Gully bed erosion depth is one of the most important parameters for design of debris flow control works. So far

there are few researches on gully bed erosion depth and there are no good methods for calculating the gully bed erosion depth. How to calculate the gully bed erosion depth is also a technical problem which urgently needs to be solved for debris flow preventing engineering design. The driving forces of viscous debris flow and potential resistance which may take part in the motion are analyzed. And then the calculation formula of the maximum erosion depth is obtained. The formula shows that the erosion depth of gully bed increases with the increasing of depth and density of debris flow

longitudinal slope of gully bed and viscosity of gully bed materials

while decreases with the increasing of internal frictional angle of gully bed materials. Comparing with the existing calculation methods

the formula is based on a strict theoretical derivation

the calculation result is more accurate and can be used to calculate the erosion depth in the occurrence of debris flow area for different frequencies

and provides a technical support for the design of viscous debris flow control works. The practical value of the calculation formula is illustrated.