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OCR for page 129
129 Figure 9-43. Recommended design racking curve. Figure 9-42. Racking ratios from FLAC analysis-- Case 5. For circular culverts and pipes subject to ovaling deforma- tions, the simplified close-form solutions and procedure design curve expressed by Equation (9-15), Rrec = [2Frec/ presented in Section 9.5.1 should provide reliable results (1+Frec)]. The comparison shows reasonably good agreement under general conditions, with the following notes: between the recommended simple design solution charts and In selecting the design transient ground deformation pa- the results obtained from the numerical analyses. rameter for a culvert or pipe constructed at a signifi- cant depth below the ground surface, PGV is a better parameter in the deformation-based procedure than the 9.7 Conclusions and site-adjusted PGA, because PGV can be used directly Recommendations for estimating the shearing strain in the ground (Equa- Simplified seismic analysis procedures for evaluating culvert tion 9-1). Discussions and recommendations on PGV and pipe structures subjected to transient ground deforma- values developed in Chapter 5 for retaining walls, slopes, tions induced by ground shaking proposed in this chapter. The and embankment should be used in evaluating the maxi- analysis procedures use a deformation-based methodology mum free-field shearing strain in Equation (9-1). For cul- that can provide a more reliable prediction of culvert/pipe per- verts and pipes buried at relatively shallow depths (that is, formance. The approach focuses on the deformations in the within 50 feet of the ground surface), it is more reasonable transverse section of the structure (that is, ovaling/racking de- to estimate the free-field shearing strain in the ground formations) instead of the longitudinal axial/curvature defor- using the earthquake-induced shearing stress divided by mations, due primarily to the general condition that typical the stiffness of the surrounding ground (Equation 9-2). culvert structures for transportation applications are of limited If a more accurate prediction of the maximum free-field length, and as such it is in general unlikely to develop signifi- shearing strain is required, a more refined free-field site cant transient axial/curvature deformations along the longitu- response analysis (for example, using the SHAKE com- dinal direction of the culvert structures. puter program) should be performed. Based on the results of a series of parametric soil-structure In using the simplified approach, the no-slip interface interaction analysis taking various factors into considera- assumption should be used in calculating the maximum tion, the following conclusions and recommendations are thrust/hoop forces (Tmax based on Equation 9-11) in the provided: culvert structure for conservative purposes. Results based Table 9-12. Racking stiffness of culverts and flexibility ratios. Structural Racking Stiffness Flexibility Ratio KS (kips/ft) FREC Case 1 172 0.97 Case 2 172 2.4 Case 3 115 2.9 Case 4 57 7.3 Case 5 43 19.3

OCR for page 129
130 on the full-slip assumption tend to under-estimate the For rectangular shape culverts subject to racking deforma- thrust/hoop forces. tions, the simplified procedure presented in Section 9.5.2 In using the simplified approach, the full-slip interface should provide reliable results under general conditions, assumption should be used in calculating the maximum with the following notes: bending moments (Mmax, based on Equation 9-10) and A series of parametric analysis was conducted verifying culvert deformation (DEQ, based on Equation 9-7) that the procedure can provide a reasonable estimate for because it provides more conservative results than the the culvert racking deformations. To derive the internal no-slip interface assumption. A flexural type failure forces in the structural elements, a simple frame analy- mode due to the combined effects of bending moment sis is all that is required (refer to Figure 9-10). and thrust force must be checked for both rigid and Based on the results of the parametric analysis, it ap- flexible culverts. The flexural failure criteria may be pears that burial depth has insignificant effects on the established using the conventional capacity evaluation culvert racking deformations and therefore no further procedures for reinforced concrete or metals. modifications to the procedure presented in Section Based on results from the soil-structure interaction 9.5.2 is necessary. analysis, the effect of shallow burial depth appears to be The seismic effects of transient racking/ovaling deforma- on the safe side, provided that the maximum free-field tions on culverts and pipes must be considered additional ground shearing strain is calculated at the most critical to the normal load effects from surcharge, pavement, and elevation (where the maximum ground shearing strain wheel loads, and then compared to the various failure cri- occurs, rather than the average ground shearing strain teria considered relevant for the type of culvert structure within the culvert depth profile). in question.