1 Introduction
2 Research Significance
3 Experimental Details
3.1 Concrete Specimens
Series | Group |
\( {\text{f}}_{\text{cd}} \)
(MPa) |
\( {\text{R}}_{\text{s}} \)
(%) |
\( {\text{W}}\text{/}{\text{C}} \)
|
\( {\text{W}} \)
(kg/m3) |
\( {\text{C}} \)
(kg/m3) |
---|---|---|---|---|---|---|
I | L | 18 | 0–100 @25 | 0.52–0.58 | 185 | 319–356 |
M | 24 | 0–100 @25 | 0.47–0.53 | 175–185 | 330–394 | |
H | 35 | 0–100 @25 | 0.35–0.41 | 170 | 415–486 | |
II | S0 | Not designed | 0 | 0.30–0.50 @0.05 | 120–200 | 400 |
S50 | Not designed | 50 | 0.30–0.50 @0.05 | 120–200 | 400 | |
III | S0-M | 24 | 0 | 0.50 | 188 | 375 |
S0-H | 35 | 0 | 0.25 | 133 | 450 | |
S100-M | 24 | 100 | 0.55 | 193 | 350 | |
S100-H | 35 | 100 | 0.32 | 144 | 450 |
3.2 Materials
Type | Maximum size (mm) | Specific gravity | Water absorption (%) | Fineness modulus |
---|---|---|---|---|
Fine aggregate | ||||
Expanded granules | 4.75 | 1.1 | 12.9 | 4.4 |
Sand | 4.75 | 1.6 | 1.5 | 2.7 |
1.20 | 1.7 | 1.6 | 2.2 | |
Coarse aggregate | ||||
Expanded granules | 19.0 | 1.0 | 17.2 | 6.4 |
9.5 | 1.1 | 16.1 | 5.8 |
3.3 Casting, Curing, and Testing
4 Test Results and Discussions
Series | Group | Specimen |
\( R_{s} \)
(%) |
\( W/C \)
|
\( d_{a} \)
(mm) |
\( S_{i} \)
(mm) |
\( v_{A} \)
(%) |
\( \rho_{c} \)
(kg/m3) |
\( f_{c}^{'} \)
(MPa) | \( \tau_{f} \) (1) (MPa) |
\( \frac{{\tau_{f} }}{{\sqrt {f_{c}^{'} } }} \)
| (\( \tau_{f} \))Pre. | (\( \tau_{f} \))Exp./(\( \tau_{f} \))Pre. | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(2) | (3) | (4) | (1)/(2) | (1)/(3) | (1)/(4) | ||||||||||||
I | L | L-0 | 0 | 0.52 | 19 | 230 | 5.8 | 1301 | 27.5 | 3.15 | 0.60 | 1.65 | 1.40 | 2.96 | 1.91 | 2.25 | 1.07 |
L-25 | 25 | 0.54 | 19 | 250 | 4.0 | 1409 | 26.2 | 3.23 | 0.63 | 1.65 | 1.48 | 3.11 | 1.96 | 2.19 | 1.04 | ||
L-50 | 50 | 0.55 | 19 | 245 | 5.0 | 1486 | 25.4 | 3.41 | 0.68 | 1.65 | 1.55 | 3.20 | 2.07 | 2.20 | 1.07 | ||
L-75 | 75 | 0.57 | 19 | 255 | 4.0 | 1528 | 24.8 | 3.87 | 0.78 | 1.65 | 1.63 | 3.23 | 2.35 | 2.38 | 1.20 | ||
L-100 | 100 | 0.58 | 19 | 250 | 6.2 | 1540 | 23.5 | 4.01 | 0.83 | 1.65 | 1.70 | 3.17 | 2.43 | 2.36 | 1.26 | ||
M | M-0 | 0 | 0.47 | 19 | 235 | 4.5 | 1366 | 34.1 | 3.22 | 0.55 | 1.65 | 1.40 | 3.32 | 1.95 | 2.30 | 0.97 | |
M-25 | 25 | 0.49 | 19 | 210 | 4.9 | 1491 | 33.4 | 3.66 | 0.63 | 1.65 | 1.48 | 3.58 | 2.22 | 2.48 | 1.02 | ||
M-50 | 50 | 0.50 | 19 | 230 | 4.3 | 1611 | 33.0 | 3.80 | 0.66 | 1.65 | 1.55 | 3.81 | 2.30 | 2.45 | 1.00 | ||
M-75 | 75 | 0.52 | 19 | 245 | 4.6 | 1641 | 32.4 | 3.87 | 0.68 | 1.65 | 1.63 | 3.84 | 2.35 | 2.38 | 1.01 | ||
M-100 | 100 | 0.53 | 19 | 240 | 4.6 | 1698 | 32.1 | 4.12 | 0.73 | 1.65 | 1.70 | 3.93 | 2.50 | 2.42 | 1.05 | ||
H | H-0 | 0 | 0.35 | 19 | 165 | 4.8 | 1605 | 46.3 | 3.60 | 0.53 | 1.65 | 1.40 | 4.25 | 2.18 | 2.57 | 0.85 | |
H-25 | 25 | 0.36 | 19 | 175 | 4.8 | 1667 | 45.8 | 4.09 | 0.60 | 1.65 | 1.48 | 4.40 | 2.48 | 2.77 | 0.93 | ||
H-50 | 50 | 0.38 | 19 | 210 | 5.1 | 1686 | 44.8 | 4.12 | 0.62 | 1.65 | 1.55 | 4.42 | 2.50 | 2.66 | 0.93 | ||
H-75 | 75 | 0.39 | 19 | 215 | 4.8 | 1757 | 43.8 | 4.41 | 0.67 | 1.65 | 1.63 | 4.56 | 2.67 | 2.71 | 0.97 | ||
H-100 | 100 | 0.41 | 19 | 225 | 5.0 | 1783 | 43.6 | 4.65 | 0.70 | 1.65 | 1.70 | 4.61 | 2.82 | 2.74 | 1.01 | ||
II | S0 | S0-50 | 0 | 0.50 | 19 | 220 | 4.7 | 1312 | 24.8 | 2.72 | 0.55 | 1.65 | 1.40 | 2.87 | 1.65 | 1.94 | 0.95 |
S0-45 | 0 | 0.45 | 19 | 225 | 4.0 | 1288 | 26.4 | 2.86 | 0.56 | 1.65 | 1.40 | 2.89 | 1.73 | 2.04 | 0.99 | ||
S0-40 | 0 | 0.40 | 19 | 205 | 4.5 | 1309 | 30.3 | 2.91 | 0.53 | 1.65 | 1.40 | 3.07 | 1.76 | 2.08 | 0.95 | ||
S0-35 | 0 | 0.35 | 19 | 165 | 4.6 | 1330 | 33.5 | 3.16 | 0.55 | 1.65 | 1.40 | 3.21 | 1.92 | 2.26 | 0.98 | ||
S0-30 | 0 | 0.30 | 19 | 15 | 5.0 | 1394 | 34.1 | 3.31 | 0.57 | 1.65 | 1.40 | 3.38 | 2.01 | 2.36 | 0.98 | ||
S50 | S50-50 | 50 | 0.50 | 19 | 250 | 4.5 | 1571 | 34.5 | 3.66 | 0.62 | 1.65 | 1.55 | 3.79 | 2.22 | 2.36 | 0.97 | |
S50-45 | 50 | 0.45 | 19 | 250 | 5.0 | 1619 | 38.5 | 2.79 | 0.45 | 1.65 | 1.55 | 4.05 | 1.69 | 1.80 | 0.69 | ||
S50-40 | 50 | 0.40 | 19 | 195 | 5.0 | 1706 | 42.9 | 4.23 | 0.65 | 1.65 | 1.55 | 4.41 | 2.56 | 2.73 | 0.96 | ||
S50-35 | 50 | 0.35 | 19 | 180 | 4.9 | 1727 | 45.7 | 4.61 | 0.68 | 1.65 | 1.55 | 4.55 | 2.79 | 2.97 | 1.01 | ||
S50-30 | 50 | 0.30 | 19 | 40 | 4.9 | 1736 | 49.8 | 4.64 | 0.66 | 1.65 | 1.55 | 4.69 | 2.81 | 2.99 | 0.99 | ||
III | S0-M | S0-M-19 | 0 | 0.50 | 19 | 240 | 4.1 | 1441 | 25.6 | 3.81 | 0.62 | 1.65 | 1.40 | 3.14 | 1.90 | 2.24 | 1.22 |
S0-M-10 | 0 | 0.50 | 9.5 | 245 | 4.2 | 1486 | 24.3 | 3.03 | 0.52 | 1.65 | 1.40 | 2.42 | 1.54 | 1.81 | 1.25 | ||
S0-M-5 | 0 | 0.50 | 4.75 | 250 | 4.5 | 1498 | 24.1 | 2.51 | 0.47 | 1.65 | 1.40 | 1.85 | 1.41 | 1.66 | 1.36 | ||
S0-H | S0-H-19 | 0 | 0.25 | 19 | 120 | 4.1 | 1633 | 36.8 | 4.12 | 0.68 | 1.65 | 1.40 | 4.02 | 2.50 | 2.94 | 1.03 | |
S0-H-10 | 0 | 0.25 | 9.5 | 135 | 4.3 | 1645 | 35.1 | 3.21 | 0.62 | 1.65 | 1.40 | 3.05 | 2.22 | 2.61 | 1.05 | ||
S0-H-5 | 0 | 0.25 | 4.75 | 145 | 4.4 | 1606 | 34.3 | 2.87 | 0.46 | 1.65 | 1.40 | 2.25 | 1.76 | 2.08 | 1.27 | ||
S100-M | S100-M-19 | 100 | 0.55 | 19 | 245 | 4.0 | 1717 | 29.1 | 4.52 | 0.65 | 1.65 | 1.70 | 3.79 | 2.13 | 2.06 | 1.19 | |
S100-M-10 | 100 | 0.55 | 9.5 | 250 | 4.2 | 1703 | 26.2 | 3.49 | 0.52 | 1.65 | 1.70 | 2.77 | 1.62 | 1.57 | 1.26 | ||
S100-M-5 | 100 | 0.55 | 4.75 | 250 | 4.2 | 1722 | 24.8 | 2.81 | 0.46 | 1.65 | 1.70 | 2.08 | 1.40 | 1.36 | 1.35 | ||
S100-H | S100-H-19 | 100 | 0.32 | 19 | 140 | 4.1 | 1831 | 39.0 | 4.77 | 0.69 | 1.65 | 1.70 | 4.53 | 2.62 | 2.55 | 1.05 | |
S100-H-10 | 100 | 0.32 | 9.5 | 165 | 4.0 | 1809 | 36.2 | 3.68 | 0.60 | 1.65 | 1.70 | 3.34 | 2.20 | 2.14 | 1.10 | ||
S100-H-5 | 100 | 0.32 | 4.75 | 185 | 4.4 | 1881 | 36.1 | 3.24 | 0.51 | 1.65 | 1.70 | 2.62 | 1.85 | 1.79 | 1.23 |
4.1 Typical Failure Mode
4.2 Effect of \( R_{s} \) (\( \rho_{c} \)) on \( {{\tau_{f} }}/{f_{c}^{'}} \)
4.3 Effect of \( W/C \) on \( {{\tau_{f} }}/{f_{c}^{'}} \)
4.4 Effect of \( d_{a} \) on \( {{\tau_{f} }}/{f_{c}^{'}} \)
5 Modeling of Shear Friction Parameters
5.1 Model Back Ground
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 \( m = 1 - 2\frac{{f_{t}^{*} }}{{f_{c}^{*} }}\frac{1}{1 - \sin \phi } \). | |
---|---|
For LWAC-BS | For LWAC-CF (Kwon et al. model) |
\( v_{c} = 1.0EXP\left[ { - 0.055\left( {\frac{{f_{c}^{'} }}{{f_{0} }}} \right)\left( {\frac{{\rho_{0} }}{{\rho_{c} }}} \right)^{1.5} } \right] \); \( \frac{{f_{t}^{*} }}{{f_{c}^{*} }} = 0.11\left[ {\left( {\frac{{f_{c}^{'} }}{{f_{0} }}} \right)^{0.8} \left( {\frac{{c_{0} }}{{d_{a} }} \cdot \frac{{\rho_{0} }}{{\rho_{c} }}} \right)} \right]^{ - 0.83} \);
\( \phi = 21.6\left( {\frac{{f_{t}^{*} }}{{f_{c}^{*} }}} \right)^{ - 0.2} \)
| \( v_{c} = 0.79EXP\left[ { - 0.029\left( {\frac{{f_{c}^{'} }}{{f_{0} }}} \right)^{0.9} \left( {\frac{{\rho_{0} }}{{\rho_{c} }}} \right)^{1.6} } \right] \); \( \frac{{f_{t}^{*} }}{{f_{c}^{*} }} = 0.064\left[ {\left( {\frac{{f_{c}^{'} }}{{f_{0} }}} \right)\left( {\frac{{c_{0} }}{{d_{a} }}} \right)^{1.7} \left( {\frac{{\rho_{c} }}{{\rho_{0} }}} \right)^{0.1} } \right]^{ - 0.43} \);
\( \phi = 20.65\left( {\frac{{f_{t}^{*} }}{{f_{c}^{*} }}} \right)^{ - 0.21} \)
|