Analytical Model of Piezoresistivity for an Inner-Adhesive-Type Carbon Fibre Reinforced Plastic Tunnel Reinforcement

Cracks in a tunnel lining often emerge under the coupling action of earth and water pressures in a complex stratum environment, and accidents often occur in the process of repairing cracks. In this study, we used the force-sensitive properties of embedded carbon fibre to conduct early-warning research on lining reinforcement to prevent secondary damage during tunnel lining reinforcement. According to the earth load characteristics, a bond stress–slip model of the embedded carbon fibre under bidirectional earth pressure was established on the basis of the thick-walled cylinder theory and the semi-inverse method in elastic theory. The length change of a single fibre was obtained on the basis of the principle that the volume of a single carbon fibre is constant during the deformation process. The resistance and strain model of the single carbon fibre under the action of an external force was then established following the relationship between the resistance, the length change and the volume change of the single carbon fibre. The resistance of carbon fibre composite materials, according to their production technology and unidirectional force properties, was assumed to be a mixture of the series and parallel resistances of the single carbon fibre, and a piezoresistive model of carbon fibre composite materials was formed by using the multidimensional Taylor series expansion and the idea of the average equivalent. The comparison between the theoretical and monitoring values of the piezoresistive model in a tunnel project in Tibet, China revealed that the resistance of various types of carbon fibres increases with the radius of the lining reinforcement and earth pressure and decreases with an increase in the lining reinforcement thickness. Meanwhile, the angles at different positions of the lining reinforcement also have certain effects on the resistance value of the carbon fibre. The variation curve of the piezoresistive model was exponential in both deeply and shallowly buried tunnels, which verifies the rationality of the model.