A local homogenization approach for simulating the reinforcement effect of the fully grouted bolt in deep underground openings

Fully grouted bolts are a key component of the support system for underground openings.Although considerable effort has been made in the simulation of the reinforcement effect of the fully grouted bolts on the rock masses surrounding underground openings,most of the work has limited significance since the structural element approach is used.This study proposes a local homogenization approach(L-H approach)that integrates elastoplastic mechanics,composite mechanics,and analytical approaches with numerical simulation to effectively simulate the reinforcement effect of the fully grouted bolt on deep surrounding rock masses.In the L-H approach,the representative volume of bolted rock mass(RVBRM)with a fully grouted bolt is established based on the original mesh model utilized in the rockbolt element approach.The RVBRM is a regular quadrangular prism with a cross-sectional size equal to the bolt spacing and a length equal to the bolt length.The RVBRM is homogenized by the L-H approach from a unidirectional bolt-reinforced composite into a homogeneous transversely isotropic medium whose mechanical properties are described by a new transversely isotropic elastoplastic model.The L-H parameters for the RVBRM are obtained using analytical approaches,composite mechanics,and known parameters of the rock mass and bolt.Using the L-H approach,the reinforcement effect of the fully grouted bolt on the bolted rock specimen and the surrounding rock mass in Jinping II Diversion Tunnel#2 with a depth greater than 2000 m is simulated.The results show that the predictions of the L-H approach are more in agreement with the physical model results of bolted rock specimen and provide a more realistic response of the bolted surrounding rock mass.The L-H approach demonstrates that fully grouted bolts with common bolt spacings and diameters substantially enhance the elastic modulus,shear strength,and tensile strength of the rock mass in the direction of the bolt axis.