A novel framework towards the design of more sustainable concrete infrastructure

Abstract

This study presents a novel framework for the design of reinforced concrete (RC) structures which aims at ensuring that future RC structures have the lowest possible carbon footprint, energy use and impact on the environment. The key focus of the study is on RC structures where there is often a lack of grasp of materials aspects, and environmental aspects of construction. In the proposed framework, a set of quantifiable design parameters and variables (binder type, concrete grade, diffusivity, concrete cover depth, area of steel in the structural component) are selected with respect to a set of performance measures which cover the functionality and availability of the structure to the user during its service life. The outputs generated from the framework are optimised material types and properties which not only meet the design performance requirements but also lead to minimised life-cycle environmental impacts. A RC beam is used to demonstrate the proposed design methodology. The application of the framework for design in the material specifications of the RC beam showed a reduced volume of materials in construction compared to the current materials and structures design practice.

Appendix

1.1 Bending moment constraint

M _Rd is evaluated using simplified design formulations based on the rectangular stress-block. The maximum M _Ed due to g _k and q _k occurs at mid-span of the beam and is given as:

$$M_{\text{Ed}} = \left( {\gamma_{g} g_{k} + \gamma_{q} q_{k} } \right){\raise0.7ex\hbox{${l^{2} }$} \!\mathord{\left/ {\vphantom {{l^{2} } 8}}\right.\kern-0pt} \!\lower0.7ex\hbox{$8$}}$$

(16)

where, γ _g (−) is the partial load factor for the dead load and is given as γ _g  = 1.35, in EN 1992-1-1:2004 [14], γ _q (−) is the partial load factor for the live load and is given as γ _q  = 1.5, in EN 1992-1-1:2004 [14], l (m) is the effective span of the beam.

‘q _k ’ is assumed to be 30 kN/m whereas the dead load, ‘g _k ’, is a variable represented as:

$$g_{\text{k}} = \frac{{\rho_{\text{c}} }}{100}\left( {\frac{b}{1000} \times \frac{h}{1000}} \right)\frac{{\rho_{\text{s}} }}{100}\left( {\frac{{A_{\text{st}} + A_{\text{sc}} }}{1000}} \right)\;{\text{kN}}/{\text{m}} + 60\;{\text{kN}}/{\text{m}}$$

(17)

where, ρ _c (kg/m³) is the density of concrete; ρ _s (kg/m³) is the density of steel; and the other variables are as defined in Fig. 3.

In summary, C₁ is a non-linear limit-state function represented by Eq. (18).

$${\text{C}}_{ 1} \equiv \left[ {\left( {\gamma_{g} g_{k} + \gamma_{q} q_{k} } \right)\frac{{l^{2} }}{8}} \right] - \left[ {0.87A_{\text{st}} f_{\text{ym}} d - 0.67\frac{{A_{\text{st}}^{2} f_{\text{ym}}^{2} }}{{bf_{\text{cm}} }}} \right] \le 0$$

(18)

where, f _cm (MPa) is the design mean strength of concrete and is equal to (f _ck + 8) MPa; f _ym (MPa) is the mean strength of steel and is taken as f _yk; d (mm) is the effective depth of the beam; and the other variables are as defined in Fig. 3 and Eq. (18).

1.2 Maximum and minimum bending reinforcement

$$\begin{gathered} {\text{A}}_{\text{s,min}} = 0.13\;\% \;b\left( {d + \frac{\phi }{2} + x_{\hbox{min} } } \right) \hfill \\ {\text{A}}_{\text{s,max}} = 4\;\% \;b\left( {d + \frac{\phi }{2} + x_{\hbox{min} } } \right) \hfill \\ \end{gathered}$$

(19)

where, the design parameters, b, d, x _min and Ø are as shown in Fig. 3.

A _s,min minimizes thermal and shrinkage cracking whereas A _s,max allows for adequate placing and compaction of concrete around the reinforcement.

1.3 Global warming potential

The global warming potential (GWP) is defined as an index, based upon radiative properties of well-mixed greenhouse gases, measuring the radiative forcing of a unit mass of a given well-mixed greenhouse gas in the present-day atmosphere integrated over a chosen time horizon, relative to that of carbon dioxide. The GWP represents the combined effect of the differing times these gases remain in the atmosphere and their relative effectiveness in absorbing outgoing thermal infrared radiation (IPCC 4th Assessment Report, 2007).

1.4 Design variables

1.4.1 Chloride diffusion coefficient

The chloride diffusion coefficient (D _o) (m²/s) is related to mix design proportions as follows Papadakis et al. [20]

$$D_{o} = 0.15\frac{{1 + \rho_{\text{c}} {\raise0.7ex\hbox{$c$} \!\mathord{\left/ {\vphantom {c w}}\right.\kern-0pt} \!\lower0.7ex\hbox{$w$}}}}{{1 + \rho_{\text{c}} {\raise0.7ex\hbox{$w$} \!\mathord{\left/ {\vphantom {w c}}\right.\kern-0pt} \!\lower0.7ex\hbox{$c$}} + \frac{{\rho_{\text{c}} }}{{\rho_{a} }}{\raise0.7ex\hbox{$a$} \!\mathord{\left/ {\vphantom {a c}}\right.\kern-0pt} \!\lower0.7ex\hbox{$c$}}}}\left( {\frac{{\rho_{\text{c}} {\raise0.7ex\hbox{$w$} \!\mathord{\left/ {\vphantom {w c}}\right.\kern-0pt} \!\lower0.7ex\hbox{$c$}} - 0.85}}{{1 + \rho_{\text{c}} {\raise0.7ex\hbox{$w$} \!\mathord{\left/ {\vphantom {w c}}\right.\kern-0pt} \!\lower0.7ex\hbox{$c$}}}}} \right)^{3} D{}_{{{\text{H}}_{ 2} {\text{O}}}}$$

(20)

where, w (kg) is the water content, c (kg) is the cement content, a (kg) is the aggregate content, ρ _c (kg/m³) is the density of cement, ρ _a (kg/m³) is the density of aggregates, $D{}_{{{\text{H}}_{ 2} {\text{O}}}}$ is the (m²/s) diffusion coefficient in an ionic solution of 0.5 M NaCl and is equal to 1.6 × 10⁻⁹ m²/s (50,458 mm²/year).

Equation (20) was selected for this study to predict the chloride diffusion coefficient in concrete as it accounts for the concrete mix proportions (aggregate-to-cement ratio; water-to-cement ratio and mass densities of cement and aggregates).

1.4.2 Concrete compressive strength

The study applies Eq. (21) to predict the strength of concrete for all the different cement types Papadakis and Tsimas [21].

$$f_{\text{ck}} = K_{\text{B}} \left( {\frac{1}{{{w \mathord{\left/ {\vphantom {w {\left( {c + kP} \right)}}} \right. \kern-0pt} {\left( {c + kP} \right)}}}} - a} \right)$$

(21)

where, K _B is the Bolomey coefficient that depends on the aggregate type and concrete strength (MPa), and is assumed to be 21.3 MPa for all concrete types; w is the water content (kg/m³); c is the cement content (kg/m³); P is the content of the supplementary cementitious material (SCM) in concrete (kg/m³); and a depends on the time and curing of the concrete and is estimated as 0.5 for f _ck at 28 days Papadakis and Tsimas [21]; k is the cementing efficiency coefficient¹ of the respective SCM.