘funneled flow’ (Kung 1990). However, if the inflow into the capillary layer is too high, water is
Proceedings Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium/ 2 - 6 October 2017 S. Margherita di Pula, Cagliari, Italy / © 2017 by CISA Publisher, Italy
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
breaking through the interface. Capillary barriers are not only a curious soil hydrologic phenomenon; they are also an interesting component for cover systems of landfills and contaminated sites. Cover systems are multi-layer systems consisting of layers that perform specific tasks. Especially on steep slopes capillary barriers can be used as a component of the liner, if necessary overlain by a layer to limit the inflow into the capillary layer (so-called ‘extended capillary barrier’). For the use in cover systems, capillary barriers have to be dimensioned; that means suitable material combinations for the capillary layer and capillary block and suitable maximum distances to the drain that removes the water from the systems have to be determined dependent on site-specific conditions. Relevant are the following parameters: § Soil hydrological properties of the materials for the capillary layer and capillary block; § Slope; § Slope length / Maximum distance to the drain; § Shape of the slope (convex – concave; convergent – divergent); § Infiltration rate into the capillary layer; it depends on the climate of the site and on the layers above the capillary barrier. There are several methods available for dimensioning capillary barriers that have specific advantages and disadvantages, especially empirical investigations with large test fields (lysimeters), empirical investigations with tipping troughs in pilot plant scale, and simulations with two- or three-dimensional soil hydrological models like HYDRUS (2D/3D) (Sejna et al. 2016; see also Radcliffe and Simunek 2010). Empirical investigations with large test fields were performed e.g. on the landfill Georgswerder in Hamburg, Germany, using six test fields, each 50 m long and 10 m wide, one having an extended capillary barrier (Melchior 1993, Berger et al. 2009). Compared to empirical investigations simulations with a 2D or 3D model have major advantages in terms of required time and costs. However, the model has to be sufficiently validated for the type of application to assure that the simulation results are close to reality and can be transferred into the field. Validation is a complex procedure (see e.g. Berger 1999). However, most important are output comparisons of simulation and measurement results. Such an output comparison was performed using outflow data of a capillary barrier constructed in a 10 m long tipping trough.
2. EXPERIMENTS WITH A 10 M LONG TIPPING TROUGH Design, experiments and measurement results with the tipping trough are described in detail in Steinert et al. (1997a, 1997b) and Steinert (1999). Just the main characteristics are given here. The tipping trough (see Figure 1) was 10 m long; the capillary barrier constructed inside had a height of 1 m (0.3 m capillary block, 0.7 m capillary layer), the trough was 0.5 m deep with a central measurement area of 0.3 m depth and two margins at the front and on the back of 0.1 m depth each, separated by steel panels. The slope was continuously adjustable by a crank handle up to 1:3 (33 %). The entire trough stood on weighing cells with a resolution of 1 kg. The empty trough weighted about 4 t; the trough filled with materials and irrigated weighted around 13 t depending on the mass of the water in the trough. There were 9 capillary barrier segments, each 1 m long with a separate outflow, and 1 final capillary layer segment, also 1 m long with a separate outflow. Outflow rates were measured with a maximum resolution of 0.1 l. On the top
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
of the trough was an irrigation system that allowed a uniform irrigation of the surface of the capillary layer with a continuously adjustable irrigation rate between 0.1 and 30 mm/d. Experiments with a material combination for the capillary layer and capillary block took several months without interruption. The evaluation was focussed on the outflow rates of the capillary layer and the capillary block at different inflow rates.
Figure 1. Front view to the filled 10-m tipping trough (dark brown material: capillary block; lightcoloured material: capillary layer and collection sump; on the left side a dye tracer experiment with a red tracer is depicted; Photo: Jens Heisterkamp, Institute of Soil Science, Universität Hamburg). 3. SIMULATION WITH SWMS_2D 3.1 Material and Methods In 1995 simulations with SWMS_2D (Vs. 1.1, Simunek et al. 1992) were performed for one material combination, two slopes and only for periods where stationary flow could be assumed. The capillary layer was constructed from medium sand that was recycled from dredged material of the river Elbe in a mechanical treatment plant for harbour sediments (called ‘METHA’, see Berger et al. 2017). The capillary block consisted of gravel with main grain diameters of 1 to 3 mm. Both materials were well sorted. In the simulation they were assumed to be homogeneous and isotropic. Two slopes were investigated, steep, i.e. 1:5 (20 %) and flat, i.e. 1:25 (4 %), respectively. Only periods with a constant irrigation rate from the top and a maximum weighing difference of the entire tipping trough of 5 kg were simulated in separate simulation runs. The simulation period was set to 34,560 minutes (24 days) to assure a steady state at the end of each simulation run. Outflows of the capillary layer and capillary block were modelled as seepage faces. The evaluation was focussed on the outflow rates at the end of each simulation run. Water content–pressure head relationships and saturated hydraulic conductivities were measured and evaluated with RETC (van Genuchten et al. 1991).
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
Two groups of simulation series were performed: 1. A preliminary simulation series to check the impact of the FE mesh (for one stationary period
with slope 1:25 and inflow rate 21.3 mm/d); 2. Four validation series for all inflow rates and the two slopes; one series with the average
values of the van Genuchten-Mualem parameters and the saturated hydraulic conductivity, and three series considering the spatial heterogeneity of these parameters using that FE mesh from the preliminary series with a good match of measured and simulated outflow rates. In the preliminary simulation series nine FE meshes from 392 nodes and 347 rectangular elements to 1118 nodes and 1039 rectangular elements were used. All FE meshes had refinements the along the upper boundary (irrigation), the interface between the two layers, and the outflows of the capillary layer and the capillary block (seepage faces). The four validation simulation series were performed with that FE mesh from the preliminary series that led to a reasonable compromise of robustness (avoidance of run-time errors), exactness (small water balance errors) and computing time (mesh with 536 nodes and 483 rectangular elements). One simulation series was run with the average soil hydrological parameters of both layers (van Genuchten-Mualem parameters α and n (van Genuchten 1980), and saturated hydraulic conductivity ks) and three series with soil hydrological parameters reflecting the statistical variation of these parameters. In these three series the simulated outflow rates were calibrated to the measured outflow rates for the same stationary period as in the preliminary series (slope 1:25, inflow rate 21.3 mm/d), and afterwards the obtained parameters were used to simulate all other stationary periods (extrapolation). Actuating variables of the calibration were the saturated hydraulic conductivities ks of the capillary layer (simulation series ‘Best fit ks of capillary layer’) and of the capillary block (simulation series ‘Best fit ks of capillary block’), respectively, and the van Genuchten-Mualem parameters α and n (set to the upper values of the 95 % confidence interval for the capillary layer and to the lower values for the capillary block, respectively), slightly boosted by the ks of both layers (simulation series ‘Best fit of hydrological separation of capillary layer and capillary block’); see Table 1. Table 1. Soil hydrological parameters of the four validation simulation series with SWMS_2D. Simulations series
Average values Best fit ks capillary layer Best fit ks capillary block Best fit hydrological separation of capillary layer and cap. block
Capillary layer (METHA sand) α n ks -1 (cm ) (1) (cm/min) 0.03018 5.11346 0.78 0.03018 5.11346 0.41 0.03018 5.11346 0.78 0.0321 5.9491 0.6975
Capillary block (1/3 gravel) α n ks -1 (cm ) (1) (cm/min) 0.20570 3.75010 72.0 0.20570 3.75010 72.0 0.20570 3.75010 800 0.1972 3.4224 80.0
3.2 Results and Discussion The outflow rates of the nine FE meshes of the preliminary simulation series differ for less than 10 %. The finest FE mesh led to the largest balance error (0.493 %, the minimum balance error was 0.232 %, the average balance error 0.323 %). The measured and simulated outflow rates dependent on the inflow rates of the four validation series are shown in Figure 2, in the left column for the slope 1:25, in the right column for the slope 1:5, in the upper row for the capillary layer and in the lower row for the capillary block. Each pair of outflow rates of the capillary layer and the capillary block belonging to an
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
inflow rate sum up to the inflow rate (steady state). For illustration the inflow rate is shown at the bottom in mm/d. The measured data show a typical flow pattern: At small inflow rates (almost) all infiltrating water is moving laterally downward in the capillary layer along the interface, no outflow is measured in the capillary block. At a first threshold of the inflow rate water is breaking through the interface into the capillary block leading to an increase of the capillary block outflow. At a second higher threshold of the inflow rate the very most (slope 1:25) or all (slope 1:5) of the additional water infiltrating into the capillary layer is breaking through into the capillary block and the outflow rates of the capillary layer increase only slightly (slope 1:25) or remain constant (slope 1:5). Objective of the simulations was to reproduce this flow pattern and to identify the two thresholds. However, the simulated outflow rates show a different flow pattern with a smooth increase of the outflow rates of the capillary layer as well as of the capillary block without any thresholds. The simulation series with the average values of the van Genuchten-Mualem parameters reproduced the outflow rates at small inflow rates well. However, especially for the steep slope (20 %) at high inflow rates SWMS_2D overestimated the outflow rate of the capillary layer and underestimated that of the capillary block. Thus the model overestimated the efficiency of the capillary barrier just for that condition (steep slopes) where capillary barriers shall be used. The three simulation series with different calibrations for the stationary period with the highest inflow rate at a slope of 1:25 show a similar smooth flow pattern, too. Thus, the validation attempt failed for SWMS_2D. Slope 1:5
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Figure 2. Comparison of measured and with SWMS_2D simulated outflow rates of the capillary layer and the capillary block dependent on the inflow rates (four validation series, symbols mark stationary periods).
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
4. SIMULATION WITH HYDRUS (2D/3D) 4.1 Material and Methods A possible reason for the mismatch of the measured and simulated outflow rates obtained with SWMS_2D is the assumption of homogeneous materials. Actually, homogeneity is a concept that cannot be found in pure form in nature. Due to spatial inhomogeneity the breakthrough of the capillary barrier may occur in fingers that are self-reinforcing with increasing inflow flow rates. HYDRUS (2D/3D) allows the stochastically distribution of scaling factors that can be used to model spatial heterogeneity. Therefore, in 2017 three simulation series were performed with HYDRUS (2D/3D) (Vs. 2.05; Sejna et al. 2016) with a 2D general geometry for the same materials, slopes and periods with stationary flow as formerly with SWMS_2D: 1. A preliminary simulation series to check the impact of the FE mesh (for one stationary period with slope 1:5 and inflow rate 14.2 mm/d) 2. Simulation series for all inflow rates and the two slopes with the average values of the van Genuchten-Mualem parameters and without scaling using the FE mesh from the preliminary series with a good match of measured and simulated outflow rates that, moreover, resulted in the smallest relative water balance error at the end of the simulation (0.001 %). 3. Simulation series as series 2, but with the scaling option of HYDRUS (2D/3D) and stochastic distribution of scaling factors with Miller-Miller similitude (MMS, using default parameters of the GUI except for the standard deviation of the hydraulic conductivity scaling factor, which was set after some tests to 0.125 instead of the default of 0.25). The FE meshes were defined with refinements along the interface of the capillary layer and capillary block and along the upper boundary (inflow). In some FE meshes stretching along the length of the tipping trough was applied (default stretching factor in x-direction of 3). HYDRUS (2D/3D) generated slightly different meshes for the slopes 1:25 and 1:5, respectively. In the simulation series with scaling the same stochastically distribution of scaling factors was applied for all simulation runs of a slope (i.e. the distribution was not recalculated for each steady state period). Note that the FE meshes generated by HYDRUS (2D/3D) and generated for SWMS_2D are different. 4.2 Results and Discussion The measured and simulated outflow rates dependent on the inflow rates of the two validation series are shown in Figure 3 analogously to Figure 2. Similar to the results of the SWMS_2D simulations, the outflow rates simulated with HYDRUS (2D/3D) show a smooth increase for the capillary layer as well as for the capillary block without any thresholds. The outflow rates of the simulation without and with scaling are close together. This means, if fingering occurs in the simulation, it does not play the assumed important role. Thus, the validation attempt failed for HYDRUS (2D/3D), too.
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
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Figure 3. Comparison of measured and with HYDRUS (2D/3D) simulated outflow rates of the capillary layer and the capillary block dependent on the inflow rates (two validation series, symbols mark stationary periods) 5. POSSIBLE REASONS FOR THE MISMATCH OF MEASURED AND SIMULATED OUTFLOW RATES Due to the systematic measurement and simulation results, the mismatch of measured and simulated outflow rates is very probably caused by systematic and not by random errors. There are three groups of possible reasons to explain the mismatch of measured and simulated outflow rates. 1.) Errors in the empirical investigation The 10-m tipping trough is a well-defined but large device, and there may be many sources of error and uncertainties in the experiments, like spatial heterogeneous materials e.g. due to the filling of the device or the impact of temperature on the water flow. Furthermore, in the assumed stationary periods there might have been no stationary flow, but redistribution of water inside the tipping trough without impact on the outflow rates. However, the typical measured flow pattern with distinct threshold values of the inflow rates indicating the effectiveness of the capillary barrier and depending on the material combination and the slope is well confirmed (Steinert 1999). 2.) Errors in the application of the models The simulation task is quite well defined, for example the shape of the tipping trough and of the capillary barrier inside. However, some material properties were not considered in the simulations due to missing measurement data, like hysteresis of the soil hydrologic functions and the anisotropy of the hydraulic conductivity of the capillary layer material at the interface. Both materials (METHA-sand and 1/3 gravel) were technically pre-treated and therefore had a specific grain-size and pore-size distribution. This may be one reason why the parametrization
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
of the van Genuchten-Mualem model for the soil hydrologic functions was not unique (see below in 3.). The spatial inhomogeneity of material properties was modelled with scaling. If fingering plays an important role in the flow across the interface of capillary layer and capillary block, twodimensional simulations are not sufficient because they reflect constant conditions along the depth of the slope. Fingers as separate three-dimensional entities require three-dimensional simulations. 3.) Errors in the models like incompleteness, unsuitable approaches and FEM problems This is a broad and complex field. Only a few topics will be addressed here. The van Genuchten-Mualem model may not be suitable to describe the soil hydrologic relationships of the technical pre-treated materials used in the capillary barrier. The fitting of the van Genuchten-Mualem model to three different measured data sets for the METHA-sand resulted in significantly different parameter values for α, n, θs and θr. These data sets comprise water content - pressure head data from pressure cells (used in the simulations), and, obtained only after the simulations with SWMS_2D, unsaturated hydraulic conductivity data from tensioninfiltrometer measurements, and unsaturated hydraulic conductivity data from a transient evaporation experiment; the latter results, however, are uncertain. In the regular HYDRUS (2D/3D) version material properties are assigned to the nodes, not to the elements of the FE mesh. According to Heiberger (1996, p. 52) this approach does not allow a sharp interface between two layers, but leads to an interface layer with alternating intermediate material properties. An alternative HYDRUS version is available on request that assigns the material properties to the elements instead of the nodes of the FE mesh. Simulations with this version are under way. In the author’s opinion none of the reasons mentioned in this brief discussion is essential to explain the mismatch of measured and simulated flow patterns of the capillary barrier. The simulation results of the alternative HYDRUS version, however, have to be awaited. 6. CONCLUSIONS The model application described in this paper is quite simple: The shape of the tipping trough and of the capillary barrier inside are well defined, the two materials are quite well defined, and only stationary periods are simulated. The critical point of modelling capillary barriers is the flow process along and across the interface of the capillary layer and the capillary block. Neither SWMS_2D nor HYDRUS (2D/3D) could reproduce the measured outflow patterns and could identify the threshold values indicating the effectiveness of the capillary barrier. Possible sources of error explaining the mismatch of measured and simulated outflow patterns were discussed; errors could exist in the empirical investigation, the application of the models or in the models themselves. However, in the author’s opinion the essential reason(s) for the mismatch of simulated and measured outflow rates could not be identified yet. Additional simulations with the alternative HYDRUS version assigning material properties to the FE elements are under way. Due to the unsuccessful validation attempts of SWMS_2D and HYDRUS (2D/3D) both models should currently not be used in engineering practice for the dimensioning of capillary barriers.
Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017
ACKNOWLEDGEMENTS The empirical investigation in the tipping trough and the simulations with SWMS_2D were funded by the German Federal Ministry for Education, Science, Research and Technology (BMBF) within the integrated research project ‘Advanced Landfill Liner Systems’ under the project number 1440 569A-39. The author thanks Dr. habil. Stefan Melchior and Prof. Dr. Günter Miehlich, who led the empirical investigation, and Dr. Bernd Steinert, Matthias Türk, Karin Burger and all involved staff members for their work. The author also thanks Prof. Jirka Simunek (Ph.D.) and all other developers of SWMS_2D and HYDRUS (2D/3D). REFERENCES Berger K. (1999). Validation of the Hydrologic Evaluation of Landfill Performance (HELP) model for simulating the water balance of cover systems. Environmental Geology, Springer, 39 (11), 1261-1274. Berger K., Melchior S., Sokollek V., Steinert B. and Vielhaber B. (2009). Water Balance and Effectiveness of Landfill Cover Systems: 20 Years Measurements at the Landfill HamburgGeorgswerder. Sardinia 2009 / Twelfth International Waste Management and Landfill Symposium / 5 - 9 October 2009. CISA, Padova, Italy. Paper 316. Berger K., Groengroeft A., Gebert J., Harms C. and Eschenbach A. (2017). 20 years of longterm water balance measurements of a landfill cover system with components constructed from pre-treated dredged material. Sardinia 2017 / Sixteenth International Waste Management and Landfill Symposium / 2 - 6 October 2017. CISA, Padova, Italy. Paper 226. Heiberger T. S. (1996). Simulating the effects of a capillary barrier using the two-dimensional variably saturated flow model SWMS_2D / HYDRUS-2D. Master thesis, Oregon State University, 124 pp. Kung K.-J.S., (1990). Preferential Flow in a Sandy Vadose Zone: 2. Mechanism and Implications. Geoderma, 46 (1-3), 59-71. Melchior S. (1993). Wasserhaushalt und Wirksamkeit mehrschichtiger Abdecksysteme für Deponien und Altlasten. Dissertation, Universität Hamburg. Hamburger Bodenkundliche Arbeiten 22, 330 pp. [in German] Oldenburg C.M., Pruess K. (1993). On Numerical Modeling of Capillary Barriers. Water Resour. Res., 29 (4), 1045-1056. Radcliffe D. E. and Simunek J. (2010). Soil Physics with HYDRUS. Modeling and Applications. CRC Press, Boca Raton, FL, 372 pp. Sejna M., Simunek J. and van Genuchten M. Th. (2016). The HYDRUS Software Package for Simulating the Two- and Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Porous Media. User Manual, Version 2.05. PC Progress, Prague, Czech Republic, 306 pp. Simunek J., Vogel T. and van Genuchten M. T. (1992). The SWMS_2D code for simulating water flow and solute transport in two-dimensional variably saturated media. Vs. 1.1. Research report 126, U.S. Salinity Lab., Riverside, CA, 169 pp. Steinert B., Melchior S., Burger K., Berger K., Türk M. and Miehlich G. (1997a). Dimensionierung von Kapillarsperren zur Oberflächenabdichtung von Deponien und Altlasten. Hamburger Bodenkundliche Arbeiten 32, 420 pp. [in German] Steinert B., Melchior S., Burger K., Berger K., Türk M. and Miehlich G. (1997b). Design of capillary barriers for capping of landfills and contaminated sites. In: August H., Holzlöhner U.
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and Meggyes T. (Eds.): Advanced Landfill Liner Systems. Th. Telford, London, pp. 286-301. Steinert B. (1999). Kapillarsperren für die Oberflächenabdichtung von Deponien und Altlasten Bodenphysikalische Grundlagen und Kipprinnenuntersuchungen. Dissertation, Universität Hamburg. Hamburger Bodenkundliche Arbeiten 45, 250 pp. [in German] van Genuchten M.Th. (1980). A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Sci. Soc. Am. J., 44, 892-898. van Genuchten M.Th., Leij F.J. and Yates S.R. (1991). The RETC Code for Quantifying the Hydraulic Functions of Unsaturated Soils. EPA Report No. 600/2-91/065, U.S. Salinity Laboratory, Riverside, California, 83 pp. Yeh T.-C.J., Guzman A., Srivastava R. and Gagnard P.E. (1994). Numerical Simulation of the Wicking Effect in Liner Systems. Ground Water, 32 (1), 2-11.
