Unlined Tunnels: Sounds Cool, Until the Rock Cracks

Let’s start

A pressure tunnel, lined it or leave it unlined? A decision which could cost you millions during or after project construction.

When you’re working on a pressure tunnel design, one of the biggest calls you'll make is whether to line the tunnel and how far. It’s not just a technical detail; it can seriously affect whether a project is financially viable or not. In hydropower projects especially, this decision can make or break the budget.

As engineers, we’re always under pressure to make the right call often early in the design stage, with limited information. That’s why I wanted to share a few key ideas around pressure tunnel lining and walk you through some simple 3D models I’ve built to help visualize these concepts.

So, What’s a Pressure Tunnel?

Pressure tunnels are designed to carry water, often under high internal pressure. You’ll mostly see them in pump hydropower projects, where they connect intakes to turbines. Depending on the setup, they can be fully or partially pressurized during operation. Since PHS projects are becoming increasingly popular in Australia these days, I’ll focus specifically on pressure tunnels within PHS schemes for this post.

Pump Hydropower storage scheme

In general, a pump hydropower storage project consists of several key components, though not all are always necessary. Their inclusion and positioning often depend on the site’s topography. The diagram below highlights the typical elements of a PHS scheme. As mentioned, some of these components may be excluded or relocated to better suit the terrain. In these series of posts, I’ll be focusing specifically on the pressure tunnel and shaft, with an emphasis on the type of lining required based on project conditions. Before diving in, it’s worth clarifying that a pressure shaft can often be replaced with a steeply inclined pressure tunnel. The commonly accepted threshold for this transition is around 15 degrees.

Now let’s go over the different types of lining typically used in pressure tunnels. Broadly speaking, there are three main categories:

1.       Unlined tunnel: These tunnels are usually constructed in very high-quality, low-permeability rock. In the past, they were limited to only the most favourable geological conditions. These days, unlined tunnels have been attempted in less ideal rock as well, but with increased risk. Support systems typically include rock bolts and shotcrete.

2.       Semi-lined tunnel: When rock conditions begin to deteriorate, such as when weak or soluble materials are present, rock bolts and shotcrete alone may not be sufficient. At this stage, heavier lining is considered. This often means adding reinforced concrete lining to improve tensile strength, along with grouting around the tunnel perimeter to reduce pore pressure and improve confinement.

3.       Lined tunnel: Sometimes, no matter what you do, the ground conditions simply demand a more robust solution. In these cases, a fully lined tunnel is required, often involving a steel liner embedded in concrete. This type of lining is typically used to completely prevent leakage and ensure durability under high-pressure conditions.

Now that we’ve clarified what we mean by a lined tunnel, let’s talk about where a fully lined tunnel is actually needed. This is one of the most important decisions made early in any PHS project, often during the feasibility stage when teams are still assessing whether the project is even worth pursuing. Unfortunately, that’s also the point where many things are still uncertain, and data is limited. Because of this, the decision often has to be made using the simplest available methods, approaches that require minimal input but can still provide useful guidance on whether full lining is necessary.

So, Why Do We Need Lining in the First Place?

Like with any tunnel, lining in a pressure tunnel plays a key role in ensuring global stability. But in the context of PHS projects, lining has an additional and equally critical job: preventing extensive water leakage.

Let’s first define what we mean by "extensive leakage." In this case, it refers to the loss of internal water pressure due to water escaping into the surrounding rock. That may not sound dramatic at first, but it can lead to major safety, environmental, and financial issues.

This kind of leakage can happen for two main reasons:

• High Permeability in the Host Rock: If the surrounding rock is highly permeable or if features like fault zones, shear bands, or crushed rock intersect the tunnel, there’s a high chance that pressurized water will find its way out. This can significantly reduce the efficiency of the system and potentially cause damage to both the structure and the surrounding environment.
• Hydraulic Failure of the Rock Mass: This is when the stress state in the surrounding rock reaches a critical level either creating new fractures or opening up existing ones, allowing water to escape. Hydraulic failure itself can happen in two ways:

1. Hydraulic Jacking: This occurs when the internal water pressure in the tunnel is greater than the normal stress acting across joint surfaces in the rock. In simpler terms, when the minimum principal stress is less than the internal pressure , joints can open. This is especially a concern in areas with low in-situ stress or poor confinement.
2. Hydraulic shearing: In some cases, σ₃ might be higher than the internal pressure, so jacking doesn’t occur, but the maximum principal stress (σ₁) is so high that it triggers shear failure along existing weaknesses.

In this article, I’ll focus on the first type of hydraulic failure: hydraulic jacking. This is because it’s one of the few failure modes that can still be reasonably assessed during the preliminary design stage, even when detailed in-situ stress data isn't available. At this stage, it’s common to assume that vertical stress represents the minimum principal stress (σ₃) which, while a simplification, gives us a useful starting point.

To avoid hydraulic jacking along a pressure tunnel, the minimum principal stress must always be greater than the internal water pressure. If that condition isn't met, fractures may open, and significant leakage could occur.

This simple but powerful concept has long been used to determine where a tunnel must be fully lined. One of the most well-known approaches based on this principle is the Norwegian Method, or the Minimum Cover Method. This method calculates the minimum required rock cover to prevent hydraulic jacking using the following formula:

As you can see, this method relies entirely on topography and gravity-driven parameters to determine the minimum cover needed to transition from a lined to an unlined tunnel. While it's simple and easy to apply, it doesn't take into account several critical factors including rock quality, permeability, tectonic stress, geological structures, pore pressure, or even the size of the excavation. Yet every one of these parameters can significantly influence whether a tunnel should be lined and if so, where and how extensively. There’s been plenty of research into how each of these factors affects tunnel lining behaviour. In this article, I want to take that a step further and use 3D numerical modelling to help highlight their impact in a more visual and intuitive way.

Let’s Start with a Simple Example

 For this example, let’s assume a slope with a 30 degree angle and a height of approximately 60 m. The upper reservoir is located about 98 m away from the crest of the slope. We’ll also assume that the rock mass is fully saturated, and that the groundwater table is located right at the ground surface.

To keep things straightforward, we’re using the Mohr-Coulomb (MC) constitutive model for the material behaviour. The material properties used in the model are shown in the table below:

To simplify the analysis and reduce computational cost, fluid flow was not activated in the model. Instead, pore pressure was applied purely to establish the initial effective stress state. This is a conservative assumption, as it doesn't account for changes in pore pressure due to excavation. The resulting static pore pressure distribution is shown in the figure below:

Using the Norwegian (Minimum Cover) Method, we can estimate the minimum rock cover required to avoid hydraulic jacking, purely based on gravitational factors. This method doesn't consider geological or structural conditions such as fault zones, weak layers, or permeability and it’s a topography-driven approach. Let’s apply it to two points along our example shaft: the top (20 m depth) and the bottom (50 m depth).

Effect of excavation dimension

Let’s first explore how excavation size can influence the reliability of the minimum cover prediction. For this comparison, we consider two circular tunnel sections with different diameters:

• One with a 5 m diameter
• One with a 10 m diameter

In both cases, the depth of cover remains constant, based on the values we previously calculated using the Norwegian Method (14.5 m for the top, and 36 m for the bottom of the shaft).

To simplify the analysis, we assume that the in-situ stress condition is hydrostatic. That means the initial effective vertical stress is determined solely by the depth and the unit weight of the rock:

After completing the excavation in both cases, we compared the minimum principal stress values estimated from the 3D numerical models to those predicted using the Norwegian Method. The results are presented in the graph below:

As shown in the graph, the Norwegian Method consistently overestimates the minimum principal stress, and this discrepancy increases with depth. This overestimation could lead to critical consequences, such as structural failure if the tunnel is left unlined. Interestingly, we observed that increasing the tunnel diameter (from 5 m to 10 m) did not significantly affect the estimated minimum principal stress. Several factors may explain this:

1.       Excavation Geometry: Both cases used circular tunnel shapes, maintaining a constant width-to-height ratio. For non-circular shapes, differences could be more pronounced.

2.       Hydrostatic Stress Assumption: A uniform initial stress field combined with symmetrical tunnel geometry results in consistent stress redistribution regardless of tunnel size.

3.       Continuum Model: The numerical model does not account for discontinuities or jointed rock mass behaviour, which can have a major influence in real-world scenarios.

That said, increasing tunnel size does impact the extent of the crushed (or yield) zone around the tunnel perimeter, even under hydrostatic conditions. Additionally, the risk of progressive failure is notably higher in larger tunnels, especially if local weaknesses exist or anisotropic conditions are introduced.

What Happens If There’s a Weak Layer?

Let’s spice things up a bit more by introducing a weak layer into the model. This layer is placed in the middle of the inclined section, with a thickness of 7 m, and is modelled as a sub-horizontal feature, a scenario not uncommon in real projects, especially in sedimentary or structurally complex rock formations.

The material properties used for this weak layer in the model are:

 For consistency, the stress state in this layer follows the same hydrostatic trend as the host rock. This helps isolate the effect of the weak layer without introducing too many new variables.

So, what happened?

The results clearly show a significant increase in the extent of the yielded (crushed) zone around the tunnel in the weak layer. That’s a big deal.

Why? Because this zone can easily become a preferred path for pressurized water to escape into the surrounding rock mass. And if this water reaches the slope face, things can go south quickly, slope instability, or even landslides, are very real possibilities.

The graph below highlights a noticeable jump in the minimum principal stress near the weak layer, yet even with this jump, the stress remains well below what’s predicted by the classic minimum cover method. This reinforces how overly simplified that method can be.

Final Takeaways

• Traditional methods like the Norwegian Cover Rule offer simplicity, but can severely underestimate risks, especially at depth or in weak ground.
•    Numerical models reveal that excavation size, stress regime, and geological weaknesses significantly impact lining needs.
• A conservative assumption early on may prevent costly failure during construction, but over-conservatism can inflate budgets unnecessarily.
• Future analyses with discontinuum modelling (e.g., 3DEC) will help capture the effect of structural weaknesses more accurately.

What’s next?

In the next post, I’ll take things further by modelling the same setup in a discontinuum-based software (3DEC). I’ll introduce bedding parting planes and explore how discontinuities influence the lined vs unlined tunnel decision under pressure tunnel conditions.