Quantifying Fire Insulation Effects on the Fire Response of Hybrid-Fiber Reinforced Reactive Powder Concrete Beams

Abstract

The fire performance of reinforced reactive powder concrete (RPC) beams has raised much concern due to the sensitivity of these beams to high temperature and relatively lower fire resistance. To achieve the fire-resistance ratings as specified in building design codes, a fire insulation layer is often required. However, very limited research has been conducted on the effect of fire insulation on the fire resistance of reinforced RPC beams. Hence, using the commercial software ABAQUS, a three-dimensional sequentially coupled thermal-stress finite element (FE) model was developed to simulate the response of insulated reinforced RPC beams to fire. Comparisons between the FE predictions and the existing fire test results are presented to demonstrate the accuracy of the proposed FE model. In addition, the validated FE model was used to study the effect of fire insulation parameters, including the thermal properties, thickness, height, setting mode, and local fire insulation damage, on the fire response of reinforced RPC beams. The results showed that the failure of reinforced RPC beams with partial loss of fire insulation occurred at the area of missing fire protection. Additionally, the effect of the following important parameters on the fire resistance of insulated reinforced RPC beams was investigated: compressive strength of RPC, reinforcement ratio, load ratio, thickness of RPC cover, beam width, and span-depth ratio.

Appendix: Stress–Strain Relationship of RPC at Elevated Temperatures

• (1) Compressive strength of RPC at elevated temperatures [55]

  $$\frac{{f_{\text{c,T}}^{{}} }}{{f_{{{\text{c}},20}}^{{}} }} = \, 0.96 - 0.958\left( {\frac{T}{1000}} \right)\quad 20\,^{ \circ } {\text{C}} \le T \le 800\,^{ \circ } {\text{C}}$$

  (2)

  where $f_{{{\text{c}},20}}^{{}}$ and $f_{\text{c,T}}^{{}}$ are the compressive strength of RPC at 20 °C and temperature T (unit: °C), respectively.

• (2) Peak compressive strain of RPC at elevated temperatures [55]

  $$\frac{{\varepsilon_{\text{c,T}} }}{{\varepsilon_{0} }} = \, 0.696 + 12.1\left( {\frac{T}{1000}} \right) - 39.7\left( {\frac{T}{1000}} \right)^{2} + 48.8\left( {\frac{T}{1000}} \right)^{3} \quad 20\,^{ \circ } {\text{C}} \le T \le 800\,^{ \circ } {\text{C}}$$

  (3)

  where $\varepsilon_{ 0}$ and $\varepsilon_{\text{c,T}}$ are the peak compressive strain of RPC at 20 °C and temperature T, respectively.

• (3) Elastic modulus of RPC at elevated temperatures [55]

  The elastic modulus of RPC at temperature T$(E_{\text{c,T}}^{{}} )$ is set to be the tangent modulus at the 0.5 $f_{\text{c,T}}$ point of the compressive stress–strain curve at temperature T.

• (4) Compressive stress–strain relationship of hybrid-fiber reinforced RPC at elevated temperatures [55]

  $$y = \left\{ {\begin{array}{*{20}c} {mx + (3 - 2m)x^{2} + (m - 2)x^{3} \;\;\;{\kern 1pt} 0{\kern 1pt} \le x \le 1} \\ {\frac{x}{{n(x - 1)^{2} + x}}{\kern 1pt} \;\;{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\kern 1pt} {\kern 1pt} \;\;x \ge 1} \\ \end{array} } \right.$$

  (4)

  where $x = \varepsilon /\varepsilon_{\text{c,T}}$, $y = \sigma /f_{\text{c,T}}$; $\varepsilon$ is the compressive strain, $\sigma$ is the compressive stress; m and n are parameters corresponding to the ascending and descending curves respectively, which can be obtained from Table 5.

  Table 5 Equation parameters in different temperature ranges

• (5) Tensile strength of RPC at elevated temperatures [55]

  $$\frac{{f_{\text{t,T}}^{{}} }}{{f_{{{\text{t}},20}}^{{}} }} = \, 0.972 - 0.82\left( {\frac{T}{1000}} \right)\quad 20\,^{ \circ } {\text{C}} \le T \le 800\,^{ \circ } {\text{C}}$$

  (5)

  where $f_{t,20}^{{}}$ and $f_{t,T}^{{}}$ are the tensile strength of RPC at 20 °C and temperature T, respectively.

• (6) Peak tensile strain of RPC at elevated temperatures

  $$\varepsilon_{\text{t,T}} = \frac{{f_{\text{t,T}}^{{}} }}{{E_{\text{c,T}} }}$$

  (6)

  where $\varepsilon_{\text{t,T}}$ is peak tensile strain of RPC at temperature T.

• (7) Tensile strength stress–strain relationship of RPC at elevated temperatures [49]

  $$y = \left\{ {\begin{array}{*{20}c} {1.17x + 0.65x^{2} - 0.83x^{3} \;\;\;{\kern 1pt} 0{\kern 1pt} \le x \le 1} \\ {\frac{x}{{5.5(x - 1)^{2.2} + x}}{\kern 1pt} \;\;\;\;{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \;\;\;\;\;\;\;\;\;\;\;\;\;\;x \ge 1} \\ \end{array} } \right.$$

  (7)

  where $x = {\varepsilon \mathord{\left/ {\vphantom {\varepsilon {\varepsilon_{\text{t,T}} }}} \right. \kern-0pt} {\varepsilon_{\text{t,T}} }}$,$y = {\sigma \mathord{\left/ {\vphantom {\sigma {f_{\text{t,T}}^{{}} }}} \right. \kern-0pt} {f_{\text{t,T}}^{{}} }}$; $\varepsilon$ is the tensile strain, $\sigma$ is the tensile stress.