Analytical Solution for Borehole Contraction Caused by Radial Unloading

摘要

The elastoplastic analysis of a borehole was conducted using the elasto-brittle-plastic softening model and the Mohr-Coulomb strength theory, combined with earth pressure formulas derived from the cavity wall formula and Berezantsev's formula. The analytical solutions for the plastic zone radius and radial displacement are presented. Using the curves of the plastic zone radius and the wall displacement of the borehole versus borehole depth, the influence of various factors such as different earth pressure calculation methods, the unloading process, the borehole radius, and the dilatation and softening effects are discussed in detail. According to the results, the use of the cavity wall formula leads to convergence easily and both the knee points for the plastic zone radius and the wall displacement of the borehole occur in the shallower part of the borehole. On the other hand, according to Berezantsev's formula, the earth pressure increases along the shaft, following a hyperbolic curve, and continues to increase at the bottom of the borehole. Because there is a significant difference between the results of the previous two methods, an integrated method for estimating the earth pressure should be derived using the in situ results. The unloading process, borehole radius used in the design, dilatation and softening effects, etc., also have a great influence on the plastic zone radius and the wall displacement of the borehole. Moreover, the borehole radius has huge impact on the boundary force.