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<br />HYDRAULIC ENGINEERING '94
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<br />downstream at increased velocities (Clark et al. 1987). Upstream and downstream
<br />of Petersburg, the 3050m (10000 ft) wide valley floor narrows dramatically and
<br />the South Branch flows through constrictions approximately 152m (500 ft) wide
<br />at Petersburg Gap downstream of the city and 114m (375 ft) wide near Marvin
<br />Chapel upstream of the city, (Figure I)
<br />Using the graphical pre- and post-processor FastT ABS, a finite element
<br />mesh representing the flood plain and channel between Marvin Chapel ,and
<br />Petersburg Gap was constructed using a combination of HEC-2 cross sectlon input
<br />data previously used for the one-dimensional modeling of the area, topographic
<br />infonnation from orthophoto maps, and field survey data. Aerial photos were used
<br />to reconstruct conditions prior to the 1985 (-400 yr) flood and levee alignment
<br />infonnation was digitized from design maps.
<br />Modelinil Procedure
<br />RMA2 is a numerical model which uses the finite element method to solve
<br />the two-.dimensional. vertically averaged Navier-Stokes equations for free surface
<br />flow (Thomas and McAnally 1985), The model can generate both steady state and
<br />transient solutions which give water depth and velocity at eac;h node in the finite
<br />element mesh used to represent the study area. For comparison with the HEC-2
<br />results, steady state solutions were modeled in this study. Meshes are constructed
<br />by using combinations of quadrilateral and triangular elements of varying sizes.
<br />This allows for more accurate representation of topography and pennits greater
<br />mesh density in areas where more detailed information is desired. Manning's n
<br />values are assigned for individual elements allowing spatial variation in roughness,
<br />and for this study were based on field data collected for the U,S, Anny Corps'
<br />flood protection study. Eddy viscosity can also be assigned for individual
<br />elements. In order to achieve a solution with accurate representation of flow
<br />separdtion. the eddy viscosity values were lowered as far a possible given the
<br />constraint of obtaining a stable solution. Wetting and drying of meshes is allowed
<br />via tWQ options. both of which were employed in this study. ]n one, when water
<br />depth for a node drops below a user-specified level, the node goes dry and is
<br />removed from the mesh, creating lateral movement in the mesh boundary.
<br />Likewise. when water depth at a node exceeds a certain level. the node is re-
<br />incorporated into the mesh, The other option ror wetting and drying is the "marsh
<br />element" option. With this option, elements are not removed from the mesh. but
<br />as the water surface drops. the area of the element available for flow decreases so
<br />that dry elements are effectively removed from the mesh (King and Roig 1988),
<br />RMA2 accepts inflows and water surface elevations as boundary
<br />conditions, Data from a gage located near the upstream gap and high water marks
<br />recorded at the downstream gap were used to formulate boundary conditions to
<br />simulate the 1949 (-50 yr), 100 yr, and 1985 floods fnr meshes representing the
<br />topography before and after the 1985 flood and with the proposed levees,
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<br />LEVEE DESIGN-2D MODEL
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<br />759
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<br />Enml Dischanre Hi~h Wat~r Mark
<br />1949 Flood (-50yr) IJI2cms 281.5m
<br />100 Yr Flood 2208 ems 281.6m
<br />1985 Flood (-400 yr) " 3652 ems 281,8m
<br />Table 1. Boundary ConWbons used in lhe simulation of the 50 yr tOO d 400
<br />, yr, an yr floods.
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<br />RmdIli
<br />Several key observations emerge from the modeling efforts:
<br />-In several a~e~s of the. mesh, the pattern of flow and the water surface elevation
<br />contours exhibit two~dlmensional features that are important ~o d' F
<br />' F' 2 resign. or
<br />t,,;o~~anson. (g. ,shows .water surface elevations for the 100 yr flood under
<br />cXlsllng topographic c~ndltions and the location of the original cross sections
<br />used for HEC-2 modehng,
<br />. The two-dimensional nature of flow, the effect nf changing topography and the
<br />IOfluence of lbe upstream gap are illustrated in Fig, 3, The upstream gap direclS
<br />h'gh veloclly flow across the flood plain, In the 1985 flood chann I 'dth'
<br />I .. . e WI In
<br />Il~t ,:"glon IOcreased by roughly 200%, As illustrated in the figure, an
<br />lIlerease 10 channel Width (post-I 985 mesh) decreases the f1 I'
<br />h flood I . ow ve oclty across
<br />I c pam.
<br />.The levees alter both the pattern and velocity of flow as well as th t
<br />I I. . e wa er
<br />~u.r ace e e~attons. Fig. 4 shows flow pattems and velocities for the 1985 flood
<br />~ ~(~ ~nd Without levees in th~ area of the bridge over the South Branch in
<br />I c~c~.s~u~g, In general, ~~re IS a decrease in velocity on the flood. plain and an
<br />IIKrc. ase In channel velOCIties. The levees effectively fonn an add't' I
<br />" h. . . Ilona
<br />t.;OJlslncUon W Ich exhibits some of the ~ame features as the gaps. ]n a(krf
<br />Ihe computed water surface elevations are different on the north and sout~ 1~~
<br />01 rhe channel. SI
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<br />M' As outlined in the above examples, the two-<iimensional modeling provides
<br />.1. 1~I.onal mformati.on about ~he pattern of flow and the water surface eJevations
<br />rh.lt I~ not captured m a one-dnnensional model, infonnation of use in both
<br />~Jt~~lIn.g and evaluati.n~ ~~od pm~tion pl~ns. Additional analyses in preparation
<br />. lI~h ,I.oll~~ from thiS 1~ltlal study mclude Investigation of the effect of flood Jain
<br />1.:. 'ral.l~I()OS and contractions. evaluation of model sensitivity to boundary P
<br />l(J~I.~/I(llo.ns and hydraulic parameters, and the incorporation of digital elevation
<br />llltlUC S Into mesh construction.
<br />References Cited
<br />
<br />1'1 Kd 'T' n~d" I,.P. and Roig, L.e. (1988) ~Two-Dimensional Finile Elemenl Models for Flood
<br />.lIn, an I a Wetlands" P d' I '
<br />. f/ A I . ,rocee m8s nternalwnal Conference on Computational Methods
<br />,II ''',",' 11(1 ysu, Okflyama. Japan.
<br />("mfl'dl"~)mas, W.A. and McAnally, W.H. (1985) Users Manual/or/he Generalized
<br />.\, W. .mgram Syst~m, Open Channel Flow and Sedimentation. TABS.2. Deparunenl of the
<br />TIly, illcrways Expenmenl Station, Corps of Engineers.
<br />1', ltullWt. ~.l~~ A;;~ C(~~Of Engineers, Ballimore Districl and Inlerstate COmmission on the
<br />, ('mlll,lity Rt!~ :slRd E ~ Local Flood Protection Petersburg, West Virgini4: Integrated
<br />r"T an nVlronmentallmpact Statement.
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