Subject matter

As early as in 1958, Verbeck mentioned that H₂O and CO₂ Gas Diffusion in Porous media was (GDP) a key physical process of concrete carbonation; 10 years later Hamada proved the diffusive nature of the carbonation of concrete by identifying the square root of time behavior of the “depth of neutralization”. 60 years later, different methods for measuring gas diffusion coefficient of cementitious materials have been developed but no technical consensus exists on those methods. This RILEM TC GDP would like to provide an overview of the available gas diffusion methods for building materials along with their pitfalls, benefits and drawbacks by a group of international experts.

The gas diffusion coefficient is a general indicator of the resistance to gas transfer of a given microstructure of a porous media. It is also a specific durability indicator of cement based materials. The TC would focus on reviewing the literature, benchmarking test methods on both reference inert materials and cementitious materials over a large range of gas diffusion coefficients ([10^-11, 10^-6] m².s^-1). The group would also focus on calculation method to analyze experimental results, on the evaluation of sources of uncertainty from the procedure, the diffusion cell design or the materials themselves, such as geometries or conditioning.

It is beyond the scope of this group to correlate the results of this test method to the results of actual durability performance of cementitious materials, such as carbonation depth in natural or accelerated conditions. Nevertheless, the field of application of the method will be included in the state of the art review.

Terms of reference

The activity of the TC is planned for three years as the objective is focused on building a consensus on gas diffusion test method by comparing testing principles, by quantifying uncertainties and by simulating tests with numerical models. First a state of the art report based on published literature will be issued on gas diffusivity in porous media, looking at the physics at play, the testing methods, range of values for building materials and usage of values for evaluating material performance. Not many labs are currently equipped with gas diffusion test methods. Therefore a benchmark of methods on reference inert materials and non-ageing cementitious materials is proposed. In the future, gas diffusion could be used as specific indicator of building material performance. The results of this TC will deliver experimental evidence and state of knowledge useful for the definition of future standards.

Confirmed partners are coming from 6 countries (France, Greece, Spain, Switzerland, UK and USA) and prospective partners have been identified in China, India, Hong Kong and Japan.

Detailed working programme

The working programme is organised in six tasks. After a joined effort of the TC GDP on literature review, the other 5 tasks can run for the most part in parallel until completion.

4.1. State of the art

Collecting information on existing gas diffusion tests is a key task. Thus, the first efforts of the TC will focus on a state of the art review. Although a rich literature on gas diffusion in porous materials existed in the 20th century and before, gas diffusion tests for cementitious materials were developed only from the 1970’s.

To our knowledge, the work of C.D. Lawrence was one of the forerunners and remains today the most cited. C.D. Lawrence designed a diffusion test whose principle is still used. This test consists in submitting both opposite sides of a specimen to two flowing gas streams. The gas diffusion coefficient is then deduced from the First Fick Law, when a steady state regime is reached. Another testing procedure consists in measuring the time-evolution of gas concentration at the downstream side of a specimen, while the gas concentration is maintained constant at the upstream side. The diffusion coefficient is calculated using the Second Fick Law from the obtained accumulation curve. In addition to these methods (steady state flux / accumulation), other test principles can be found in literature. For each procedure, benefits and drawbacks will be listed.

Beyond the compilation of diffusion tests designed for cementitious materials, the state of the art review will cover the gas diffusion phenomenon in porous solids. In particular, the following topics will be addressed:

• prevalence of diffusion mechanisms (Knudsen or molecular diffusion);
• effect of pressure and temperature on gas diffusion;
• conversion of gas diffusivity from species A to species B;
• physical sorption of diffusing species on cement matrix;
• effect of internal RH, phase assemblage and microstructure on gas diffusion;
• comparison of gas permeation and gas diffusion.

Applications of gas diffusion tests will be also addressed in the literature review. In the scope of academic research, gas diffusion could be used to enhance the understanding of microstructure of cement based materials. For engineering applications, gas diffusion coefficient could be a relevant durability indicator, for instance in a performance based-approach of the design of reinforced concrete structures. Modelling is the main tool to predict the service life duration of concrete structures. Examples of use of gas diffusion coefficient in analytical and numerical modelling will be provided.

4.2. Benchmark of existing methods on materials

Benchmarking exercises will be organized to compare the various gas diffusion methods used by the members of the TC group. First, reference dried specimens made with inert or non ageing materials will be tested by each participant. In particular, this will permit a comparison between transient and steady-state methods of gas diffusion.

Then, brainstorm will be required to define the cement materials which will be tested in a second phase. The main issues are the following: mix composition, drying state, hydration and carbonation state.

Beyond the diffusion tests with “usual” gas such as O₂, diffusion tests will be also carried with reactive gas, such as CO₂ or water vapor. For the latter, tests could be carried with the cup-test method. This will allow comparing gas diffusion coefficient and vapor permeability in dry conditions

4.3. Gas diffusion cells and procedure

Results of gas diffusion test can be affected by any pressure gradient between up and downstream compartment. Thus, works will be conducted to assess the effect of low pressure difference for each test method, resulting from the setup or multi-species diffusion. For that purpose, diffusion cells could be modified and pressure sensors could be installed if necessary. In the same manner, RH control probes could be installed in the diffusion cells, in order to investigate the influence of RH on diffusion.

4.4. Specifications of samples and materials

This task will include the following topics:

• effect of drying on diffusion coefficient and role of isotherm hysteresis;
• reactivity of the cement matrix with diffusing gas species;
• choice and calculation of the representative elementary volume with respect to specimen size;
• specimen geometry.

4.5. Uncertainties: ranking and evaluation of possible sources

Reliable tests require a knowledge of uncertainties. Among the uncertainties sources, the following will be assessed:

• pressure gradient;
• material variability;
• lateral leakage (in the case of 1D test);
• uniformity of water saturation degree within the specimen after a preconditioning period;
• comparison of 1D and 2D numerical of diffusion test (for instance, to assess the effect of sealing problem).

Different methods are considered to evaluate those uncertainties, including the analysis of existing dataset shared by participants and the use of numerical models. For example, the role of pressure or liquid saturation gradient can be investigated with numerical models. Uncertainty evaluation will also rely on experimental data from tasks 4.4 and 4.5. Furthermore, the range of measurement (i.e. upper and lower limits) have to be justified for each method and accompanied with a precision.

4.6. Calculation methods

Results of all existing diffusion tests are used to calculate the effective gas diffusion usually from Fisk’s Laws. This task will focus on different calculation methods of the diffusion coefficient.  Moreover, numerical simulations of the various diffusion tests will be carried out to address the following issues :

• effect of the initial gas concentration in the specimen;
• effect of gravity, gas density or gas homogenization in the downstream compartment;
• choice of approach for gas diffusion modelling (one gas species diffusion or multiple gas species inter-diffusion);
• effect of entry parameters such as porosity, water saturation, reference gas diffusion coefficient;
• need to account for gas equilibrium with pore water for steady state or transient analysis.