A novel constitutive law of confined grouted rock bolt under pull-out load based on a fully nonlinear bond–slip model

Rock bolts are widely applied in deep underground excavations for rock reinforcement. Here, a constitutive model that quantifies the pull-out load–displacement relationship of the grouted rock bolt has been developed though theoretically analyzing the load transfer behaviour along the bolt–grout interface. An improved nonlinear continuously yielding criteria was employed as a bond–slip model where the role of confining pressure playing in slip was accounted. The performance of the proposed constitutive model was demonstrated by comparing with three sets of laboratory pull-out tests on the fully grouted rock bolts under different confining pressure levels (including a short-encapsulated pull-out test designed in our laboratory). The input parameters in the model were determinable within the laboratory environment. The analytical simulation results of pull-out load–displacement performance, the axial stress in the rock bolt and shear stress along the bolt–grout interface agreed well with the laboratory data. We also found that the confining pressure significantly affects the critical embedment length, and the higher the confining pressure, the shorter the critical embedment length. The findings enrich the understanding on the mechanical properties of grouted rock bolts and hence aid the rock engineers in rock reinforcement design in underground excavations.