Although much effort has been made to develop various frost heave models in the past decades, a simple yet versatile model is still needed for engineering applications. This paper presents a method to estimate frost heave in frozen soil using a macroscopic water flux function that extends the segregation potential to make it applicable for both steady state and transient freezing and thawing states. The formation of an individual ice lens is modelled by combining previously developed stress and strain criteria. The water flux function, which includes various factors in accordance with the porosity rate function, can describe the growth of both new and old ice lenses. More importantly, every component of the water flux function is physically explained by the theory of pre-melting dynamics, where all the influencing factors are traced back to their impacts on the ice volume distribution. The performance of the model is demonstrated via simulations of one-dimensional freezing and thawing processes after the model is validated by a specific case from previous literature. Although adequate data are not available for a stricter experimental verification of the model, it is observed that the simulations predict the general course of events together with significant specific features that were identified in previous experimental studies.