This blog is inspired by this article “Simulating composite behaviour in SCL tunnels with sprayed waterproofing membrane interface: A state-of-the-art review”, by Su and Bloodworth. I recommend all tunnel engineers involved with sprayed concrete lining to have a look, as it beautifully summarises the latest practice.
Transverse shear in tunnel waterproofing
A lot of tunnels, especially ones with sprayed concrete lining (my previous blog on sprayed concrete: https://www.si-eng.org/blog/sprayed-concrete), use a ‘double shell’ system – a sprayed primary lining against the ground, followed by a waterproofing layer, followed by sprayed or in-situ secondary lining. The waterproofing layer largely speaking is either sheet membrane or spray-applied. Sheet membrane is used more often, because relatively speaking sprayed waterproofing is typically slower to apply, and when the primary lining leaks, sprayed waterproofing can fail to stick. Nevertheless, sprayed waterproofing is sometimes preferred over for two advantages in practice: (1) no working-at-height required (2) more reliable quality for complex geometry and sharp bends. From the structural perspective, it could bring another benefit – making the primary and secondary linings behave in composite action, or at least more towards it. The concept and benefit of composite structure has been explained in my previous blog – see the link below. The sprayed waterproofing could potentially facilitate the composite action by providing transverse shear capacity – a concept also explained in my previous blog linked below.
Tunnel is a tubular structure subject mainly to radial actions from the ground or groundwater, which converts into circumferential compression due to the arching effect. So tunnel lining is required to resist primarily axial compression. In addition, it is normally required to resist, to certain extent, bending in circumferential direction. The bending comes from asymmetric loadings from the ground (such as when K0 does not equal 1), or eccentricity (due to deformation or construction tolerance).
In tunnel design, the thickness of the tunnel lining is typically governed by the bending resistance rather than the compressive capacity. The utilisation of compressive strength of the tunnel primary lining is usually no more than a quarter of its capacity. Bending resistance is where the value of composite action shines – it can reduce the thickness of tunnel lining.
From a design perspective, if the waterproof layer is considered as a ‘slip membrane’, i.e. no shear transfer with concrete is considered, the two tunnel linings are considered to behave in a ‘combined’ manner. Typically sheet membrane is assumed to behave this way, as sheet membrane is relatively slippery, having negligible friction.
The better the waterproof layer is able to bond with concrete, the more the structural behaviour shifts towards composite manner. This is normally only achievable with sprayed waterproofing.
Achieving full composite behaviour with full bond requires the waterproofing layer, as well as its interface with the concrete, to have at least the same tensile and shear strength as the concrete itself. Simply put, this requires the plastics or rubber stuck to concrete to be as strong as concrete– this is without a doubt as challenging as it sounds.
Can composite action really reduce lining thickness?
Even if composite action can be achieved, it is still limited by a few things to realise its perceived benefit – reduction of lining thickness.
A hurdle to be overcome for the parimary lining:
The purpose of the primary lining is typically intended to provide sufficient structural capacity in the temporary state (also permanent if it is designed to be permanent works), where both the ground and the supporting lining, working as composite materials, deform and settle when an equilibrium is reached. Note that deformation is inevitable, but is a matter of to what extent is acceptable. With specific regard to the deformation, there are usually two requirements: (1) the GEO condition under ultimate limit state requirement of Eurocode 2, which basically means the deformation should be controlled to a degree small enough not to cause collapse of the ground; (2) volume loss (typically applicable for tunnelling in urban environment), which basically means that tunnelling under or adjacent to other assets should not cause excessive ground deformation to damage the assets. The deformation control is especially important for soft ground, and linked with construction sequence and timing. My previous blog on ‘Time-space Effect’ explains this issue:
As you can imagine, there must be a minimum thickness of the primary lining, in order to control volume loss, as the thicker the primary lining is, the stiffer it is, and the less it deforms. So there is a lower bound limit of how much the primary lining thickness can be reduced to.
Two hurdles to be overcome for the secondary lining:
(1) Composite action puts the entire secondary lining in fuller and higher tension, making cracks wider and more visible. Although cracks in the secondary lining are unlikely to be detrimental to the serviceability of the tunnel, as water-tightness is already provided by the waterproof membrane, cracks on the secondary lining is directly visible to people inside the tunnel, creating unpleasantness and anxiety, and in some extreme cases may cause tensile failure (Ultimate Limit State condition).
(2) Shear resistance at the interface will result in restraint to the secondary lining, causing ‘restrained deformation’ cracks (Concrete shrinks/contracts due to thermal or shrinkage effect. see my previous blog https://www.si-eng.org/blog/crack-control-of-concrete-using-reinforcement-to-achieve-water-tightness-2) . When the waterproofing membrane is fully slippery, the secondary lining is free to contract and slide against the primary lining. However, when the transverse shear is in full action due to the bonding of the membrane, tension builds up in the secondary lining when it contracts. I imagine the restraining effect should be more significant in tunnels with large cross sections, as there is less arching effect (which puts more compression in the lining) and the linings behave more akin to flat slabs/beams. This may sometimes require bar reinforcement be used in the secondary lining in order to control the restrained deformation, if the bonding condition of the membrane is too good!
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