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.