LAUSR

ABSTRACT Estimating erosion rate of solid particles in a porous medium is of interest to geotechnical engineers; which use analytical or numerical models for this purpose. Constitutive law of erosion is a key component in the development of such models. These models estimate the solid erosion rate as a function of various modelling parameters such as fluid velocity and time. Using the principles of dimensional analysis, a constitutive law is proposed for assessment of the rate of erosion in relation to the fluid velocity and a dimensionless proportionality constant called the erosion coefficient,. Based on physics of the erosion process, experimental observations and approximation theory, is expressed as a function of grain density, particle Reynolds number and porosity variation. Then, the proposed constitutive model is combined with the principle of conservation of mass to arrive at an analytical model for estimation of internal erosion rate. The analytical model shows that the erosion rate has a non-linear direct relationship with fluid velocity and a non-linear inverse relationship with time. The proposed analytical model is calibrated and validated using experimental data available in the literature. The validation results show that the model estimations of erosion rate can closely reproduce experimental data.