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Table 9 The enhancement coefficient \(W\) by fitting the fiber hybrid effect function.

From: Experimental Investigation on the Mechanical Properties of Polypropylene Hybrid Fiber-Reinforced Roller-Compacted Concrete Pavements

Mechanical indexes The enhancement coefficient \(W\) of PFRCC \(R^{2}\)
\(f_{t}\) \(\begin{gathered} W_{{f_{t} }} = 1{ + 0}{\text{.0907}} \times \lambda_{i} { + }1.0588 \times \lambda_{j} { + }1.0618 \times \lambda_{k} - {0}{\text{.063}} \times \lambda_{i}^{2} \hfill \\ \, - {2}{\text{.816}} \times \lambda_{j}^{2} - {1}{\text{.344}} \times \lambda_{k}^{2} - {0}{\text{.824}} \times \lambda_{i} \lambda_{j} { + 4}{\text{.064}} \times \lambda_{j} \lambda_{k} \hfill \\ \, - {0}{\text{.520}} \times \lambda_{k} \lambda_{i} - {5}{\text{.243}} \times \lambda_{i} \lambda_{j} \lambda_{k} \hfill \\ \end{gathered}\) 0.999
\(\varepsilon_{t}\) \(\begin{gathered} W_{{\varepsilon_{t} }} = 1 + 0.3744 \times \lambda_{i} + 1.2946 \times \lambda_{j} + 0.8485 \times \lambda_{k} - {0}{\text{.260}} \times \lambda_{i}^{2} \hfill \\ \, - {3}{\text{.443}} \times \lambda_{j}^{2} - {1}{\text{.074}} \times \lambda_{k}^{2} + 1.741 \times \lambda_{i} \lambda_{j} - {4}{\text{.064}} \times \lambda_{j} \lambda_{k} \hfill \\ \, + 1.637 \times \lambda_{k} \lambda_{i} - {0}{\text{.075}} \times \lambda_{i} \lambda_{j} \lambda_{k} \hfill \\ \end{gathered}\) 0.988
\(\alpha_{t}\) \(\begin{gathered} W_{{\alpha_{t} }} = 1 - 0.0605 \times \lambda_{i} - 2.2195 \times \lambda_{j} - 2.7421 \times \lambda_{k} + 0.042 \times \lambda_{i}^{2} \hfill \\ \, + 5.903 \times \lambda_{j}^{2} + 3.471 \times \lambda_{k}^{2} - 1.678 \times \lambda_{i} \lambda_{j} + 4.353 \times \lambda_{j} \lambda_{k} \hfill \\ \, + 2.089 \times \lambda_{k} \lambda_{i} - {10}{\text{.035}} \times \lambda_{i} \lambda_{j} \lambda_{k} \hfill \\ \end{gathered}\) 0.798
\(E_{c}\) \(\begin{gathered} W_{{E_{c} }} = 1 + 0.0547 \times \lambda_{i} + 0.4674 \times \lambda_{j} + 0.1311 \times \lambda_{k} - {0}{\text{.038}} \times \lambda_{i}^{2} \hfill \\ \, - {1}{\text{.243}} \times \lambda_{j}^{2} - {0}{\text{.166}} \times \lambda_{k}^{2} + 0.827 \times \lambda_{i} \lambda_{j} + 2.621 \times \lambda_{j} \lambda_{k} \hfill \\ \, - 0.154 \times \lambda_{k} \lambda_{i} - {12}{\text{.991}} \times \lambda_{i} \lambda_{j} \lambda_{k} \hfill \\ \end{gathered}\) 0.979