THE EFFECT OF THE SUSPENDED SEDIMENT TRANSPORT ON BED EVOLUTION DURING FLOOD STAGE

Abstract: The transition from gravel river-bed to sand river-bed in Taiwanese rivers often occurs in several kilometers. Therefore, the effect on bed evolution of suspended load transport should be considered. This paper develops a two-dimensional depth-averaged mathematical model for bed evolution of alluvial rivers by solving convective-diffusion equations for suspended-sediment to obtain suspended load transport. Then, the effect of suspended load transport can be discussed. The applicability of the model can be performed by simulating the bed evolution in Pa-Chang River, which is one of the principle rivers in Taiwan, with and without suspended load transport during the period of Herb Typhoon (the peak discharge is 1650 cms) and 2-year frequency flood (the peak discharge is 476 cms). The apparent discrepancy in calculated results of bed variation during the flood stage is obtained when suspended load transport is considering in the numerical bed evolution model. The findings indicate that not only the quantitative effect is the influence of the suspended load transport on bed evolution but also qualitative effect. The comparisons of the simulated results show that it is necessary to consider suspended load transport in the simulation of bed evolution for alluvial rivers as bed material includes sand and silt.

Keywords: alluvial rivers, suspended load transport, two-dimensional bed evolution model.

1 INTRODUCTION

The ways of sediment transport by water flow in alluvial rivers can be separated into bed load and suspended load. The main sediment transport for bed evolution in ordinary river flow is bed load. However, a lot of suspended sediment transport will occur in flood stage when the river bed material includes sand and silt. Also, the bed evolution of Taiwanese rivers usually occurred in flood stage because of its disproportionate in rainfall. Therefore, the effect of suspended load on bed evolution can not be neglected. Many bed evolution models, including one-dimensional models and two-dimensional models, have been developed to simulate sediment transport in alluvial rivers [1,2,3]. Unfortunately, most of them are not taking account of suspended load. Since the river bed material of upstream reaches in principle Taiwanese rivers is gravel, and downstream reach is sand, the suspended load caused by erosion of upstream reaches can lead to heavy effect on bed evolution in downstream reaches. The suspended sediment transport should be considered in bed evolution model, as clearly demonstrated from aforementioned discussion. Hence, this paper is aimed at developing a two-dimensional depth-averaged model to consider both bed load and suspended load transports for simulating bed evolution in alluvial rivers. Besides, the effect of suspended sediment transport on bed evolution is also discusses by simulating the bed variations of Pa-Chang River during the period of Herb Typhoon and 2-year frequency flood.

2 MATHEMATICAL MODEL

The depth-averaged continuity and motion equations are given as the following [4]:

in which the depth-averaged quantities are denoted by the overbar; h = the depth of flow; H = the stage of flow; u and v = velocity components in x- and y-direction, respectively;

is the eddy viscosity of water;

and

are the components of bed shear stresses in the x- and y-directions, respectively; g is the acceleration of gravity; ρ = fluid density; and t = time. The convective-diffusion equations for suspended-sediment is:

C = volumetric concentration of suspended sediment;

and

are the deposition and entrainment terms of river bed, respectively. The continuity equation for sediment transport can be written as:

Z = the channel bed elevation;

= the porosity of bed material;

and

= the components of unit-width sediment discharge

in x- and y-direction, respectively;

is calculated by Meyer-Peter and Muller formula;

= the fall velocity of sediment;

= the reference concentration. The MacCormack explicit finite-difference method is used to discretize the governing equations. Therefore, the explicit finite-difference of the governing equations may be written as [5]:

Subscripts i and j refer to the grid points in the x- and y-directions, respectively; the superscript

refers to the value of the variables at the unknown time level whereas

refers to the known time level; and

、

is the function of the known value of the variables at time level

(see details in [5]).

3 THE DESCRIPTION OF PA-CHANG RIVER

Pa-Chung River is one of the principle rivers in Taiwan. The river flows through Tainan County and Chia-I County, the density populated cities along the riverbanks, and many important transportation systems pass through this part. From July 31 to August 1, Herb Typhoon passed through the northeastern part of Taiwan. The strong intensity of rainfall brought a tremendous damage to Taiwan, and it caused the vast deposition in the reach of river between Chun-Hui Bridge and Tung-Ho Bridge. The model is applied to simulate the bed evolution in the river reach between Chun-Hui Bridge and cross-section No. 79 during the period of Herb Typhoon and 2-year frequency flood (the peak discharge is 476 cms). The reach is about 3500 m long and 350 m wide, and bed topography is shown as figure 1. A little mountain named garbage mountain is located at x = 1650 m. Figure 2 shows the flood discharge hydrograph in Chun-Hui Bridge during the period of Herb Typhoon. The peak discharge measured in the hydrological station of Chun-Hui Bridge is 1650 cms. This amount about equals to the 50-year frequency flood (50-year frequency flood is 1 200 cms). Figure 3 shows the water stage hydrograph of cross-section No. 79.

4 COMPARISONS BETWEEN THE SIMULATED RESULTS

The upstream boundary condition for simulation is the flood inflow discharge in Chun-Hui Bridge, and the downstream boundary condition is the flood stage in cross-section No. 79. The simulating cases include Herb Typhoon and 2-year frequency flood, and the mean diameter in the simulated reach is 0.1 mm. Figure 4 indicates the comparison of computed bed variations during 2-year frequency flood. The evident differences are in general. The effect of suspended sediment on bed evolution is visible. Similarly, the comparisons of numerical results in 36-hour bed evolution simulating during Herb Typhoon are shown in Figure 5. The calculations for bed evolution of cross-section are shown in Figure 6, and CR indicates the distance from the left riverbank. The same results also indicate the importance of suspended load in the simulation of bed evolution. Table 1 shows the change of sedimentary volume in river bed, reasonably accurate simulation can be obtained when suspended load is concerned in the bed evolution model.

5 CONCLUDING REMARKS

Although the suspended sediment transport has less effect on bed evolution in alluvial rivers during ordinary river flow, there are obvious effects on bed evolution based on the simulated results of bed variations in Pa-Chung River during the period of Herb Typhoon and 2-year frequency flood. Moreover, the change of bed evolution is not only the quantitative effect but also qualitative effect. The apparent discrepancy in simulated results of bed variation reveals that suspended load transport can not be neglected in the sand river-bed evolution modeling. Therefore, suspended sediment transport should be concerned in the satisfactory movable-bed model for simulating bed evolution to obtain more accurate results.

[1] Parker, G.,“The ACRONYM Series of Pascal Programs for Computing Bedload Transport in Gravel Rivers,”Saint Anthony Falls Hydraulic Laboratory, No. M-220, The University of Minnesota, U.S.A. (1990).

[2] Karim, M. F. and Kennedy, J. F.,“IALLUVIAL: A Computer-Based Flow and Sediment Routing Model for Alluvial Streams and its Application to the Missouri River,”Iowa Institute of Hydraulic Research, No. 250, The University of Iowa, U.S.A. (1982).

[3] Lai, C. T.,“A Numerical Scale Model for Simulating Unsteady Alluvial-Channel Flow,”Twelve Selected Computer Stream Sedimentation Models Developed in the United States, Edited by Fan, S. S., Federal Energy Regulatory Commission, pp. 189-260 (1988).

[4] Tsai, C. H., Kau, W. T. and Tsai, C. T.,“Two-dimensional Piecewise-Uncoupled Model for Bed Evolution in Alluvial Rivers,”The Chinese Journal of Mechanics, Series B, Vol. 14, No. 2, pp. 109-124 (1998).

[5] Tsai, C. H.,“Numerical Simulation of Flow and Bed Evolution in Alluvial River with Levees,”Ph. D. Thesis, Department of Hydraulics and Ocean Engineering, National Cheng-Kung University, Tainan, Taiwan (2000).

Table 1 The comparisons of change in sedimentary volume during Herb Typhoon (unit：m³)

Cross-section No.	Field measured	with suspended load transport	without suspended load transport
86-85	Erosion	Erosion (82 )	Erosion (17 )
85-79	Deposition (700 )	Deposition (223 )	Erosion (24 )


Fig. 2 The flood discharge hydrograph in Chun-Hui Bridge during Herb Typhoon	Fig. 3 The flood stage hydrograph of cross-section No. 79 during Herb Typhoon



Fig. 6 The comparison of bed evolution in cross-sections during Herb Typhoon