Si Shen is leader of the tunnelling and geotechnics team for TYPSA in the UK and Ireland. He has worked on major projects in the UK such as HS2, the Thames Tideway and Crossrail projects in London, and internationally on Brisbane’s Cross River Rail. On these major projects, he has led or participated in the design of many shaft structures with either flat or domed base slabs.

Building upon those experiences, Shen put the spotlight on the how base slab geometry is chosen, notably the choice between flat and domed shapes. In presenting the BTSYM lecture, he looks at the principles and forces involved, the materials and design, and the construction challenges.

INTRODUCTION

Shen began by explaining that the presentation was primarily intended for young members of the tunnelling industry and, therefore, overly complicated technical terms would be avoided where possible. The key would be to understand the content and absorb a range of knowledge to then hold a framework of understanding that is not available in textbooks about looking at the choices between flat and domed base slabs.

He covered the common points that must be considered for both flat and domed base slabs and then the pros and cons for the two options.

He said: “Whichever your preference is, I’d like you to keep an open mind between the two options, because each of them has its place in certain situations.”

To follow his overview of questions about shaft geometry, Shen said details on specific points could be followed up by examining standards and textbooks.

LOADING CONDITIONS

In discussing the loading conditions, Shen said the loading on base slabs is mainly from groundwater, the shaft being like a submerged vessel; buoyancy will press with an upwards force on the underside of the base slab.

Depending on the ground condition, there may be some heave as well, he added. Heave, in simple terms, he continued, is the swelling of the ground and can result from varied causes. In the geology of London, there is mainly consolidation heave which is more pronounced in London Clay and chalk.

In very simple terms, fine grained soil is like a slow-acting sponge – ‘When you are digging out a shaft you are digging out soil and you are unloading the soil underneath”.

When the excavation is done, the soil is unloaded and has a tendency to bounce back, but the presence of groundwater, though, as pore water, has a suction effect that holds back the soil – “but only temporarily.” The pore water will be released gradually, creating a swelling effect of the soil over time.

“But usually, the construction speed is much faster than the speed it is getting released. The base slab will be in there soon enough, before full release happens.” The presence of the base slab, therefore, provides a constraint against the swelling and there will be heaving pressure exerted on the underside of the base slab.

Developing on from loading conditions, Shen addressed key considerations on choices of shaft geometry including structural behaviour, analytical approaches, restrained deformation behaviour, uplift stability, waterproofing, ease of construction, and safety of construction.

STRUCTURAL BEHAVIOUR

The structural behaviour of a flat base slab is relatively easy to understand. Shen said. When loaded, the shear capacity of the slab is mobilised, converting vertical loadings into horizontal stress flows, whereby flexural capacity is generated to resist vertical loadings.

Shen said: “Berar in mind, that when the slab gets really thick, as when the aspect ratio (depth compared to width or length) gets really low, it will start to mobilise more of arching rather than shear behaviour.” He added that when a slab is really thick it may be more appropriate to model it as ‘strut and tie’.

Domes are famous for creating large span column-less structures and have been used throughout human history. They can also be commonly found in tunnel structures, Shen said – the shaft base slab but also tunnel headwalls, especially in sprayed concrete lined tunnels, and in large caverns.

In terms of structural behaviour, he added, domes can be thought of as myriad different arches combined and then, when pressed, will tend to crack around the perimeters – almost as if to split the curved form of the dome into individual arches.

In general, when subject to vertical loadings, a normally oriented dome such as for a building roof is in compression in the meridian (the up and down, or radial) direction – like longitudinal lines of the Earth. In the hoop direction (like latitude lines, or circles), the upper and centre parts of the dome are in compression whereas in the lower parts along the perimeter there is a tension band, he explained.

However, there are a number of major factors that influence dome behaviour significantly:

  • Loading direction – if the loadings are not vertical but perpendicular to the dome surface, the tension band will be greatly reduced
  • Dome geometry – If the geometry is not a half circle (hemisphere) but flatter, the tension will be greater
  • Boundary condition – if the dome is laterally restrained at the support, the tension will be reduced. Soil support or pressure plus connection of the slab to a shaft wall lining are further challenges in studying the nature and degree of restraints.

In terms of the use of a dome shape for shaft base slabs, there are a number of distinctive points of consideration:

  • Concrete is the material to use by default. The simulation of direct tension of concrete can be complicated
  • Water resistance is normally required for underground Structures
  • How to simulate the support to the dome from the ground – springed support can normally provide a reasonably accurate simulation of ground support

SIMULATION OF AXIAL TENSION OF CONCRETE

It is particularly challenging to analyse reinforced concrete in axial tension, said Shen. Typical locations underground where axial tension is found include tunnel junctions, shaft openings and headwalls, said Shen.

From a shaft to a horizontal tunnel opening, there will be axial tension along two sides of the opening in the vertical direction, he added; where a horizontal tunnel leads to another tunnel, there will be horizontal tensile forces at the top and bottom of the opening; and, at a headwall, because it is a dome, there is a tension band around the perimeter.

Reinforced concrete cracks in tension, after which its stiffness substantially reduces. The cracked behaviour of reinforced concrete can be explained with a concept called ‘tension stiffening’, which means:

  • Concrete itself has almost zero axial stiffness in tension once cracked
  • Stiffness of the rebars remain fully
  • Some concrete still bonds to rebars after cracking
  • Composite stiffness of reinforced concrete is to be calculated as a value somewhere between zero and full.

Given the tension stiffening effect, commonly used analytical approaches of concrete in axial tension include:

  • Linear elastic – this approach does not take cracking of the concrete into account and can grossly overestimate the amount of tension.
  • Linear elastic with artificially reduced stiffness – this approach artificially reduces the stiffness of concrete within the anticipated tension area, in order to reduce the level of conservatism compared to the method above. It is another simplistic approach and the reduction is the ‘tension stiffening’ referred to i.e., about finding the right stiffness for cracked concrete.
  • Elastoplastic (Linear with yielding criteria) – this approach effectively puts a cap on the maximum amount to tension an element is able to take. Once tension reaches the cap, the effective stiffness of the element reduces to zero.
  • Non-linear elastic – this an advanced approach that accounts for the change in stiffness in accordance with the level of strain. This will be discussed in further details below.
  • Other more sophisticated approaches have been adopted or proposed in various situations but are not common in current practice

‘FULL’ STRESS-STRAIN RELATIONSHIP OF CONCRETE

Eurocode 2 provides three different models of the concrete stress-strain behaviour, with increasing sophistication and degree of matching to the ‘real’ behaviour of concrete based on testing results. The stress-strain relationship of concrete is naturally non-linear. However, there is a very important aspect to these stress-strain curves that is often overlooked. That is that all of the stress-strain curves of concrete are only for concrete in compression – none describes what happens for concrete in tension.

Adding the tension side into the diagram, the ‘full’ stress-strain relationship of concrete can be considered.

Firstly, unreinforced concrete is a brittle material. The stress-strain relationship is linear but the tensile capacity is very low. Once the applied tensile stress exceeds the tensile stress capacity, the plain concrete will simply snap and its stiffness will drastically reduce to zero as the material will break into pieces.

However, in the case of reinforced concrete, the behaviour is much more ductile (hence a primary reason for having reinforcement in concrete). As soon as the tensile capacity of the reinforced concrete is exceeded, the cracks will be captured and bridged by reinforcement.

The reinforced concrete develops micro cracks at first and as strain increases develops the first major crack at certain strain. At this point, Shen said, the stiffness “falls off a cliff” but the trend gets intercepted by reinforcement, resulting in the ‘tension stiffening’ effect. The reinforced concrete then behaves at a reduced stiffness for certain further strain before another major crack develops.

The stiffness reductions continue, in steps, each time with strain picked up again by the reinforcement. This cyclic reduction of stiffness continues until the concrete is completely destroyed and what’s left in action is only reinforcement. The ultimate failure is the yield of reinforcement.

Model Code 2010 – “a very useful document, which I recommend to read by all interested in concrete” – simplifies the stated cyclic tensile behaviour of concrete into a bi-linear relationship. This relationship also correlates tensile strain (from analysis) and crack width (for design), which is a very useful feature to ensure compliance with design requirements, especially related to water tightness.

“Furthermore, we should not forget that reinforced concrete is naturally a composite material,” added Shen. Its stiffness should be a combination between concrete and reinforcement.

Crack control of concrete is a very important subject for underground structures, because it is a way of providing water resistance and is “usually quite challenging,” said Shen.

“Whenever we design deep basement, tube stations or shafts, water tightness is usually a key design requirement, because water either leaves a stain or compromises functionality of the structure,” he added.

WATER RESISTANCE OF UNDERGROUND STRUCTURES

Crack control of concrete is a very important subject for underground structures, because it is a way of providing water resistance and is “usually quite challenging,” said Shen.

“Whenever we design deep basement, tube stations or shafts, water tightness is usually a key design requirement, because water either leaves a stain or compromises functionality of the structure,” he added.

There are generally speaking three different ways of providing water tightness:

  1. Explicit waterproofing. A double-shell structure is usually provided, including using an intermediate layer of sheet or sprayed membrane. This prevent water from reaching the inner shell. Or a cavity can be provided between the layers to drain away the leaked water.
  2. Seepage prevention by crack-elimination. Concrete is virtually water-proof when it is uncracked and perfectly compacted. However, in practice you can never achieve this. One way to prevent concrete from cracking would be to pre-stress it. But this is normally used for domes or silos above ground and generally not feasible for underground structures. Another approach is to use admixtures to adjust the mix design of the concrete.
  3. Crack self-healing. This is achieved by using reinforcement to control the progression and size of cracking in the concrete, restricting crack widths to very small scale, so that after the crack leaks for a bit, it gets blocked up either by fine particles or chemical reactions. With this approach, a small amount of leakage must be permitted, initially, and the Eurocode has stringent requirements.

Shen said he usually uses EC2-3 supplemented by CIRIA guide C766.

EC2-3 clearly differentiates between two types of cracks – the non through type, which blocks water seepage; and the through type, which is comparatively less restrictive on flow.

For the non through type, this is possible where a structural element is subject to bending, one side in compression and the other side in tension. Cracks open on the tension side but with the other part of the concrete section in compression they do not propagate fully through the entire section. The section is considered water resistant. The limit of crack width for such type is typically 0.3mm for durability reasons.

However, where a concrete section is subject to axial tension, it is a different story, said Shen. The entire section is in tension. The cracks go through the entire section, creating water paths. Therefore the ‘through crack’ condition is a much more unfavourable condition in comparison for underground structures.

For through crack conditions, the Eurocode has a set of very stringent requirement for crack control. The limits are onerous, ranging from 0.05mm to 0.2mm, and the amount of rebar needed to achieve the former is far more than required for the latter. For underground structures at a great depth, cracks may need to be controlled to 0.05mm.

RESTRAINED DEFORMATION CRACKS

Restrained deformation cracking has detailed guidance in CIRIA C766. It used to be called the ‘early age thermal’ cracks. In very simple terms, concrete continues to lose moisture over its life and during this process it shrinks in size, and also expands when curing and cools down after that, during which process it shrinks back, said Shen. Whenever concrete tries to shrink but is prevented from doing so by a restraint, it will crack to relieve the strain. The restraint can come from external sources, such as an adjoining stiff element, or internal sources, which can happen for a thick element.

Flat base slabs tend to be thicker in comparison, which leads to higher risk of restrained deformation cracks and excessive heat release, he added. For infrastructure construction, durability is usually a high requirement, which requires high concrete grade, leading to high cement content and heat release. Therefore, it is desirable to have high percentage of cement replacement, such as pulverised fuel ash (PFA) or ground granulated blast-furnace slag (GGBS) in the mix – this is also desirable from carbon footprint perspective.

PRACTICAL CONSIDERATIONS

From a practical perspective, the following issues should be considered.

  • Application of waterproofing membrane: the flat base slab is typically easier to apply waterproofing membrane, due to its flat substrate. The domed base slab requires more careful planning to avoid wrinkles and creases due to the curved surface.
  • Buoyancy uplift: the flat base slab is usually thicker in comparison, which puts more counterweight in to resist uplift pressure from ground water and heave.
  • Working platform: the flat slab offers a flat working platform whereas the domed slab presents more challenges for plant operations.

For a circular shaft, there are two typical ways of providing base slab reinforcement:

  • Orthogonal reinforcement is relatively ‘conventional’. However, in most cases it needs to be fixed on site. This can be particularly labour intensive and hazardous for large scale shafts
  • Polar reinforcement has a ring of reinforcement around the perimeter whereas the centre piece has orthogonal reinforcement. This arrangement, when combined with a thinner base slab, can help facilitate prefabrication and reduce health and safety hazards on site

CONCLUSION

In summary, the domed base slab generally has the following advantages:

  • Less concrete pour
  • Less excavation
  • Less thermal effect
  • Smaller/lighter rebar cage
  • Option to pre-fab rebar cage

In contrast, the flat base slab generally has the following advantages:

  • No through cracks – better water resistance
  • More counterweight against uplift
  • Flat working surface
  • Simpler details
  • Easier to apply waterproof membrane

Having focused on the loading, analysis and design considerations for the different types of shaft base geometry, Shen then finished his lecture with a brief spotlight, with images and photos, related to shafts on projects in London, such as a flat base slab for Moorgate station on the Crossrail project, and domed slabs on the Thames Tideway.