A novel time-varying inverse Peck formula for forecasting freezing-induced ground heave in tunnel construction

The Peck formula is widely used to predict subsurface settlement in tunnel excavation without freezing techniques. However, predicting surface uplift during tunnel construction with artificial ground freezing is still a challenge. This investigation introduces a groundbreaking methodology by creatively inverting the Peck formula. By integrating the inverted Peck formula with the principles of plane freezing theory and considering stratum constraint conditions, we’ve developed a time-varying model to quantify the volume of stratum frost heave and the subsequent surface uplift. Through a meticulous back-analysis coupled with maximum likelihood estimation, this approach enhances the precision in gauging the extent of the frost heave mound, thereby improving the accuracy and simplicity of predicting surface uplift deformation in the tunnel construction process employing ground freezing. The robustness and credibility of this innovative approach are substantiated through an exhaustive comparative analysis juxtaposed with empirical engineering monitoring data and calculations based on the stochastic medium theory. The outcomes demonstrate that the proposed inverted Peck formula excels in its explicit clarity and practical relevance, more closely aligning with the empirical data on surface uplift than predictions derived from the stochastic medium theory, thus offering enhanced predictive performance. This study provides a novel theoretical model for anticipating surface uplift deformations in tunnel construction endeavors using ground freezing techniques, delivering valuable insights and a promising predictive tool for both engineering professionals and academic researchers.