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Impact of subgrade and backfill stiffness on values and distribution of bending moments in integral box bridge

Andrzej Helowicz
Andrzej Helowicz
   | Jun 30, 2021
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Article Category: Original Study
Published Online: Jun 30, 2021
Page range: 90 - 98
Received: Mar 26, 2020
Accepted: Jan 31, 2021
DOI: https://doi.org/10.2478/sgem-2021-0001
Keywords
© 2021 Andrzej Helowicz, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Longitudinal section of the bridge.
Longitudinal section of the bridge.

Figure 2

Cross-section of the bridge.
Cross-section of the bridge.

Figure 3

Bridge location (Microsoft Bing Maps) [18]
Bridge location (Microsoft Bing Maps) [18]

Figure 4

Partial load factors consistent with diagram A/4a [8].
Partial load factors consistent with diagram A/4a [8].

Figure 5

Load denotations and load action directions.
Load denotations and load action directions.

Figure 6

Elastic constrains location.
Elastic constrains location.

Figure 7

Beams and nodes location and elastic constraints distribution in cross-section.
Beams and nodes location and elastic constraints distribution in cross-section.

Figure 8

Distribution of bending moments in bridge's upper floor slab.
Distribution of bending moments in bridge's upper floor slab.

Figure 9

Distribution of bending moments in bridge's left abutment wall.
Distribution of bending moments in bridge's left abutment wall.

Figure 10

Distribution of bending moments in bridge's right abutment wall.
Distribution of bending moments in bridge's right abutment wall.

Figure 11

Distribution of bending moments in bridge's bottom slab.
Distribution of bending moments in bridge's bottom slab.

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
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