Rockbolting is routine practice for supporting of underground excavations. For the stabilizing of rock cavern roof arches, long rockbolts or cables may not necessarily be beneficial. A proper design of rockbolt support should therefore be based on a clear understanding of both the mechanism of the rock roof arch structure and the features of rockbolt reinforcement. In this paper, the classical voussoir arch theory is applied to investigate the mechanism of roof arching, and criteria for the forming of a natural rock roof arch are established. Design of rockbolt support based on the arching theory and the commonly used Convergence Confinement Method (CCM) with regard to bolt length and density are discussed. Application of analytical solutions In rockbolt support design of a large cavern roof is carried out with the objective of enlightening the efficiency of short and closely spaced fully grouted rockbolts in rock arch reinforcement.


Empirical methods are commonly applied when rockbolt support for the roof arch of underground opening in rock is designed. Among these, analytical methods provide fundamental approaches to investigate the mechanism of roof arching and the characteristics of rockbolting reinforcement, even though some assumptions have to be made to Simplify problems. Analytic solutions are also useful to identify important parameters in the design and to verify the results of numerical modelling. In this paper, limit equilibrium analyses of roof arch and the Convergence Confinement Method - CCM, are applied to rock support analysis of rock cavern roofs with focus on mechanism of roof arch forming and reinforcing as well as design of length and spacing of the rockbolts.


The classical voussoir arch theory was found helpful for the understanding of the mechanism of forming a natural rock roof arch, and to identify factors that contribute to the reinforcement of a rock roof arch. By derivation of the arch thrust line, it is noted that in-situ horizontal stresses play an important role in arch forming, and there is a required minimum thickness of a Roman arch necessary for stability.

2.1 Voussoir arch action

Voussoir arch (Figure 1) action arises directly from the properties of the material. Voussoir, or masonry blocks, are laid in weak mortar or placed one on another to form the arch. This method of construction ensured that the structure would sustain no tension and sliding between blocks. Stability of the whole arch is assured by the compaction under gravity of the various elements and high capacity of compressive strength of masonry blocks. Coulomb, in his memoir on statics in 1773, examined the behaviour of the masonry structure in the light of three assumptions:

  • masonry has no tensile strength;

  • masonry has an unlimited compressive strength, and

  • sliding failure does not occur.

The action of the arch can be described by the line of thrust, representing the equilibrium of given loading. The thrust line for a general shape of underground cavern roof arch may be derived based on limit equilibrium analysis.

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