Reliability-based Support Optimization of Rockbolt Reinforcement around Tunnels in Rock Masses


  • Hongbo Zhao

    Henan Polytechnic University

  • Zhongliang Ru

    Henan Polytechnic University

  • Changxing Zhu

    Henan Polytechnic University


Traditionally, the design of tunnels is based on determinate parameter values. In practice, both the performance and safety of tunnels are affected by numerous uncertainties: for example,it is difficult for engineers to predict uncertainties in geological conditions and rock mass properties. The purpose of reliability-based optimization (RBO) is to find a balanced design that is not only economical but also reliable in the presence of uncertainty. In the past few decades, numerous reliability optimization techniques have been proposed for taking uncertainty into account in the design of engineering structures. In the present study, the first-order reliability method (FORM) was used to compute the reliability index using Excel Solver. The least squares support vector machine (LSSVM) approach was adopted to build a relationship between reliability index and design variables,and the artificial bee colony (ABC) algorithm was employed for the reliability-based optimization. A proposed LSSVM/ABC-based reliability optimization method was applied to the case of a tunnel with rockbolt reinforcement. The mechanical parameters of the rock mass, in-situ stress and internal pressure were considered as the random variables. The reliability index of tunnel was analysed. The length, distance out of plane and the number of rockbolts were determined and optimized considering the uncertainty based on RBO. The proposed method improved the efficiency of RBO while maintaining high accuracy. The results showed that the proposed method not only meets the design accuracy, but also improves the efficiency of reliability-based optimization.


reliability-based optimization; reliability analysis; first-order reliability method; artificial bee colony; least squares support vector machine

Published Online


How to Cite

Zhao, H., Ru, Z., Zhu, C. “Reliability-based Support Optimization of Rockbolt Reinforcement around Tunnels in Rock Masses”, Periodica Polytechnica Civil Engineering, 62(1), pp. 250–258, 2018.



Research Article