Figure 1
Figure 2
Figure 3
![Bridge location (Microsoft Bing Maps) [18]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/6473793b4e662f30ba53f835/j_sgem-2021-0001_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKHTUB44VK%2F20260316%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260316T034852Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEP%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIQCzJZ4bVC6Upw1ddg7F2AXjcyG5Jd%2BkYifCLCmIYhcSHQIgRicZHSGGdymvEmpyUj8WrnWiSIaXbn%2BHqGQSAdHOaQ4qxAUIyP%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDNv4uuVPgghO5o3m2SqYBWySS8qaLe3K3%2B2KpuYM3E7ALk6xGA%2BWp5FgDLAR5RJQ7Hfyxhykr8o5k07o46M6TE1W1t99hvtk45GSzQvmb0RDG8DT6ZnP0%2FyWs%2BX5JBM6EswuEAWBzLxKN76sQ2j6qAnZqTalraPMSIOAjC8nIqa0m907lmu2zqesdXx2nZyqSSNalLjvzyZM0OMZGxgJ2cuXKv29xGShwFnQGNKebx5pMqgNKCieMpQB4AQxaTb4VEJDlOO%2BdZJ9ZdrpuMy%2FcA%2FsJLokSwresrbC8T19Cu1%2Bqvj39w2vAfjFwti0Fx8xdy6OWMWnISeXTuQchbtFZSMfWhTi97aGif%2BUTk3JcRG4ATHFScwL%2BaEE%2FGDDI6cmFnXDksZ7%2FUg9pkSCbc3pQuF2fYQncJektDdkEDLHI1OGE2IqBeAgeV0GykqdTxkJLh5l2%2Fevp8lgi6QFH9%2FjTWr1VcnWvYqGhScBJsQx%2BRex%2FU9b1t1yq27O7Ac2RY63xjxHTRoVOvLaoPvRGMEG%2FSscRLhkN2ssInVCzlGyIBH7lEJ5qsaMprY8l%2FR%2BC4hQuADGNIDBQIUiQn1kaw0dLCjU9%2BQhuQ0MhK0%2FN9P4tnpb%2Bxljvx5Jctovv3DKTqgkhifaHc5KQ%2BIzwg%2FAija4CZvsVagXspvNbYXkBWBqQ%2BV3%2FYsrldlV0vPN8KNi8oSUwHrahhMX6vdocwtO4NvLV%2FRn3W0RD93I8llwSzBkUAq5Q%2FbodOUmhHDO9TIevmirtd6DAvJUisKEGCU5lQOClY7%2BnthKIJ2fWk9DzOFkFzTlo8nSBy3%2BuyGslPo7XHs12hsWMP3d0G9bKTdj7wAZMTkFKTN%2Fx8Fa8bni6RggLwXMYhBF3zAzCM4FtN2HXM5g4gepJqxfCeow4%2FTczQY6sQEhaRPmku%2BUsY291osXumyhcrbioiCybhOb%2FcKz8tK30IRUTgHjkN%2FNbDp85EmHe7FO9OIjlVmntY2%2BFifqeu7AxRS64yfeP3l360TYPLi0nWEoP5Pj4zi8n4TwUQ8y7Lzg6k60TIe5fzJjONL%2Frt%2FtrBsb1VITyTnAJoKvbOsF1or7I2kOWdfU4UJMEroaeyFubzxDu357ze2B3UkklAvzKxSF2UmZSzJ9AE51mRePPpY%3D&X-Amz-Signature=3966f8b8bdc4aea1db8e9ee50f9541a159867d387a60a2057081dadc57cab586&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 4
![Partial load factors consistent with diagram A/4a [8].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/6473793b4e662f30ba53f835/j_sgem-2021-0001_fig_004.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKHTUB44VK%2F20260316%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260316T034852Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEP%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIQCzJZ4bVC6Upw1ddg7F2AXjcyG5Jd%2BkYifCLCmIYhcSHQIgRicZHSGGdymvEmpyUj8WrnWiSIaXbn%2BHqGQSAdHOaQ4qxAUIyP%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDNv4uuVPgghO5o3m2SqYBWySS8qaLe3K3%2B2KpuYM3E7ALk6xGA%2BWp5FgDLAR5RJQ7Hfyxhykr8o5k07o46M6TE1W1t99hvtk45GSzQvmb0RDG8DT6ZnP0%2FyWs%2BX5JBM6EswuEAWBzLxKN76sQ2j6qAnZqTalraPMSIOAjC8nIqa0m907lmu2zqesdXx2nZyqSSNalLjvzyZM0OMZGxgJ2cuXKv29xGShwFnQGNKebx5pMqgNKCieMpQB4AQxaTb4VEJDlOO%2BdZJ9ZdrpuMy%2FcA%2FsJLokSwresrbC8T19Cu1%2Bqvj39w2vAfjFwti0Fx8xdy6OWMWnISeXTuQchbtFZSMfWhTi97aGif%2BUTk3JcRG4ATHFScwL%2BaEE%2FGDDI6cmFnXDksZ7%2FUg9pkSCbc3pQuF2fYQncJektDdkEDLHI1OGE2IqBeAgeV0GykqdTxkJLh5l2%2Fevp8lgi6QFH9%2FjTWr1VcnWvYqGhScBJsQx%2BRex%2FU9b1t1yq27O7Ac2RY63xjxHTRoVOvLaoPvRGMEG%2FSscRLhkN2ssInVCzlGyIBH7lEJ5qsaMprY8l%2FR%2BC4hQuADGNIDBQIUiQn1kaw0dLCjU9%2BQhuQ0MhK0%2FN9P4tnpb%2Bxljvx5Jctovv3DKTqgkhifaHc5KQ%2BIzwg%2FAija4CZvsVagXspvNbYXkBWBqQ%2BV3%2FYsrldlV0vPN8KNi8oSUwHrahhMX6vdocwtO4NvLV%2FRn3W0RD93I8llwSzBkUAq5Q%2FbodOUmhHDO9TIevmirtd6DAvJUisKEGCU5lQOClY7%2BnthKIJ2fWk9DzOFkFzTlo8nSBy3%2BuyGslPo7XHs12hsWMP3d0G9bKTdj7wAZMTkFKTN%2Fx8Fa8bni6RggLwXMYhBF3zAzCM4FtN2HXM5g4gepJqxfCeow4%2FTczQY6sQEhaRPmku%2BUsY291osXumyhcrbioiCybhOb%2FcKz8tK30IRUTgHjkN%2FNbDp85EmHe7FO9OIjlVmntY2%2BFifqeu7AxRS64yfeP3l360TYPLi0nWEoP5Pj4zi8n4TwUQ8y7Lzg6k60TIe5fzJjONL%2Frt%2FtrBsb1VITyTnAJoKvbOsF1or7I2kOWdfU4UJMEroaeyFubzxDu357ze2B3UkklAvzKxSF2UmZSzJ9AE51mRePPpY%3D&X-Amz-Signature=e4221f01502837fd9bbb50952b85ef9d5b478b8beb4b17f35634ba69f32bff91&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
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Figure 11
| kh | Modulus of horizontal subgrade reaction (backfill material) |
| a, b | Coefficients dependent on soil type and consistency, e.g. gravel a = 1/4, b = 1/2 |
| Ep | Pressuremeter modulus of soil, Ep ≈ β qc, |
| qc | Cone soil penetration resistance determined by cone penetration test (CPT) |
| r0 | Reference radius, r0 = 0.3m |
| D | Bridge abutment wall height, D = 5.9 m, |
| r | Radius, a half of abutment wall height r = D / 2 = 5.9 / 2 = 2.95 m |
Bending moment values used for bridge design_
| Member | Value [kNm] |
|---|---|
| Upper floor slab, midspan | 362 |
| Upper floor slab, at support | 333 |
| Bottom slab, midspan | 196 |
| Bottom slab, at support | 287 |
| Abutment wall at midspan | 182 |
Basic bridge parameters_
| Elements | |
|---|---|
| Effective span length | Lt=6.45 [m] |
| Overall span length | Lp=6.9 [m] |
| Skew angle | a=90° |
| Wall, upper floor slab, and bottom slab thickness | h=0.45 [m] |
| Minimal soil surcharge height over bridge structure | Hn=1.1 [m] |
| Length of bridge without wing walls | Lo=30.6 [m] |
| Overall length of wing walls | Ls=8.49 [m] |
| Angle of rotation of wing walls relative to bridge length | b=45° |
| Span height to length ratio | 1:15 |
| Embankment height | 6.0 [m] |
| Bottom slab and wing wall strip footing concrete class | C32/40 |
| Bridge wall, upper floor slab, wing wall, and string course concrete class | C40/50 |
| Live load type | HA and HB45 |
Grading of 6N and 6P class backfills [14]_
| Square mesh sieve [mm] | Percent passing sieve [%] | |
|---|---|---|
| 6N | 6P | |
| 125 | 100 | |
| 100 | 100 | |
| 75 | 65–100 | |
| 37,5 | 45–100 | |
| 10 | 15–75 | |
| 5 | 10–60 | |
| 0.6 | 0–30 | |
| 0.063 | 0–15 | |
Stiffness of elastic constraints for M-5 model_
| Symbol | Range of influence [m] | Modulus of subgrade reaction [kN/m3] | Stiffness of elastic constraints [kN/m2] |
|---|---|---|---|
| k1 | 0.3375 | kh = 80,000 | 0.3375 • 80,000 = 27,000 |
| k2 | 0.3625 | 0.3625 • 80,000 = 29,000 | |
| k3 | 0.5 | 0.5 • 80,000 = 40,000 | |
| k4 | 0.3375 | kv = 37,068 | 0.3375 • 37,068 = 12,510 |
| k5 | 0.3625 | 0.3625 • 37,068 = 13,437 | |
| k6 | 0.5 | 0.5 • 37,068 = 18,536 |
Concrete modulus of elasticity and Poisson's ratios [11]_
| Member | ||
|---|---|---|
| Bottom slab, | 33.34 [GPa] | |
| concrete C32/40 | Ecm, | 0.2 |
| Abutment walls, upper floor slab, | ν | 35.22 [GPa] |
| concrete C40/50 | 0.2 |
Model and parameters analyzed_
| Model | kh [kN/m3] | kv [kN/m3] |
|---|---|---|
| M-1 | 10,000 | 10,000 |
| M-2 | 37,000 | 10,000 |
| M-3 | 120,000 | 10,000 |
| M-4 | 10,000 | 80,000 |
| M-5 | 37,068 | 80,000 |
| M-6 | 120,000 | 80,000 |
| M-7 | 10,000 | 120,000 |
| M-8 | 37,000 | 120,000 |
| M-9 | 120,000 | 120,000 |
| M-10 | 0 | ∞ |
Permanent load_
| Load | Values [kN/m] | |
|---|---|---|
| Road pavement | V1 | 2.3 • 0.2 • 9.81 • 1.75 • 1.1 = 8.7 |
| Surcharge over bridge | V2 | 2.0 • 1.1 • 9.81 • 1.2 • 1.1 = 28.5 |
| Earth pressure behind left abutment wall | HL1 | (2.3 • 0.2+2.0 • 1.1) • 9.81 • 0.33 • 1.5 • 1.1 = 14.2 |
| HL2 | (2.3 • 0.2+2.0 • (1.1 + 5.9)) • 9.81 • 0.33 • 1.5 • 1.1 = 77.2 | |
| Earth pressure behind right abutment wall | HP1 | (2.3 • 0.2+2.0 • 1.1) • 9.81 • 0.6 • 1.0 • 1.0 = 15.7 |
| HP2 | (2.3 • 0.2+2.0 • (1.1 + 5.9)) • 9.81 • 0.6 • 1.0 • 1.0 = 85.1 | |
| Self-weight of concrete | CW | 2.4 • 1 • 0.45 • 9.81 • 1.2 • 1.1 = 13.99 |