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.

Modern tunnels in hard rock are usually constructed by drill and blast with the rock reinforced by shotcrete (sprayed concrete) in combination with rock bolts. The irregular rock surface and the projection method of shotcrete leads to a tunnel lining of varying thickness with unevenly distributed stresses that affect the risk of cracking during shrinkage of the young and hardening material. Depending on water conditions, shotcrete is either sprayed directly onto the rock surface or over a drainage system, creating a fully restrained or an end-restrained structural system. In this paper, a method for non-linear numerical simulations has been demonstrated, for the study of differences in stress build up and cracking behaviour of restrained shotcrete slabs subjected to shrinkage. Special focus was given to the effects of the irregular shape and varying thickness of the shotcrete. The effects of glass fibre reinforcement and bond were implemented in the study by changing the fracture energy in bending and in the interaction between shotcrete and the substrate. The study verifies that an end-restrained shotcrete slab is prone to shrinkage induced cracking, and shows the importance of a continuous bond to avoid wide shrinkage cracks when shotcrete is sprayed directly onto the rock. 

Tunnels in hard, jointed rock are commonly reinforced with shotcrete (sprayed concrete) applied directly on the irregular rock surface. The thickness for such linings can be as small as 50 mm, which result in a fast drying. The resulting shrinkage of the restrained lining is a well-known phenomenon, which leads to cracking. The installation of drainage systems also results in an end-restrained shotcrete lining that is more prone to shrinkage cracking. The drying process is a complex problem that depends on multiple factors such as cement content, porosity and ambient air conditions (i.e. temperature, relative humidity and wind speed). Two numerical models capable of capturing the structural effects of drying shrinkage were compared in this study. It was found that inclusion of non-linear drying shrinkage is important for accurately describing crack initiation in an end-restrained shotcrete slab. The best fit to the experimental data was obtained when the rate of drying was described as a non-linear decreasing function.

Fibre reinforced shotcrete (sprayed concrete) is often used to support tunnels in hard rock. The shotcrete should be designed to carry the load from a loose block, which is assumed to be transferred to the surrounding rock mass over a narrow band. It is commonly accepted that the width of this band is constant, and independent of the shotcrete thickness. In this paper, numerical simulations are used to show that the width of this band and the load capacity is strongly correlated to the mean shotcrete thickness around the perimeter of the block. Furthermore, it is also shown that a strong linear correlation exists between the mean bond strength and the rock support capacity. This indicates that, under certain conditions, local areas with low thickness and bond strength can exist around the block perimeter without having any significant effect on the rock support capacity.

Falling or sliding of loose blocks is one of the most common failure modes in a rock tunnel. For tunnels in hard and jointed rock, fibre-reinforced shotcrete (sprayed concrete) in combination with rock bolts is one of the most commonly used supports to prevent such failures. The structural behaviour, and especially the failure, of this type of rock support, is complex and involves several failure mechanisms; such as cracking of the shotcrete and interface failure along the shotcrete-rock, bolt-grout and rock-grout interface. Therefore, rock supports are normally designed using analytical solutions based on the independent failure modes. However, these failure modes are derived based on experimental testing and the assumption that no interaction between the failure modes occur. This assumption has not been verified. Therefore, this paper presents a numerical model capable of simulating the failure of a bolt-anchored and fibre-reinforced shotcrete lining. The model includes bond failure between shotcrete and rock, cracking of the shotcrete and pull-out failure of rock bolts. The structural behaviour for each failure mode and the complete structure have been verified against experiments from the literature. This shows that the model is capable of simulating the different phases of failure, and show good agreement with results from full-scale experimental tests from the literature. Furthermore, results from the numerical simulation confirms that the design of the shotcrete lining can be based on individual failure mechanisms. Moreover, it was shown that a design based on the residual strength of the fibre-reinforced shotcrete is conservative compared to a design based on the bond strength.