A very simple sounding, but usually not that straightforward problem tunnel engineers face at the very beginning of the design procedure is:

What shape and size should the tunnel profile be?

The cross-sectional geometry, i.e., the profile of a tunnel can be the function of several circumstances, such as:

• Ground environment

• Type of required/preferred support system
• Excavation methodology
• Structural considerations
• Technical capabilities on site
• Internal space requirements (spaceproofing)

Certainly, there are construction methodologies where the shape and size is given (i.e. TBM tunnels, jacked tunnels, precast and submerged tunnels etc.).

Mined tunnels however can have all different shapes and sizes and it can also vary along the same tunnel alignment.

There’s no debate about that the ideal cross-sectional geometry for a tunnel is a circle, where the evolution of the arching effect in the surrounding ground is the most substantial. However, in reality, a mined tunnel is almost never a circle for practical reasons, although designers try to make it as close to it as possible.

What does this mean?

It means, that the curves (assume arcs and straight lines) that make up of the perimeter of the tunnel, need to be transitioned into each other in a way, that is the least disturbing for the continuity of the perimeter, thus the most beneficial for the stability of the surrounding ground, and the tunnel lining. Such transition is a tangential connection. This essentially means that the attaching curves should meet at a point where their tangent is the same (see Figure 2).

Where two curves connect to each other in an angle, stress accumulation happens (see Figure 2/b), therefore it should be avoided. This usually means development of increased bending moment or shear force in the lining, interruption in the arching effect, and shear stress buildup in the ground.

Our main goal is to transform the vertical and horizontal ground stress components into the combination of compressive tangential stresses in the ground, and compressive axial forces in the lining. We should avoid ‘broken’ lines in the profile geometry.

Because how gravity works, at least the middle and top parts of a tunnel usually comply with this rule. On the other hand, where we expect the lining to withstand large hydrostatic (undrained tunnels) or earth pressures, the invert part of the tunnel can also be designed as curved to increase stability.

Where the design intentionally introduces ‘corners’ into the profile geometry, those locations are usually considered as hinges in the structural calculations, where no bending moment can be transferred.

Sometimes the tunnel is not designed to withstand water pressure around its full perimeter (drained tunnel), and no invert lining is required. Tangential continuity in this case is not always required (see table of typical mined tunnel types in Figure 4).

To summarize the above, the general rule is:

The closer the shape of a hole in the ground is to a circle, the more stable the ground around it becomes.

Also, due to economic reasons, the cross-sectional area of the profile is aimed to be as small as possible (the less amount excavated, the cheaper it is), by providing the absolute minimum required space for the internal functions of the tunnel.

So, this is how shape and size come together and provide the requirements for the actual geometry.

Now, that we understand the driving principles, let’s have a look at how this works in reality.

In many cases, some properties of the tunnel profile are given, such as:

• Height
• Height from the knees
• Width at tunnel axis
• Width at invert
• Cross sectional area
• Radius of crown arc
• Or the combination of the above

In order to examine the possible scenarios, and the theory behind their solution, we will consider the following profile types, which typically are applied for mined tunnels: