为从理论上确定水沙动力、阻力和边界条件对冲积河流推移质输沙最优河道形态和最小比降的影响，基于 水力半径分割方法将河床整体糙率划分为河岸糙率和河底糙率；采用河道形态自动调整变分方法，以等腰梯形为 河道过水断面，推导推移质输沙率与河道形态的关系，分析河岸与河底相对糙率、河岸坡角、流量、输沙率、中值 粒径和河底糙率对最优河道形态和最小比降的影响。结果表明：最优河道形态和最小比降随河岸与河底相对糙 率的增大而减小，随河岸坡角的增大而增大。流量或者河底糙率的增加将使最小比降减小，同时造成最优河道形 态趋向窄深。输沙率或者中值粒径的增加将使最小比降增大，但两者对最优河道形态演变的影响不同，输沙率增 大将使最优河道形态向宽浅发展，而中值粒径增加将使最优河道形态向窄深发展。

The optimal channel of rivers dominated by bed load is determined by many factors. In addition to hydrodynamic conditions, it is also closely related to water and sediment inflows and boundary conditions. Since the rivers on the alluvial plains in the United States and India transport overloaded sediment via wide and shallow channels, some foreign scholars believe that wide and shallow channels are ideal for transporting overloaded sediment. However, the sediment transport capacity of the channel is inversely proportional to the width-depth ratio of the channel in the lower reaches of the Yellow River. The reduction of the width-depth ratio can improve the maximum sediment transport capacity of the channel. The relationship between the sediment transport capacity and the optimal section of rivers in different regions manifests different or even opposite relationships, and the channel boundary conditions may be a major factor. When the scouring resistance of the river bank is high, the transverse deformation of the river channel is greatly constrained, and the corresponding channel form is relatively narrow and deep. On the contrary, the river channel is subjected to relatively weak horizontal constraints and is prone to widening. To theoretically determine the influence of different factors on the optimal channel form for alluvial rivers and the corresponding minimum gradient, the methods of hydraulic radius segmentation and the river automatic adjustment variational are used to derive the relationship between bed load sediment transport rate and channel form. By taking the isosceles trapezoid as the cross-section, the relative roughness of the river bank to the river bottom, the bank slope angle, the flow discharge, the sediment transport rate, the median particle size, and the roughness of the river bottom are analyzed to ascertain how they affect the optimal channel form and the minimum gradient, respectively. The results show that the optimal channel form and minimum gradient decline with the increase of relative roughness of river-bank to river-bottom, and rise with the increase of bank slope angle. The increase of flow discharge or river-bottom roughness will cause the minimum gradient to decrease and the optimal channel form to become narrow and deep. The increase in sediment transport rate or median particle size will increase the minimum gradient, but their effects on the evolution of the optimal channel form are different since the increase of sediment transport rate will yield a wide and shallow optimal channel form while the increase of median particle size will make the optimal channel form narrow and deep. This study only conducts a quantitative analysis of the response of the optimal channel form of rivers dominated by bed load and the corresponding minimum gradient to multiple factors of hydrodynamics and river boundary. The response of the sediment transport capacity of the sediment-laden river dominated by suspended load transport to these factors needs further investigation.