天然河流中悬移质泥沙均由非均匀颗粒组成，不同颗粒在输移过程中表现出不同的运动特征。由于非均匀沙运动的复杂性、研究方法的局限性，目前对于非均匀沙运动中的质量和动量传递机理尚不清晰，缺乏有力的理论分析方法和工具。本文基于水沙两相流的双流体方程，推导得到了非均匀悬移质泥沙的输沙方程，并讨论了河床边界与其相互作用的数学与力学描述，得到如下主要结果：首先，引入非均匀泥沙的弥散速度概念，建立了非均匀悬移质泥沙弥散速度本构方程，进而基于水沙两相流方程建立了非均匀挟沙水流两相浑水模型。由于方程包含了颗粒与水流作用力及不同颗粒相互作用力，因而能够从力学本质上反映非均匀沙不同粒径颗粒的相互作用对颗粒悬浮的影响机制，为分析非均匀悬移质泥沙输沙机理提供了理论工具。其次，分析了非均匀沙悬浮的主要动力机制。非均匀沙悬浮本质上是浑水紊动、颗粒自身作用、其他粒径颗粒作用三种作用共同影响的结果，相对于均匀沙弥散速度，非均匀沙弥散速度本构方程包含了不同粒径颗粒相互作用项。再次，分析了明渠恒定均匀流中各粒径组浓度垂线分布规律。与均匀沙情况相比，在低浓度、各粒径组粒径差异不大的条件下，非均匀沙输沙方程与均匀沙输沙方程计算结果区别不大；在含沙浓度高、粒径差异明显的条件下，非均匀沙输沙方程能更好地反映泥沙非均匀性的影响。非均匀沙相互作用强度与浓度呈正相关关系，在低浓度条件下，非均匀沙相互作用对颗粒悬浮影响并不明显，随着浓度升高，非均匀沙相互作用逐渐增大。在相同浓度下，泥沙非均匀性增强时，非均匀沙相互作用对颗粒悬浮影响更明显。在空间变化上表现为，床面附近颗粒非均匀性带来的影响较为明显，在主流区逐渐减弱。最后，论文讨论了影响非均匀悬移质输沙的两个关键床面过程，即河床混合层床沙级配变化的动力学过程及床沙冲刷与沉积的过程。将沙波运动视作河床混合层内泥沙垂向掺混的主要动力，得到了河床混合层垂向掺混动力方程，分析了河床混合层掺混对床沙级配时空分布变化的影响。基于动理学理论建立了床沙冲刷通量和沉积通量的表达式，从力学本质上分析了水流强度及颗粒大小对床沙通量的影响规律，研究了床沙与悬沙交换对非均匀沙运动的影响，为认识悬移质泥沙运动与河床相互作用提供了理论分析工具。

In natural rivers, suspended sediment are generally composed of non-uniform grains, and the non-uniformity can exert great effect on different fluvial processes. However, research on non-uniform sediment suspension is limited and always conducted in a similar way as the uniform particles, without considering the interactions between particles in different grain sizes. The transport mechanism of non-uniform suspended sediment has not been fully elucidated. Therefore, this paper aims to address the key theoretical issues in the transport of non-uniform suspended sediment and interactions between suspended load and bed materials, with the main contents and innovations concluded as follows:On the basis of two-phase flow theory, a non-uniform two-phase mixture model is developed to describe the transport of non-uniform sediment-laden flows, in composition of governing equations for flows and non-uniform sediment in different grain sizes. Specifically, the particle-particle interactions between sediment in different grain sizes are included as a function of the relative velocity between particles in different grain sizes. For the closure of the equations, drift velocity is introduced as the relative velocity between each phase and the sediment-laden flows. By methods of Sherman–Morrison formula and the perturbation asymptotic technique, the constitutive relation of drift velocity is derived, from which the physical suspension mechanism of non-uniform particles can be well analyzed. Based on the constitutive equation for drift velocity of each grain size, the suspension of the non-uniform sediment can be attributed to influences imposed by both the fluid turbulence, the sediment particles themselves, and more importantly, interactions between particles in different grain sizes, which is main difference from the research on uniform sediment transport. Transport equations for the non-uniform sediment are developed based on the constitutive relation of drift velocity, and the vertical concentration distribution of each grain size is derived. The calculated concentration profile is compared to the experimental data, and well consistency can be observed between the two. The concentration profiles between the uniform calculations and non-uniform calculations are compared, result shows in the low concentration condition, rare discrepancy is observed, while with the concentration increases, especially in the high concentration conditions, the difference of the concentration calculations between the uniform and non-uniform methods becomes obvious. With the analysis of the non-uniform items in the transport equation, it shows that the interaction between different particles is positively correlated to the concentration, exerting obvious effect on the suspension of non-uniform sediment particles in the high-concentration conditions. Moreover, with the ratio of different grain sizes increases, the non-uniformity effect on each grain size increases as well. For the boundary conditions, the variations of grain size distributions should be considered. A diffusion-type partial-differential equation is developed to describe the vertical mixing in the active layer and its significant influences on the variations of grain size distributions, with migration of bed forms considered as the dominant driving force. Changes of grain size distributions on the bed surface develop into inner part of the active layer in a manner of diffusion, which makes the active layer no longer a well-mixed homogeneous layer as has been assumed in many previous studies. Moreover, new entrainment function and settlement function are derived on the basis of Kinetic Theory for sediment transport, which have the advantage over other methods in that it helps to provide a new approach to statistically associate the dynamic processes of micro?scopic motion of particles to macroscopic features of sediment transport.