1 – Introduction
Requirements for the long-term efficiency and qualitqy of underground structures have increased in recent decades. Today, the standard lifetime requirement of road and rail tunnels is 100 years and in some cases even higher (up to 150 years). This calls for high increased attention to the durability of the whole structure and of each individual element.
This attention also needs to be paid to waterproofing systems, which play an essential role in the durability and quality of the structures, as demonstrated by the very high impact that water inflows have on the damage of linings and infrastructure (Howard, 1991; Sandrone and Labiouse, 2011). This issue is even more relevant when taking into account that in many cases it is impossible or very difficult to repair or replace waterproofing elements once the tunnel is finished because those elements are installed in between the primary and the final lining.
Despite these reasons for interest, there is currently, at the state-of-the-art, a clear lack of knowledge on the long-term performances of waterproofing systems underground.
In the following article, the timedependent degradation of waterproofing geomembranes will be analysed through laboratory tests focused on Plasticised Polyvinyl chloride (PVC-P) geomembranes.
2 – PVC-P Waterproofing Geomembranes degradation
PVC-P geomembranes are one of the more widely-used technologies for waterproofing underground structures, due to their workability and weld-ability. They are recognised as effective systems to achieve the long-term quality and performances required for modern standards (Dammyr et al., 2014). Moreover, these geomembranes are flexible in all but the most extreme jobsite temperatures and consequently easy to adapt to the geometry of the substrate. PVC-P geomembranes, installed in rolls of about 2m, are welded on the job site to act as a barrier to water between the primary and final lining. The base of the waterproofing system is completed by a regularisation layer at the extrados of the geomembrane, in order to protect it from damage from the substrate (Luciani et al., 2018). More advanced layouts have additional PVC layers for protection at the intrados, double waterproofing geomembranes and injection hoses. These further protect the PVC-P geomembrane from accidental damage, increase the effectiveness of the system and allow the repair of water leakage by injections, without damaging the lining and with lower times and costs (Luciani and Peila, 2019).
Two types of PVC-P geomembranes are used in underground: translucent and coloured. The former guarantees the purity of the material (due to the absence of pigments and fillers) and permits a worker to visually check the welding and for the presence of burnt material (Mahuet, 1984). Conversely, coloured geomembranes allow the detection of damage to the surface through the use of the signal layer, i.e., the membrane is composed of two layers of different colours and therefore, if the surface is damaged (due to a dropped tool or rebar installation) the back colour shows through and allows timely repair work before casting.
In geomembranes, PVC resin is used in combination with additives: plasticisers, fillers, stabilisers, pigments and others. The most important of the additives, and the most relevant in terms of quantity is plasticisers. This is a family of different polymers used to change the mechanical behaviour of the resin from a rigid material to one that is rubber-like (Hsuan et al., 2008; Wypych, 2015). Plasticisers in PVC-P geomembranes account for about 25-35% of the weight. It is not chemically bonded to the PVC chains and thus it can migrate outside the membrane.
This is one of the main phenomena affecting long-term behaviour of geomembranes. Its rate depends on temperature, environmental conditions, plasticiser concentration and plasticiser type (Storey, Mauritz and Cox, 1989). Other degradation phenomena, e.g., photo-oxidation, thermaloxidation, biological attack) are usually not relevant in underground applications.
3 Plasticiser loss estimation
The study of long-term plasticiser loss is usually done by accelerated ageing tests because the process is very slow, and data coming from natural ageing after 30-40 years are seldom available (Usman and Galler, 2014; Maehner, Peter and Sauerlaender, 2018) while data for longer times do not yet exist. Tests are performed at higher temperatures to accelerate plasticiser loss and then the results are projected to the long-time using the Arrhenius equation (Hsuan et al., 2008). Several tests have been proposed to simulate different ageing conditions and Luciani (2019) developed a test device specifically designed to reproduce tunnel waterproofing conditions.
However, a different approach can be used to analyse this issue focusing on the physical mechanism occurring: plasticiser loss is a diffusion problem and can be therefore analysed using Fick’s law.
This law, with the correct boundary and initial conditions, can be used to analyse the concentration of plasticiser at each point of the geomembrane at each time. The ruling parameter is the diffusion coefficient D, that describes on a macroscopic scale all the chemical and physical forces slowing down the diffusion. Diffusion coefficient is in many cases considered a constant, but in the specific case of polymers it is a function of temperature, plasticiser type and concentration of the plasticiser.
The conditions to be used to integrate Fick’s equation for geomembranes are: monodimensional flux (the thickness is much smaller than the other directions), initial uniform concentration in the geomembrane, concentration outside the geomembrane always equal to 0 and no flux on the intrados surface, where the absence of water or air circulation inhibits plasticiser removal.
4 Plasticiser absorption test
4.1 Test procedure
The diffusion coefficient of plasticiser can be evaluated through plasticiser absorption tests. Small specimens of geomembrane of regular and known surface are cut with a metallic hollow cutter, cleaned on the surface, dried in a desiccator and weighted. Then the specimens are totally immersed in a tank filled with plasticiser and the increase in weight with time is measured. From the rate of weight increase the diffusion coefficient can be computed (Griffiths, Krikor and Park, 1984; Storey, Mauritz and Cox, 1989).
The procedure has been repeated with the plasticiser kept at four different temperatures: 20°C, 45°C, 60°C and 75°C.
4.2 Tested materials
Two commercial PVC-P geomembranes produced by Mapei have been tested:
- a 2mm coloured geomembrane, with calcium carbonate filler and an initial plasticiser content of 24.0% in weight;
- a 2mm translucent geomembrane, without filler and with an initial plasticiser content of 26.7% in weight.
Furthermore, in order to analyse the effect of plasticiser concentration on plasticiser loss, eight specifically designed and produced formulations have been studied (Table 1). These materials have four different plasticiser concentrations and are both with and without filler. The plasticiser used to produce all of the materials is the same, and it is the one used in the absorption tests.
4.3 Results
Tests on the same material at different temperatures show that the diffusion coefficient variation with temperature T can be described by the Arrhenius equation as:
D = D0e -E/RT where D0 is a constant, E the activation energy and R the gas constant. As expected, higher temperatures call for higher diffusion coefficients.
From the analysis of the tests performed on the tailor-made materials, the law correlating plasticiser concentration CP in the geomembrane and diffusion coefficient has been obtained as:
D = D1CPb where D1 and b are constants. This equation shows that, as the plasticiser is lost and its concentration in the geomembrane reduces, the diffusion coefficient reduces. The reduction of diffusion coefficient is explained by the internal interaction among PVC chains and plasticiser: as plasticiser concentration reduces, PVC-P resin becomes stiffer and therefore it is harder to the remaining plasticiser molecules to move inside the membrane. This means that the rate of diffusion slows down with time. This is a crucial aspect because it assesses that Arrhenius’s extrapolation commonly used is too conservative since it hypothesises a constant reaction rate. Conversely, the reaction rate reduces with time both due to the reduction of gradient of concentration of plasticiser inside and outside the material and due to the reduction of diffusion coefficient.
5 Discussion
5.1 Long-term extrapolation
Known the diffusion coefficient and its dependence on temperature and plasticiser concentration, plasticiser loss can be evaluated along time using Fick’s law in different conditions. Comparing the results obtained from plasticiser absorption tests with accelerated ageing tests on the same materials, the former give higher plasticiser loss (Luciani, 2019). This is due to the fact that plasticiser absorption tests are performed in laboratory conditions on perfectly clean and dry specimens, that is not the real condition on the job site, where the presence of moist and dirt surface reduces the plasticiser migration. The few cases of naturally aged materials reported in literature (Usman and Galler, 2014; Maehner, Peter and Sauerlaender, 2018) confirm that plasticiser absorption tests partially overestimate the plasticiser loss and can be therefore considered as an upper limit of the possible loss.
In order to assess the end-of-life time of a geomembrane a threshold value has to be defined. It is commonly used, in the absence of other data the value of 0.5 plasticiser loss ratio, while Luciani (2019), on the basis of mechanical properties of the studied PVC-P geomembranes, suggests a conservative value of 0.45.
Figure 5 shows the loss of plasticiser with time evaluated at a job site temperature of 15°C (that is a typical temperature for urban tunnels). Both the studied commercial geomembranes are within the threshold value after 100 years, proofing that the loss of plasticiser is not enough in this time span to damage the PVC-P geomembrane. The geomembrane without filler behaves better showing a very low plasticiser loss.
5.2 Effect of thickness of the geomembrane
Since the diffusion coefficient is not influenced by the thickness of the geomembrane, the same method can be used to analyse the effect of thickness on the plasticiser loss.
As an example, Figure 6 shows the long-term plasticiser loss ratio of the membrane with filler at 15°C for different thicknesses. With the increase of thickness, the effect of the degradation reduces, however, the variation is not constant: it is relevant from 1 mm to 2 mm while it is quite negligible from 2 mm to 3 mm.
Since the standard minimum thickness required for geomembranes is 2 mm, increase the thickness is not much effective in terms of slowing plasticiser loss. However, the increase in thickness has great impact in reducing the probability of damage of the geomembranes due to punctual loads during installation.
6. Conclusion
The performed tests allowed the evaluation of the long-term degradation behaviour of PVC-P waterproofing geomembranes. The two studied commercial geomembranes are still effective after 100 years and therefore fulfil modern requirements for underground structures. Geomembranes without filler show lower plasticiser loss with time. An increase in the thickness of a geomembrane has an effective impact on durability for very small dimensions, while for geomembranes between 2mm and 3mm, there is a far smaller variation in durability.
