Numerical Modeling in Geoenvironmental Practice By Craig H. Benson, Ph.D., P.E., M.ASCE o deling o f non-linear systems is now a regular Software Resources part of geoenvironmental engineering practice M due to Lh e ava il ability of inexpensive, high-speed A variety of powerful codes are available. The most PCs that utilize user-friendly software and graphical user common codes used for analysis o f vadose zone hydrol­ interfaces. Robust and effici ent solvers for no n-linear par­ ogy and unsaturated flow are 1-JYDRUS (www.pc-progress. lial d ifferential equations have also had a major irnpact com), UNSAT-H. (www.hydrology.pnl.gov or www.uwgeo on the practicality of geoenvironmental software packages. soft.org), VADOSE/W (www.geoslope.com), SEEP/W (www. Consequentl y, detailed analyses are being done in practice geoslope.corn), and SVFLUX (www.soilvision.com). that were not possible a decade ago. These include realistic HYDRUS is the most cornmonly used code in vadose zone assessrn ents of potential perfo rrn ance as well as "what if" hydrology worldwide, and can also be used to simulate scenarios. The rnost common analyses are associated with heat flow and contarninant transport in unsaturated rn edia. vadose-zone hydrology to predict the movement of water Other software packages cornrnonly used for contaminant in the vadose zone and i nteractions with the atmosphere. transpo 11 sirnulation in va riably saturated media include However, contarninant transport analyses in variably satu­ CTRAN/W (www.geoslope.com), CHEMFLUX (www.so il rated systerns are also becorning cornmonplace. vision.com), and STOMP (www.stomp.pnl.gov). Three­ di rnensio nal sirnulations are possible with fllt))e,,t~l*fa,.f,fP>.ll),(,,.aplļpckQ)tk,,Wtt*' 1--l YDRUS, SEEPW, SVFLUX, C f-1 EMFLUX, ~~ ~~ i,:ļltfo.iajŖi!il~ and STOMP. Versions of I IYDRUS are also lw•Cc:rl.«f available that sirnulate variably saturated reactive transport using equilibrium and kinetic geochemical algorithrns (www.sck cen.be/hp 1/). Applications Typical output frorn a HYRDUS-20 sirnulatio n is shown in Fi gure 1. Th is simulatio n considered a sloping landfill cover with a capi ll a1y break (fine layer over coarse layer). The image shows the con­ trast in water content at the capillary break (orange colors for higher water contents in the upper finer-grained layer; blue col­ o rs for low water contents in the coarse­ grained underlying layer) . Accumulation of water down slope in the finer-grained upper layer is also evident. The accumula­ Figure 1. Example of distribution of volumetric water content in a sloping section of a water balance cover employing a capillary barrier located in Monterey, CA. tion is caused by lateral diversion in the Predictions were made with HYDRUS-2D. Low water contents exist in the coarse­ finer-grained layer that is induced by the grained layer near the base that forms the capillary break. Higher water contents exist in the fine-textured layer used for water storage. The variation in color in the capillary break between the layers. Another fine-texture layer ( orange-red color) shows the down-slope diversion of water due to example of output from HYDRUS-2D is the capillary break. shown in Figure 2. The image shows sulfate 1 6 -Strata e11ce is normally made using a capillary­ 300 tube modei and parameters describing the soil water characteristic curve. The 250 most common modei is the van Genu­ () C chten-Mualem function, an analytical 3 200 C expression relating unsaturated hydrau­ !!I <' lic conductivity to suction or volumet­ CD 150 ;;u ric water content. An important variable C :::, 0 in this function is the pore interaction 100 =i: 3 term, which generally is assumed to be 2, 0.5. Recent studies have shown, how­ 50 ever, that this term can range from 0.5 to 3 .0, which can have a dramatic effect 0 1/1 /04 on the rate at which the unsaturated hydraulic co11ductivity decreases as the sucti o 11 increases. The predictions in Figure 4, made with UNSAT-H, show that cumulative 350 10 evapotranspiration varies by as much as (b) Soil Water Storage and Percolation 0 30% depending 011 the mag11itude ofthe 300 8 C 3 pore i11teraction parameter used in the E C s 250 2I simulatio11. A vari atio n this large could Q) /Soil Water Storage :.::· Ol 6 CD have a sig11ifi ca11 t effect 011 the viability ~ -u .8 200 CD o f the cover design. This example illus­ (/) c=; 0 trates that expertis e i11 parameteriza­ ciī 4 2I ro 5· tion can be as importanl as expertise i11 150 :::, s 11umerical methods when making pre­ 0 2 3 (/) 100 2- dictions in geoenvi ronme11tal engineer­ ing using numerical models. 50 0 1 /1/01 7 /1 /01 1 /1 /02 7/1/02 1 /1 /03 7 /1 /03 1 /1 /04 Training Predictions made with numerical Figure 3a and 3b. Water balance quantities predicted with UNSAT-H for a monolithic final cover over a solid-waste landftll at a semi-arid location: (a) precipitation, evapo­ models depend 011 a variety of factors, transpiration, and runoff; (b) soil water storage and percolation. Soil water storage is i11cluding the parameters used as input, the total volume of water in lhe cover per unit area. The varialion in soil water storage reflects the seasonal variation in degree of saturation wilhin the cover profile. the bou11dary co11ditio11s selected, and the spatial and temporal discretization "realistic." Understandi11g the accuracy a11d limitations of employed. Understandi11g how these factors affect predic­ numerical models is o-itical, particularly sophisticated mod­ tions is essential. For example, an engineer recently ca ll ed to els of highly non-linear systems that have many options. ask: "what is this va11 Genuchten a parameter in the u11satu­ Most certainly, modei predictions must always be tempered rated hydraulic properties i11put?" Clearly, this engineer did with engi11 eeri11g judgment and checked by others with not have the training necessary to be conducting numerical modeling expertise. modeli11g of unsaturated flow problems. Numerical model­ ing requires more tha11 a perso11 to "turn the crank" and Parameterization collate the output. Even if the software can easily be run by point-and-click input, the modeler needs training to e11sure Parameterization remai11s a major factor affecting the that the modei is set up properly, the input is realistic, and accuracy o f predictions made whe11 modeli11g geoenvi­ the predictions are accurate and reasonable. ronmental systems. Scale effects and bias can have a sig- 11 i ficant impact o n the primary variables that are com­ Conclusion monly measured (e.g., saturated hydraulic co11ductivity, The 11umerical models available to today's geoenviron­ the soil water characteri stic curve, partition coefficients). m ental engineer are extremely powerful. They can be used H owever, other less conspicuous variables can also have to solve problems that could not be analyzed in practice an important effect 011 the accuracy of predictions. For a decade ago. Ma11y of the models also have sophisticated example, the unsaturated hydraulic conductivity fu11ction interfaces that make input and operation simple and effi­ is rarely determined experimentally because of the diffi­ cient, and the output can appear extremely realistic. How­ culties ;i.ssociated with its measureme11t. lnstead, a11 infer- ever, engineers must 11ot forget that models are always an 1 8 ~-Strata concentrations in a taili ngs disposal facil­ Hydros20. [solmore]. Gr11phlcal O,splay of Results • [Concentrat1om. · 1 solute>) - ~~ ity. The analysis considered variably satu­ rated flow due to drainage of the tailings, water and oxygen ingress from an overly­ ing cap, and geochemical reactions within the tailings due to the oxygen source in the cap. Non-linear numerical models are essen­ tial for analyzing scenarios such as those shown in Figures 1 and 2. They ca nnot be analyzed directly with analytical solutions. Many of the software packages used to con­ duct non-linear modeling have been devel­ oped commercially and must be licensed. 1[ow ever, some are available in the pub­ lic domain. For example, HYDRUS-1 D is an extremely powerful public-domain software package that can handle non-li n­ ea r flow and transport problems in one dimension. The software can simulate a variety of sophisticated problems, includ­ ing colloidal transport (using filtration Figure 2. Sulfate concentrations (g/L) in a tailings disposal facility during drainage of the theory), atmospheric interactions includ­ tailings. HYDRUS-2D was used to simulate unsaturated f\ow and contaminant transport within the tailings facility. (Courtesy ofHong Kim, HKK Consultants, Reno, NV.) ing snow melt and root water uptake, heat transport, C02 transport, a nd carbon- ate chemistry. Forward simulations can be conducted for percolation rate through the cover not exceed 3 mm/yr. As prediction, and inverse simulations can be performed for shown i11 Figure 3b, the design criterion is met. at least for parameter estimation from field and/or laborat01y data. the three year period simulated. The output shown in Figures 3a and 3b appear remark­ Modei Predictions Versus Reality ably realistic. The runoff and soil water storage curves One of the most common geoengineering applications appear jagged which reflect the rapid response of these of software for vadose zone hydrology is for the design of water balance variables to episodic precipitation events. ln water balance covers used for landfill closures. Water bal­ contrast, the evapotranspiration and percolation curves are ance covers function by storing infiltration in unsaturated smoother, reflecting how damping and averaging within fine-textured soil with minimal percolation into the under­ the proflle affect these fluxes.