Explain how the support reaction curve and the ground reaction curve are utilized in the design of tunnel support systems.

The support reaction curve and the ground reaction curve are essential tools used in the design of tunnel support systems because they illustrate the interaction between the ground and the support, allowing engineers to select a support system that provides adequate stability. The ground reaction curve (GRC) represents the relationship between the internal pressure applied to the tunnel wall by the ground and the radial deformation (inward movement) of the tunnel wall. It illustrates how the ground responds to the excavation process. As the tunnel is excavated, the ground loses support, leading to deformation. The GRC shows how much pressure the ground can exert at different levels of deformation. Initially, the ground can withstand a high pressure with little deformation. However, as deformation increases, the ground pressure decreases as the rock mass begins to yield and loosen. The shape of the GRC depends on several factors, including the rock type, the stress conditions, the groundwater conditions, and the excavation method. Stronger, more competent rock masses will have GRCs that show higher pressures and lower deformations. Weaker, more fractured rock masses will have GRCs that show lower pressures and higher deformations. The support reaction curve (SRC) represents the relationship between the support pressure provided by the tunnel support system and the radial deformation of the tunnel wall. It illustrates how the support system responds to the ground deformation. Different types of support systems, such as rock bolts, shotcrete, or steel sets, will have different SRCs. A stiff support system, such as a thick layer of shotcrete, will provide high support pressure with little deformation. A flexible support system, such as rock bolts, will allow for more deformation with lower support pressure. The design of the tunnel support system involves selecting a support system whose SRC intersects the GRC at a point that provides adequate stability. The intersection point represents the equilibrium state between the ground and the support. The support system should be able to provide enough support pressure to prevent excessive deformation of the tunnel wall. The factor of safety is then considered. The factor of safety is the ratio of the support capacity to the support demand. A higher factor of safety indicates a more stable tunnel. The design of the tunnel support system should aim to achieve a desired factor of safety. The factor of safety is influenced by the shape of the GRC and the SRC, as well as the uncertainty in the rock mass properties. In some cases, the GRC and SRC may not intersect, indicating that the tunnel is unstable. In these cases, the tunnel support system must be redesigned to provide more support pressure or to reduce the ground deformation. For example, the tunnel may need to be excavated using a different method, or the ground may need to be improved using ground improvement techniques. The selection of support is based on these curves.