This study introduces a unified cylindrical and spherical cavity reverse expansion model to simulate the formation of compaction grouting bodies and grout diffusion along pile shafts. Stress field expression employs the superposition method, while displacement field analysis utilizes the nonassociated Mohr-Coulomb criterion. By combining the displacement expression for cylindrical cavity reverse expansion with the fluid flow equation, a calculation method is proposed to compute the upward and downward diffusion heights of grout, considering the unloading effect. The parameter analysis demonstrates that ultimate grouting pressure increases with increasing soil strength and grouting depth, with the ultimate grouting pressure at the pile tip being greater than that at the pile side. The value of grout diffusion height is negatively correlated with unloading ratio and grouting depth while positively correlated with grouting pressure and pile diameter. The deeper the grouting depth, the greater the impact of unloading on grout diffusion height. Three case studies validate the effectiveness of the proposed model. Analysis reveals that when grouting pressure exceeds the ultimate pressure, the size of the grout body is related to the grouting volume. Neglecting the unloading effect in the prediction of grout diffusion height for pile foundations would lead to conservative results.

The accurate prediction of grouting upward diffusion height is crucial for estimating the bearing capacity of tipgrouted piles. Borehole construction during the installation of bored piles induces soil unloading, resulting in both radial stress loss in the surrounding soil and an impact on grouting fluid diffusion. In this study, a modified model is developed for predicting grout diffusion height. This model incorporates the classical rheological equation of power-law cement grout and the cavity reverse expansion model to account for different degrees of unloading. A series of single-pile tip grouting and static load tests are conducted with varying initial grouting pressures. The test results demonstrate a significant effect of vertical grout diffusion on improving pile lateral friction resistance and bearing capacity. Increasing the grouting pressure leads to an increase in the vertical height of the grout. A comparison between the predicted values using the proposed model and the actual measured results reveals a model error ranging from -12.3% to 8.0%. Parametric analysis shows that grout diffusion height increases with an increase in the degree of unloading, with a more pronounced effect observed at higher grouting pressures. Two case studies are presented to verify the applicability of the proposed model. Field measurements of grout diffusion height correspond to unloading ratios of 0.68 and 0.71, respectively, as predicted by the model. Neglecting the unloading effect would result in a conservative estimate.