Transport Properties of Concrete (eBook)

Measurements and Applications

Peter A. Claisse (Autor)

eBook Download: PDF | EPUB

2014 | 1. Auflage
312 Seiten
Elsevier Science (Verlag)
978-1-78242-319-5 (ISBN)

Infos

Transport Properties of Concrete covers how to measure the ability of ions and fluids to move through concrete material, and how to use the results to model performance. These transport properties largely determine the durability of concrete and of steel embedded within it, as well as the effectiveness of structures such as landfill containment barriers. The book begins by explaining in detail what transport properties are and how to write computer models for transport processes. Early chapters present and explain computer models written in basic code. Coverage then proceeds to a wide range of tests for the transport properties of concrete, and methods for calculating the values for these properties from the test results using analytical and numerical models. The final chapters then show how the values obtained can be used to predict the durability of reinforced concrete, to model the effect of gas pressure, and to model waste containment structures. A number of practical examples are given, in which the calculations and computer models have been applied to real experimental data. Transport Properties of Concrete provides a comprehensive examination of the subject, and will be of use to all concerned with the durability and effectiveness of concrete structures. - Provides a detailed understanding of the various transport mechanisms that take place during testing in concrete - Shows how to obtain fundamental transport properties

Peter A. Claisse is Professor Emeritus at Coventry University and the author of more than 100 publications on construction and materials, including the Woodhead title Transport Properties of Concrete: Measurements and Applications. He graduated with a degree in Physics from Oxford University and then spent the next 9 years working as a Civil Engineer on major UK construction sites including 4 years on the Torness nuclear power station.?After obtaining a PhD in Civil Engineering at Leeds University, studying Silica Fume in concrete, he then went to the AEA Technology Harwell laboratory for 3 years to work on Nuclear waste containment.?He was at Coventry University for 20 years, teaching Civil Engineering Materials and researching transport processes in concrete and the use of secondary materials in cement.

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2

Computer models to predict the transport processes in concrete

Abstract:

In this chapter, the basic methods used to develop computer models are explained by considering an example. It is shown that the models use the simple equations given in Chapter 1 rather than their integrated forms. A model for pressure-driven flow and diffusion through a waste containment barrier is considered. The lines of code correspond exactly to the equations that are being applied and the key equations and their corresponding code are discussed. Example calculations from the model are presented which show the key influence of adsorption on transport.

Key words

permeability; diffusion; computer model; finite difference; finite step

2.1 Introduction

Having defined the basic physical equations in Chapter 1, there are two possible ways to make use of them: they may be integrated either analytically or numerically. Both approaches are used in different chapters of this book. In this chapter, a simple approach to numerical integration using BASIC computer code is described. This numerical integration may also be described as finite step modelling. The computer modelling was carried out using code written in Visual Basic running as a macro in Microsoft Excel on a standard desktop computer.

There are many different software packages available which can be used for modelling of this type. However, the author is not aware of any that can model the particular complexities that arise in the transport processes in concrete. In particular for the electromigration model, which is used in several of the later chapters of this book, there do not appear to be any packages that can adequately account for charge conservation. Also when considering pressure-driven flow combined with diffusion in a multilayer containment barrier, no packages were found that could be used for modelling. It must also be observed that a simple model for, say, pressure-driven flow combined with diffusion can be written in a few hours and will run on any computer with Microsoft Excel without the need to locate and purchase a package. The main limitation of this type of programme is that it is one-dimensional and can only model situations in which the flow is linear or there is, for example, circular, cylindrical or spherical symmetry.

To give an example of how the code can be written, combined pressure-driven flow and diffusion through a barrier is considered. The use of this particular model is described in Chapter 15 which also explains the purpose of the three layers. The same programme was used to analyse the three-layer barriers used in the site trials and the single-layer samples tested in the laboratory.

The structure of the programme is shown in Fig. 2.1; it loops through the sample in time and space. Examples of the code are discussed in Section 2.2.

2.1 Block diagram of the computer code.

2.2 Expressing the basic equations as computer code

2.2.1 Input data

The barrier is constructed with up to three layers. Each layer is characterised with parameters as follows. For any layer j:

layer thickness = xj

capacity factor = αj

permeability = kj

intrinsic diffusion coefficient = Dj

porosity = εj

Within the programme, each layer is divided vertically into a large number of cells. The calculation is carried out for a unit cross-sectional area (1 m2) so the cell volumes are numerically equal to their thicknesses.

2.2.2 Code example 1: calculation of Darcy velocity

The computer code is complicated by the fact that this code was written for a multi-layer barrier. The Darcy velocity is calculated as follows:

=k1×(h+x1+x2+x3)x1+(x2×k1k2)+(x3×k1k3) [2.1]

[2.1]

where h is the total height of the water column on the sample which is added to the height (thickness) of the sample itself if the flow through it is vertical, but not if it is horizontal (as in lab tests).

The variables are expressed in the computer code as follows:

k1

PERM (1)

element 1 in an array of permeabilities

H + x1 + x2 + x3

tHeight

the total height (thickness) of the barrier

x1

THICK (1)

the thickness of layer 1

Thus the code for equation (2.1) becomes:

V = PERM (1) * (tHeight) / (THICK (1) = (THICK (2) * PERM (l) / PERM (2)) + (THICK (3) * PERM (l) / PERM (3))) [Code example 1]

2.2.3 Code example 2: updating input to cell

The sample is divided up into cells as shown in Fig. 2.2, where cin and cout are the total flows due to pressure-driven flow during the time step and din and dout are the flows for diffusion. As the programme moves to consider the next cell, the flow out of the previous one becomes the flow into the next. The code for this is:

cin = cout

din = dout [Code example 2]

2.2 Schematic diagram of programme for cell i.

2.2.4 Code example 3: advection and diffusion calculation

Advection calculation

The advection from cell i to cell i + 1 during a single time step dt is calculated as:

×dt=dt×V×Cli [2.2]

[2.2]

The variable dt is expressed as dtd in the code so it becomes:

cout = V * dtd * CL (I) [Code example 3a]

where:

CL (I) = Cli, the concentration in the liquid in cell i

V is the Darcy velocity of the flow and

dtd is the time step.

Diffusion calculation

The cells may be in different layers of the barrier with different porosities, diffusion coefficients and cell thicknesses. The formula assumes that cell sizes have been set so all cells are entirely in a single layer and thus do not have a layer boundary in them.

The diffusion from cell i to cell i + 1 during a single time step dt is calculated as:

dt=dtC1i−C1(i+1)(Cti(2Diεi)+Cti+1(2Di+1εi+1)) [2.3]

[2.3]

where Cti is the cell thickness.

For the code, clayer is the layer in which the current cell (I) is located and nlayer is the layer in which the next cell (I + 1) is located. IDIF (clayer), POR (clayer) and CTHICK (clayer) are the intrinsic diffusion coefficient, porosity and cell thickness for the layer in which the cell I is located. The code for equation (2.3) therefore becomes:

dout = dtd * (CL (I) = CL (I + l)) / ((CTHICK (clayer) / (2 * IDIF (clayer) * POR (clayer))) = (CTHICK (nlayer) / (2 * IDIF (nlayer) * POR (nlayer)))) [Code example 3b]

For the upper and lower cells (numbers 1 and n), the diffusion is doubled because the diffusion path to the centre of the cell only runs through half the distance of solid.

2.2.5 Code example 4: calculating change in contents of cell

change (I) is the change in concentration in cell (I) during the single time step. Thus the code is:

change (I) = (din − dout + cin − cout) / CTHICK (clayer) [Code example 4]

Where CTHICK (clayer) is the cell thickness in the layer in which the cell is located and is equal to the volume because a unit cross-sectional area is considered.

2.2.6 Code example 5: updating concentration in cell

The total concentration Cs in cell (I) is CS (I) and is increased by change (I). The concentration C1 in the liquid CL (I) is then calculated using the capacity factor α, CAP (clayer). Thus the code is:

CS (I) = CS (I) + change (I)

CL (I) = CS (I) / CAP (clayer) [Code example 5]

A few additional lines of code (probably in a subroutine) could be used for a non-linear adsorption isotherm (i.e. α varying with concentration).

2.3 Other elements of the code

2.3.1 Checking the code

Transport by advection alone reaches a steady state when the concentration throughout the barrier si = the concentration above it s0. Thus:

=V×Cs0 [2.4]

[2.4]

Transport by diffusion alone reaches a steady state when there is a linear concentration gradient through the barrier. The flux is given by:

=C10(x1D1×ε1)+(x2D2×ε2)+(x3D3×ε3) [2.5]

[2.5]

These values are calculated at the start of the programme and can be used for...

Produkt-Details

• Erscheint lt. Verlag: 9.5.2014
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
• Themenwelt: Technik ► Architektur
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 1-78242-319-2 / 1782423192
• ISBN-13: 978-1-78242-319-5 / 9781782423195