Probability distributions of shotcrete parameters for reliability-based analyses of rock tunnel support

Abstract

A common support measure for underground excavations in jointed rock masses to support loose blocks is to apply a thin shotcrete layer to the periphery of the excavation and systematically install rockbolts into the surrounding rock mass. In this support system, large blocks are carried by the rockbolts and small blocks are carried by the thin shotcrete layer. To verify the shotcrete layer’s load-bearing capacity and to stringently account for the large uncertainties incorporated in the variables involved in determining its capacity, analytical calculations in combination with reliability-based methods can be used. However, a lack of knowledge exists regarding the magnitude and uncertainty of shotcrete characteristics (thickness, adhesion, flexural tensile strength, residual flexural tensile strength, and compressive strength), making it difficult to apply reliability-based methods. A statistical quantification of these characteristics is therefore important to facilitate reliability-based methods in design and verification of shotcrete support. In this paper, we illustrate how shotcrete support against small loose blocks can be viewed as a correlated conditional structural system and how this system can be analyzed using reliability-based methods. In addition, we present a unique amount of data for the aforementioned variables, which are all incorporated in the design and verification of a shotcrete layer’s ability to sustain loads from small loose blocks. Based on the presented data, we statistically quantify and propose suitable probability distributions for each variable. Lastly, we illustrate how the proposed probability distributions can be used in the design process to calculate the probability of exceeding the shotcrete’s load-bearing capacity. Both the probabilistic quantification and the defined correlated conditional structural system along with the illustrative calculation example are followed by a discussion of their implications.