1 Introduction
2 Calculation of Interface Shear Stress
2.1 Mattock et al. Equation
2.2 Walraven’s Equation
2.3 Loov and Patnaik’s Equation
2.4 Kahn and Mitchell’s Equation
2.5 ACI Design Code
2.6 AASHTO Design Code
2.7 Determination of Interface Shear Stress
3 Experimental Program
3.1 Variables
Specimens designation | Shear interface condition | Target lightweight slab concrete strength (MPa) | Quantities of shear reinforcement |
---|---|---|---|
R-30-5 | Rough | 30 | 5 ϕ 10 double-legged stirrups |
R-40-0 | Rough | 40 | 0 |
R-40-5 | Rough | 40 | 5 ϕ 10 double-legged stirrups |
R-40-9 | Rough | 40 | 9 ϕ 10 double-legged stirrups |
R-40-17 | Rough | 40 | 17 ϕ 10 double-legged stirrups |
R-50-5 | Rough | 50 | 5 ϕ 10 double-legged stirrups |
S-30-5 | Smooth | 30 | 5 ϕ 10 double-legged stirrups |
S-40-0 | Smooth | 40 | 0 |
S-40-5 | Smooth | 40 | 5 ϕ 10 double-legged stirrups |
S-40-9 | Smooth | 40 | 9 ϕ 10 double-legged stirrups |
S-40-17 | Smooth | 40 | 17 ϕ 10 double-legged stirrups |
S-50-5 | Smooth | 50 | 5 ϕ 10 double-legged stirrups |
3.2 Test Beams
Specimens | Concrete strength (MPa) | Stirrups crossing interface | Reinforcement ratio ρ (%) | Clamping stress ρfy (MPa) | ||||
---|---|---|---|---|---|---|---|---|
Web | Flange | Spacing (mm) | Area (mm2) | Yield strength (MPa) | Ultimate strength fu (MPa) | |||
R-30-5 | 50.32 | 30.03 | 500 | 628 | 345.86 | 543.18 | 0.174 | 0.60 |
R-40-0 | 47.30 | 40.10 | – | – | – | – | 0 | 0 |
R-40-5 | 47.89 | 42.24 | 500 | 628 | 345.86 | 543.18 | 0.174 | 0.60 |
R-40-9 | 48.28 | 40.73 | 250 | 1256 | 345.86 | 543.18 | 0.349 | 1.21 |
R-40-17 | 51.05 | 40.64 | 125 | 2512 | 345.86 | 543.18 | 0.698 | 2.41 |
R-50-5 | 51.97 | 50.71 | 500 | 628 | 345.86 | 543.18 | 0.174 | 0.60 |
S-30-5 | 50.32 | 30.03 | 500 | 628 | 345.86 | 543.18 | 0.174 | 0.60 |
S-40-0 | 47.30 | 40.10 | – | – | – | – | 0 | 0 |
S-40-5 | 47.89 | 42.24 | 500 | 628 | 345.86 | 543.18 | 0.174 | 0.60 |
S-40-9 | 48.28 | 40.73 | 250 | 1256 | 345.86 | 543.18 | 0.349 | 1.21 |
S-40-17 | 51.05 | 40.64 | 125 | 2512 | 345.86 | 543.18 | 0.698 | 2.41 |
S-50-5 | 51.98 | 50.71 | 500 | 628 | 345.86 | 543.18 | 0.174 | 0.60 |
3.3 Materials
Concrete type | Mixture quantities (kg/m3) | Density of concrete (kg/m3) | Target fc (MPa) | fc’ (MPa) |
f
t
(MPa) |
E
c
(MPa) |
µ
| ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Coarse aggregate | Fine aggregate | Water | Cement | Fly ash | Water reducer | W/C | |||||||
C50 web concrete | 1095 | 616 | 154 | 459 | 103 | 13.15 | 0.33 | 2440 | 50 | 49.47 | 4.09 | 37,389 | 0.20 |
L30 slab concrete | 543 | 808 | 211 | 306 | – | – | 0.69 | 1868 | 30 | 30.03 | 3.46 | 26,344 | 0.21 |
L40 slab concrete | 512 | 826 | 206 | 359 | – | – | 0.57 | 1903 | 40 | 40.93 | 4.20 | 27,949 | 0.19 |
L50 slab concrete | 508 | 787 | 201 | 428 | – | – | 0.47 | 1924 | 50 | 50.71 | 4.02 | 31,449 | 0.20 |
Type | Yield strength (MPa) | Ultimate tensile strength (MPa) | Elasticity of modulus (MPa) |
---|---|---|---|
Grade 40 steel bars (ϕ10) | 345.86 | 543.18 | 1.87 × 105 |
Grade 40 steel bars (
10) | 456.39 | 567.52 | 1.82 × 105 |
Grade 40 steel bars (
25) | 409.12 | 557.31 | 1.79 × 105 |
3.4 Specimens Fabrication
3.5 Test Procedure
4 Experimental Results and Discussion
4.1 Observed Behavior
4.2 Deflection Characteristics
4.3 Horizontal Shear Stress
Specimens | Concrete strength \( f^{\prime}_{c} \) (MPa) | Interface width b (mm) | Interface length l (mm) | Area of longitudinal steel As (mm2) | Cracked transformed section properties | |||
---|---|---|---|---|---|---|---|---|
Web | Flange | h0 (mm) | I × 106 (mm4) | C × 104 (N) | ||||
R-30-5 | 50.32 | 30.03 | 150 | 1200 | 1964 | 110 | 610 | 87.0 |
R-40-0 | 47.30 | 40.10 | 150 | 1200 | 1964 | 107 | 585 | 54.6 |
R-40-5 | 47.89 | 42.24 | 150 | 1200 | 1964 | 107 | 585 | 95.0 |
R-40-9 | 48.28 | 40.73 | 150 | 1200 | 1964 | 107 | 585 | 87.6 |
R-40-17 | 51.05 | 40.64 | 150 | 1200 | 1964 | 107 | 585 | 102.1 |
R-50-5 | 51.97 | 50.71 | 150 | 1200 | 1964 | 102 | 537 | 84.1 |
S-30-5 | 50.32 | 30.03 | 150 | 1200 | 1964 | 110 | 610 | 57.7 |
S-40-0 | 47.30 | 40.10 | 150 | 1200 | 1964 | 107 | 585 | 44.0 |
S-40-5 | 47.89 | 42.24 | 150 | 1200 | 1964 | 107 | 585 | 57.5 |
S-40-9 | 48.28 | 40.73 | 150 | 1200 | 1964 | 107 | 585 | 59.9 |
S-40-17 | 51.05 | 40.64 | 150 | 1200 | 1964 | 107 | 585 | 79.3 |
S-50-5 | 51.98 | 50.71 | 150 | 1200 | 1964 | 102 | 537 | 54.2 |
Specimens | Experimental vn | Mattock et al. Eq. (1) | Walraven Eq. (2) | Loov and Patnaik Eq. (3) | Kahn and Mitchell Eq. (4) | ACI Eq. (5) | ACI shear-friction Eq. (6) | AASHTO LRFD Eq. (7) | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
v
Eq. (1)
|
v
n
/v
Eq. (1)
|
v
Eq. (2)
|
v
n
/v
Eq. (2)
|
v
Eq. (3)
|
v
n
/v
Eq. (3)
|
v
Eq. (4)
|
v
n
/v
Eq. (4)
|
v
Eq. (5)
|
v
n
/v
Eq. (5)
|
v
Eq. (6)
|
v
n
/v
Eq. (6)
|
v
Eq. (7)
|
v
n
/v
Eq. (7)
| ||
R-30-5 | 4.83 | 2.20 | 2.19 | 2.76 | 1.75 | 1.95 | 2.48 | 2.34 | 2.06 | 1.83 | 2.64 | 0.51 | 9.44 | 2.50 | 1.93 |
R-40-0 | 3.03 | 1.72 | 1.76 | 0.00 | 0.00 | 0.85 | 3.56 | 2.01 | 1.51 | 1.52 | 1.99 | 0.00 | 0.00 | 1.90 | 1.59 |
R-40-5 | 5.28 | 2.20 | 2.40 | 3.08 | 1.71 | 2.31 | 2.28 | 2.95 | 1.79 | 1.83 | 2.89 | 0.51 | 10.32 | 2.50 | 2.11 |
R-40-9 | 4.62 | 2.69 | 1.72 | 4.36 | 1.06 | 3.10 | 1.49 | 3.73 | 1.24 | 2.14 | 2.16 | 1.03 | 4.50 | 3.11 | 1.49 |
R-40-17 | 5.67 | 3.65 | 1.55 | 6.21 | 0.91 | 4.30 | 1.32 | 5.41 | 1.05 | 2.75 | 2.06 | 2.05 | 2.76 | 4.31 | 1.31 |
R-50-5 | 4.67 | 2.20 | 2.12 | 3.27 | 1.43 | 2.54 | 1.84 | 3.38 | 1.38 | 1.83 | 2.55 | 0.51 | 9.13 | 2.50 | 1.87 |
Mean | 1.96 | 1.37 | 2.16 | 1.50 | 2.38 | 7.23 | 1.72 | ||||||||
Standard deviation | 0.09 | 0.11 | 0.56 | 0.11 | 0.11 | 9.09 | 0.08 | ||||||||
Coefficient of variation | 0.15 | 0.25 | 0.34 | 0.22 | 0.14 | 0.42 | 0.16 | ||||||||
S-30-5 | 2.42 | 2.20 | 1.10 | 2.76 | 0.88 | 1.95 | 1.24 | 2.34 | 1.03 | 1.83 | 1.32 | 0.31 | 7.88 | 0.88 | 2.75 |
S-40-0 | 1.66 | 1.72 | 0.97 | 0.00 | 0.00 | 0.85 | 1.95 | 2.01 | 0.83 | 1.52 | 1.09 | 0.00 | 0.00 | 0.52 | 3.19 |
S-40-5 | 3.06 | 2.20 | 1.39 | 3.08 | 0.99 | 2.31 | 1.32 | 2.95 | 1.04 | 1.83 | 1.67 | 0.31 | 9.97 | 0.88 | 3.47 |
S-40-9 | 2.43 | 2.69 | 0.90 | 4.36 | 0.56 | 3.10 | 0.78 | 3.73 | 0.65 | 2.14 | 1.14 | 0.62 | 3.95 | 1.24 | 1.95 |
S-40-17 | 3.58 | 3.65 | 0.98 | 6.21 | 0.58 | 4.30 | 0.83 | 5.41 | 0.66 | 2.75 | 1.30 | 1.23 | 2.91 | 1.97 | 1.82 |
S-50-5 | 2.75 | 2.20 | 1.25 | 3.27 | 0.84 | 2.54 | 1.08 | 3.38 | 0.81 | 1.83 | 1.50 | 0.31 | 8.96 | 0.88 | 3.12 |
Mean | 1.10 | 0.77 | 1.20 | 0.84 | 1.34 | 6.73 | 2.72 | ||||||||
Standard deviation | 0.03 | 0.03 | 0.15 | 0.02 | 0.04 | 7.83 | 0.39 | ||||||||
Coefficient of variation | 0.16 | 0.22 | 0.32 | 0.18 | 0.15 | 0.42 | 0.23 |
4.4 Horizontal Shear Stress νn-Slip Relations
Specimens number | ρfy (MPa) | Concrete strength \( f^{\prime}_{c} \) (MPa) | Horizontal shear stress (MPa) | Slip (mm) | Failure mode | ||||
---|---|---|---|---|---|---|---|---|---|
At 0.13 mm slip | At 0.5 mm slip | At failure | Maximum | At failure | At maximum shear stress | ||||
R-30-5 | 0.60 | 30.03 | 1.59 | 4.65 | 4.83 | 4.83 | 0.63 | 0.63 | Horizontal shear |
R-40-0 | 0.00 | 40.10 | 0.48 | 1.38 | 3.03 | 3.03 | 0.82 | 0.82 | Horizontal shear |
R-40-5 | 0.60 | 42.24 | 0.82 | 2.08 | 5.28 | 5.28 | 1.13 | 1.13 | Horizontal shear |
R-40-9 | 1.21 | 40.73 | 0.49 | 1.20 | 4.62 | 4.87 | 1.65 | 2.88 | Horizontal shear |
R-40-17 | 2.41 | 40.64 | 0.36 | 1.57 | 5.67 | 5.67 | 1.40 | 1.40 | Flexure |
R-50-5 | 0.60 | 50.71 | 0.39 | 0.86 | 4.67 | 4.67 | 1.38 | 1.38 | Horizontal shear |
S-30-5 | 0.60 | 30.03 | 0.71 | 1.50 | 2.42 | 3.21 | 1.48 | 6.38 | Horizontal shear |
S-40-0 | 0.00 | 40.10 | 0.75 | 1.49 | 1.66 | 2.44 | 0.62 | 5.38 | Horizontal shear |
S-40-5 | 0.60 | 42.24 | 0.28 | 1.31 | 3.06 | 3.20 | 1.01 | 5.91 | Horizontal shear |
S-40-9 | 1.21 | 40.73 | 1.10 | 2.25 | 2.43 | 3.33 | 1.17 | 5.37 | Horizontal shear |
S-40-17 | 2.41 | 40.64 | 0.67 | 2.21 | 3.58 | 4.41 | 1.53 | 5.04 | Horizontal shear |
S-50-5 | 0.60 | 50.71 | 0.44 | 1.48 | 2.75 | 3.01 | 0.81 | 4.66 | Horizontal shear |
4.5 Stirrup Stresses
5 Recommendation
5.1 Proposed Shear Capacity Equation and Verification
5.2 Validation of the Proposed Equation
Concrete type | Author | Specimens | f′c (MPa) |
ρ
| fy (MPa) | ρfy (MPa) | v (MPa) |
---|---|---|---|---|---|---|---|
NWB | Saemann and Washa (1964) | 8A | 20.13 | 0.0108 | 293.73 | 3.18 | 4.26 |
6A | 20.00 | 0.0102 | 293.73 | 3.00 | 6.57 | ||
Loov and Patnaik (1994) | Beam 1 | 37.40 | 0.0100 | 438.00 | 4.36 | 7.76 | |
Beam 2 | 34.90 | 0.0038 | 438.00 | 1.66 | 4.27 | ||
Beam 3 | 30.50 | 0.0064 | 432.00 | 2.76 | 6.82 | ||
Beam 5 | 34.80 | 0.0038 | 430.00 | 1.63 | 5.54 | ||
Beam 6 | 37.10 | 0.0038 | 428.00 | 1.62 | 5.25 | ||
beam 7 | 35.80 | 0.0140 | 432.00 | 6.06 | 9.25 | ||
Beam 8 | 35.60 | 0.0019 | 407.00 | 0.77 | 3.12 | ||
Beam 9 | 37.10 | 0.0038 | 428.00 | 1.62 | 4.64 | ||
Beam 10 | 37.60 | 0.0019 | 409.00 | 0.77 | 3.46 | ||
Beam 12 | 34.60 | 0.0189 | 408.00 | 7.72 | 9.20 | ||
Beam 13 | 19.20 | 0.0019 | 431.00 | 0.82 | 2.92 | ||
Kahn and Slapkus (2004) | 7-5 | 50.20 | 0.0019 | 556.00 | 1.03 | 4.09 | |
7-7 | 50.20 | 0.0028 | 556.00 | 1.55 | 6.77 | ||
7-9 | 50.20 | 0.0037 | 556.00 | 2.06 | 6.90 | ||
LCP | Mattock et al. (1976) | A0 | 29.17 | 0.0000 | 0.00 | 0.00 | 3.45 |
A1 | 25.79 | 0.0044 | 328.89 | 1.45 | 5.23 | ||
A2 | 28.24 | 0.0088 | 369.57 | 3.25 | 6.30 | ||
A3 | 26.96 | 0.0132 | 366.81 | 4.84 | 7.03 | ||
A4 | 28.27 | 0.0176 | 350.96 | 6.18 | 7.58 | ||
A5 | 27.30 | 0.0220 | 350.96 | 7.72 | 8.21 | ||
A6 | 29.30 | 0.0264 | 357.16 | 9.43 | 9.27 | ||
Shaw and Sneed (2014) | S-5-R-1 | 31.37 | 0.0133 | 456.00 | 6.06 | 7.17 | |
S-5-R-2 | 31.37 | 0.0133 | 456.00 | 6.06 | 7.03 | ||
S-5-R-3 | 31.37 | 0.0133 | 456.00 | 6.06 | 7.52 | ||
S-8-R-1 | 49.71 | 0.0133 | 456.00 | 6.06 | 10.07 | ||
S-8-R-2 | 49.71 | 0.0133 | 456.00 | 6.06 | 9.38 | ||
S-8-R-3 | 49.71 | 0.0133 | 456.00 | 6.06 | 9.31 | ||
Sneed et al. (2016) | S-SL-CJ-R-9-1 | 37.10 | 0.0090 | 498.00 | 4.48 | 6.90 | |
S-SL-CJ-R-9-2 | 37.10 | 0.0090 | 498.00 | 4.48 | 7.03 | ||
S-SL-CJ-R-13-1 | 38.41 | 0.0130 | 498.00 | 6.47 | 8.80 | ||
S-SL-CJ-R-13-2 | 38.41 | 0.0130 | 498.00 | 6.47 | 8.27 | ||
S-SL-CJ-R-17-1 | 34.13 | 0.0170 | 498.00 | 8.47 | 8.69 | ||
S-SL-CJ-R-17-2 | 34.13 | 0.0170 | 498.00 | 8.47 | 9.10 | ||
S-SL-CJ-R-22-1 | 34.48 | 0.0220 | 498.00 | 10.96 | 8.96 | ||
S-SL-CJ-R-22-2 | 34.48 | 0.0220 | 498.00 | 10.96 | 8.00 | ||
S-CL-CJ-R-9-1 | 32.89 | 0.009 | 498.00 | 4.48 | 5.17 | ||
S-CL-CJ-R-9-2 | 32.89 | 0.0090 | 498.00 | 4.48 | 6.76 | ||
S-CL-CJ-R-13-1 | 31.99 | 0.0130 | 498.00 | 6.47 | 7.07 | ||
S-CL-CJ-R-13-2 | 31.99 | 0.0130 | 498.00 | 6.47 | 6.53 | ||
NWP | Mattock et al. (1976) | M0 | 27.13 | 0.0000 | 0.00 | 0.00 | 4.07 |
M1 | 28.82 | 0.0044 | 350.96 | 1.54 | 5.24 | ||
M2 | 26.89 | 0.0088 | 363.37 | 3.20 | 6.76 | ||
M3 | 27.55 | 0.0132 | 360.61 | 4.76 | 7.65 | ||
M4 | 28.61 | 0.0176 | 350.96 | 6.18 | 7.86 | ||
M5 | 27.13 | 0.0220 | 363.37 | 8.00 | 8.48 | ||
M6 | 28.41 | 0.0264 | 363.37 | 9.60 | 9.10 | ||
Mattock (1976) | B1 | 40.27 | 0.0044 | 353.51 | 1.56 | 3.36 | |
B2 | 40.27 | 0.0088 | 348.54 | 3.07 | 4.83 | ||
B3 | 41.75 | 0.0132 | 353.51 | 4.66 | 7.27 | ||
B4 | 41.75 | 0.0176 | 371.09 | 6.53 | 8.80 | ||
B5 | 40.65 | 0.0256 | 339.58 | 8.70 | 10.83 | ||
B6 | 40.65 | 0.0320 | 339.58 | 10.87 | 11.72 | ||
D1 | 25.99 | 0.0044 | 353.51 | 1.55 | 4.07 | ||
D2 | 25.99 | 0.0088 | 353.51 | 3.11 | 6.34 | ||
D3 | 20.27 | 0.0132 | 386.12 | 5.10 | 6.96 | ||
D4A | 17.20 | 0.0176 | 372.33 | 6.55 | 6.85 | ||
D4 | 20.27 | 0.0176 | 386.12 | 6.79 | 6.91 | ||
Mansur et al. (2008) | AN-2 | 40.20 | 0.0089 | 530.00 | 4.71 | 8.18 | |
AN-4 | 40.20 | 0.0178 | 530.00 | 9.42 | 10.17 | ||
AN-6 | 40.20 | 0.0267 | 530.00 | 14.13 | 12.92 | ||
Shaw and Sneed (2014) | N-5-R-4 | 33.51 | 0.0133 | 456.00 | 6.06 | 8.21 | |
N-5-R-5 | 33.51 | 0.0133 | 456.00 | 6.06 | 7.45 | ||
N-5-R-6 | 33.51 | 0.0133 | 456.00 | 6.06 | 7.45 | ||
N-8-R-1 | 52.06 | 0.0133 | 456.00 | 6.06 | 10.34 | ||
N-8-R-2 | 52.06 | 0.0133 | 456.00 | 6.06 | 7.79 | ||
N-8-R-3 | 52.06 | 0.0133 | 456.00 | 6.06 | 8.96 | ||
HSP | Kahn and Mitchell (2002) | SF-7-1-CJ | 80.91 | 0.0051 | 413.70 | 2.10 | 6.21 |
SF-7-2-CJ | 80.91 | 0.0102 | 413.70 | 4.20 | 9.43 | ||
SF-7-3-CJ | 85.99 | 0.0152 | 413.70 | 6.30 | 12.67 | ||
SF-7-4-CJ | 85.99 | 0.0203 | 413.70 | 8.39 | 15.24 | ||
SF-10-3-CJ | 89.31 | 0.0152 | 413.70 | 6.30 | 13.09 | ||
SF-10-4-CJ | 89.31 | 0.0203 | 413.70 | 8.39 | 14.49 | ||
SF-14-1-CJ | 101.74 | 0.0051 | 413.70 | 2.10 | 10.45 | ||
SF-14-2-CJ | 101.74 | 0.0102 | 413.70 | 4.20 | 11.40 | ||
SF-14-3-CJ | 104.93 | 0.0152 | 413.70 | 6.30 | 15.48 | ||
SF-14-4-CJ | 104.93 | 0.0203 | 413.70 | 8.39 | 17.60 | ||
Mansur et al. (2008) | AM-2 | 69.00 | 0.0089 | 530.00 | 4.71 | 7.50 | |
AM-3 | 69.00 | 0.0133 | 530.00 | 7.07 | 11.50 | ||
AM-4 | 69.00 | 0.0178 | 530.00 | 9.42 | 14.03 | ||
AH-2 | 87.00 | 0.0089 | 530.00 | 4.71 | 7.78 | ||
AH-3 | 87.00 | 0.0133 | 530.00 | 7.07 | 12.36 | ||
AH-4 | 87.00 | 0.0178 | 530.00 | 9.42 | 14.17 | ||
B1-4 | 73.20 | 0.0089 | 300.00 | 2.67 | 6.73 | ||
B2-2 | 84.90 | 0.0042 | 300.00 | 1.34 | 5.17 | ||
B2-4 | 84.90 | 0.0089 | 300.00 | 2.67 | 7.32 | ||
B2-5 | 84.90 | 0.0112 | 300.00 | 3.36 | 8.21 | ||
B2-6 | 84.90 | 0.0134 | 300.00 | 4.02 | 9.17 | ||
B3-4 | 95.20 | 0.0089 | 300.00 | 2.67 | 7.97 | ||
B4-2 | 106.40 | 0.0045 | 300.00 | 1.34 | 6.01 | ||
B4-4 | 106.40 | 0.0089 | 300.00 | 2.67 | 8.43 | ||
B4-5 | 106.40 | 0.0112 | 300.00 | 3.36 | 9.24 | ||
B4-6 | 106.40 | 0.0134 | 300.00 | 4.02 | 9.96 |
Concrete type | Author | Specimens | f′c (MPa) |
ρ
| fy (MPa) | ρfy (MPa) | v (MPa) |
---|---|---|---|---|---|---|---|
NWB | Loov and Patnaik (1994) | Beam 14 | 19.60 | 0.0019 | 431.00 | 0.82 | 1.93 |
Patnaik (2001) | SR1.1 | 19.80 | 0.0005 | 558.00 | 0.30 | 1.78 | |
SR1.2 | 19.80 | 0.0005 | 558.00 | 0.30 | 2.37 | ||
SR2.1 | 23.50 | 0.0014 | 520.00 | 0.75 | 1.89 | ||
SR2.2 | 23.50 | 0.0014 | 520.00 | 0.75 | 1.61 | ||
SR3.1 | 17.00 | 0.0008 | 704.00 | 0.59 | 1.91 | ||
SR3.2 | 17.00 | 0.0008 | 704.00 | 0.59 | 1.73 | ||
SR4.1 | 34.80 | 0.0007 | 641.00 | 0.44 | 1.74 | ||
SR4.2 | 26.70 | 0.0007 | 641.00 | 0.44 | 1.35 | ||
SR4.3 | 34.80 | 0.0012 | 641.00 | 0.79 | 1.48 | ||
SR4.4 | 26.70 | 0.0012 | 641.00 | 0.79 | 1.53 | ||
SR4.5 | 34.80 | 0.0018 | 641.00 | 1.14 | 2.99 | ||
SR4.6 | 26.70 | 0.0018 | 641.00 | 1.14 | 1.94 | ||
SR5.1 | 34.80 | 0.0025 | 641.00 | 1.59 | 2.11 | ||
SR5.2 | 26.70 | 0.0025 | 641.00 | 1.59 | 2.25 | ||
SR5.3 | 34.80 | 0.0031 | 641.00 | 1.99 | 3.01 | ||
SR5.4 | 26.70 | 0.0031 | 641.00 | 1.99 | 2.81 | ||
SR5.5 | 34.80 | 0.0041 | 641.00 | 2.65 | 4.56 | ||
SR5.6 | 26.70 | 0.0041 | 641.00 | 2.65 | 4.13 | ||
ST1.1 | 34.40 | 0.0052 | 340.00 | 1.78 | 3.16 | ||
ST1.2 | 32.40 | 0.0052 | 340.00 | 1.78 | 3.61 | ||
ST2.1 | 33.90 | 0.0070 | 340.00 | 2.37 | 4.70 | ||
ST2.2 | 31.60 | 0.0070 | 340.00 | 2.37 | 5.08 | ||
ST3.1 | 26.90 | 0.0105 | 340.00 | 3.56 | 5.90 | ||
ST3.2 | 30.30 | 0.0105 | 340.00 | 3.56 | 6.30 | ||
LCP | Mattock et al. (1976) | B1 | 25.79 | 0.0044 | 341.99 | 1.50 | 3.10 |
B2 | 23.17 | 0.0088 | 350.96 | 3.09 | 4.50 | ||
B3 | 26.96 | 0.0132 | 350.96 | 4.63 | 5.79 | ||
B4 | 28.27 | 0.0176 | 338.54 | 5.96 | 6.48 | ||
B5 | 27.30 | 0.0220 | 348.20 | 7.66 | 6.90 | ||
B6 | 29.30 | 0.0264 | 357.16 | 9.43 | 7.96 | ||
D1 | 41.34 | 0.0044 | 357.16 | 1.57 | 2.55 | ||
D2 | 41.34 | 0.0088 | 360.61 | 3.17 | 4.61 | ||
D3 | 39.37 | 0.0132 | 360.61 | 4.76 | 5.32 | ||
D4 | 39.37 | 0.0176 | 360.61 | 6.34 | 7.05 | ||
D5 | 38.61 | 0.0220 | 360.61 | 7.94 | 7.46 | ||
D6 | 38.61 | 0.0264 | 357.16 | 9.43 | 8.41 | ||
Hoff (1992) | LWC1-1 | 58.54 | 0.0052 | 370.00 | 1.94 | 1.98 | |
LWC1-2 | 58.68 | 0.0052 | 370.00 | 1.94 | 2.52 | ||
LWC1-3 | 57.16 | 0.0052 | 370.00 | 1.94 | 2.85 | ||
LWC1-4 | 58.54 | 0.0095 | 469.00 | 4.47 | 5.25 | ||
LWC1-5 | 58.68 | 0.0095 | 476.00 | 4.53 | 4.69 | ||
LWC1-6 | 57.16 | 0.0095 | 469.00 | 4.47 | 5.01 | ||
LWC2-1 | 63.92 | 0.0052 | 370.00 | 1.93 | 3.37 | ||
LWC2-2 | 60.40 | 0.0052 | 370.00 | 1.93 | 2.31 | ||
LWC2-3 | 60.19 | 0.0052 | 370.00 | 1.93 | 2.06 | ||
LWC2-4 | 57.02 | 0.0095 | 469.00 | 4.47 | 5.10 | ||
LWC2-5 | 60.40 | 0.0095 | 472.00 | 4.50 | 4.77 | ||
LWC2-6 | 60.19 | 0.0095 | 472.00 | 4.50 | 4.69 | ||
LWC3-1 | 71.09 | 0.0053 | 497.00 | 2.61 | 4.61 | ||
LWC3-2 | 75.22 | 0.0053 | 497.00 | 2.61 | 3.78 | ||
LWC3-3 | 75.98 | 0.0053 | 497.00 | 2.61 | 4.03 | ||
LWC3-4 | 71.09 | 0.0095 | 461.00 | 4.36 | 6.00 | ||
LWC3-5 | 75.22 | 0.0096 | 461.00 | 4.41 | 6.00 | ||
LWC3-6 | 75.98 | 0.0095 | 461.00 | 4.39 | 6.16 | ||
Shaw and Sneed (2014) | S-5-S-1 | 31.37 | 0.0133 | 456.00 | 6.06 | 5.38 | |
S-5-S-2 | 31.37 | 0.0133 | 456.00 | 6.06 | 4.76 | ||
S-5-S-3 | 31.37 | 0.0133 | 456.00 | 6.06 | 5.52 | ||
S-8-S-1 | 49.71 | 0.0133 | 456.00 | 6.06 | 9.31 | ||
S-8-S-2 | 49.71 | 0.0133 | 456.00 | 6.06 | 8.07 | ||
S-8-S-3 | 49.71 | 0.0133 | 456.00 | 6.06 | 8.21 | ||
Sneed et al. (2016) | S-SL-CJ-S-9-1 | 37.10 | 0.009 | 498.00 | 4.48 | 3.72 | |
S-SL-CJ-S-9-2 | 37.10 | 0.009 | 498.00 | 4.48 | 4.55 | ||
S-SL-CJ-S-13-1 | 38.41 | 0.013 | 498.00 | 6.47 | 5.50 | ||
S-SL-CJ-S-13-2 | 38.41 | 0.013 | 498.00 | 6.47 | 6.79 | ||
S-SL-CJ-S-17-1 | 34.13 | 0.017 | 498.00 | 8.47 | 6.62 | ||
S-SL-CJ-S-17-2 | 34.13 | 0.017 | 498.00 | 8.47 | 6.55 | ||
S-SL-CJ-S-22-1 | 34.48 | 0.022 | 498.00 | 10.96 | 6.96 | ||
S-SL-CJ-S-22-2 | 34.48 | 0.022 | 498.00 | 10.96 | 7.86 | ||
S-CL-CJ-S-9-1 | 32.89 | 0.009 | 498.00 | 4.48 | 4.48 | ||
S-CL-CJ-S-9-2 | 32.89 | 0.009 | 498.00 | 4.48 | 5.31 | ||
S-CL-CJ-S-13-1 | 31.99 | 0.013 | 498.00 | 6.47 | 5.71 | ||
S-CL-CJ-S-13-2 | 31.99 | 0.013 | 498.00 | 6.47 | 5.63 | ||
S-CL-CJ-S-17-1 | 31.37 | 0.017 | 498.00 | 8.47 | 6.00 | ||
S-CL-CJ-S-17-2 | 31.37 | 0.017 | 498.00 | 8.47 | 6.83 | ||
NWP | Mattock et al. (1976) | N1 | 28.82 | 0.0044 | 350.96 | 1.54 | 3.17 |
N2 | 26.89 | 0.0088 | 363.37 | 3.20 | 5.38 | ||
N3 | 27.55 | 0.0132 | 360.61 | 4.76 | 6.62 | ||
N4 | 28.61 | 0.0176 | 350.96 | 6.18 | 7.93 | ||
N5 | 27.13 | 0.0220 | 350.96 | 7.72 | 8.10 | ||
N6 | 28.41 | 0.0264 | 344.75 | 9.10 | 8.21 | ||
Kahn and Mitchell (2002) | SF-4-1-C | 46.92 | 0.00,425 | 413.70 | 1.76 | 4.02 | |
SF-4-2-C | 46.92 | 0.00850 | 413.70 | 3.52 | 6.40 | ||
SF-4-3-C | 46.92 | 0.01275 | 413.70 | 5.27 | 8.18 | ||
Shaw and Sneed (2014) | N-5-S-4 | 33.51 | 0.0133 | 456.00 | 6.06 | 4.55 | |
N-5-S-5 | 33.51 | 0.0133 | 456.00 | 6.06 | 4.83 | ||
N-5-S-6 | 33.51 | 0.0133 | 456.00 | 6.06 | 5.45 | ||
N-8-S-1 | 52.06 | 0.0133 | 456.00 | 6.06 | 9.10 | ||
N-8-S-2 | 52.06 | 0.0133 | 456.00 | 6.06 | 7.45 | ||
N-8-S-3 | 52.06 | 0.0133 | 456.00 | 6.06 | 7.72 | ||
HSP | Kahn and Mitchell (2002) | SF-10-1-CJ | 98.78 | 0.00507 | 413.70 | 2.10 | 3.65 |
SF-10-2-CJ | 83.11 | 0.01015 | 413.70 | 4.20 | 5.67 |
Interface condition | Concrete type | Author | Mean | Standard deviation | Coefficient of variation | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Rough interface | NWB | Saemann and Washa (1964) | 0.99 | 1.00 | 0.94 | 0.15 | 0.19 | 0.19 | 0.15 | 0.19 | 0.20 |
Loov and Patnaik (1994) | 0.93 | 0.17 | 0.18 | ||||||||
Kahn and Slapkus (2004) | 1.17 | 0.27 | 0.23 | ||||||||
LCP | Mattock et al. (1976) | 1.10 | 0.98 | 0.13 | 0.13 | 0.12 | 0.14 | ||||
Shaw and Sneed (2014) | 0.97 | 0.10 | 0.10 | ||||||||
Sneed et al. (2016) | 0.90 | 0.09 | 0.10 | ||||||||
NWP | Mattock et al. (1976) | 1.17 | 1.00 | 0.16 | 0.18 | 0.14 | 0.18 | ||||
Mattock (1976) | 0.89 | 0.08 | 0.09 | ||||||||
Mansur et al. (2008) | 0.95 | 0.16 | 0.17 | ||||||||
Shaw and Sneed (2014) | 0.98 | 0.10 | 0.10 | ||||||||
HSP | Kahn and Mitchell (2002) | 0.91 | 0.79 | 0.14 | 0.16 | 0.15 | 0.20 | ||||
Mansur et al. (2008) | 0.72 | 0.12 | 0.17 | ||||||||
Smooth interface | NWB | Loov and Patnaik (1994) | 1.31 | 1.25 | 1.11 | 0.00 | 0.34 | 0.30 | 0.00 | 0.27 | 0.27 |
Patnaik (2001) | 1.25 | 0.35 | 0.28 | ||||||||
LCP | Mattock et al. (1976) | 1.20 | 1.00 | 0.21 | 0.24 | 0.18 | 0.23 | ||||
Hoff (1992) | 1.03 | 0.10 | 0.10 | ||||||||
Shaw and Sneed (2014) | 1.20 | 0.17 | 0.14 | ||||||||
Sneed et al. (2016) | 0.78 | 0.16 | 0.20 | ||||||||
NWP | Mattock et al. (1976) | 1.51 | 1.32 | 0.10 | 0.24 | 0.06 | 0.18 | ||||
Kahn and Mitchell (2002) | 1.11 | 0.21 | 0.19 | ||||||||
Shaw and Sneed (2014) | 1.37 | 0.13 | 0.10 | ||||||||
HSP | Kahn and Mitchell (2002) | 0.72 | 0.70 | 0.13 | 0.13 | 0.18 | 0.19 |