Seismic Analysis and Design of Retaining Walls, Buried Structures, Slopes, and Embankments (2008) / Chapter Skim
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Pages 105-130
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From page 105... ...
These results consider both flexible and rigid culverts, burial depths that range from 0.5 to 5 diameters, various cross-sectional geometries (for example, circular and rectangular) and wall stiffnesses, and different properties of the surrounding soil.
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From page 106... ...
. Flexible culverts and pipes respond to loads differently than rigid culverts and pipes.
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From page 107... ...
Ovaling and racking deformations.
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From page 108... ...
When subject to ovaling/racking deformations, a flexural type failure mode due to the combined effects of bending moment and thrust force must be checked. The flexural failure mode is typically the main concern for rigid culverts and pipes, such as those constructed with reinforced concrete.
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From page 109... ...
The latter is a very important failure mode that must be considered for rigid culverts and pipes (such as those constructed with reinforced concrete)
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From page 110... ...
; γt = total unit weight of soil; H = soil cover thickness measured from the ground surface to the crown elevation; d = diameter of the circular culvert or pipe; Rd = depth-dependent stress reduction factor; = 1.0 − 0.00233z for z <30 feet where z is the depth to the midpoint of the culvert or pipe; = 1.174 − 0.00814z for 30 feet < z <75 feet; and Gm = effective, strain-compatible shear modulus of the ground surrounding the culvert or pipe. Alternatively, the maximum free-field shearing strain also can be estimated by a more refined free-field site response analysis (for example, conducting SHAKE analyses)
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From page 111... ...
tends to be the governing factor for the bending response of the lining (distortion) while the compressibility ratio (C)
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From page 112... ...
and the expression of k2 suggests that the maximum lining thrust/hoop force response is a function of compressibility ratio, flexibility ratio, and Poisson's Ratio. Figures 9-4 through 9-6 graphically describe their interrelationships.
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From page 113... ...
Step 4: Based on the flexibility ratio obtained form Step 3 above, determine the racking ratio (Rrec) for the structure using Figure 9-5 or the following expression: The racking ratio is defined as the ratio of actual racking deformation of the structure to the free-field racking deformation in the ground.
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From page 114... ...
114 Figure 9-8. Relative stiffness of soil versus rectangular frame.
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From page 115... ...
started with a 10-foot diameter corrugated steel pipe (or an equivalent liner plate lining) and a 10-foot diameter precast concrete pipe to represent a flexible and a rigid culvert structure, respectively.
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From page 116... ...
Culvert Properties Rigid Culvert (Concrete Pipe) Flexible Culvert (Corrugated Steel Pipe)
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From page 117... ...
Figures 9-11 through 9-15 show the finite difference meshes (using computer program FLAC) used for the parametric analysis accounting for the variable culvert embedment depths.
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From page 118... ...
From these analyses the following observations were made: • Flexible culverts experience greater deformation than the ground deformation in the free-field for both full-slip and no-slip cases. • Rigid culverts experience less deformation than the ground deformation in the free-field for both full-slip and no-slip cases.
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From page 119... ...
Based on the results from the analysis, it appears that the potential for overestimation of bending demand would occur for rigid types of culvert structures buried at shallow depths by as much as 30 to 35 percent. Figure 9-24 also suggests that the effects of embedment depth on bending response are insignificant when the embedment depth ratio is greater than about 3.
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From page 120... ...
Culvert lining bending moment distribution (for flexible culvert in Set 1, Case 1 geometry)
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From page 121... ...
9-7 Culvert Diameter Change (ft) for No-Slip Interface Using FLAC Analysis Diameter Change Ratio for No-Slip to Full-Slip For Flexible Culvert Case 1 (H/d=5)
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From page 122... ...
, the Set 2 results indicated that: • The ratios of the actual culvert deformation to free-field ground deformation were significantly reduced, reflecting the effect of higher culvert lining stiffness because of the reduced culvert diameter. • The bending and thrust force response of the smaller 5-foot diameter culvert, when normalized to the closeform solutions, show similar trends to that of the larger culvert (10-foot diameter)
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From page 123... ...
Embedment effects on culvert maximum bending moments (parametric analysis -- Set 2)
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From page 124... ...
Embedment effects on culvert maximum bending moments (parametric analysis -- Set 3)
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From page 125... ...
Based on the discussions presented in Section 9-4, when the flexibility ratio is close to 1.0, the ovaling deformation of the lining should be about the same as that of the surrounding ground. Results from the FLAC analysis in Figure 9-34 show that for the rigid culvert the ratio of the culvert deformation to the ground deformation is very close to 1.0, verifying the validity Culvert Properties Flexible Culvert (Corrugated HDPE)
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From page 126... ...
Embedment effects on culvert maximum thrust/hoop forces (parametric analysis -- Set 5)
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From page 127... ...
Figure 9-36. Embedment effects on culvert maximum bending moments (parametric analysis -- Set 5)
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From page 128... ...
For Cases 2 through 5, the flexibility ratios are all greater than 1.0, suggesting that the structure would deform more than the ground in the free-field, and results shown in Figures 9-39 through 9-42 support this theory. Figure 9-43 plots the racking ratio as a function of the flexibility ratio based on the results obtained from the FLAC analysis and then compares them with the recommended
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From page 129... ...
Racking stiffness of culverts and flexibility ratios.
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From page 130... ...
. – Based on the results of the parametric analysis, it appears that burial depth has insignificant effects on the culvert racking deformations and therefore no further modifications to the procedure presented in Section 9.5.2 is necessary.
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