6.12 WSPRO Bridge Modeling
The Water Surface Profile (WSPRO) Program was developed specifically for bridge design and the determination of the effects of a bridge on water surface profiles (FHWA, 1990). The procedures for WSPRO have been incorporated into HEC-RAS to provide WSPRO methods within HEC-RAS. WSPRO's low flow analysis procedures are only valid for Class A conditions (subcritical flow). When the bridge opening becomes submerged, pressure and weir flow methods are used. WSPRO has major advantages over other methods of bridge computation in that it allows analysis of the abutment shape, upstream spur dikes, and other special bridge features. The use of WSPRO within the HEC-RAS package requires only a limited amount of additional input.
WSPRO Modeling Procedures
Computational procedures in WSPRO focus on the energy equation to determine water surface elevations, although the energy computations employed have slightly different assumptions and methods than have previously been presented. Contraction losses into the bridge are assumed to be negligible and are not included. Only friction losses between sections 1 and 4 and an expansion loss between sections 1 and 2 are employed to evaluate bridge effects. Coefficients are included to determine the effects of abutment shape and upstream spur dikes. In addition, the locations of sections 1 and 4 as defined by the WSPRO method are different than the locations for these two sections presented earlier.
WSPRO Required Cross Sections.
A minimum of four sections are required to model a bridge using WSPRO. These four sections are located at the beginning of the contraction and the end of the expansion (sections 4 and 1, respectively), a section defining the full floodplain just downstream of the bridge face (designated section 2F in WSPRO), and a section defining the bridge opening (designated section 2 in WSPRO). These locations are shown in Figure 6.38. In HEC-RAS, however, the Bridge Editor supplies WSPRO section 2 by developing sections BU and BD, and the modeler supplies section 3, just upstream of the bridge, which is not used in WSPRO. Therefore, for this discussion, the same section nomenclature is used, rather than as defined by WSPRO. Thus, WSPRO section 2F is 2 and WSPRO section 2 is BD.
Figure 6.38 WSPRO section locations for a stream crossing with a single waterway opening.
WSPRO Cross Section Locations.
The start of contraction and end of expansion section locations are defined as one bridge-opening width from both the upstream and downstream bridge face in WSPRO, as shown on Figure 6.38a. For instance, if the bridge-opening width is 500 ft, sections 1 and 4 are located 500 ft from the downstream and upstream bridge face, respectively. For wide valley sections or for sparsely vegetated floodplains, this distance may underestimate losses through the bridge. Although the modeler may choose to use the other techniques described earlier in this chapter to locate Sections 1 and 4, these methods do not comply with WSPRO methodology. Therefore, when the modeler specifies the use of WSPRO along with the other three techniques in HEC-RAS for analyzing Class A low flow, the bridge cross-section locations must be set up as defined in Section 6.4, or a separate geometric model for the WSPRO analysis will be needed. If a separate model is used, the modeler will need to compare the WSPRO results to the HEC-RAS results (for the energy, momentum, or Yarnell methods).
When locating the cross section at the end of expansion, the WSPRO method will likely result in a cross-section location that is closer to the bridge than the equations shown earlier for expansion lengths, or for the USACE rule of thumb previously presented. Where spur dikes are used to prevent significant flow from moving parallel to the roadway embankment and into the bridge opening, the contraction section is located one bridge opening width upstream of the end of the spur dike (Figure 6.38b). The studies for the length of contraction (Lc) and length of expansion (Le) performed by the HEC found no justification for locating either the expansion or contraction sections as defined in WSPRO.
However, even with the computational and cross-section location differences, all the major water surface profile programs or methods give adequate results. A comparison of water surface profiles through bridges as computed by WSPRO, HEC-2, and HEC-RAS was conducted by the HEC (USACE, 1995c). Detailed data from the USGS were used for 13 bridge sites on thickly vegetated floodplains in the states of Louisiana, Mississippi, and Alabama. The general conclusions from the study were that all three programs computed accurate profiles
...within the tolerance of the observed data. The variation of the water surface at any given cross section was on the order of 0.1 to 0.3 ft (0.03 to 0.1 m). The mean absolute error in computed versus observed water surface elevations varied from 0.24 ft (0.07 m) with HEC-RAS to 0.33 ft (0.1 m) with WSPRO. Given the small variance in the results, it is concluded that any of the models can be used to compute adequate water surface profiles at bridge locations and that no one model performed significantly better than another.
WSPRO Coefficients.
Contraction coefficients are not used in WSPRO, so a value of zero should be supplied for Cc. An expansion loss is computed in the following subsection with Equation 6.19. Manning's n may be adjusted at the bridge, similar to the discussion in Section 6.5, when WSPRO is used.
WSPRO Computation Procedures
Loss computations in WSPRO proceed in a similar fashion as for energy analysis earlier in this chapter and in Chapter 2. The total energy equation between the exit and approach sections (sections 1 and 4) is
(6.17)
The losses between sections 1 and 4 represent the sum of the friction losses between the two cross sections plus the expansion losses between sections 1 and 2. From sections 1 to 2, the friction loss is found by applying the geometric mean friction slope to the flow at a weighted distance between the two sections. The geometric mean friction slope equation is one of four methods within HEC-RAS used to compute friction loss and it is the specified technique for use in WSPRO. The equation for friction slope between sections 1 and 2 is
(6.18)
The expansion loss between sections 1 and 2 is given by the equation
(6.19)
The variables a2 and b2 are related to the bridge geometry through expressions developed empirically by Kindswater, et al. (1953) and later modified by Matthai (1968):
(6.20)
and
(6.21)
The variable C is an empirical discharge coefficient and varies depending on the bridge opening type and the embankment slope. The references by Kindwater, et. al and Matthai, or Appendix D in the Hydraulic Reference Manual (USACE 2002) may be consulted for additional information on the selection of C. WSPRO friction losses from sections 2 to 4 (within HEC-RAS) are calculated by adding the losses from 2 to BD, BD to BU, BU to 3 and 3 to 4. Friction losses between each of the two locations are computed using Equation 6.18, with total conveyance used at the appropriate sections.
Specification of WSPRO Computations.
In HEC-RAS, WSPRO is one of the four methods available to compute water surface profiles through a bridge for Class A low flow conditions. As was the case for the use of the momentum and Yarnell equations, additional information must be supplied to implement the WSPRO method. On the Deck/Roadway Geometry Editor (refer to Figure 6.24), the embankment side slopes are specified, which are used for computation purposes in WSPRO only. After WSPRO is selected as a computation method on the Bridge Modeling Approach Editor (see Figure 6.39), the WSPRO Variables icon is selected. The WSPRO template opens, and the additional information necessary for using WSPRO is specified-abutments, wing walls, guide banks (spur dikes), and other data. Figure 6.40 shows the WSPRO data template with data items needed to model the bridge shown in Figure 6.29 in WSPRO.
Figure 6.39 Bridge Modeling Approach Editor specifying the use of WSPRO.
Figure 6.40 Additional WSPRO bridge hydraulic parameters editor for the example bridge.
