Figure 1: Padma (Ganges) and Jamuna (Brahmaputra) Rivers, and the site of the proposed Paksey Bridge crossing of the Padma.

Figure 2: The Hardinge Bridge crossing of the Padma River near Paksey, Bangladesh, provides no capacity for vehicular or pedestrian traffic.

Figure 3: Friable banks composed of silt and fine sand lead to shifting channels and a need for long channel revetments.

Figure 4: The proposed Paksey Bridge across the Padma (Ganges) River in western Bangladesh. The Hardinge Railway Bridge, built in 1915, is shown in the background, 300 m upstream.

Figure 5: Curvilinear MIKE 21C grid (223 H 34 cells) with Paksey Bridge guide bank extension. Cells at the bridges are about 50 m square (540 square feet).

Figure 6: Simulated bathymetry at 100-year flood peak.

Figure 7: Finite element network of the Padma River in the vicinity of the proposed Paksey Bridge crossing without bridges in place.

Figure 8: Isocolor plot of bed elevations that range from - 32 m (106 feet) in the deepest parts of the winding thalweg to more than 20 m (66 feet).

Figure 9: Isocolor plot of of bed elevations in the vicinity of the Hardinge and proposed Paksey Bridges. Water flows from north to south. Large amounts of erosion along the west side of the channel during floods makes estimating both general and local scour depths critical tasks.

Figure 10: Comparison of measured and computed depth-averaged velocities of the 1998 flood at Transect 4 located about 700 m downstream of the Hardinge Bridge. Velocities were measured with an ADCP with global positioning satellite georeferencing.

Figure 11: Finite element network in the vicinity of the Hardinge and Paksey Bridges showing various element types.

Figure 12: Velocity vectors and isocolors of water speeds for the simulated 100-year flood peak flow with the proposed Paksey Bridge in place.

Figure 13: Pier B: - four vertical cylindrical piles each 3 m (10 feet) in diameter with a hexagonal cap 4 m (13 feet) high (looking upstream in the flume.)

Figure 14: Pier A: four battered cylindrical piles each 2.25 m (7.4 feet) in diameter with a tapered cylindrical cap 7.5 m (24.75 feet) high (looking upstream in the flume.)

Figure 15: Flume transects showing bed elevations along the upstream and downstream faces of the two piles after equilibrium conditions had been reached. Piers were aligned with approaching streamflow (H = 0o) in this run.

The Ganges and Brahmaputra Rivers both receive new names once they pass into Bangla-desh: the Ganges becomes the Padma, while the Brahmaputra is known as the Jamuna. South of the capital city, Dhaka, the lower Padma joins the Meghna River, which flows from the northeast. Lower reaches of the Meghna expand in width from less than 1 km (0.6 mile) to around 8 km (5 miles) during the wet season and much more during large floods. The combined river delta is the largest in the world, beginning more than 320 km (192 miles) from the Bay of Bengal.

Flooding along the Padma and Jamuna and the countless distributary channels that flow from them during the monsoon season (which lasts from mid-April to mid-October) often causes enormous hardship and hinders economic development in Bangladesh. However, deposits of rich silt from floods replenish fertile but overworked farmland soils. Thus, the great river system is both the principal resource of the country and its greatest hazard.

Highway transportation is complicated by the deltaic geography, which requires frequent crossings of streams and rivers, especially in east-west travel. Both the Padma and Jamuna are notorious for their shifting subchannels and for formation of large silt islands called chars. Because of changing river courses and expansive channels, bridges are costly and, consequently, few in number.

The economy of Bangladesh is largely dependent on agriculture, which accounts for more than a third of the gross domestic product and provides employment for two-thirds of the labor force. Various crops, including rice, wheat and bananas, are grown in the northwestern region of Bangladesh; however, agricultural development there has been impeded by an inadequate road system that lacks critical bridge crossings of major rivers.

The Padma, which divides western Bangladesh, is bridged only at a site north of Kushtia at the town of Paksey. The span, known as the Hardinge Bridge (Figure 2), carries a broad-gauge railroad across the river, but has no capacity for vehicular or pedestrian traffic. Consequently, passengers and goods need to be ferried across the river. River crossings are often delayed because of flooding during the monsoon season or because of maintenance dredging needed to provide access to ferry landings (known as ghats) during the dry season.

Improved agricultural production in the northwest region of the country would be assisted by a direct roadway connection to the southwestern port city of Mongla. A proposed bridge across the Padma a short distance downstream from the Hardinge Bridge will be an important link in the road network. Funded by the Overseas Economic Cooperation Fund (OECF) of Japan, this new bridge will provide an uninterrupted transportation route between Bangladesh's three largest cities: Dhaka, Chittagong and Khulna.

The overwhelming economic need for a highway crossing of the Padma in Bangladesh makes the Paksey Bridge a crucial project. However, friable and unstable banks (Figure 3), sediment loads of extraordinary size and constantly shifting channels in one of the world's largest rivers make design of a sound and dependable crossing challenging.

Hydraulic and Scour Analyses

PB conducted a comprehensive hydraulic and scour analyses of the proposed crossing in collaboration with the Surface Water Modelling Center (a not-for-profit research institute in Dhaka established in 1996 by the Bangladesh Ministry of Water Resource), and the River Research Institute (a division of the Bangladesh Ministry of Water Resources) for the Roads and Highways Department of the Bangladesh Ministry of Communications. This analysis consisted of three modeling components:

Water-surface elevations, water velocities, hydrodynamic forces, and potential depths of local and general scour were calculated based on results from the numerical and physical models.

Data from two recent monsoon floods, consisting of water-surface elevations, streambed elevations in the vicinity of the crossing and acoustic-Doppler current profile measurements along numerous channel transects were available to calibrate and test the numerical models. Close agreement between measured and calculated water-surface elevations, depth-averaged velocities and streambed elevation variations suggested that maximum scour depths around pier foundations could be decided with a high degree of confidence, and that the new bridge would not create adverse impacts on the existing railway bridge that would remain upstream of the new Paksey Bridge.

Paksey Bridge Site

The proposed Paksey Bridge (Figure 4) will be built 300 m (990 feet) downstream of and parallel to the Hardinge Bridge. The bridge will have an overall length of 1786 m (5,893 feet) consisting of 15 spans, each 109.5 m (361 feet) long and 2 end spans, each 72 m (239 feet) long, and it will carry two 7.5-m- (24.75-feet-) wide vehicular traffic lanes and two 1.0-m- (3.3-foot-) wide pedestrian walkways. Constrictions created by the massive pier foundations of the Hardinge Bridge produce high-speed flow regions downstream of the bridge, as shown by the hydraulic models. Consequently, spans and piers of the Paksey Bridge are matched to those of the Hardinge Bridge to avoid placing foundations in locations of potentially large scour depths.

Dense sand having a median particle diameter D₅₀ = 0.16 mm (0.0064 inch) is present to considerable depth at the bridge site. Concrete piers will be placed on pile foundations with two pile design options considered, driven steel piles and bored, cast-in-place concrete piles. Each design consists of groups of four piles. Cylindrical steel piles, each 2.25 m (7.4 feet) in diameter, will be battered at 1:6 slopes (horizontal:vertical), while vertical concrete piles will be 3 m (10 feet) in diameter.

The Padma (Ganges) River has undergone considerable lateral movement upstream of the bridge site during the last two centuries. The deepest part of the channel at the Hardinge Bridge has moved back and forth between the abutments several times since the bridge was built. Variable approach flow conditions have led to construction of extensive guide banks upstream of the bridge. Guide banks covered by concrete block revetement that control the course of flows through the Hardinge Bridge and prevent bank erosion will be extended downstream through the new crossing.

Stream gauge records have been collected at the Hardinge Bridge continually since 1934. Based on the historical record, the 100-year flood peak discharge is estimated to be Q₁₀₀ = 89 200 m³/s, and the 500-year flood peak Q₅₀₀ = 101 500 m³/s. Other hydrometric data available for model calibration and testing include:

Bathymetric data from three surveys and limited topographic measurements were used to develop a digital elevation model of the Padma and surrounding floodplains. Satellite images were used to establish bank lines and estimate flow resistance of floodplains and chars.

Geomorphologic Model

Long-term changes in bed elevations and hydraulic conditions of the Padma at the Paksey Bridge site were evaluated using the two-dimensional depth-averaged flow and sediment transport model MIKE 21C ("MIKE 21C - User Guide and Reference Manual," 1996). Geometry of the study reach is represented by a curvilinear finite difference grid containing 223 H 34 cells (Figure 5). Evolution of bed elevations during characteristic monsoon floods lasting nearly four months was simulated to evaluate general scour at both the proposed Paksey Bridge crossing and the existing Hardinge Bridge. Hydrodynamic and sediment transport calculations were carried out sequentially in an uncoupled fashion using a time step of 20 minutes, and bed elevations were updated continually throughout the simulations.

Testing of the morphological model was carried out by simulating changes in bed elevations during the 1995 monsoon flood. The curvilinear grid used in the test did not include the Paksey Bridge guide bank extension. Comparison of the simulated and measured bed elevations at the end of the flood, however, show the model to predict the morphological changes accurately.

Time-dependent simulations show bed elevations at the Paksey bridge to vary continuously during floods, increasing as scour holes fill, then decreasing as flow rates increase significantly, then increasing initially as floods recede. Bed elevations generally reach their lowest levels near the flood peaks. Simulated bed elevations at the peak of the 100-year design flood with the Paksey Bridge guide bank extensions in place are shown in Figure 6. Minimum bed elevations at the Paksey Bridge were found to be -41 m (-135 feet) during the 100-year flood, and -44 m (-145 feet) during the 500-year flood. Because some coefficients of the sediment transport algorithms are not known with certainty, these parameters were varied to study the effects of changes. Based on the findings, minimum bed elevations for the 100-year flood at the Paksey Bridge could be as low as -48 m (158 feet).

Detailed Hydraulic Model

Detailed hydraulic analyses of the bridge crossing for current and future conditions were carried out using the two-dimensional depth-averaged flow and sediment transport module (Flo2DH) of the Finite Element Surface-water Modeling System (FESWMS) developed by Froehlich (1999) for the U.S. Federal Highway Administration (FHWA). Flo2DH uses the finite element method to solve numerically the set of partial differential equations that describe the flow of water and sediment average over water.

An advantage of the finite element method in analyzing river flows at bridge crossings is the use of an unstructured network or mesh to discretize the area being studied. The reach of the Padma studied in detail is more than 16 km (10 miles) long, and the finite element network consists of more than 4,000 elements (Figure 7). Ground elevations range from more than +20 m (+66 feet) to less than -32 m (-106 feet) referenced to mean sea level (Figures 8 and 9). Elements are smallest in size in the central and narrowest portion of the study reach at the locations of the Hardinge Bridge and the proposed highway bridge. Elements are larger near the upstream and downstream boundaries.

Historical trends and morphological simulations give reasons for believing the shallow east side of the Padma under the Hardinge Bridge, which is currently a large point bar, would be stable for the foreseeable future. Simulations show the Paksey Bridge would increase 100-year flood velocities along the east bank enough to erode the eastside of the channel. Experience suggests that subsequent deposition of eroded bed material might encourage formation of a new char downstream of the Paksey Bridge with successive monsoon floods.

Physical Model

Small-scale physical model studies of local scour at two pier configurations considered for the Paksey Bridge (Piers A and B as shown in Figures 13 and 14) were carried out at the River Research Institute in Faridpur in a 2.2 -m- (7.25-foot-) wide laboratory flume. Various combinations of water depth and velocity were studied with the two model piers aligned with approaching stream flow at angles of 0, 5, 10, 20, and 30 degrees. Sediment was applied at the upstream end of the flume at a predetermined rate throughout a run. Bed elevations were measured periodically along transects on the upstream and downstream faces of the piers (Figure 15) until equilibrium conditions were reached.

Results of the experiment indicate that during 100-year flood conditions local scour depths at Pier A (four battered cylindrical piles) could reach 9 m (30 feet) along the downstream face when pier alignment angles are 10º to 20º, and that local scour depths at Pier B (four vertical piles) could be as much as 12 m (40 feet) along the downstream face when piers are aligned at 30º to approaching stream flow. Local scour depth was calculated as the vertical distance between the ambient bed elevation at each pier estimated from the transect, and the lowest point measurement along the transect at each pier. Numerical model results give reason to believe that stream flows could approach any of the piers at angles up to 30º.

A Summary and Conclusions

Three models (a numerical model of long-term geomorphic channel changes, a detailed numerical model of hydraulic conditions at bridges, and a physical model of local pier scour) were used to study hydraulics and scour at the proposed Paksey Bridge on the Padma River in Bangladesh. The approach establishes a comprehensive analytical procedure for assuring safe and sound designs of bridges spanning large rivers with easily erodible beds and banks.