A semi‐elliptical surface compound diffusion model for synchronous grouting filling stage in specially shaped shield tunnelling

In constructing super‐large section shield tunnels, it is difficult to guarantee the filling efficiency and uniformity of grouting behind the segments. Studies on grout diffusion models often simplify the grout filling process, leading to inaccurate results, especially for shield tail void with special noncircular profiles. This paper presents a theoretical study on the grout filling diffusion mechanism and its mechanical behaviour, with a particular focus on the grout actual motion process at the synchronous grouting filling stage when the shield is advancing. A semi‐elliptical surface compound diffusion model without the predetermined flowing passage was developed, and this model was used to derive the grout filling pressure and diffusion distance formulas. To address the time‐varying diffusion surface and irregular integral region issues in derived equations, a stepwise solution algorithm based on the spatiotemporal discretisation operation was proposed. Finally, the grout pressure distribution patterns and some critical influence factors were analysed using a case study in the soft silty clay area to compare the presence and absence of circumferential‐longitudinal correlations in the grout filling diffusion process. The results show that the diffusion mechanical behaviour and force transmission significantly affected the total and per‐unit‐area grout pressures, and the proposed theoretical model is more consistent with the field‐measured data. The local trend and fluctuation characteristics of grout filling pressure are clearly different from those of a circular tunnel. The grout filling diffusion mechanism was determined to be the main cause of pressure distribution changes under the premise of a certain initial grouting pressure.