Levee overtopping can lead to failure and cause catastrophic damage, as was the case during Hurricane Katrina. We present a computer simulation of erosion to study the development of the rills and gullies that form along an earthen embankment during overtopping. We have coupled 3D Smoothed Particle Hydrodynamics with an erodibility model to produce our simulation. Through comparison between simulations and between simulation and analogous laboratory experiments, we provide quantitative and qualitative results, evaluating the accuracy of our simulation

Chen, Zhongxian

Cutler, Barbara

Franklin, W. Randolph

Gross, Jared

Stuetzle, Christopher S.

Zimmie, Thomas F.

English

Merrimack College: Merrimack ScholarWorks

Merrimack College Merrimack ScholarWorks Computer Science Faculty Publications Computer Science 11-2010 Quantitative analysis of simulated erosion for different soils Zhongxian Chen Christopher S. Stuetzle Barbara Cutler Jared Gross W. Randolph Franklin See next page for additional authors Follow this and additional works at: https://scholarworks.merrimack.edu/cs_facpub  Part of the Computer Sciences Commons Authors Zhongxian Chen, Christopher S. Stuetzle, Barbara Cutler, Jared Gross, W. Randolph Franklin, and Thomas F. Zimmie See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/221590007Quantitative analysis of simulated erosion for different soilsConference Paper · January 2010DOI: 10.1145/1869790.1869867 · Source: DBLPCITATIONS7READS286 authors, including:Some of the authors of this publication are also working on these related projects:Computer Science Pedagogy View projectDeep Mathematical Representation of Terrain View projectZhongxian ChenPinterest Inc.22 PUBLICATIONS   150 CITATIONS   SEE PROFILEChristopher StuetzleMerrimack College21 PUBLICATIONS   34 CITATIONS   SEE PROFILEBarbara CutlerRensselaer Polytechnic Institute53 PUBLICATIONS   1,216 CITATIONS   SEE PROFILEThomas ZimmieRensselaer Polytechnic Institute81 PUBLICATIONS   503 CITATIONS   SEE PROFILEAll content following this page was uploaded by Christopher Stuetzle on 12 May 2020.The user has requested enhancement of the downloaded file.Quantitative Analysis of Simulated Erosionfor Different SoilsZhongxian Chenchenz5@cs.rpi.eduChristopher Stuetzlestuetc@cs.rpi.eduBarbara Cutlercutler@cs.rpi.eduJared Grossgrossj@rpi.eduW. Randolph Franklinfranklin@cs.rpi.eduThomas Zimmiezimmit@rpi.eduABSTRACTRensselaer Polytechnic InstituteTroy, NYLevee overtopping can lead to failure and cause catas-trophic damage, as was the case during Hurricane Katrina.We present a computer simulation of erosion to study the de-velopment of the rills and gullies that form along an earthenembankment during overtopping. We have coupled 3DSmoothed Particle Hydrodynamics with an erodibility modelto produce our simulation. Through comparison betweensimulations and between simulation and analogous labora-tory experiments, we provide quantitative and qualitativeresults, evaluating the accuracy of our simulation.Categories and Subject DescriptorsI.3.5 [Computer Graphics]: Computational Geometry andObject Modeling—physically based modeling ;I.6.4 [Simulation and Modeling]: Model Validation andAnalysis and Simulation Output AnalysisKeywordshydraulic erosion simulation, physical modeling1. INTRODUCTIONDuring Hurricane Katrina in 2006, the overtopping, seep-age, and eventual failure of earthen levees protecting NewOrleans, LA, caused vast devastation to the city and its sur-rounding areas. A better understanding of the evolutionof rills and gullies, which form during levee overtopping, isnecessary to enable the design of structures that can moreeffectively withstand storm conditions.Erosion Literature During storm conditions, a leveeovertops the moment the level of water has reached and ex-ceeds the crest (highest part of the levee) and flows over thedownslope side. Hanson et al. [7] presented a four-stage ero-sion process that occurs during overtopping of an embank-ment. Wang et al. [12, 13] presented two dimensional math-ematical models for the erosion of an embankment. BriaudPermission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.ACM GIS ’10 , November 2-5, 2010. San Jose, CA, USA(c) 2010 ACM ISBN 978-1-4503-0428-3/10/11 ...$10.00.sinksourcecrestupslopedownslopeA BCD0.670m0.356m0.950m0.038m0.051m0.131m0.257m0.174m0.257m0.131mFigure 1: Diagram of the geometric dimensions ofthe levee for our computer simulations and physicalexperiments. Note the labels A, B, C, and D alongthe profile of the levee.et al. [1] expanded the traditional definition of a soil’s“erodi-bility” to account for water velocity that varies throughoutthe flow field, instead defining erodibility as a function ofshear stress over the surface of the soil. This model is appli-cable to small-scale erosion simulations, and is the erosionmodel implemented in our simulation.One important metric for the effectiveness of a levee isthe average time to breach during storm conditions. Fread,from the National Weather Service, defined time to breachas the duration of time between the initial formation of arill and the time at which the rill has reached the upslope ofthe levee, forming a clear channel along with breaching wa-ter runs [4]. We base our quantitative analysis of computersimulations and laboratory experiments on this accepted ob-servational definition.Computer Modeling of Hydraulic Erosion Fluidflow and hydraulic erosion simulations have been developedfor computer graphics, though the primary goal has been tocreate physically plausible terrains mimicking features formedthrough erosion processes. Fluid simulation techniques canbe divided into two categories. In the first category are grid-based Eulerian techniques, as used by Foster and Metaxaswith the Marker-And-Cell method to solve 3-D Navier-Stokesequations [3]. An alternative to Eulerian methods, the highresolution particle-based Lagrangian methods based onSmooth Particle Hydrodynamics (SPH) [5, 9], is becomingmore popular. Kristof et al. [8] was the first to present anerosion simulation using SPH. The soil, water, and soil-waterboundary were all represented by particles, the soil and wa-ter particles have mass and velocity while the boundary par-ticles are designed solely for the two phases to interact. ThisFigure 2: Physical experiment using pure sand.method is most similar to our simulation method. To rep-resent terrain, we use a Segmented Height Field (SHF) [10].Evaluation and Validation One of the most importantgoals of our work is to evaluate the accuracy of our com-puter simulations through comparisons with experimentaldata, collected from laboratory trials. To our knowledge,validation of the accuracy of the detailed computer simula-tions of erosion, especially those for computer graphics use,has received little attention. One notable exception is theSODA project [11], in which a patch of soil was pelted withrain both in a laboratory and in a cellular automata com-puter simulation, and the results are visually compared.2. EXPERIMENTAL METHODOLOGYTo study the formation and propagation of rills and gulliesin the surface of an earthen embankment and enable vali-dation of our computer simulations, we conducted a seriesof physical laboratory experiments, which are described inour earlier work [6], shown in Figures 1 & 2. We performedanalogous computer simulations [2] for five different sets oferosion parameters that span the estimates of the soil pa-rameters in our physical laboratory experiments (Figure 3).We performed two trials for each simulation as an initial in-vestigation of the variance of these simulations and averagetheir results.Table 1 presents several interesting quantitative measure-ments for each simulation. We calculate the maximum ver-tical erosion depth and the total volume of eroded soil foreach trial after ten minutes of simulation (from the pointof initial overtopping). The last three columns of the tablepresent the elapsed time for three specific milestones thatindicate breach of the levee.To characterize and evaluate the physical accuracy of ourerosion simulation, we provide results for our computer sim-ulation trials with different soil parameters and confirm thatthe system behavior changes as expected with regard to rilland gully formation, maximum erosion depth, total erosionvolume, and two objective and quantitative time to breachmetrics. Furthermore, we compare the results from our com-puter simulations to our laboratory laboratory erosion ex-periments.3. ANALYSIS AND DISCUSSIONComparison of Computer Simulations We analyzethe results of our computer simulations of erosion by visu-alizing and comparing the erosion through different quanti-Figure 3: A computer simulation result showingdeep channels in a soil with medium erodibility.tative metrics, and draw conclusions on the validity of ourerosion model and simulation results. As shown in Table 1,the values of maximum vertical erosion depth and total ero-sion volume at 10 minutes after the initial overtopping gen-erally increase with increased erodibility and also, logically,the time to breach (for each of the three metrics) is shorterfor soils with higher erodibility.We perform a detailed analysis of several easy-to-monitorgeometric and simulation properties. In Figure 4, we plotthe values of maximum vertical erosion depth in differentzones of the levee with respect to time. Each of the five plotspresents results for a specific set of soil parameters. As canbe observed from the plots, the crest of the levee is the mostvulnerable to erosion when compared to the upslope anddownslope and, as expected, the erosion is most aggressiveon the downslope and the crest. Furthermore, the erosiondepth for highly erodible soils increases dramatically in thefirst five minutes and then levels off. In contrast, the erosiondepth for less erodible soils proceeds at a more constant pacethroughout the 10 minute simulation.Time to Breach Metrics To identify the moment ofbreach, we follow the somewhat subjective definition of theDam-Break Flood Forecasting Model [4] (Table 1, 6th col-umn). In addition to this classic definition, we propose twoquantitative metrics related to levee breach that can be cal-culated directly from the computer simulations, illustratedin Figure 5. In the left plot, we monitor the upslope faceof the levee to determine when significant erosion occursin this zone, as this will indicate the formation of a chan-nel across the crest of the levee. We define the moment ofbreach as the moment when this upslope erosion exceeds aspecific threshold (Table 1, 7th column). Next, we observethat levee breach is typically accompanied by a dramaticincrease in the magnitude of the velocity of water particlescrossing the crest of the levee. In our simulation, velocity ofwater flow can be approximated by the average velocity ofindividual water particles in the zone of the levee crest (be-tween positions B and C in Figure 1). In the right plot ofFigure 5, we observe that the velocity for simulations withlarger erodibilities peaks earlier than for those with smallererodibilities (Table 1, 8th column).Visual Comparison of Erosion In Figure 6, we presenta visual comparison of the development of the number, shape,branching pattern, and depth of the rills and gullies in dif-ferent computer trials. Several interesting observations canbe made from these images. First, as the erodibility of thesoil increases, the gullies become deeper and wider. Early insand-clay mixture#1: a=93, τc=3.00 #3: a=137, τc=2.50pure sand#5: a=187, τc=2.00Figure 4: We plot the maximum erosion depth along the length of the levee for the different soil types. Theless erodible soils display a smaller maximum depth of erosion and a smaller total volume of erosion (notshown). Note that in all cases the erosion begins on the downslope of the levee, progresses across the crestof the levee, and finally erodes the upslope to breach the levee.the trial with highly erodible soil we can also see numeroussmall channels, but as the erosion progresses fewer, deeperprimary channels emerge, allowing the secondary channelsto dry up. If we continued the trials beyond 10 minutes,this pattern may well follow for the less erodible soils aswell. Because the water’s velocity should be greatest at thebase of the downslope (point D), yielding higher shear stressand maximum erosion, we expect to first observe erosion atthe base of the downslope and then watch it progress upto the crest of the levee (point C). However, in our com-puter simulations the erosion on the downslope was uniformfrom crest to base and ultimately the greatest depth of ver-tical erosion occurs along the crest and the top part of thedownslope. These observations may be due to the overallscale and proportions if the geometry. For simulations offull-scale levees (for which we will create analogous simu-lations with small-scale models using our geotechnical cen-trifuge [14]) we expect to see increased velocities and moresignificant initial erosion at the base of the downslope, andpossibly more varied channel formation.Comparison of Computer Simulations and Physi-cal Experiments Finally, we compare our computer sim-ulation trials with the laboratory experiment shown in Fig-ure 2. During the erosion of the physical model, the time tobreach was 6:25 for fine-grain sand with an estimated erodi-bility of a = 187, which can be compared to the time tobreach for Simulation #1.Figure 5: We evaluate two quantitative metrics todefine the moment of breach of the levee. The left-most plot displays the maximum depth of erosionwithin the zone of the upslope of the levee. Themiddle plot shows the average velocity of water par-ticles in the zone of the levee crest.Visually, the progression of the geometric data appearssomewhat similar. During the physical experiment, severalshallow channels gave way to or joined with a single deepchannel that formed along the downslope and slowly erodedback along the crest. Conversely, several computer trials ex-hibited behavior in which a series of channels formed, thoughin many cases lesser channel formation did give way to fewermore pronounced channels, with the lesser channels dryingup as the experiment progressed. The behavior of the simu-lated erosion is comparable to that seen in the experiment,especially with regard to the formation and progression ofthe rills and gullies beginning on the downslope and pro-gressing back across the crest. In both the simulations andthe experiment the rill formation starts as the water over-sand-clay pure sand#1 #2 #3 #4 #5a = 93 a = 115 a = 137 a = 159 a = 187τc = 3.00 τc = 2.75 τc = 2.50 τc = 2.25 τc = 3.002min4min6min8min10minFigure 6: Visualization of the progression of erosionfor each of our computer simulations. White indi-cates no erosion, Erosion ranges from shallow (lightblue) to deep (red). Four dashed lines (from left toright) in each image respectively indicate labels A,B, C and D in Figure 1.Table 1: Erosion parameters and numerical data for the erosion and breaching of our computer simulations.Maximum erosion Total erosion Time to breach (m:ss)Simulation a τc depth (m) volume (m3) crest channel upslope erosion water velocity#1 sand-clay mixture 93 3.00 0.0450 0.0022 8:36 9:06 7:15#2 115 2.75 0.0607 0.0053 3:13 4:20 3:41#3 137 2.50 0.0586 0.0047 2:44 4:08 3:06#4 159 2.25 0.0577 0.0050 2:35 3:42 2:24#5 pure sand 187 2.00 0.0663 0.0091 1:11 1:06 0:51tops the levee, and continues until the rill has eroded backalong the crest. When the rill had reached the upslope, thusbreaching the levee, the progression ceased and the watercontinued to flow along the same channels, slowly cuttingaway at the edges and bottom and expanding the channels.The more highly erodible soils in our simulation trialsshowed significant erosion on the upslope, whereas very lit-tle was observed during the experiment. Also, the overallvolume of erosion and the depth of erosion of the chan-nels formed during the computer simulation exceeded thatof the laboratory experiment, as the channels were carvedout faster during the simulation. These discrepancies canbe attributed to a number of factors not taken into accountby our simulation, such as soil moisture content of the soil,soil porosity, and the presence of a clay or wood levee core,which will have a substantial impact on the erodibility of thesoil and the behavior of the water in the system. Also miss-ing from the simulation was deposition, which has a clearimpact on the behavior of the water once it reaches the bot-tom of the downslope, and may or may not affect the erosionalong the downslope.4. FUTURE WORKTo improve the accuracy of results, we will extend oursimulation engine to include sediment transport and de-position and soil permeability. We will also implement amore physically-accurate model of crumbling overhangs andslumping. To enhance simulation efficiency, we will furtheroptimize our implementation and improve the paralleliza-tion strategy to use a super computer or GPUs, allowing usto work with larger datasets at higher resolutions. Further-more, we will conduct additional physical experiments andacquire higher-resolution digital scans to facilitate precisegeometric comparison.5. ACKNOWLEDGMENTSThis research was supported by NSF grant CMMI-0835762.6. REFERENCES[1] J. L. Briaud, H.-C. Chen, A. V. Govindasamy, andR. Storesund. Levee Erosion by Overtopping in NewOrleans during the Katrina Hurricane. Journal ofGeotechnical and Geoenvironmental Engineering,134(618), 2008.[2] Z. Chen, C. S. Stuetzle, B. M. Cutler, J. A. Gross,W. R. Franklin, and T. F. Zimmie. Analyses,simulations and physical modeling validation of leveeand embankment erosion. In To appear in GeoFrontiers 2011, Dallas, Texas, US, 2011. To appear.[3] N. Foster and D. Metaxas. Realistic animation ofliquids. Graphical Models and Image Processing,(58):471–483, 1996.[4] D. L. Fred. Dambrk: The nws dam-break floodforcasting model. National Weather Service, Office ofHydrology, Silver Spring, Md, 1984.[5] R. A. Gingold and J. J. Monaghan. Smoothed particlehydrodynamics: Theory and application tono-spherical stars. Mon. Not. R. Astr. Soc.,(181):375–389, 1977.[6] J. A. Gross, C. S. Stuetzle, Z. Chen, B. Cutler, W. R.Franklin, and T. Zimmie. Simulating levee erosionwith physical modeling validation. In The 5thInternational Conference on Scour and Erosion (ICSE2010), San Fransisco, CA, November 2010. (toappear).[7] G. J. Hanson, K. R. Cook, and S. L. Hunt. Physicalmodeling of overtopping erosion and breach formationof cohesive embankments. Transactions of the ASAE,48(5):1783–1794, 2005.[8] P. Kristof, B. Benes, J. Krivanek, and O. St’ava.Hydraulic erosion using smoothed particlehydrodynamics. Computer Graphics Forum,28(2):219–228, 2009.[9] L. B. Lucy. A numerical approach to the testing of thefission hypothesis. Astronomical Journal,(82):1013–1024, 1977.[10] C. S. Stuetzle, Z. Chen, B. Cutler, W. R. Franklin,J. Gross, K. Perez, and T. Zimmie. Computersimulations and physical modelling of erosion. In 7thInternational Conference on Physical Modelling inGeotechnics (ICPMG 2010), Zurich, June 2010. (toappear).[11] G. Valette, S. Prevost, L. Lucas, and J. Leonard.SoDA project: A simulation of soil surfacedegradation by rainfall. Computers & Graphics,30(4):494–506, August 2006.[12] P. Wang and R. Kahawita. Modeling the hydraulicsand erosion process in breach formation due toovertopping. In Sedimentation and SedimentTransport, Proceedings, pages 211–220, 2003.[13] P. Wang, R. Kahawita, A. Moktari, T. M. Phat, andT. T.Quach. Modeling breach formation inembankments due to overtopping. Transactions of theInternational Congress on Large Dams, 22(3):377–396,2006.[14] T. F. Zimmie. Geo-environmental research usingcentrifuges. In The Encyclopedia of EnvironmentalControl Technology, volume 9, pages 335–366. GulfPublishing Co., 1995.View publication stats

Quantitative analysis of simulated erosion for different soils

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Quantitative analysis of simulated erosion for different soils

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