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Analysis of numerical models of an integral bridge resting on an elastic half-space

Andrzej Helowicz

Andrzej Helowicz

Wroclaw University of Science and Technology, Faculty of Civil EngineeringWrocław, Poland
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Helowicz, Andrzej
  
22 dic 2024
Analysis of numerical models of an integral bridge resting on an elastic half-space's Cover Image
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Categoría del artículo: Original Study
Publicado en línea: 22 dic 2024
Páginas: 337 - 348
Recibido: 17 abr 2024
Aceptado: 11 nov 2024
DOI: https://doi.org/10.2478/sgem-2024-0026
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© 2024 Andrzej Helowicz, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1:

Analyzed integral bridge.
Analyzed integral bridge.

Figure 2:

Soil layer used in numerical models A and C.
Soil layer used in numerical models A and C.

Figure 3:

Finite element mesh of complex models A and C.
Finite element mesh of complex models A and C.

Figure 4:

Finite element mesh of simple model B.
Finite element mesh of simple model B.

Figure 5:

Location of the applied springs under the footing foundations in simple model B.
Location of the applied springs under the footing foundations in simple model B.

Figure 6:

Actual soil deformation and according to the theory of elasticity.
Actual soil deformation and according to the theory of elasticity.

Figure 7:

Bending moments in piers C1 and C2 where A and C are complex bridge models and B is a simple bridge model.
Bending moments in piers C1 and C2 where A and C are complex bridge models and B is a simple bridge model.

Figure 8:

Shear and axial forces in piers C1 and C2.
Shear and axial forces in piers C1 and C2.

Figure 9:

Horizontal and vertical displacements in piers C1 and C2 where Ux and Uy are horizontal displacements along the X-axis and Y-axis direction and Uz is the vertical displacement along the Z-axis direction.
Horizontal and vertical displacements in piers C1 and C2 where Ux and Uy are horizontal displacements along the X-axis and Y-axis direction and Uz is the vertical displacement along the Z-axis direction.

Spring constants_

Element Pier footing Abutment footing
βx (L/B) L=8 m, B=4 m L=10 m, B=3 m
βx =0.944 βx =0.976
βy (L/B) L=4 m, B=8 m L=3 m, B=10 m
βy =1.012 βy =1.096
βz (L/B) L=4 m, B=8 m L=3 m, B=10 m
βz =2.175 βz =2.3
βφx (L/B) L=4 m, B=8 m L=3 m, B=10 m
βφx =0.435 βφx =0.402
βφy (L/B) L=8 m, B=4 m L=10 m, B=3 m
βφy =0.595 βφy =0.721
kx (kN/m) 427,021 427,819
ky (kN/m) 457,832 480,236
kz (kN/m) 560,860 574,345
kφx (kN/m/rad) 2,540,626 1,650,517
kφy (kN/m/rad) 6,944,437 9,854,189

Material properties used in the analysis_

Model A, B, C
Soil Loose sand and gravel [27]
Es (MN/m2) 80 (Middle range value)
ν 0.35
ϕ 40 (model A)
G (MN/m2) 30.8
L (m) 3 and 4
B (m) 10 and 8
Bridge structure Concrete C50/60
Ecm (MN/m2) 37,000
ν 0.2

Load applied to the structure_

Load type Value
SW of the bridge structure SW 24 kN/m3
UDL 1 10 kN/m2
UDL 2 25 kN/m2
The characteristic value of the maximum expansion range of the uniform bridge temperature component ∆TN,exp=36°C

Equations for spring constants for a rectangular footing [21], [22]_

Spring constants Motion Reference
Vertical stiffness Barkan (1962)
kz=G1−νβzBL {k_z} = {G \over {\left( {1 - \nu } \right)}}{\beta _z}\sqrt {BL}
Horizontal stiffness Barkan (1962)
ky=21+νGβyBL {k_y} = 2\left( {1 + \nu } \right)G{\beta _y}\sqrt {BL}
Rocking stiffness Gorbunov-Posadov (1961)
kϕ=G1−νβϕBL2 {k_\phi } = {G \over {\left( {1 - \nu } \right)}}{\beta _\phi }B{L^2}
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Temas de la revista:
Geociencias, Geociencias, otros, Ciencia de los materiales, Compuestos, Materiales porosos, Física, Mecánica y dinámica de fluidos
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