Correction: An Extended Damage Plasticity Model for Shotcrete: Formulation and Comparison with Other Shotcrete Models

The authors would like to correct following typing errors: For (3) and (4), the correct expressions are given as

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill f_{\mathrm{p}}({\stackrel{\_}{\sigma }}_{\mathrm{m}},\stackrel{\_}{\rho },\theta ,q_{\mathrm{h}}\left({\alpha }_{\mathrm{p}}\right),t)=& {\left((1-q_{\mathrm{h}}\left({\alpha }_{\mathrm{p}}\right)){\left(\frac{\stackrel{\_}{\rho }}{\sqrt{6}{f}_{\mathrm{cu}}\left(t\right)}+\frac{{\stackrel{\_}{\sigma }}_{\mathrm{m}}}{f_{\mathrm{cu}}\left(t\right)}\right)}^2+\sqrt{\frac{3}{2}}\frac{\stackrel{\_}{\rho }}{f_{\mathrm{cu}}\left(t\right)}\right)}^2\hfill \\ & +m_0{q}_{\mathrm{h}}^2\left({\alpha }_{\mathrm{p}}\right)\left(\frac{\stackrel{\_}{\rho }}{\sqrt{6}{f}_{\mathrm{cu}}\left(t\right)}r\left(\theta \right)+\frac{{\stackrel{\_}{\sigma }}_{\mathrm{m}}}{f_{\mathrm{cu}}\left(t\right)}\right)-q_{\mathrm{h}}^2\left({\alpha }_{\mathrm{p}}\right),\hfill \end{array}\end{array}$$

(1)

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill g_{\mathrm{p}}({\stackrel{\_}{\sigma }}_{\mathrm{m}},\stackrel{\_}{\rho },q_{\mathrm{h}}\left({\alpha }_{\mathrm{p}}\right),t)=& {\left((1-q_{\mathrm{h}}\left({\alpha }_{\mathrm{p}}\right)){\left(\frac{\stackrel{\_}{\rho }}{\sqrt{6}{f}_{\mathrm{cu}}\left(t\right)}+\frac{{\stackrel{\_}{\sigma }}_{\mathrm{m}}}{f_{\mathrm{cu}}\left(t\right)}\right)}^2+\sqrt{\frac{3}{2}}\frac{\stackrel{\_}{\sigma }}{f_{\mathrm{cu}}\left(t\right)}\right)}^2\hfill \\ & +q_{\mathrm{h}}^2\left({\alpha }_{\mathrm{p}}\right)\left(\frac{m_0\stackrel{\_}{\sigma }}{\sqrt{6}{f}_{\mathrm{cu}}\left(t\right)}+\frac{m_{\mathrm{g}}\left({\stackrel{\_}{\sigma }}_{\mathrm{m}}\right)}{f_{\mathrm{cu}}\left(t\right)}\right),\hfill \end{array}\end{array}$$

(2)

corresponding to the respective time-independent equations in [1].

For (14), parameter $c_{\mathrm{f}}$ is computed as

$$c_{\mathrm{f}}=\frac{\mathrm{d}{\beta }_{\mathrm{f}}^{\mathrm{II}}}{\mathrm{d}t}{|}_{t=t_{\mathrm{f}}}-2d_{\mathrm{f}}{t}_{\mathrm{f}}.$$

(3)

The authors would like to express their gratitude to Anna-Lena Hammer from Ruhr University Bochum, Germany for finding this error.

The changes do not affect the results. The manuscript will be updated, and the original one will remain available on the article webpage.