Analytical solution for expandable polyurethane grouting in a rock fracture

Abstract

Expandable polyurethane grout has been extensively utilized for the reinforcement and sealing of rock fractures. The diffusion mechanism of this grout is particularly unique, owing to the time-dependent characteristics of both its density and viscosity. However, the non-synchronous relationship between the change in diffusion radius and pressure poses challenges in deriving analytical solutions. In light of this, our study presents an innovative analytical model to effectively simulate the diffusion behavior of expandable polyurethane within rock fractures. Notably, this model considers both the self-expanding source and the convective driving force. The outcomes of our research demonstrate that spread and pressure exhibit distinct characteristic times, allowing us to employ the same equations with diverse parameters, yielding a semi-deterministic approach. In this approach, the first run of the model is deterministic while the second entails empirical considerations. Further, a comparison of analytical results with experimental injections was made involving varying grouting quantities, revealing excellent agreement between the measured and calculated pressures. The present model can be employed for fitting and real-time monitoring after calibration, enabling the exploration of conventional stop criteria, as well as refusal and mass criteria. Additionally, this model facilitates the formulation of conditions to effectively achieve the target, considering vital factors such as the time-spread relation, expansion ratio, and gel time.