One of the main issues involved during tunnel construction with tunnel boring machines is the tail gap grouting. This gap is between the external diameter of tunnel lining and the excavation boundary that is filled with high-pressure grouting materials. In this work, three different approaches of gap grouting modeling in the FLAC3D software are investigated with a special attention to the influence of the grout material hardening process. In the first approach, the grout is modeled as a liquid during injection, and considering the TBM advancement and its hardening time, the grout characteristics are changed to the properties of the solid grouting. In the second approach, the grouting material from the beginning of injection is considered with the properties of solid grouting in the model, and the liquid phase is ignored. In the third approach, without considering the back-filled grouting area in the model geometry, only the injection pressure is applied to the end of the shield and behind the installed segments. The validity of the approaches is evaluated with respect to the maximum ground surface settlement. All the three approaches estimate different surface settlement but the result of the first approach is closer to the monitoring data. Also as a sensitivity analysis, in this work, we investigate the effect of the elastic modulus of liquid and solid grouting materials on the amount of surface settlement that can help to gain a more accurate insight into the effect of grout mixture.