Scientific Investigations Report 2006-5023

**U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2006-5023**

The U.S. Army Corps of Engineers’ Hydrologic Engineering Center River Analysis System (HEC-RAS) model (Brunner, 1997) was used as the one-dimensional flow model for this project. This model is based on the standard step-backwater computation. It balances the energy equation from one cross section to the next. Energy losses between sections are from friction, expansion, and contraction. Friction losses are computed with Manning’s equation. Expansion and contraction losses are determined by applying a coefficient to the change in velocity head. The model requires that the following assumptions are valid (Brunner, 1997):

- Flow is steady in time.
- Flow is gradually varied in space. This assumption is not required at hydraulic structures such as bridges or culverts because the momentum or other empirical equations can be used. HEC-RAS does the computations and can be set to use the most applicable method.
- Flow is one dimensional (velocity is always perpendicular with the cross section).
- Channel slope is less than 10 percent.

The two-dimensional model chosen for this project was RMA2 (Donnell and others, 2000) with the Surface Water Modeling System (SMS; Environmental Modeling Research Laboratory, 1999), a graphical user interface. RMA2 is a two‑dimensional, depth-averaged, finite-element hydrodynamic numerical model (Donnell and others, 2000). The model solves for flow properties of two-dimensional elements, rather than for entire cross sections as does a one-dimensional model. Depth-averaged velocity is computed in the X and Y horizontal directions. Velocities in the vertical (Z) direction are not accounted for and are assumed negligible. The model also assumes gradually varied sub‑critical flow. Flow can be either steady (constant with time) or unsteady (varying with time). This program’s computational procedure is based on the solutions of the Reynolds form of the Navier-Stokes equations for turbulent flows (Donnell and others, 2000). SMS is used as a pre- and post-processor, automating much of the set-up process for a finite-element network and providing various graphical outputs.

Data requirements for one- and two-dimensional models are similar, except that a two-dimensional model requires more geometry information. One-dimensional models essentially require two-dimensional geometry data, whereas two-dimensional models require three-dimensional data. Both models require various additional information such as bridge geometry, bed roughness, and discharge. Water‑surface profiles for a known discharge are used to calibrate each model type.

Two methods were used to survey channel geometry. Dry-land surface was surveyed with a total station using standard techniques. Channel geometry was surveyed with a vessel mounted acoustic Doppler current profiler (ADCP). This device uses sonar to measure water depth, vessel velocity in relation to the bed, and water velocity. Water-surface elevations were surveyed at each cross section. Twenty cross sections were surveyed using this method. Additional points along the banks between cross-sections also were surveyed for the two-dimensional model.

Bridge datum provided by ADOT&PF was used for vertical datum. Horizontal coordinates were established at the downstream left-bank corner of the main bridge deck at N 10,000 ft, E 10,000 ft.

The roughness value in a one-dimensional model accounts for various factors that provide resistance to flow. These factors include (Arcement and Schneider, 1989):

- Basic bed-material roughness,
- Surface irregularities,
- Variation in cross section shape and size,
- Obstructions to the flow,
- Vegetation and flow conditions, and
- Meandering of the channel.

Channel roughness can be estimated using established techniques (Arcement and Schneider, 1989), or computed with a hydraulic model using surveyed water-surface elevations for a measured discharge. If roughness is determined with a hydraulic model, then all these factors affect the value. The difficulty with computing a roughness is that flood flows usually are quite different from surveyed flows. Higher flows can change bed geometry and are less affected by obstructions and small surface irregularities. Extreme flows may go over the banks, for which only estimated roughness is available. Less confidence can be placed in a model run at flows that vary greatly from the calibration discharge.

A two-dimensional model also relies on roughness values to compute energy loss. Similar factors apply, except that, because the model computes velocity in both X and Y directions, several factors do not affect the apparent roughness value. As noted above, roughness in a one-dimensional model accounts for factors such as channel meanders and flow that is not perpendicular to the cross sections. The two-dimensional model simulates the effect of these losses with non-perpendicular velocity, so they are not reflected in the roughness value. As a result, the roughness value used in the two-dimensional model often will be lower for the same conditions than the value used in the one-dimensional model.

Both model types require boundary conditions: a discharge and an initial water-surface elevation. Flow at this study site is sub-critical for all discharges; each model requires a discharge at the upstream boundary and a water-surface elevation at the downstream boundary. The six discharges used in the models were the discharge measured on August 19, 1998, the discharge measured during the flood on August 17, 1967, and floods with return intervals of 100 and 500 years on the Tanana River, with low and high discharges on the Nenana River (table 2). The Tanana River flood-frequency calculations were based on 32 years of record, 1962-94, at USGS streamflow-gaging station Tanana River at Nenana (15515500), using standard flood-frequency analyses (Interagency Advisory Committee on Water Data, 1982).

The only direct measurement of discharge at the mouth
of the Nenana River was made on August 19, 1998. Discharges for the Nenana River
for the other discharge scenarios were either estimated or determined as follows.
Floods with return intervals of 100 and 500 years for the Nenana River were
estimated using the regional regression flood estimates outlined in Jones and
Fahl (1994). Nenana River discharge on August 17, 1967, was estimated at 30,800
ft^{3}/s, based on the ratio between the computed 100- and 500-year
floods at the mouth and those at streamflow-gaging station Nenana River at Healy
(15518000). This ratio then was applied to the flow from the gage record for
August 16, 1967, to determine discharge at the mouth for the models. Low discharge
for Nenana River (12,000 ft^{3}/s) was determined by rounding the measured
discharge from the survey. High discharge was the computed 100-year flood at
the mouth (69,000 ft^{3}/s).

Initial water-surface elevations either were known (at the surveyed discharge) or were estimated as the normal depth. Normal depths were computed using the water-surface slope from the discharge measurement made on August 17, 1967, and the roughness value from the calibrated model.

Geometry for the one-dimensional model was a combination of surveyed and interpolated channel data and pier and abutment geometries from the as-built plans. The only bridge parts affecting flow characteristics are the piers and the south abutment of the main bridge. The other bridge abutments (the north one on the main bridge and both on the slough bridge) had little effect on the flow because they either are not in the water or do not project from the bank. The low-steel elevations for the bridges are 389.58 ft (main bridge) and 379.74 ft (slough bridge). (Low steel is the lowest part of the bridge superstructure between supports over the river.) These are well above the water surface, even during extreme floods; the water-surface elevation on August 17, 1967, was 356.9 ft.

Twenty cross sections were surveyed for use in the one-dimensional model, but the model can better simulate expansions and contractions with additional sections. HEC‑RAS includes a routine that interpolates between cross sections to generate synthetic cross sections (Brunner, 1997). Channel geometry between the surveyed cross sections changed little, so the interpolation is valid through this reach. In all, 43 cross sections were used in the one-dimensional model analysis (fig. 4).

Once the geometry data were input to HEC-RAS, boundary conditions and discharges were entered to calibrate the model. Two discharges were used for model calibration: the discharge at the time of the survey on August 19, 1998, and the discharge measured on August 17, 1967. Four flooding situations were then modeled for the scour estimation. The 100- and 500-year recurrence-interval flows on the Tanana River were simulated with a high and a low discharge in the Nenana River. Simulated discharges and associated initial downstream water-surface elevations used as boundary conditions are summarized in table 2. Initial downstream water-surface elevation used with the discharge on August 19, 1998, was surveyed. Starting water-surface elevations for the other scenarios were estimated from the computed water-surface slope of the August 17, 1967, discharge measurement.

The model computed flow in the Tanana Slough using an iterative process beginning with an assumed flow division between the main channel and the slough. Water-surface elevations then were computed along each channel to the upstream junction. If the total energy head at the upstream cross section in each channel is equal, the flow division between channels is assumed to be correct. If they are not equal, the model changed the flow division and recomputed the water-surface profiles in the channels. Iterations continued until the total energy heads balanced.

The model was calibrated by running it with a given discharge having a known water-surface elevation and then adjusting the streambed roughness until the output closely matched the known elevation. Roughness can change with depth, so a calibration discharge near the magnitude of the flood discharge is desirable. The high-measurement discharge (August 17, 1967) was between the 100- and 500-year recurrence-interval flows, so the roughness was calibrated to this discharge (table 3).

The calibrated model was used to simulate four discharge
scenarios on the Nenana River: the 100-year recurrence-interval flow with both
low and high flows and the 500-year recurrence interval-flow with both low and
high flows (Q_{100}/_{500}, Nenana Low/High in table
2). Pier and contraction scour were computed using output from these scenarios,
and the results were used to compare the one-dimensional model with the two-dimensional
model.

Surveyed cross sections were spaced too widely to create an adequate topographic map to run the RMA2 model, so 56 additional cross sections were interpolated from the surveyed cross sections by the HEC-RAS software. Interpolated cross sections, surveyed cross sections, and additional surveyed points along the banks were input to Computer Aided Drafting (CAD) software to add breaklines and boundaries to the data set. (Breaklines are where the simulated topographic surface slope is allowed to change abruptly. For example, the top of a cut bank. A boundary is a line defining the edge of the data.) The data set then was exported into SMS.

The next step in setting up the two-dimensional model was to generate a computational mesh (fig. 5). The mesh consisted of triangular and quadrilateral elements that cover the entire simulated area. A well-designed mesh will increase model stability. Properties of a well designed mesh are discussed in Donnell and others (2000).

Elevations and material properties then were assigned
to the mesh nodes. Elevations were assigned by overlaying the mesh with the
geometry data set. SMS interpolates elevations for nodes that do not reside
directly over a known point. Roughness and eddy viscosity were assigned to each
element. Roughness was entered as a Manning’s *n*, but, as discussed
earlier, the value for the two-dimensional model tends to be lower than the
value for a one-dimensional model. Eddy viscosity is a term used to define the
effect that velocity in one element will have on adjacent elements. Eddy viscosity
and roughness values were defined as properties of a specific material type.
Each element in the mesh was then given a material type (table
3). This allowed the modeler to rapidly change the properties of all similar
material types during calibration runs.

Boundary conditions are defined by assigning flow to the upstream model boundaries and a water-surface elevation to the downstream boundaries. The two-dimensional model used two upstream boundaries (Tanana River and Nenana River) and one downstream boundary (Tanana River below the confluence). Discharges and downstream water surfaces for this model were the same as was used for the HEC-RAS model (table 2).

Model calibration begins with selecting a tolerance
level for the change in water-surface elevations between computational iterations.
When this tolerance level is met, the model has converged on a solution. The
two-dimensional model was considered converged when the change was less than
0.1 ft. Increasing eddy viscosity causes the model to converge more easily,
but a value that is too high causes the velocity vectors to be parallel and
the model to appear one-dimensional. Values used with this model were the lowest
that would result in model convergence. Eddy viscosities ranged from 20 to 100
(lb/s)/ft^{2} (table 3), which are well within
the range of the 0.2 to 1,000 (lb/s)/ft^{2} suggested by Donnell and
others (2000).

The model was calibrated using the measured discharges
(August 19, 1998, and August 17, 1967) and their associated water-surface elevations.
The model divided flow between the main channel of the Tanana River and the
slough. Changing the roughness in the main channel of the Tanana River varied
the simulated water-surface elevation. The simulated flow division was varied
by changing the roughness of the slough channel and a logjam at the upper end
of the slough. Values used to calibrate the two-dimensional model are presented
in table 4, and a comparison of water-surface profiles
simulated by the one- and two-dimensional models is presented in figure
6*A*. Different roughness values were required for low and high discharge
in the two-dimensional model. The survey data and mesh design were developed
to optimize model use for high flows. As a result, the model did not perform
well simulating low discharges. Channel roughness used in the low discharge
simulation is lower than that used in the high-discharge scenarios. Roughness
was reduced to offset the affects of using a coarse mesh designed for the high-flow
simulations. Roughness was reduced to account for ragged edges of coarse high-flow
mesh and to accommodate a decreased flow area produced by turning off edge elements
to increase model stability. To accurately simulate low discharge conditions,
a denser topographic data set would have to be gathered and a finer computational
mesh built.

Once the model was calibrated, runs were made with the five discharge scenarios that represent floods (table 2). Results from these simulations were used to determine flow depths and angles of attack for input to the scour calculations. The results show definite areas of two-dimensional flow that cannot be described with the one-dimensional model.

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