Abstract: Proper selection of grouting pressure is required to ensure the good performance of back-fill grouting. It is suggested that that the back-fill grouting compacts the surrounding soil first, and then fracture the soil when the grouting pressure exceeds a certain value. To determine the optimal grouting pressure, a formulation for calculating the upper critical value of the grouting pressure is developed based on the elastio-plastic theory with considering the unlimited expansion of the grouts. By combining the shear resistance of bolts and the grouting pressure acting on the segments, the upper critical value of the grouting pressure is determined with considering the shear failure of the bolts. Based on active and passive earth pressures, the formulations of upper and lower critical value for the grouting pressure, which meet the requirement for soil strata stability, are developed. The calculating method of the optimal grouting pressure is also presented. A practical engineering case is analyzed, illustrating the effects of elastic modulus, cohesion, internal friction angle of soil, initial underground water pressure, and tunnel depth buried on the critical grouting pressure. It is found that the critical value of grouting pressure is influenced by many factors such as the elastic modulus, cohesion, internal friction angle of soil, initial pressure of ground water, segmental structure performance, and tunnel depth. The upper pressure limit increases with the increase of the elastic modulus, cohesion, internal friction angle of soil, initial pressure of ground water, and tunnel depth, while the lower pressure limit increases with the increase of tunnel depth as well.

Key words: shield tunnel, back-fill grouting, grouting pressure, upper pressure limit, lower pressure limit