A method and apparatus for measuring the total erosion rate and downstream transport of suspended and bedload sediments using an adjustable shear stress erosion and transport (ASSET) flume with a variable-depth sediment core sample. Water is forced past a variable-depth sediment core sample in a closed channel, eroding sediments, and introducing suspended and bedload sediments into the flow stream. The core sample is continuously pushed into the flow stream, while keeping the surface level with the bottom of the channel. Eroded bedload sediments are transported downstream and then gravitationally separated from the flow stream into one or more quiescent traps. The captured bedload sediments (particles and aggregates) are weighed and compared to the total mass of sediment eroded, and also to the concentration of sediments suspended in the flow stream.