Elastoplastic coupling analysis of surrounding rock-prestressed yielding anchor bolts/cables based on unified strength theory

A whole-process analytical theory for the coupled deformation of deep circular tunnel surrounding rock and prestressed yielding anchor bolt (cable) system is derived based on the unified strength theory and non-associated flow rule. This theory considers the strain softening characteristic of rock mass, the yielding rein-forced characteristics of anchor bolt (cable), and the support timing. An analytical method is proposed to calculate the difference in displacement of anchor bolts (cables). This study highlights the importance of monitoring anchor bolts (cables) elongation rate in high-stress tunnels by integrating theoretical analysis with engineering practice. The displacement difference that occurs during the coordinated deformation of the bolts (cables) and the surrounding rock provides the support resistance. Therefore, the safety margin standard of elongation rate can be used to assess the integrity and effectiveness of the support structure during the real-time bolts (cables) action. The present study aims to validate the rationality of the analytical theory by conducting numerical simulations using ABAQUS software. Specifically, we focus on analyzing the ground response curves (GRC) under the bolt (cable) support and the elongation rate of the bolt (cable). Various factors such as prestress, yielding amount, support timing, intermediate principal stress coefficient, radial/longitudinal spacing, and length are considered to compare and analyze their effects on the GRC. The results showed that anchor bolts (cables) can significantly reduce the surrounding rock convergence. With prestressed bolt (cable) support, the GRC exhibits a stepwise drop, significantly and timely reducing the support force required for the surrounding rock equilibrium. After setting the yielding structure, the increase in anchor cable stress was limited, thereby slightly increasing the surrounding rock displacement. However, the anchor cable elongation rate significantly decreased, thereby greatly enhancing the support structure safety. The support timing affects the starting point of bolts (cables) function. The displacement control effect is more pronounced when support is provided earlier. However, this also leads to an increase in the elongation rate of the bolt (cable). The intermediate principal stress coefficient reflects the self-bearing capacity of the surrounding rock, and increasing this value can improve the deformation control performance of the surrounding rock under anchor bolt (cable) support as a whole and reduce the elongation rate through the coupled function of the surrounding rock-anchor bolt (cable) system. The spacing between anchor cables significantly impacts the convergence control of surrounding rock. Smaller spacing leads to better control of the surrounding rock deformation and lower stress of the anchor cables. As the length of the anchor cables increases, the elongation rate and stress of the anchor cables continuously decrease. However, the surrounding rock deformation exhibits an initially decreasing and increasing pattern. This paper presents a theoretical and computational approach to analyze the effect of prestressed yielding anchor bolt (cable) support and the safety of support structures in tunnel engineering. The findings of this study can serve as a valuable reference for the convergence analysis of circular tunnels in underground engineering.