Concrete Structures Subjected to Fire Loading: From Thermo-Mechanical Modeling of Strain Behavior of Concrete Towards Structural Safety Assessment

Abstract

In this chapter, results obtained within a 4-year research project on the safety of underground structures subjected to fire loading are presented. For this project, a consortium consisting of three scientific partners (Vienna University of Technology, University of Innsbruck, University of Natural Resources and Life Sciences, Vienna) and eight industrial partners (ÖBB-Infrastruktur AG, ASFINAG, Wiener Linien, Arge Bautech, VÖZFI, Büro Dr. Lindlbauer, Schimetta Consult, ZT Reissmann) was established. Whereas the mentioned research project followed a holistic approach, covering simulation of the fire event, experimental investigation of concrete and concrete structures at high temperatures, and modeling and simulation work at both the material and the structural scale (Amouzandeh, Development and application of a computational fluid dynamics code to predict the thermal impact of underground structures in case of fire, Ph.D. thesis, Vienna University of Technology, Vienna, 2012; Ring et al. Brandversuche zum Abplatz- und Strukturverhalten von Tunnel mit Rechtecksquerschnitt [Fire experiments investigating the spalling and structural behavior of rectangular tunnels], Technical Report, Vienna University of Technology and Vereinigung der österreichischen Zementindustrie (VÖZFI), Vienna, 2012; Ring, Experimental characterization and modeling of concrete at high temperatures: Structural safety assessment of different tunnel cross-sections subjected to fire loading, Ph.D. thesis, Vienna University of Technology, Vienna, 2012; Zhang, Simulations for durability assessment of concrete structures: multifield framework and strong discontinuity embedded approach, Ph.D. thesis, Vienna University of Technology, Vienna, 2013), this chapter focuses on one aspect of the project, namely modeling and simulation of the behavior of concrete and concrete structures under combined thermal and mechanical loading:

• 1. First, a micromechanical model taking the composite nature of concrete into account is presented. Based on experimental results obtained for cement paste and aggregate subjected to thermal/mechanical loading, a two-scale model formulated within the framework of continuum micromechanics is developed, giving access to the effective elastic and thermal-dilation properties of concrete as a function of temperature.

• 2. In a second step, these model-based properties are considered within a differential formulation of the underlying stress–strain law, accounting for the influence of mechanical loading on the thermal-strain evolution. The proposed micromechanical approach and its implementation are validated by experimental results obtained from concrete specimens subjected to combined thermo-mechanical loading.

• 3. Finally, the effect of the underlying model assumptions at the structural scale is illustrated by means of the safety assessment of underground support structures under fire attack.

The obtained results are nowadays considered in the formulation of standards and guidelines for the assessment of the safety of underground structures subjected to fire loading (ÖBV-Richtlinie: Fire protection with concrete for underground traffic infrastructure [Erhöhter baulicher Brandschutz mit Beton für unterirdische Verkehrsbauwerke], Austrian Society for Construction Technology, Vienna, 2013).

Appendix: Effective Prescribed Strains in Two-Phase Materials

According to [14], the effective strain E _eff is related to the prescribed strain $\bar{\varepsilon }$ in the material phases as:

$$\displaystyle{ K_{\mathrm{eff}}E_{\mathrm{eff}} =\langle A: K:\bar{\varepsilon }\rangle _{V }\,. }$$

(6.19)

Considering a two-phase material with matrix m and inclusion i, with

$$\displaystyle{ \bar{\varepsilon }=\bar{\varepsilon } _{m}\ \mbox{ in}\ V _{m},\ \bar{\varepsilon }=\bar{\varepsilon } _{i}\ \mbox{ in}\ V _{i}, }$$

(6.20)

$\bar{\varepsilon }_{i}$ may be substituted by

$$\displaystyle{ \bar{\varepsilon }_{i} =\bar{\varepsilon } _{m} +\varDelta \bar{\varepsilon } _{i}. }$$

(6.21)

Rewriting Eq. (6.19) and considering Eq. (6.21) gives

$$\displaystyle{ K_{\mathrm{eff}}E_{\mathrm{eff}} =\langle A: K\rangle _{V }\bar{\varepsilon }_{m} + f_{i}\langle A: K\rangle _{V _{i}}\varDelta \bar{\varepsilon }_{i}\,. }$$

(6.22)

Considering $K_{\mathrm{eff}} =\langle A: K\rangle _{V }$ in Eq. (6.22), one gets

$$\displaystyle{ E_{\mathrm{eff}} =\bar{\varepsilon } _{m} + f_{i}\langle A\rangle _{V _{i}} \frac{K_{i}} {K_{\mathrm{eff}}}(\bar{\varepsilon }_{i} -\bar{\varepsilon }_{m}), }$$

(6.23)

where $\langle A\rangle _{V i}$ is given in [14].