Table 4 Summary of shear friction strength model of LWAC.
Fundamental model: \( \tau_{f} = \frac{1}{2}f_{c}^{*} \frac{1}{\cos \alpha }[l - m\sin \alpha ] \); \( \alpha = 2\tan^{ - 1} \left[ {\frac{x}{{\left( {x^{2} + y^{2} } \right)^{1/2} + y}}} \right] \); \( x = \frac{m}{l} \); \( y = \frac{{\left( {l^{2} - m^{2} } \right)^{1/2} }}{l} \); \( l = 1 - 2\frac{{f_{t}^{*} }}{{f_{c}^{*} }}\frac{\sin \phi }{1 - \sin \phi } \); and \( m = 1 - 2\frac{{f_{t}^{*} }}{{f_{c}^{*} }}\frac{1}{1 - \sin \phi } \). | |
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For LWAC-BS | For LWAC-CF (Kwon et al. model) |
\( v_{c} = 1.0EXP\left[ { - 0.055\left( {\frac{{f_{c}^{'} }}{{f_{0} }}} \right)\left( {\frac{{\rho_{0} }}{{\rho_{c} }}} \right)^{1.5} } \right] \); \( \frac{{f_{t}^{*} }}{{f_{c}^{*} }} = 0.11\left[ {\left( {\frac{{f_{c}^{'} }}{{f_{0} }}} \right)^{0.8} \left( {\frac{{c_{0} }}{{d_{a} }} \cdot \frac{{\rho_{0} }}{{\rho_{c} }}} \right)} \right]^{ - 0.83} \); \( \phi = 21.6\left( {\frac{{f_{t}^{*} }}{{f_{c}^{*} }}} \right)^{ - 0.2} \) | \( v_{c} = 0.79EXP\left[ { - 0.029\left( {\frac{{f_{c}^{'} }}{{f_{0} }}} \right)^{0.9} \left( {\frac{{\rho_{0} }}{{\rho_{c} }}} \right)^{1.6} } \right] \); \( \frac{{f_{t}^{*} }}{{f_{c}^{*} }} = 0.064\left[ {\left( {\frac{{f_{c}^{'} }}{{f_{0} }}} \right)\left( {\frac{{c_{0} }}{{d_{a} }}} \right)^{1.7} \left( {\frac{{\rho_{c} }}{{\rho_{0} }}} \right)^{0.1} } \right]^{ - 0.43} \); \( \phi = 20.65\left( {\frac{{f_{t}^{*} }}{{f_{c}^{*} }}} \right)^{ - 0.21} \) |