Half-spherical surface diffusion model of shield tunnel back-fill grouting based on infiltration effect

Studies on shield tunnel back-fill grouting often simplified soil and grout as homogeneous single-phase media and ignored the interactions between soil pores and solid-liquids in grouts, thus leading to inaccurate results. Using shield method construction characteristics as a basis, this paper presents a theoretical study on the diffusion mechanism of back-fill grouting, with a particular focus on the diffusion process of grout at the penetration stage. To this end, a half-spherical surface diffusion model considering the infiltration effect of back-fill grouting in shield tunnel construction was developed. The model was then used to derive formulae based on soil porosity and volume fractions of grout grains to determine distributions of grouting pressure and define a concept of effective grout diffusion radius. Finally, the relationship between the pressure applied to tunnel segments as a result of the back-fill grouting of the shield tunnel and the important factors was analysed using a case study comparing the presence and absence of infiltration. The results show that the total and per-unit-area pressure on tunnel segments from back-fill grouting of the shield tunnel are significantly affected by the infiltration effect. Grouting pressure was determined to be the cause of changes in segment pressure and pressure intensity.