A new analytical model for stress distribution in the rock bolt under axial loading

This study presents a novel analytical model to simulate the axial strain and stress distribution along the full embedment length of the grouted rock bolt under axial loading. The model is derived based on the force equilibrium equation at one infinitesimal section of the rock bolt to grout interface and solved using second order partial differential equation method. Such a model is advanced in a way that all the input parameters can be pre-determined by rock bolt geometry information and direct shear testing of the grout without the need to conduct any pull-out test. In addition, this model is the first one in literature addressing the influence of the confining pressure applied to the grouted rock bolt on the axial strain and stress distribution in the rock bolt. Such a model also corrects the correlation between the axial load and axial stress at the loading end of the rock bolt as many past research underestimate the stress level. The features of the proposed model enable its engineering application to be user-friendly and universal. The close agreement between the simulation results of the proposed model and the experimental data in the literature validates the model's capability for successfully and accurately mapping out the axial strain and stress distribution along the grouted rock bolt under axial loading.