Based on the theory of cylindrical cavity expansion which considers the influence of initial radius

and according to the similarity between the mechanism of the critical depth of pressuremeter test and the penetration effect of pile-sinking

the interface of soil heave of pile-sinking with pre-drilling is obtained; and then a simple formula to estimate the range and magnitude of soil heave is derived. The law of soil heave due to initial radius of pre-drilling is analyzed. The initial radius is just the pre-drilling one

so the formula is universal to estimate soil heave which derived in this paper. When initial radius is zero

the formula can be used to analyze general pile-sinking. It is demonstrated that the calculated soil heave is less than the measured value

but more close to it than the FEM result. So a simple and practical formula to estimate the range and magnitude of soil heave for the engineering is given