The rapids shoal is the main navigation-hampering shoal in mountainous rivers,while the criterion of rapids abating is a technical parameter which has an influence on the regulation design of the rapids shoal channel,and it is also one of the most important focuses in the research of rapids.The paper analyzes the convenience and feasibility of a comprehensive index which combines rapids and hillside flow parameters as well as its difficulty of theoretical discrimination in practical using,and further it proposes the simplified basic discriminant.Based on the facts,the paper also points out that there are some preferable discriminants,such as parabola,straight line,broken line,etc.,the precise meaning of which in mathematics is given.And it should be regarded as different parameters of rapids abating in river-crossing area of ascending rapids which uses “expanding the springboard” method.