An analytical solution for the critical anchorage length of grouted rockbolts

Determining the critical anchorage length of grouted rockbolts is of great theoretical and practical value for the design of anchorage structures. First, the elastic solution for the critical anchorage length is derived according to the shear stress distribution of the anchorage-body interface, and the factors affecting the critical anchorage length are analyzed. Second, the critical anchorage length and its influencing factors are analyzed by a numerical simulation and compared with the theoretical results. In addition, the accuracy of the critical anchorage length is verified by the field test results. Finally, based on the analysis of the safety degree and the field test, the determination of a reasonable anchorage length is discussed. It is shown that the critical anchorage length of the grouted rockbolt in the elastic state is not related to the pullout load but only to the mechanical properties of the rock and the anchorage-body diameter. The softer the rock is, the longer the critical anchorage length is. With the increase in the anchorage-body diameter, the critical anchorage length is longer. The Poisson’s ratio of the rock has little effect on the critical anchorage length. Moreover, the research also shows that the reasonable anchorage length of the grouted rockbolt determined in this study is economical and can meet the safety requirements for engineering applications.