Coupled Prediction of Grout Diffusion and Ground-Surface Heave During Fracture Grouting in Layered Soil

To establish a quantitative link between grout propagation and ground-surface heave in grouting-based settlement remediation, this study proposes a semi-analytical framework based on energy balance and volume conservation. The equivalent diffusion radius is first solved from an energy balance that partitions effective injection work among ground-confinement work, fracture-surface creation, and viscous-flow dissipation. The calculated diffusion scale is then combined with pore-structure adjustment to define a net subsurface source volume, which is transferred to an axisymmetric Gaussian surface-heave field through a heave-volume transfer efficiency. Six single-hole tests in three-layer ground were used to examine response trends; quantitative comparison of the theoretical diffusion radius and heave was restricted to the pressure-controlled cases G1–G3. The calculated equivalent diffusion radii were 22.3–24.0% greater than the measured values, indicating a systematic positive bias, while the relative errors in theoretical maximum heave were 12.3–13.6%. A three-dimensional FLAC3D equivalent-expansion model reproduced the maximum surface heave for G1–G4 with relative errors of 5.93–6.58%; however, it did not simulate grout flow or fracture propagation and was therefore used only to examine ground-deformation transfer. The available evidence supports the calculation chain at a first-order laboratory scale rather than a comprehensive independent validation. The framework remains limited by idealized fracture geometry, effective parameters requiring independent identification or calibration, the absence of experimental replication, finite-scale boundary effects, and the lack of multi-hole validation. Within these limits, it provides a structured basis for relating grout propagation extent to surface uplift under single-hole fracture-grouting conditions.