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  • Writer's pictureSi Shen

Convergence confinement method (1)

What convergence and what confinement?

Convergence-Confinement is a well-known theory in tunnelling, and widely applicable regardless of the ground condition (for both soil and rock). Convergence refers to the observed tendency of the ground closing into a tunnel after it is dug. Confinement means the ability of the installed support to prevent or limit the closing in of the ground.

In essence, Convergence-Confinement is all about the interaction between the ground and the support (structure) during the sequential construction. Convergence and Confinement are two opposing forces that try to push against each other all the time and reach a final state of equilibrium. When there is strong confinement, the convergence is lower; the later confinement comes into existence, the more convergence there will be.

The basic concept is as simple as this. However, the Convergence-confinement theory extends way beyond it. I plan to use a few blogs to explain the basics of it.

The time-space theory of tunnel convergence

The degree of mobilisation of the ground’s capacity has positive correlation with two factors - space and time:

  • The duration that the ground is left exposed and unsupported. The time gap may come from:

o Physical limitation of how quickly support can be installed and become effective. Very often, the support can only be installed gradually after the excavation has already been done, such as segmental ring tunnel and sprayed concrete lined tunnel.

o Planned or unplanned disruption/pause in construction activities

  • The dimension/distance that the ground is left exposed and unsupported

  • The majority of ground movement comes from a combination of the above two factors (there are other relatively minor factors at play, such as deformation of the support).

What is Convergence-confinement trying to say?

A tunnel excavation should ideally be analysed on a 3 dimensional basis, as stresses in the ground re-distribute by arching around the tunnel face in a dome shape on a 3D basis.

The stress re-distribution follows the following principles:

  • In tunnelling, it is usually the case that excavation has to be made first, before any support/propping to the ground can be installed. This results in unloading of the ground and requires the ground to be self-supporting temporarily.

  • Excavation of the ground breaks the original balance of stress in the ground in the short term. The original ground that perfectly balances the stresses are now gone, creating stress imbalance. The ground will be seeking support automatically to make up the balance. This can be achieved through two means:

1. Utilising the (shear) capacity of the ground itself, by arching and diverting the stresses to adjacent ground

2. The capacity of the man-made structural support, if there is any

o Before installation of support, the ground is self-supporting by mobilising its own capacity. Though using its own capacity, the ground deforms (converges)

o When the ground is soft with insufficient capacity, it will continue to deform over time (particularly noticeable for cohesive soil) until it ultimately fails, or be reinforced by structural supports that come into existence.

  • The more the ground is allowed to move into the excavation (converge), the more capacity of the ground contributes towards the overall balance, thus reducing contribution from the structures. This could be beneficial from a structural design perspective. However, this also results in more ground settlement, which usually has certain acceptance limit in an urban environment.

  • Methods that prevents/limits ground movement into the excavation will prevent/reduce the mobilisation of contribution from the ground capacity, thus increasing contribution from the structure. For example (in theory), a tunnel dug by shielded and pressure balanced tunnelling machines will result in high utilisation of the structural capacity compared to the same tunnel if dug with open face.

Limitations of Convergence-confinement theory

The Convergence-confinement theory is developed based on the following idealisations:

  • Homogenous ground, i.e. there is a single, continuous and consistent lump of ground everywhere, no layers of different ground, no faults.

  • Isotropic stress conditions of a deep tunnel , i.e. stress is same in all directions. K0 equals 1 – this is usually not the case for real soil.

  • Full and open face excavation of a circular tunnel – this is usually not the case for a real tunnel

Although none of the above would be true for a real-life situation, they provide an approximation close enough.

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