Installation-Delay Effects on Passive-Bolt Anchorage in Squeezing Railway Tunnels: An Analytical Framework for Support Transition and Cost Optimization

Deep beneath the earth, where rock masses are fractured and under immense pressure, building a tunnel is a delicate negotiation between human engineering and geological force. When engineers dig through such "squeezing" ground, the rock does not simply sit still; it slowly deforms inward, trying to close the space created by the excavation. To keep the tunnel open, builders rely on a system of immediate support, typically involving layers of sprayed concrete and steel bolts drilled into the rock to hold it together. A fundamental challenge in this work is timing. The moment a tunnel face is exposed, the rock begins to relax and move. If the support system is not installed instantly, the rock moves further before the bolts and concrete can take hold. This delay changes how the support system behaves, often in ways that standard calculations do not predict. Engineers need to know exactly when a simple system of short bolts and concrete will fail and when they must switch to a more robust, deeper anchoring system to prevent collapse, all while keeping the project financially viable.

In a new study, researchers have developed a practical framework to answer these questions for high-speed railway tunnels, specifically looking at how installation delays affect the performance of passive rock bolts. The team combined a well-known analytical method for predicting ground movement with a detailed economic model to simulate what happens when support is not applied immediately. They focused on a scenario where the rock quality is poor and the tunnel is deep, conditions that are common in the tectonically active regions of Vietnam where a new north-south high-speed rail line is being planned. The researchers wanted to see if the standard approach—using short bolts and a layer of shotcrete—could survive the extra movement caused by construction delays, or if the rock would move so much that the bolts would simply pull out of the ground before they could do their job.

The study reveals that the timing of construction is just as critical as the strength of the materials. In their simulations, the researchers found that as the quality of the rock deteriorates, the zone of broken, unstable rock around the tunnel expands rapidly. For the standard 3.95-meter bolts used in their baseline model, there is a specific tipping point. When the rock quality drops below a certain rating, the broken zone grows so large that it swallows the entire length of the bolt that is supposed to be anchored in solid rock. Once this happens, the bolt loses its grip and can no longer hold the tunnel together, regardless of how strong the concrete lining is. The researchers identified this dangerous transition zone to occur when the rock mass rating falls between 48.2 and 50.1. In this narrow band, the delay in installing support causes the rock to move just enough to render the standard short bolts useless, forcing a switch to a different strategy.

To understand the financial impact of this mechanical failure, the team created a normalized cost model that strips away currency fluctuations and inflation to compare the true resource cost of different support strategies. They tested a severe scenario where the rock quality was very poor, with a rating of 35. In this situation, the standard short bolts failed completely because the broken rock zone was far too deep. Simply adding more short bolts or making the concrete thicker did not solve the problem, as these measures did not reach deep enough into the stable rock to provide a secure anchor. The only solution that worked in the simulation was to switch to deep, prestressed cable anchors. The mathematical optimum for this deep anchorage was a length of 9.61 meters. However, because construction requires practical, whole numbers and accounts for material waste, the researchers calculated that a standard 10-meter cable tendon would be the field-ready solution. This adjustment brought the estimated cost to 3,105.4 cost units per meter of tunnel, a figure that represents the most efficient way to secure the tunnel in these difficult conditions without overspending on ineffective measures.

The researchers validated their approach by comparing their results against real-world data from the Driskos Twin Tunnel in Greece, a site known for its severe squeezing ground and poor rock quality. In that tunnel, engineers had to install long, tensioned cables because the initial short bolts and concrete were insufficient to stop the deformation. The new model successfully reproduced the overall trend of the ground movement observed in Greece, predicting a final tunnel deformation that was within 8.2 percent of the actual measurements recorded there. This close match suggests that the framework is reliable for predicting when a support system will fail due to installation delays. The study confirms that in poor ground, waiting even a short time to install support can push the rock past the point where short bolts can hold, necessitating a more expensive but necessary switch to deep anchorage.

Ultimately, this work provides a tool for engineers to make better decisions during the early design phase of large tunnels. It moves beyond the assumption that all parts of a support system work together perfectly from the moment they are installed. Instead, it acknowledges that in the real world, delays happen, and those delays can change the physics of the problem entirely. By identifying the specific rock quality thresholds where short bolts fail, the study helps engineers plan for the right type of support before construction begins. This prevents the costly mistake of building a tunnel with a system that looks adequate on paper but fails in practice because the rock moved too much before the bolts could engage. The findings suggest that for tunnels in squeezing ground, the key to safety and cost-efficiency lies in recognizing when the rock is too broken for simple solutions and having the foresight to use deeper, more active anchorage systems.