The empirical power law relationship model and non-equilibrium sediment transport theory are two different methods used to describe the suspended sediment transport in alluvial rivers. The mathematical comparison results show that, for steady uniform flow, the derivatives of sediment concentration of the two above mentioned methods are first order approximate when sediment transport state is near equilibrium condition, and the variation of the saturation recovery coefficient is considered in power law relationship when sediment transport state is far away from the equilibrium condition. Based on the equivalence property, the calculation formula of exponent in power law function is established, showing that the value of exponent varies with the saturation recovery coefficient, sediment fall velocity, unit width discharge and longitudinal distance. Based on the derivative of power law function for the structural features of sediment concentration, the calculation expression of saturation recovery coefficient which is far away from the equilibrium condition is extracted and expressed. Finally, a new power law relationship model with changing exponent is proposed and applied to the sand basin. The application result revealed that the computed suspended sediment concentration along the distance of the sand basin is in suitable agreement with the measured values.