Study on channel-forming process and a mathematical model for conservation storage for long-term utilized reservoirs

ABSTRACT

It was conventionally believed that a large multi-purpose reservoir would eventually be abandoned because of the sediment deposition caused by the long-term elevation of water level. The concept of the reservoir life was introduced based on this convention. The concept of long-term utilization of reservoirs was first proposed by some Chinese researchers, who also investigated the sedimentation process during the long-term operation of reservoirs and applied the long-term operation strategy in the planning and operation practices for large reservoirs. Based on the general law of reservoir sedimentation, the mechanism of the long-term utilization of reservoirs was discussed in this paper. The channel-forming process for long-term utilized reservoirs was investigated, the first and the second channel-forming discharges were introduced, and the formation of the relative equilibrium longitudinal channel profile and cross-section was analysed. A quantitative relation was derived for the conservation cross section and storage with respect to the sediment discharge period and the control water level. A mathematical model was developed for the long-term utilization of reservoirs. As a case study, this model was applied to the planning of the long-term utilization of the Three Gorges Reservoir.

KEYWORDS:

• Long-term utilized reservoir
• conservation storage
• water level and time period for sediment discharge
• reservoir’s normal operating level
• first and second channel-forming discharges
• equilibrium longitudinal profile and cross-section

Acknowledgement

Thanks Dr. Wenkai, Qin for translating this article from Chinese to English.

Notation
$B$	=	Channel width
$B_c$	=	Stable channel width
$h_1$	=	Equilibrium water depth under the first channel-forming discharge
$h_2$	=	Equilibrium water depth under the second channel-forming discharge
$H_1\left(x\right)$	=	Water surface elevation under the first channel-forming discharge when the reservoir channel is in equilibrium
$H_2\left(x\right)$	=	Water surface elevation under the second channel-forming discharge when the reservoir cross-section in equilibrium
$H_F$	=	Flood control water level or water level for sediment discharge
$H_n$	=	Normal water level
$J_0$	=	Original river bed slope
$J_c$	=	Equilibrium slope of longitudinal profile
$J_2$	=	Equilibrium slope when the channel cross-section of reservoir is in equilibrium
$L$	=	Distance between the upstream end of sediment deposition and the dam
$L_0$	=	Distance from the dam to the intersection between the normal water level Hn and the natural river bed
$L_1$	=	Distance from the dam and the intersection between H1(x) and the normal water level Hn
$L_2$	=	Distance from the dam and the intersection between $H_2\left(x\right)$ and the normal water level Hn
$L_4$	=	Distance from the dam to the intersection between the normal water level and $Z_0\left(x\right)$
$n$	=	Manning’s roughness coefficient$Q_F{Q}_n$
$Q_1$	=	First channel-forming discharge
$Q_2$	=	Second channel-forming discharge
Qm	=	Minimum flow discharge in the sediment discharge period
QM	=	Maximum flow discharge in the sediment discharge period
$S$	=	Concentration of suspended load
$\overline{S}$	=	Average sediment concentration, in the sediment discharge period
T	=	Effective sediment discharge period
$V_{1.c}$	=	Conservation storage
$W_s$	=	Sediment quantity discharged during the effective sediment discharge period
$W_{s.0}$	=	Annual average quantity of sediment inflow
$W_{s.1}$	=	Quantity of sediment inflow in the sediment discharge period
$Z_0\left(x\right)$	=	Original bed surface
$Z_1\left(x\right)$	=	Bed surface when the reservoir channel is in equilibrium
$Z_2\left(x\right)$	=	Bed surface when the reservoir cross-section is in equilibrium
$\omega$	=	Settling velocity of suspended load
$\xi$	=	River facies coefficient
$\lambda$	=	Sediment deposition percentage
${\delta }_{1.M}$	=	Maximum difference between bed level $Z_1\left(x\right)$ and $Z_2\left(x\right)$
${\delta }_{2.M}$	=	Maximum difference between water level $H_1\left(x\right)$ and $H_2\left(x\right)$
$\mathrm{\Delta }{H}_0$	=	Maximum difference between $H_n$ and $H_1\left(x\right)$ (or $H_2\left(x\right)$)
$\mathrm{\Delta }{Z}_0$	=	Maximum difference between $Z_2\left(x\right)$ and $Z_0\left(x\right)$