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

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

Studia Geotechnica et Mechanica
Volume 46 (2024): Issue 4 (December 2024)
By: Andrzej Helowicz  
Open Access
|Dec 2024

Figures & Tables

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_

ElementPier footingAbutment footing
βx (L/B)L=8 m, B=4 mL=10 m, B=3 m
βx =0.944βx =0.976
βy (L/B)L=4 m, B=8 mL=3 m, B=10 m
βy =1.012βy =1.096
βz (L/B)L=4 m, B=8 mL=3 m, B=10 m
βz =2.175βz =2.3
βφx (L/B)L=4 m, B=8 mL=3 m, B=10 m
βφx =0.435βφx =0.402
βφy (L/B)L=8 m, B=4 mL=10 m, B=3 m
βφy =0.595βφy =0.721
kx (kN/m)427,021427,819
ky (kN/m)457,832480,236
kz (kN/m)560,860574,345
kφx (kN/m/rad)2,540,6261,650,517
kφy (kN/m/rad)6,944,4379,854,189

Material properties used in the analysis_

ModelA, B, C
SoilLoose sand and gravel [27]
Es (MN/m2)80 (Middle range value)
ν0.35
ϕ40 (model A)
G (MN/m2)30.8
L (m)3 and 4
B (m)10 and 8
Bridge structureConcrete C50/60
Ecm (MN/m2)37,000
ν0.2

Load applied to the structure_

Load typeValue
SW of the bridge structure SW24 kN/m3
UDL 110 kN/m2
UDL 225 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 constantsMotionReference
Vertical stiffnessBarkan (1962)
(3.1) kz=G1−νβzBL {k_z} = {G \over {\left( {1 - \nu } \right)}}{\beta _z}\sqrt {BL}
Horizontal stiffnessBarkan (1962)
(3.2) ky=21+νGβyBL {k_y} = 2\left( {1 + \nu } \right)G{\beta _y}\sqrt {BL}
Rocking stiffnessGorbunov-Posadov (1961)
(3.3) kϕ=G1−νβϕBL2 {k_\phi } = {G \over {\left( {1 - \nu } \right)}}{\beta _\phi }B{L^2}
DOI: https://doi.org/10.2478/sgem-2024-0026 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365
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Language: English
Page range: 337 - 348
Submitted on: Apr 17, 2024
Accepted on: Nov 11, 2024
Published on: Dec 22, 2024
Published by: Wroclaw University of Science and Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
design,
integral bridge,
intermediate support,
foundation stiffness,
pier
Related subjects:
Geosciences,
Geosciences, other,
Materials sciences,
Composites,
Porous materials,
Physics,
Mechanics and fluid dynamics

© 2024 Andrzej Helowicz, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.

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