Grout Diffusion Morphology and Numerical Characteristic Radii During Directional Grouting in Layered Water–Bearing Soft Strata

Underwater soft strata commonly occur beneath river and lake dike foundations. Coupled water–level fluctuations and seepage make these strata susceptible to differential settlement and shear failure. However, quantitative characterization of grout diffusion in layered water–bearing soft strata remains limited, particularly when borehole configuration, pressure transmission, and stratigraphic position vary simultaneously. This study investigates the diffusion behavior of 1086E underwater epoxy grouting material (UEGM) and the associated soil–stress response in a laboratory–scale layered water–bearing soft–stratum model. Three single–run directional–grouting tests were conducted in a finite three–dimensional layered soil model. A two–dimensional layered numerical model was used to examine grout transport and soil–stress redistribution, while a homogeneous single–borehole model was used to compare different numerical characteristic radii with an analytical diffusion–radius estimate. The following results were obtained: (1) During injection, the soil–stress response exhibited four stages: initial nonresponse, rapid rise, stabilization, and pressure–release decline, with stabilized readings ranging from 15.0 to 17.8 kPa. (2) Excavation revealed axially continuous but geometrically irregular cured grout consolidation bodies, whose diameters generally decreased from the inlet end toward the borehole tip. At borehole depths of 150, 250, and 350 mm, near–end grout diffusion diameters of 35, 30, and 20 mm decreased to 25, 12, and 11 mm at the borehole bottom, respectively. (3) The axial attenuation coefficient varied non–monotonically across the three borehole configurations. With one test per configuration and borehole depth varying with stratigraphic position, this pattern is interpreted in terms of the combined influence of borehole length and local stratum properties. Complementary numerical simulations described the evolution of pre–gel grout distribution during injection. In the homogeneous single–borehole benchmark, R50, defined by the 0.5 grout–volume–fraction contour, reached approximately 0.87 times the analytical diffusion radius at 60 s under the adopted geometry, material parameters, and boundary conditions. Simulations over 0.1–0.4 MPa further predicted an increase in the characteristic diffusion radius with diminishing incremental gains as pressure increased, with 0.1 MPa being the pressure used in the physical tests. These findings provide laboratory–scale observations and model–specific numerical insights into grout diffusion in layered water–bearing soft strata. However, their application to field–scale design requires replicated experiments and independent experimental verification under representative field conditions.